utils.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Mar 24 08:38:01 2023

@author: Julian Alberto Giles

Various utilities for processing weather radar data.
"""

import numpy as np
import xarray as xr
from scipy import ndimage
from scipy.integrate import cumulative_trapezoid
from functools import partial
import os
import datetime as dt
import glob
from multiprocessing import Pool
import xradar as xd
import sys
import scipy
import matplotlib as mpl
import warnings
from xhistogram.xarray import histogram
import wradlib as wrl
import regionmask as rm
from osgeo import osr
import pandas as pd
import time
try: import pyinterp
except: None
from scipy.spatial import KDTree
from osgeo import gdal
from scipy.ndimage import binary_opening
import dask

import dotenv
secrets_paths =[
    "/user/jgiles/secrets.env",
    "/p/home/jusers/giles1/juwels/secrets.env"
    ]
for secrets_path in secrets_paths:
    if os.path.exists(secrets_path):
        secrets = dotenv.dotenv_values(secrets_path)
        break

# set earthdata token (this may change, only lasts a few months)
os.environ["WRADLIB_EARTHDATA_BEARER_TOKEN"] = secrets['EARTHDATA_TOKEN']

wrldata_paths =[
    "/home/jgiles/wradlib-data-main",
    "/p/scratch/detectrea2/giles1/wradlib-data-main"
    ]
for wrldata_path in wrldata_paths:
    if os.path.exists(wrldata_path):
        os.environ['WRADLIB_DATA'] = wrldata_path
        break

#### Helper functions and definitions

# names of variables
phidp_names = ["UPHIDP_UF", "UPHIDP", "UPHIDP_UF", "PHIDP"] # names to look for the PHIDP variable, in order of preference
dbzh_names = ["DBZH"] # same but for DBZH
rhohv_names = ["RHOHV"] # same but for RHOHV
zdr_names = ["ZDR"]
th_names = ["TH", "DBTH", "DBZH"]

# function to get the names of variables from the dataset
def get_names(ds, phidp_names=phidp_names, dbzh_names=dbzh_names, rhohv_names=rhohv_names,
              zdr_names=zdr_names, th_names=th_names):
    # get PHIDP name
    for X_PHI in phidp_names:
        if X_PHI in ds.data_vars:
            break
    # get DBZH name
    for X_DBZH in dbzh_names:
        if X_DBZH in ds.data_vars:
            break

    # get RHOHV name
    for X_RHO in rhohv_names:
        if X_RHO in ds.data_vars:
            break

    # get ZDR name
    for X_ZDR in zdr_names:
        if X_ZDR in ds.data_vars:
            break

    # get TH name
    for X_TH in th_names:
        if X_TH in ds.data_vars:
            break

    return X_DBZH, X_PHI, X_RHO, X_ZDR, X_TH



# Set minimum height above the radar to be considered (mostly for filtering when calculating offsets, ML and entropy)
min_hgts = {
    'default': 200,
    '90grads': 600, # for the VP we need to set a higher min height because there are several bins of unrealistic values
    'ANK': 200, # for ANK we need higher min_hgt to avoid artifacts
    'GZT': 200 # for GZT we need higher min_hgt to avoid artifacts
}

# Set minimum range to be considered (mostly for filtering bad PHIDP close to the radar)
min_rngs = {
    'default': 1000,
    'HTY': 0, # for HTY the data looks pretty good close to the radar
    'ANK': 7000, # for ANK we need higher min_range to avoid artifacts
    'AFY': { # for AFY we need higher min_range to avoid artifacts
            2016: 6000,
            2017: 5000,
            2018: 7000,
            2019: 7000,
            2020: 7000
            },
    'SVS': 4200, # for SVS we need higher min_range to avoid artifacts
    'GZT': 3000, # for GZT we need higher min_range to avoid artifacts
}

# DEPRECATED
# # Set minimum range index to be considered for ZDR (to avoid artifacts close to the radar)
# min_irngs_ZDR = {
#     'default': 1,
#     'HTY': 1, # for HTY the data looks pretty good close to the radar
#     'ANK': 1, # for ANK we need higher min_range to avoid artifacts
#     'AFY': 8, # for AFY we need higher min_range to avoid artifacts
#     'SVS': 8, # for SVS we need higher min_range to avoid artifacts
#     'GZT': 8, # for GZT we need higher min_range to avoid artifacts
# }

# Set minimum range to be considered for ZDR (to avoid artifacts close to the radar)
min_rngs_ZDR = {
    'default': 500,
    'HTY': 300, # for HTY the data looks pretty good close to the radar
    'ANK': { # for ANK we need higher min_range to avoid artifacts
            2015: 1875,
            2016: 1875,
            2017: 1750,
            2018: 2250,
            2019: 3250,
            2020: 750
            },
    'AFY': { # for AFY we need higher min_range to avoid artifacts
            2016: 4200,
            2017: 2100,
            2018: 5100,
            2019: 6000,
            2020: 6000
            },
    'SVS': 3000, # for SVS we need higher min_range to avoid artifacts
    'GZT': 3000, # for GZT we need higher min_range to avoid artifacts
}

# Set the possible ZDR calibrations locations to include (in order of priority)
# The idea is to use a script that will try to correct according to the first offset; if not available or nan it will
# continue with the next one, and so on. Only the used offset will be outputted in the final file.
# All items in zdrofffile will be tested in each zdroffdir to load the data.
zdroffdir = ["/calibration/zdr/VP/", "/calibration/zdr/LR_consistency/", "/calibration/zdr/QVP/",]# "/calibration/zdr/falseQVP/"] # subfolder(s) where to find the zdr offset data
zdrofffile = ["*zdr_offset_belowML_00*",  "*zdr_offset_below1C_00*", "*zdr_offset_below3C_00*", "*zdr_offset_wholecol_00*",
              "*zdr_offset_belowML_noWR_0*", "*zdr_offset_below1C_noWR_0*", "*zdr_offset_below3C_noWR_0*",
              "*zdr_offset_belowML_0*", "*zdr_offset_below1C_0*", "*zdr_offset_below3C_0*",
              "*zdr_offset_belowML_noWR-*", "*zdr_offset_below1C_noWR-*", "*zdr_offset_below3C_noWR-*",
              "*zdr_offset_belowML-*", "*zdr_offset_below1C-*", "*zdr_offset_below3C-*",
              "*zdr_offset_belowML_2*", "*zdr_offset_below1C_2*", "*zdr_offset_below3C_2*", # this line is for boxpol
              ] # pattern to select the appropriate file (careful with the zdr_offset_belowML_timesteps)

# like the previous one but for timestep-based correction
zdrofffile_ts = ["*zdr_offset_belowML_timesteps_00*",  "*zdr_offset_below1C_timesteps_00*", "*zdr_offset_below3C_timesteps_00*", #"*zdr_offset_wholecol_timesteps_00*",
              "*zdr_offset_belowML_timesteps_0*", "*zdr_offset_below1C_timesteps_0*", "*zdr_offset_below3C_timesteps_0*",
              "*zdr_offset_belowML_timesteps-*", "*zdr_offset_below1C_timesteps-*", "*zdr_offset_below3C_timesteps-*",
              "*zdr_offset_belowML_timesteps_2*", "*zdr_offset_below1C_timesteps_2*", "*zdr_offset_below3C_timesteps_2*", # this line is for boxpol
              ] # pattern to select the appropriate file (careful with the zdr_offset_belowML_timesteps)

# set the RHOHV correction location
rhoncdir = "/rhohv_nc/" # subfolder where to find the noise corrected rhohv data
rhoncfile = ["*rhohv_nc_2percent*", "*rhohv_nc-*"] # pattern to select the appropriate file (careful with the rhohv_nc_2percent)

# default parameteres for phidp processing in DWD and turkish (dmi) C-band data
phase_proc_params = {}

phase_proc_params["dwd"] = {}
phase_proc_params["dwd"]["vol5minng01"] = { # for the volume scan
    "window0": 7, # number of range bins for phidp smoothing (this one is quite important!)
    "winlen0": 7, # size of range window (bins) for the kdp-phidp calculations
    "xwin0": 9, # window size (bins) for the time rolling median smoothing in ML detection
    "ywin0": 1, # window size (bins) for the height rolling mean smoothing in ML detection
    "fix_range": 750, # range from where to consider phi values (dwd data is bad in the first bin)
    "rng": 3000, # range for phidp offset correction, if None it is auto calculated based on window0
    "azmedian": True, # reduce the phidp offset by applying median along the azimuths?
    "rhohv_thresh_gia": (0.97, 1), # rhohv thresholds for ML Giangrande refinement of KDP
    "grad_thresh": 1 # additional filtering parameter for ML refinement (1=ignore)
}
phase_proc_params["dwd"]["90gradstarng01"] = { # for the vertical scan
            "window0": 17, # number of range bins for phidp smoothing (this one is quite important!)
            "winlen0": 21, # size of range window (bins) for the kdp-phidp calculations
            "xwin0": 5, # window size (bins) for the time rolling median smoothing in ML detection
            "ywin0": 5, # window size (bins) for the height rolling mean smoothing in ML detection
            "fix_range": 750, # range from where to consider phi values (dwd data is bad in the first bin)
            "rng": 3000, # range for phidp offset correction, if None it is auto calculated based on window0
            "azmedian": True, # reduce the phidp offset by applying median along the azimuths?
            "rhohv_thresh_gia": (0.97, 1), # rhohv thresholds for ML Giangrande refinement of KDP
            "grad_thresh": 1 # additional filtering parameter for ML refinement (1=ignore)
        }
phase_proc_params["dwd"]["pcpng01"] = phase_proc_params["dwd"]["90gradstarng01"] # for the precip scan

phase_proc_params["dwd-hres"] = {}
phase_proc_params["dwd-hres"]["vol5minng01"] = { # for the volume scan
    "window0": 11, # number of range bins for phidp smoothing (this one is quite important!)
    "winlen0": [9, 11], # size of range window (bins) for the kdp-phidp calculations
    "xwin0": 5, # window size (bins) for the time rolling median smoothing in ML detection
    "ywin0": 5, # window size (bins) for the height rolling mean smoothing in ML detection
    "fix_range": 1500, # range from where to consider phi values (dwd data is bad in the first bins)
    "rng": 1000, # range for phidp offset correction, if None it is auto calculated based on window0
    "azmedian": True, # reduce the phidp offset by applying median along the azimuths?
    "rhohv_thresh_gia": (0.97, 1), # rhohv thresholds for ML Giangrande refinement of KDP
    "grad_thresh": 1 # additional filtering parameter for ML refinement (1=ignore)
}
phase_proc_params["dwd-hres"]["90gradstarng01"] = phase_proc_params["dwd-hres"]["vol5minng01"] # for the precip scan
phase_proc_params["dwd-hres"]["90gradstarng10dft"] = phase_proc_params["dwd-hres"]["vol5minng01"] # for the precip scan
phase_proc_params["dwd-hres"]["pcpng01"] = phase_proc_params["dwd-hres"]["vol5minng01"] # for the precip scan

phase_proc_params["dmi"] = {
        "window0": 7000,
        "winlen0": [2500, 7000],
        "xwin0": 5,
        "ywin0": 5,
        "fix_range": 350,
        "rng": 1000, # range for phidp offset correction, if None it is auto calculated based on window0
        "azmedian": 10, # reduce the phidp offset by applying median along the azimuths?
        "rhohv_thresh_gia": (0.99, 1), # rhohv thresholds for ML Giangrande refinement of KDP
        "grad_thresh": 0.0001 # additional filtering parameter for ML refinement
}

phase_proc_params["boxpol"] = {
        "window0": 7000, # Tobi uses 11 bins
        "winlen0": [2500, 7000], # Tobi uses 31 bins
        "xwin0": 5,
        "ywin0": 5,
        "fix_range": 350,
        "rng": 1000, # range for phidp offset correction, if None it is auto calculated based on window0
        "azmedian": 10, # reduce the phidp offset by applying median along the azimuths?
        "rhohv_thresh_gia": (0.97, 1), # rhohv thresholds for ML Giangrande refinement of KDP
        "grad_thresh": 1 # additional filtering parameter for ML refinement
}


# make a function to retreive only the phase_proc_params dictionary corresponding to the a data path (not very precise, tuned to my data naming)
def get_phase_proc_params(path):
    """
    Get phase_proc_params according to path

    Parameter
    ---------
    path : str or list
        Path of the data I want to phase-process. The appropriate part of phase_proc_params
        is retreived based on the naming. If list, only the first element is used as reference.

    Returns
    ---------
    phase_proc_params : dict
        Dictionary with default values to use for phase processing.
    """
    if type(path) is list:
        path = path[0]
    elif type(path) is str:
        pass
    else:
        raise ValueError("path must be str or list")

    if "dwd" in path or "DWD" in path:
        dwd_key = "dwd"
        if "dwd-hres" in path or "DWD-hres" in path:
            dwd_key = "dwd-hres"
        elif int(path.split("dwd")[1].split("/")[1]) >= 2021:
            dwd_key = "dwd-hres"
        if "vol5minng01" in path:
            if "/tur/" in path or "/ess/" in path:
                phase_proc_params_tur = phase_proc_params[dwd_key]["vol5minng01"].copy()
                phase_proc_params_tur["azmedian"] = 5
                return phase_proc_params_tur
            else:
                return phase_proc_params[dwd_key]["vol5minng01"]
        if "90gradstarng01" in path:
            return phase_proc_params[dwd_key]["90gradstarng01"]
        if "90gradstarng10dft" in path:
            return phase_proc_params[dwd_key]["90gradstarng10dft"]
        if "pcpng01" in path:
            return phase_proc_params[dwd_key]["pcpng01"]

    elif "dmi" in path:
        return phase_proc_params["dmi"]
    elif "boxpol" in path:
        return phase_proc_params["boxpol"]
    else:
        raise ValueError("No default phase_proc_params dictionary could be inferred from path")

# Parameters for attenuation correction
attenuation_corr_linear_coefs = {
    "dwd": {"alpha": 0.08, "beta": 0.02, "alphaml": 0.08, "betaml": 0.02},
    "dmi": {"alpha": 0.14, "beta": 0.025, "alphaml": 0.25, "betaml": 0.025},
    }


# set ERA5 directory
if os.path.exists("/automount/ags/jgiles/ERA5/hourly/"):
    # then we are in local system
    era5_dir = "/automount/ags/jgiles/ERA5/hourly/loc/pressure_level_vars/" # dummy loc placeholder, it gets replaced below
elif os.path.exists("/p/scratch/detectrea/giles1/ERA5/hourly/"):
    # then we are in JSC
    era5_dir = "/p/scratch/detectrea/giles1/ERA5/hourly/loc/pressure_level_vars/" # dummy loc placeholder, it gets replaced below
elif os.path.exists("/p/largedata2/detectdata/projects/A04/ERA5/hourly/"):
    # then we are in JSC
    era5_dir = "/p/largedata2/detectdata/projects/A04/ERA5/hourly/loc/pressure_level_vars/" # dummy loc placeholder, it gets replaced below

# in case KDP is not in the dataset we defined its attributes according to DWD data:
KDP_attrs={'_Undetect': 0.0,
 'units': 'degrees per kilometer',
 'long_name': 'Specific differential phase HV',
 'standard_name': 'radar_specific_differential_phase_hv'}

# we define a funtion to look for loc inside a path string
locs = ["pro", "tur", "umd", "afy", "ank", "gzt", "hty", "svs", "ess"] # possible locs

def find_loc(locs, path):
    components = path.split(os.path.sep)
    for element in locs:
        for component in components:
            if element.lower() in component.lower():
                return element
    return None

locs_code = {"10392": "pro", "10832": "tur", "10356": "umd",
             "17187": "afy", "17138": "ank", "17259": "gzt",
             "17373": "hty", "17163": "svs"} # possible locs

def find_loc_code(locs_code, path):
    components = path.split(os.path.sep)
    for element in locs_code.keys():
        for component in components:
            if element.lower() in component.lower():
                return locs_code[element]
    return None

# define a function to split a string at a certain pattern and replace it
def edit_str(ff, replace, name):
    """
    ff: string of file path or whatever
    replace: what string part to replace
    name: new string to put
    """

    ff_parts = ff.split(replace)
    newff = (name).join(ff_parts)
    return newff


def fix_time_in_coords(ds):
    """
    Fix time coord issues and reduce time dimension if present in dataset coordinates where it is not needed

    Parameter
    ---------
    ds : xarray.DataArray or xarray.Dataset
    """

    # It may happen that some time value is missing or that time values are repeated, attempt to fix that using info in rtime
    if ds["time"].isnull().any() or (ds["time"].diff("time").compute().astype(int) <= 0).any() :
        ds.coords["time"] = ds.rtime.min(dim="azimuth", skipna=True).compute()

    # if some coord has dimension time, reduce using median
    for coord in ["latitude", "longitude", "altitude", "elevation"]:
        if "time" in ds[coord].dims:
            ds.coords[coord] = ds.coords[coord].median("time")

    # in case there are still duplicate timesteps, attemp to reduce the time dim
    ds = reduce_duplicate_timesteps(ds)

    return ds

def reduce_duplicate_timesteps(ds):
    """
    Reduce duplicate time values by combining the data variables available at each timestep. In
    case there are duplicate data vars (same name in the duplicate time value) then remove the duplicates,
    otherwise keep all variables by renaming them with _n, with n = 2,... starting from the second
    one with the same name.

    Originally made for handling turkish radar datasets.

    Parameter
    ---------
    ds : xarray.Dataset
    """
    # Check if there are duplicate time values
    if (ds.time.diff("time").astype(int)==0).any():

        # Create a new dummy dataset to concatenate the reduced data
        ds_reduced = ds.isel(time=[0]).copy()

        for tt in sorted(set(ds.time.values)):
            # Make a list for the selected variables
            reduced_vars = []

            # Select data for the current timestep
            ds_time = ds.sel(time=tt)

            # If time is not a dimension anymore
            if "time" not in ds_time.dims:
                # then just add the current ds
                ds_reduced = xr.concat([ds_reduced, ds_time], dim="time", join="outer", coords="different", compat='equals')

            else:
                # for each variable,
                for vv in ds_time.data_vars:
                    # start by removing NA
                    ds_time_nona = ds_time[vv].dropna("time", how="all")

                    if len(ds_time_nona["time"]) == 1:
                        # if the array got reduced to only 1 timestep, then attach it to reduced_vars
                        reduced_vars.append(ds_time_nona.copy())

                    elif len(ds_time_nona["time"]) == 0:
                        # if the array got reduced to 0 timestep, then skip
                        continue

                    else:
                        # if there are still more than 1 timestep, divide them into separate variables
                        for itt in range(len(ds_time.time)):
                            count = 0
                            if itt == 0:
                                # set the first one as the "pristine" variable
                                reduced_vars.append(ds_time_nona.isel(time=[itt]).copy())
                                count+=1
                            else:
                                for ivv in range(count):
                                    ivv+=ivv # we need to sum 1 because we are going backwards
                                    if ds_time_nona.isel(time=[itt]).equals(reduced_vars[-ivv]):
                                        # if it is equal to any of the already selected arrays, ignore it
                                        break
                                    else:
                                        # if it is not equal to previous arrays, append it as a variant of that variable
                                        reduced_vars.append(ds_time_nona.isel(time=[itt]).rename(vv+"_"+str(count)).copy())
                                        count+=1

                # Merge all variables into a single dataset
                reduced_vars_ds = xr.merge(reduced_vars, compat='no_conflicts')

                # Add the current timestep data to the new dataset
                ds_reduced = xr.concat([ds_reduced, reduced_vars_ds], dim="time", join="outer", coords="different", compat='equals')

        # delete the dummy data from the first timestep
        # Here I could also use .drop_isel but there is a bug and it does not work https://github.com/pydata/xarray/issues/6605
        ds_reduced = ds_reduced.drop_duplicates("time", keep="last")

        return ds_reduced

    else: # in case there are no duplicate timesteps, just return ds
        return ds


def align(ds):
    """
    Reduce and align dataset coordinates

    Parameter
    ---------
    ds : xarray.DataArray or xarray.Dataset
    """
    ds["time"] = ds["time"].load().min() # reduce time in the azimuth
    ds["elevation"] = ds["elevation"].load().median() # remove elevation in time
    ds["azimuth"] = ds["azimuth"].load().round(1)
    ds = xd.util.remove_duplicate_rays(ds) # in case there are duplicate rays, remove them
    ds["time"] = np.unique(ds["time"]) # in case there are duplicate times
    return ds.set_coords(["sweep_mode", "sweep_number", "prt_mode", "follow_mode", "sweep_fixed_angle"])

def check_time_dimension_alignment(datasets, tolerance="S"):
    """
    From a list of xarray DataArray or Datasets, check that it is possible to align their time
    dimensions to a unique one (e.g. to the one with the earliest time values).

    Parameter
    ---------
    datasets : list of xarray.DataArray or xarray.Dataset
    tolerance : keyword argument for time rounding. "S" for seconds, "T" for minutes.
    """
    if not datasets:
        return False, "No datasets provided."

    # Check that all datasets have the same length of the time dimension
    time_lengths = [ds.sizes['time'] for ds in datasets]
    if len(set(time_lengths)) != 1:
        return False, "Datasets have different lengths of the time dimension."

    # Check that each time array is shifted by the same delta time (or a multiple of it)
    time_deltas = [ds['time'].dt.round(tolerance).diff(dim='time').median().item() for ds in datasets]
    time_inis = [ds['time'][0].dt.round(tolerance).item() for ds in datasets]
    # print(time_deltas)
    # print(time_inis)
    base_delta = time_deltas[0]
    for n, delta in enumerate(time_deltas):
        if not (delta % base_delta == 0 or base_delta % delta == 0):
            return False, "Datasets have inconsistent delta times."
        if n>0:
            # print((time_inis[n] - time_inis[n-1]))
            if not abs(time_inis[n] - time_inis[n-1]) <= base_delta:
                return False, "Datasets have inconsistent delta times."

    return True, "Datasets have consistent time dimensions and delta times. It is possible to align them."

def unfold_phidp(ds, phidp_names=phidp_names, rhohv_names=rhohv_names, wrap_interval=360.0, rhohv_thresh=0.8, window=3):
    """
    Unfold PHIDP radially (along the range dimension). Supports multiple folds.

    Parameters
    ---------
    ds : xarray.Dataset
        Dataset including the necessary variables for this function to work.
    phidp_names : list
        List of PHIDP variable names to look for in the dataset, in order of priority.
    rhohv_names : list
        List of RHOHV variable names to look for in the dataset, in order of priority.
    wrap_interval : float
        Length of the wrapping interval.
    rhohv_thresh: float
        Only values above rhohv_thresh are considered in the calculations.
    window: int
        Window for circular smoothing of PHIDP in vector space (typical value: 5). If window
        is not larger than 0, then no smoothing is applied. In case of applying unfold_phidp
        multiple times this value should be set to zero after the first unfolding!!

    Returns
    ---------
    ds : xarray.Dataset
        Original dataset with unfolded PHIDP
    """
    success = False

    # Identify valid PHIDP and RHOHV variable names
    X_PHI = next((phi for phi in phidp_names if phi in ds.data_vars), None)
    X_RHO = next((rho for rho in rhohv_names if rho in ds.data_vars), None)

    if X_PHI and X_RHO and ds[X_PHI].notnull().any():

        # 1. Mask the data based on RHOHV to avoid unwrapping pure noise, then smooth
        ds_phi = ds[X_PHI].where(ds[X_RHO] > rhohv_thresh)

        # We also take out the first bins
        gate_indices = xr.DataArray(
                    np.arange(ds_phi.sizes['range']),
                    dims=['range'],
                    coords={'range': ds_phi.coords['range']}
                )

        ds_phi = ds_phi.where(gate_indices >= 4, 0)

        # Smooth the data with circular smoothing if window > 0
        if window > 0:
            # Convert to radians and decompose into U and V components
            phi_rad = np.deg2rad(ds_phi)
            u = np.cos(phi_rad)
            v = np.sin(phi_rad)

            # Apply a rolling median to the components. A window of ~5 gates completely
            # suppresses isolated 1-2 gate spikes while preserving actual persistent folds.
            u_smooth = u.rolling(range=window, center=True, min_periods=window//2+1).median()
            v_smooth = v.rolling(range=window, center=True, min_periods=window//2+1).median()

            # Reconstruct the smoothed phase back into degrees [-180, 180]
            # xr.apply_ufunc safely handles Dask-backed arrays for arctan2
            smoothed_phi_rad = xr.apply_ufunc(
                np.arctan2, v_smooth, u_smooth, dask="allowed"
            )
            smoothed_phi = np.rad2deg(smoothed_phi_rad)
        else:
            smoothed_phi = ds_phi.copy()

        # Despeckle to remove isolated values
        smoothed_phi_dp = smoothed_phi.copy(data=wrl.util.despeckle(smoothed_phi.values))

        # 2. Forward-fill NaNs along the range dimension.
        # This is critical so a fold separated by a few NaN gates is still detected.
        # phi_ffill = ds_phi.ffill(dim="range")
        phi_ffill = smoothed_phi_dp.ffill(dim="range")

        # 3. Calculate the gate-to-gate phase difference using .shift()
        # This preserves the exact dimensions and coordinates of the original array.
        phase_diff = phi_ffill - phi_ffill.shift(range=1)

        # The first gate has nothing to subtract from, so it becomes NaN. Fill it with 0.
        phase_diff = phase_diff.fillna(0)

        # 4. Detect folds (jumps greater than half the wrap interval)
        # If the difference is strongly negative (e.g. < -180), it folded forward
        fold_up = (phase_diff < -(wrap_interval / 2.0)).astype(int)
        # If the difference is strongly positive (e.g. > 180), it folded backward
        fold_down = (phase_diff > (wrap_interval / 2.0)).astype(int)

        # Net folds at each gate
        folds = fold_up - fold_down

        # 5. Cumulatively sum the folds along the ray
        fold_counts = folds.cumsum(dim="range")

        # 6. Apply the unwrapping correction to the original masked data
        # This natively allows values to exceed 360, 720, etc.
        unwrapped_phi = ds[X_PHI] + (fold_counts * wrap_interval)

        # Reassign to dataset while keeping original attributes
        attrs = ds[X_PHI].attrs.copy()
        ds[X_PHI+"_UF"] = unwrapped_phi
        ds[X_PHI+"_UF"].attrs = attrs

        if (fold_counts!=0).any(): print(f"{X_PHI} was unfolded radially.")
        success = True

    if not success:
        warnings.warn("unfold_phidp: PHIDP and/or RHOHV variable not found. Nothing was done.")

    return ds

def unfold_phidp_old(ds, phidp_names=phidp_names, rhohv_names=rhohv_names, phidp_lims=(-30,30)):
    """
    Unfold PHIDP in case it is wrapping around the edge values, it should be defined between -180 and 180.
    The unfolding is done for the whole of ds (not per ray or per PPI).
    Only pixels with RHOHV>0.7 are taken into consideration.

    Parameter
    ---------
    ds : xarray.DataArray or xarray.Dataset
    phidp_names : list of PHIDP variable names to look for in the dataset
    rhohv_names : list of RHOHV variable names to look for in the dataset
    phidp_lims : tuple delimiting the PHIDP range to use as the center of the distribution,
                if the majority of PHIDP values are outside this range, then unfold.
    """
    success = False # define a variable to check if some PHIDP variable was found

    phidp_min = phidp_lims[0]
    phidp_max = phidp_lims[1]

    for phi in phidp_names:
        if phi in ds.data_vars:
            X_PHI = phi

            if ds[X_PHI].notnull().any():
                for X_RHO in rhohv_names: # only take pixels with rhohv>0.7 to avoid noise
                    if X_RHO in ds.data_vars:
                        ds_phi = ds[X_PHI].where(ds[X_RHO]>0.7).isel({"range":slice(4,None)}) # we also take out the first bins

                        # compute the count of values inside and outside the phidp_lims
                        values_center = ((ds_phi>phidp_min)*(ds_phi<phidp_max)).sum().compute()
                        values_sides = ((ds_phi>phidp_max)+(ds_phi<phidp_min)).sum().compute()

                        # compute also the mode (most frequent value) of the whole distribution
                        ds_phi_hist = histogram(ds_phi, bins=np.arange(-180, 184, 4), block_size=None) # block_size=None to avoid a bug
                        ds_phi_mode = ds_phi_hist[np.argmax(ds_phi_hist.values)][X_PHI+"_bin"].values

                        # if the mode is < phidp_min and the count of valid phidp values
                        # between 0-90 degrees is greater than the count between 90-180
                        # we assume the distribution of values is not folded but just shifted to the negatives
                        values_0_90 = ((ds_phi>0)*(ds_phi<90)).sum().compute()
                        values_90_180 = ((ds_phi>90)*(ds_phi<180)).sum().compute()
                        not_folded_cond = (ds_phi_mode < phidp_min) * (values_0_90 > values_90_180)

                        if values_sides > values_center:
                            if not not_folded_cond:
                                attrs = ds[X_PHI].attrs.copy()
                                ds[X_PHI] = xr.where(ds[X_PHI]<=0, ds[X_PHI]+180, ds[X_PHI]-180, keep_attrs=True).compute()
                                ds[X_PHI].attrs = attrs
                                print(X_PHI+" was unfolded")
                        success = True
                        break

    if not success:
        warnings.warn("unfold_phidp: PHIDP and/or RHOHV variable not found. Nothing was done")

    return ds

def fix_flipped_phidp(ds, phidp_names=phidp_names, rhohv_names=rhohv_names, range_name="range",
                      fix_range=3000., rng=10000., flip_kdp=True, tolerance = 0.05):
    """
    Flip PHIDP in case it is inverted. The function smooths PHIDP and calculates the
    differences between gates, for each ray. Then, the differences in the whole of ds
    are summed. If the resulting value is negative, i.e. PHIDP mostly goes down,
    then PHIDP is flipped (multiplied by -1). Only pixels with RHOHV>0.7 and
    starting from fix_range are taken into consideration. Also flips KDP if
    flip_kdp is True.

    Parameter
    ---------
    ds : xarray.DataArray or xarray.Dataset
    phidp_names : list of PHIDP variable names to look for in the dataset
    rhohv_names : list of RHOHV variable names to look for in the dataset
    range_name : str name of the range coordinate
    fix_range : float
        Minimum range from where to consider PHIDP values.
    rng : float
        Range in m for median smooting along the range dimension.
    flip_kdp : bool
        If True, test also "KDP" for flipping if there is a majority of negative values.
        Only flips if PHIDP was flipped.
    tolerance : float tolerance value to not apply the kdp flip. The count of negative
                kdp values must be higher than the count of positives *(1+tolerance) .
    """
    success = False # define a bool to check if some PHIDP variable was found
    flip_kdp_trigger = False # define a bool to trigger kdp testing and flipping

    range_step = np.diff(ds[range_name])[0]
    nprec = int(rng / range_step)
    if not nprec % 2:
        nprec += 1
    if nprec > 50: # set a maximum (important for i.e. vertical scans)
        nprec = 50

    for phi in phidp_names:
        if phi in ds.data_vars:
            X_PHI = phi

            if ds[X_PHI].notnull().any():
                for X_RHO in rhohv_names: # only take pixels with rhohv>0.7 to avoid noise
                    if X_RHO in ds.data_vars:
                        ds_phi = ds[X_PHI].where(ds[X_RHO]>0.7).where(ds[range_name]>=fix_range)
                        ds_phi_std = ds_phi.rolling({range_name:nprec}, center=True).std() # filter out pixels with std > 5
                        smooth_diff = ds_phi.where(ds_phi_std<5).rolling({range_name:nprec}, center=True).median().diff(range_name).sum()

                        if smooth_diff < 0:
                            attrs = ds[X_PHI].attrs.copy()
                            ds[X_PHI] = ds[X_PHI]*-1
                            ds[X_PHI].attrs = attrs.copy()
                            print(X_PHI+" was flipped")
                            if flip_kdp:
                                flip_kdp_trigger = True
                        success = True
                        break

    if "KDP" in ds.data_vars and flip_kdp_trigger:
        ds_kdp = ds["KDP"].where(ds[X_RHO]>0.7).where(ds[range_name]>=fix_range)
        kdp_pos = (ds_kdp>0).sum().compute()
        kdp_neg = (ds_kdp<0).sum().compute()
        if kdp_neg > kdp_pos*(1+tolerance):
            attrs = ds["KDP"].attrs.copy()
            ds["KDP"] = ds["KDP"]*-1
            ds["KDP"].attrs = attrs.copy()
            print("KDP"+" was flipped")
    if not success:
        warnings.warn("fix_flipped_phidp: PHIDP and/or RHOHV variable not found. Nothing was done")

    return ds

def xr_rolling(da, window, window2=None, method="mean", min_periods=2, rangepad="fill", **kwargs):
    """Apply rolling function `method` to 2D datasets

    Parameter
    ---------
    da : xarray.DataArray
        array with data to apply rolling function
    window : int
        size of window in range dimension

    Keyword Arguments
    -----------------
    window2 : int
        size of window in azimuth dimension
    method : str
        function name to apply
    min_periods : int
        minimum number of valid bins
    rangepad : string
        Padding method for the edges of the range dimension. "fill" will fill the
        nan values resulting from not enough bins by stretching the closest value.
        "reflect" will extend the original array by reflecting around the edges
        so there is enough bins for the calculation
    **kwargs : dict
        kwargs to feed to rolling function

    Return
    ------
    da_new : xarray.DataArray
        DataArray with applied rolling function
    """
    prng = window // 2
    srng = slice(prng, -prng)
    if rangepad == "reflect":
        da_new = da.pad(range=prng, mode='reflect', reflect_type='odd')
        isel = dict(range=srng)
    else:
        da_new = da
        isel = dict()

    dim = dict(range=window)

    if window2 is not None:
        paz = window2 // 2
        saz = slice(paz, -paz)
        da_new = da_new.pad(azimuth=paz, mode="wrap")
        dim.update(dict(azimuth=window2))
        isel.update(dict(azimuth=saz))

    rolling = da_new.rolling(dim=dim, center=True, min_periods=min_periods)

    da_new = getattr(rolling, method)(**kwargs)
    da_new = da_new.isel(**isel)

    if rangepad == "fill":
        da_new = da_new.bfill("range").ffill("range")

    return da_new

def gauss_kernel(width, sigma):
    dirac = np.zeros(width)
    dirac[int(width / 2)] = 1
    return scipy.ndimage.gaussian_filter1d(dirac, sigma=sigma)

def convolve(data, kernel, mode='same'):
    mask = np.isnan(data)
    out = np.convolve(np.where(mask, 0, data), kernel, mode=mode) / np.convolve(~mask, kernel, mode=mode)
    return out

def smooth_data(data, kernel):
    res = data.copy()
    try: # in case data is xarray
        for i, dat in enumerate(data.values):
            res[i] = convolve(dat, kernel)
    except AttributeError: # in case data is numpy array
        for i, dat in enumerate(data):
            res[i] = convolve(dat, kernel)
    return res

def n_longest_consecutive(ds, dim='time'):
    """
    Calculates the number of values in the longest consecutive sequence of
    valid values along the specified dimension.
    """
    ds = ds.notnull().cumsum(dim=dim) - ds.notnull().cumsum(dim=dim).where(ds.isnull()).ffill(dim=dim).fillna(0)
    return ds.max(dim=dim)

def give_array(start, stop, step):
    n = int((stop - start) / step)  # n jump
    num_points = n + 1
    new_stop = start + n * step
    return np.linspace(start, new_stop, num_points)

def apply_min_thresh(ds, varname, minval):
    """
    Returns ds.where(ds[varname]>minval) if varname in ds.
    If varname not in ds, returns ds and raises a warning.
    """
    if varname in ds.data_vars:
        return ds.where(ds[varname]>minval)
    else:
        warnings.warn("apply_min_thresh: "+varname+" not present in ds, no threshold was applied")
        return ds

def apply_max_thresh(ds, varname, maxval):
    """
    Returns ds.where(ds[varname]<maxval) if varname in ds.
    If varname not in ds, returns ds and raises a warning.
    """
    if varname in ds.data_vars:
        return ds.where(ds[varname]<maxval)
    else:
        warnings.warn("apply_max_thresh: "+varname+" not present in ds, no threshold was applied")
        return ds

def apply_min_max_thresh(ds, minthreshs, maxthreshs, skipfullna=False):
    """
    Applies apply_min_thresh and apply_max_thresh based on all variable-value pairs.
    If a variable not in ds it is ignored and raises a warning.

    minthreshs: dict of variable names and threshold values for apply_min_thresh
    maxthreshs: dict of variable names and threshold values for apply_max_thresh
    skipfullna: skips a variable if all of its values are NaNs.
    """
    if not isinstance(minthreshs, dict):
        raise TypeError("minthreshs must be a dict")
    if not isinstance(maxthreshs, dict):
        raise TypeError("maxthreshs must be a dict")

    ds1 = ds.copy()
    for vv in minthreshs.keys():
        if skipfullna and vv in ds1:
            if ds1[vv].notnull().any().compute():
                ds1 = apply_min_thresh(ds1, vv, minthreshs[vv])
        else:
            ds1 = apply_min_thresh(ds1, vv, minthreshs[vv])
    for vv in maxthreshs.keys():
        if skipfullna and vv in ds1:
            if ds1[vv].notnull().any().compute():
                ds1 = apply_max_thresh(ds1, vv, maxthreshs[vv])
        else:
            ds1 = apply_max_thresh(ds1, vv, maxthreshs[vv])

    return ds1

#### Loading functions
def load_dwd_preprocessed(filepath):
    """
    Load preprocessed DWD data stored in data trees. Can only concatenate several files
    in the time dimension.

    Parameter
    ---------
    filepath : str, list
            Location of the file or path with wildcards to find files using glob or list of paths
    """

    # collect files
    if type(filepath) is list:
        files = sorted(filepath)
    else:
        files = sorted(glob.glob(filepath))

    # open files
    dwddata = []
    for ff in files:

        dwd0 = xr.open_datatree(ff, chunks={})

        # check how many sweeps there are
        if len(dwd0.descendants) > 1:
            raise TypeError("More than one dataset inside the datatree. Currently not supported")
        elif len(dwd0.descendants) == 1:
            # get dataset and fix time coordinate
            dwddata.append(fix_flipped_phidp(unfold_phidp(fix_time_in_coords(dwd0.descendants[0].to_dataset()),
                                                          window=0, rhohv_thresh=0.8)))
        else:
            # get dataset and fix time coordinate
            dwddata.append(fix_flipped_phidp(unfold_phidp(fix_time_in_coords(dwd0.to_dataset()),
                                                          window=0, rhohv_thresh=0.8)))

    if len(dwddata) == 1:
        return dwddata[0]
    else:
        return xr.concat(dwddata, dim="time", join="outer", coords="different", compat='equals')

def load_dwd_raw(filepath):
    """
    Load DWD raw data.

    Parameter
    ---------
    filepath : str, list
            Location of the file or path with wildcards to find files using glob or list of paths
    """

    # collect files
    if type(filepath) is list:
        files = sorted(filepath)
    else:
        files = sorted(glob.glob(filepath))

    # extract list of moments
    moments = set(fp.split("_")[-2] for fp in files)

    # discard "allmoms" or "any" from the set if it exists
    moments.discard("allmoms") # legacy naming
    moments.discard("any")

    try:
        # for every moment, open all files in folder (all timesteps) per moment into a dataset
        vardict = {} # a dict for putting a dataset per moment
        for mom in moments:

            # open the odim files (single moment and elevation, several timesteps)
            llmom = sorted([ff for ff in files if "_"+mom+"_" in ff])

            vardict[mom] = xr.open_mfdataset(llmom, engine="odim", combine="nested", concat_dim="time", preprocess=align, compat='no_conflicts')

            vardict[mom] = fix_flipped_phidp(unfold_phidp(fix_time_in_coords(vardict[mom]),
                                                          window=0, rhohv_thresh=0.8))

    except OSError:
        pathparts = [ xx if len(xx)==8 and "20" in xx else None for xx in llmom[0].split("/") ]
        pathparts.sort(key=lambda e: (e is None, e))
        date = pathparts[0]
        print(date+" "+mom+": Error opening files. Some file is corrupt or truncated.")
        sys.exit("Script terminated early. "+date+" "+mom+": Error opening files. Some file is corrupt or truncated.")

    # merge all moments
    return xr.merge(vardict.values(), compat='no_conflicts')

def load_dmi_preprocessed(filepath):
    """
    Load DMI preprocessed data.

    Parameter
    ---------
    filepath : str, list
            Location of the file or path with wildcards to find files using glob or list of paths
    """
    # collect files
    if type(filepath) is list:
        files = sorted(filepath)
    else:
        files = sorted(glob.glob(filepath))

    # open files
    if len(files) == 1:
        dmidata = xr.open_mfdataset(files[0], compat='no_conflicts')
    if len(files) >= 1:
        dmidata = xr.open_mfdataset(files, compat='no_conflicts')

    return fix_flipped_phidp(unfold_phidp(fix_time_in_coords(dmidata), window=5, rhohv_thresh=0.9))


def load_dmi_raw(filepath): # THIS IS NOT IMPLEMENTED YET # !!!
    """
    Load DMI preprocessed data.

    Parameter
    ---------
    filepath : str, list
            Location of the file or path with wildcards to find files using glob or list of paths
    """
    raise NotImplementedError()
    # collect files
    if type(filepath) is list:
        files = sorted(filepath)
    else:
        files = sorted(glob.glob(filepath))

    # open files
    if len(files) == 1:
        dmidata = xr.open_mfdataset(files[0], compat='no_conflicts')
    if len(files) >= 1:
        dmidata = xr.open_mfdataset(files, compat='no_conflicts')

    return fix_flipped_phidp(unfold_phidp(fix_time_in_coords(dmidata), window=5, rhohv_thresh=0.9))

def load_volume(filelists, func=load_dwd_preprocessed, align_time=True, tolerance="s", verbose=False):
    """
    Full radar volume based on the data files provided.

    Parameter
    ---------
    filelists : list of list or str
            Each item of filelists must be another list containing all files paths for a single elevation, or
            a str of a file path (either uniquely defined or with wildcards).
    func : func
            Function to load each elevation. Either load_dwd_preprocessed, load_dwd_raw,
            load_dmi_preprocessed, load_dmi_raw or a user defined function that is called for
            each item in filelists.
    align_time : bool
            If True and if the time dimension has equal length in all files, align
            the time dimension according to the values of the first file. Note that
            if time alignment is not done (or not possible) the resulting dataset
            may be too large to fit in memory.
    tolerance : keyword argument for time rounding. "s" for seconds, "min" for minutes.
    verbose : If True, print additional details of the ongoing processing steps.
    """
    sweeps = []
    if type(filelists) is str:
        filelists = [filelists]

    for fn,filelist in enumerate(filelists):
        # collect files
        if type(filelist) is list:
            if any(["359." in ff for ff in filelist]):
                print("Ignoring 359. elevation")
                continue
            files = sorted(filelist)
        else:
            if "359." in filelist:
                print("Ignoring 359. elevation")
                continue
            files = sorted(glob.glob(filelist))

        if verbose: print("Loading "+str(fn+1)+" of "+str(len(filelists))+": "+str(len(files))+" files found ...")

        # load files for this elevation
        sweeps.append(func(files))

        # tidy up coords and dims
        sweeps[-1].coords["azimuth"] = sweeps[-1].coords["azimuth"].round(1) # round the azimuths to avoid slight differences
        try:
            sweeps[-1] = sweeps[-1].set_coords("sweep_fixed_angle")
            sweeps[-1].coords["sweep_fixed_angle"] = sweeps[-1].coords["sweep_fixed_angle"].mean() # reduce sweep_fixed_angle
        except:
            pass
        sweeps[-1] = sweeps[-1].expand_dims("sweep_fixed_angle") # promote sweep_fixed_angle to dim

    if align_time:
        if verbose:  print("Aligning time and concatenating datasets ...")
        if check_time_dimension_alignment(sweeps, tolerance)[0]:
            try:
                for dsn in range(len(sweeps)):
                    sweeps[dsn]["time"] = sweeps[0]["time"].dt.round(tolerance) # align all datasets to the time dim of the first one
                vol = xr.concat(sweeps, dim="sweep_fixed_angle", join="outer", coords="different", compat='equals')    # try to unify time
            except:
                warnings.warn("Not possible to align time dimension. May result in increased memory usage.")
                vol = xr.concat(sweeps, dim="sweep_fixed_angle", join="outer", coords="different", compat='equals')
    else:
        if verbose:  print("Concatenating datasets ...")
        vol = xr.concat(sweeps, dim="sweep_fixed_angle", join="outer", coords="different", compat='equals')

    # Pass meta variables to coords to avoid some issues
    vol = vol.set_coords(("sweep_mode", "sweep_number", "prt_mode", "follow_mode"))

    # Reduce coordinates so the georeferencing works
    vol["elevation"] = vol["elevation"].mean("azimuth")
    vol["rtime"] = vol["rtime"].min("azimuth")
    vol["sweep_mode"] = vol["sweep_mode"].min()

    return vol.sortby("sweep_fixed_angle")

def load_qvps(filepath, align_z=False, fix_TEMP=False, fillna=False,
              fillna_vars={"ZDR_OC": "ZDR", "RHOHV_NC": "RHOHV", "UPHIDP_OC": "UPHIDP", "PHIDP_OC": "PHIDP"}):
    """
    Load DWD or DMI QVP data.

    Parameter
    ---------
    filepath : str
            Location of the file or path with wildcards to find files using glob or list of filepaths

    Keyword Arguments
    -----------------
    align_z : bool
        If True and loading multiple files, align the z coord to the values of the first
        file. This is meant to avoid broadcasting due to random fluctuations (noise)
        in the z coordinate. If loading QVPs from multiple elevation angles, align_z should
        be False to avoid erroneous alignment.
    fix_TEMP : bool
        If True and loading multiple files, add empty (nan) TEMP coordinate in case it
        is not present in the file.
    fillna : bool
        If True, attempt to fill empty corrected variables with their non-corrected counterparts.
        E.g.: Fill empty ZDR_OC with the values from ZDR, empty RHOHV_NC with RHOHV, etc.
        Default is False
    fillna_vars : dict
        Dictionary of variables to attempt to fill in case they are empty. The keys indicate the
        variable to attempt to fill and the value indicate the filler variable.

    Return
    ------
    qvps : xarray.Dataset
        Dataset with time-concatenated QVPs

    """
    # check if filepath is a list
    if isinstance(filepath, list):
        files = sorted(filepath)
    else:
    # if not, collect files
        files = sorted(glob.glob(filepath))

    if len(files)==1:
        qvps = xr.open_mfdataset(files, compat='no_conflicts')
    else:
        # there are slight differences (noise) in z coord sometimes so we have to align all datasets
        # since the time coord has variable length, we cannot use join="override" so we define a function to copy
        # the z coord from the first dataset into the rest with preprocessing
        # There could also be some time values missing, ignore those
        # Some files do not have TEMP data, fill with nan
        first_file = xr.open_mfdataset(files[0], compat='no_conflicts')
        first_file_z = first_file.z.copy()
        def fix_coords(ds, align_z=True, fix_TEMP=True):
            if align_z:
                ds.coords["z"] = first_file_z
            ds = ds.where(ds["time"].notnull(), drop=True)
            if "TEMP" not in ds.coords and fix_TEMP:
                ds.coords["TEMP"] = xr.full_like( ds["DBZH"], np.nan ).compute()

            return ds

        try:
            qvps = xr.open_mfdataset(files, preprocess=partial(fix_coords, align_z=align_z, fix_TEMP=fix_TEMP), compat='no_conflicts', join='outer', engine='h5netcdf')
        except:
            if align_z:
                print("Aligning z coord may have failed, attempting to load without alignment...")
            try:
                qvps = xr.open_mfdataset(files, combine="nested", concat_dim="time", compat='no_conflicts', join='outer', engine='h5netcdf')
            except:
                qvps = xr.open_mfdataset(files, compat='no_conflicts', engine='h5netcdf')

    if fillna:
        assign = dict()
        for vv in fillna_vars.keys():
            if vv in qvps:
                assign[vv] = qvps[vv].fillna(qvps[fillna_vars[vv]])

        qvps = qvps.assign(assign)

    return qvps

#### Calculate beam blockage

def compute_dem(ds,
                dem_resolution=3,
                wradlib_token: str = None,
                savepath = os.path.join(os.environ['WRADLIB_DATA'], "geo/test_dem.tif")):
    """
    Compute the DEM and save it to a file. Can be then passed to calc_beam_blockage
    to avoid checking tile files and/or fetching them from the internet. By default
    saves the DEM in the wradlib-data folder.

    Parameters
    ----------
    ds : xarray.Dataset or xarray.DataArray
        Radar data in polar coordinates. Must have dims (azimuth, range) (for one elevation)
        or (time, azimuth, range) etc  but we only consider one elevation sweep at a time.
        It must have range, azimuth, and should allow georeferencing via wradlib.
    dem_resolution : int, default 3
        Resolution (arc-seconds) for SRTM fetch (1, 3, or 30).
    wradlib_token : str, optional
        WRADLIB Earthdata bearer token (if needed for DEM access).

    Returns
    -------
    None
    """
    # If token is given, set environment (for remote DEM fetch)
    if wradlib_token is not None:
        os.environ["WRADLIB_EARTHDATA_BEARER_TOKEN"] = wradlib_token

    # 1. Georeference the radar sweep
    # Let ds be a 2D sweep (azimuth × range). If it has extra dims, you may select one slice.
    # Use wradlib’s xarray accessor if available:
    # e.g., if ds is a Wradlib-xarray object:
    wgs84 = osr.SpatialReference()
    wgs84.ImportFromEPSG(4326)
    ds_geo = ds.pipe(wrl.georef.georeference, crs=wgs84)  # this gives ds with x, y, z coords attached

    # After georeferencing, ds_geo should have coords: x (az, range), y, z (altitude of beam center)
    # E.g., ds_geo.x.values, ds_geo.y.values, ds_geo.z.values

    xs = ds_geo.x.values     # shape (az, range)
    ys = ds_geo.y.values

    # 2. Determine DEM bounding box from radar footprint
    # Use wradlib.zonalstats.get_bbox which returns a dict-like:
    bbox = wrl.zonalstats.get_bbox(xs, ys)
    # bbox has keys "left", "bottom", "right", "top"
    left, bottom, right, top = bbox["left"], bbox["bottom"], bbox["right"], bbox["top"]

    # 3. Fetch DEM (SRTM) over that bounding box
    dem = wrl.io.dem.get_srtm([left, right, bottom, top], resolution=dem_resolution, merge=True)

    # 4. Save DEM to file
    gdal.Translate(savepath, dem, format="GTiff")


def calc_beam_blockage(ds,
                        dem_resolution=3,
                        dem_path=None,
                        bw=1.0,
                        wradlib_token: str = None):
    """
    Compute PBB and CBB for a polar radar dataset `ds`.

    Parameters
    ----------
    ds : xarray.Dataset or xarray.DataArray
        Radar data in polar coordinates. Must have dims (azimuth, range) (for one elevation)
        or (time, azimuth, range) etc  but we only consider one elevation sweep at a time.
        It must have range, azimuth, and should allow georeferencing via wradlib.
    dem_resolution : int, default 3
        Resolution (arc-seconds) for SRTM fetch (1, 3, or 30).
    dem_path : str
        Path to a GeoTIFF file containing a pre-calculated DEM. If provided,
        skip the DEM construction and use the provided DEM directly.
    bw : float, default 1.0
        Beam-width scaling (for half power radius).
    wradlib_token : str, optional
        WRADLIB Earthdata bearer token (if needed for DEM access).

    Returns
    -------
    pbb_da : xarray.DataArray
      Partial beam blockage fraction (dims: azimuth × range)
    cbb_da : xarray.DataArray
      Cumulative beam blockage fraction, same dims
    """

    # If token is given, set environment (for remote DEM fetch)
    if wradlib_token is not None:
        os.environ["WRADLIB_EARTHDATA_BEARER_TOKEN"] = wradlib_token

    # 1. Georeference the radar sweep
    # Let ds be a 2D sweep (azimuth × range). If it has extra dims, you may select one slice.
    # Use wradlib’s xarray accessor if available:
    # e.g., if ds is a Wradlib-xarray object:
    wgs84 = osr.SpatialReference()
    wgs84.ImportFromEPSG(4326)
    ds_geo = ds.pipe(wrl.georef.georeference, crs=wgs84)  # this gives ds with x, y, z coords attached

    # After georeferencing, ds_geo should have coords: x (az, range), y, z (altitude of beam center)
    # E.g., ds_geo.x.values, ds_geo.y.values, ds_geo.z.values

    xs = ds_geo.x.values     # shape (az, range)
    ys = ds_geo.y.values
    zs = ds_geo.z.values     # same shape or broadcastable (beam center altitudes)

    # 2. Determine DEM bounding box from radar footprint
    # Use wradlib.zonalstats.get_bbox which returns a dict-like:
    bbox = wrl.zonalstats.get_bbox(xs, ys)
    # bbox has keys "left", "bottom", "right", "top"
    left, bottom, right, top = bbox["left"], bbox["bottom"], bbox["right"], bbox["top"]

    # 3. Check if DEM was provided or fetch DEM (SRTM) over the bounding box
    if dem_path is not None:
        dem = wrl.io.open_raster(dem_path)
    else:
        dem = wrl.io.dem.get_srtm([left, right, bottom, top], resolution=dem_resolution, merge=True)

    # 4. Extract DEM raster arrays and coords
    rastervalues, rastercoords, dem_proj = wrl.georef.extract_raster_dataset(dem, nodata=-32768.0)

    # 5. Clip DEM to radar bounding box
    rlimits = (left, bottom, right, top)
    ind = wrl.util.find_bbox_indices(rastercoords, rlimits)
    rastercoords_clip = rastercoords[ind[1]:ind[3], ind[0]:ind[2], :]
    rastervalues_clip = rastervalues[ind[1]:ind[3], ind[0]:ind[2]]

    # 6. Prepare polar grid (x,y) as points for interpolation
    polcoords = np.dstack((xs, ys))  # shape (az, range, 2)

    # 7. Interpolate DEM heights to the polar coords
    # The result is the “terrain height under each bin” (shape az × range)
    # polar_terrain = wrl.ipol.cart_to_irregular_spline(
    #     rastercoords_clip, rastervalues_clip, polcoords,
    #     order=3, prefilter=False
    # )

    # 7. Interpolate DEM heights to the polar coords
    # Pass the full, unclipped arrays. Coordinates falling outside the
    # downloaded DEM (i.e., the missing open ocean) will default to 0.0.
    try:
        polar_terrain = wrl.ipol.map_coordinates(
                rastercoords, rastervalues, polcoords,
                order=3, prefilter=False
            )
    except AttributeError: # fallback to old method
        polar_terrain = wrl.ipol.cart_to_irregular_spline(
                rastercoords, rastervalues, polcoords,
                order=3, prefilter=False
            )

    # 8. Compute beam radius (half power) for each range bin
    r = ds_geo.range.values   # 1D array (range)
    beamradius = wrl.util.half_power_radius(r, bw)  # gives 1D array (range,)

    # Broadcast to 2D: for each azimuth replicate beamradius
    beamradius2d = np.broadcast_to(beamradius, xs.shape)

    # 9. Compute partial beam blockage
    PBB = wrl.qual.beam_block_frac(polar_terrain, zs, beamradius2d)
    PBB = np.ma.masked_invalid(PBB)

    # 10. Compute cumulative beam blockage
    CBB = wrl.qual.cum_beam_block_frac(PBB)

    # 11. Wrap as xarray DataArrays
    pbb_da = xr.DataArray(PBB.filled(np.nan),
                          dims=("azimuth", "range"),
                          coords={"azimuth": ds_geo.azimuth, "range": ds_geo.range},
                          name="PBB")
    cbb_da = xr.DataArray(CBB,
                          dims=("azimuth", "range"),
                          coords={"azimuth": ds_geo.azimuth, "range": ds_geo.range},
                          name="CBB")

    return pbb_da, cbb_da

#### Loading ZDR offsets and RHOHV noise corrected

def load_ZDR_offset(ds, X_ZDR, zdr_off, zdr_off_name="ZDR_offset", zdr_oc_name="ZDR_OC", attach_all_vars=False):
    """
    Load ZDR offset and correct ZDR, then attach it as a new variable in ds. Optionally
    attach also all variables in the offset file (like the offset value and quality derived quantities).

    Parameter
    ---------
    ds : xarray.Dataset
            Dataset with ZDR data.
    X_ZDR : str
            Name of the ZDR variable.
    zdr_off : str or xr.Dataset
            If str: location of the file or path with wildcards.
            If xarray.Dataset: dataset with the ZDR offset variable included.
    zdr_off_name : str
            Name of the ZDR offset variable in the offset data file.
    zdr_oc_name : str
            Name of the new offset-corrected ZDR variable in the output dataset.
    attach_all_vars : bool
            If True, attachs all variables from the zdr offset file in the output ds.
            Default is False (attachs only the offset-corrected ZDR).

    Return
    ------
    ds : xarray.Dataset
        Dataset with original data plus offset corrected ZDR
    """

    if isinstance(zdr_off, str):
        zdr_offset = xr.open_mfdataset(zdr_off, compat='no_conflicts')
    elif isinstance(zdr_off, xr.Dataset):
        zdr_offset = zdr_off.copy()
    else:
        raise TypeError("load_ZDR_offset: zdr_off must be str or xarray.Dataset")

    # check that the offset have a valid value. Otherwise skip
    if zdr_offset[zdr_off_name].isnull().all():
        raise ValueError("ZDR offset selected has no valid values")
    else:
        # create ZDR_OC variable
        if len(zdr_offset[zdr_off_name].values) > 1:
            ds = ds.assign({zdr_oc_name: ds[X_ZDR]-
                            zdr_offset[zdr_off_name].sel(time=ds["time"], method="nearest")
                            })
        else:
            ds = ds.assign({zdr_oc_name: ds[X_ZDR]-zdr_offset[zdr_off_name].values})
        ds[zdr_oc_name].attrs = ds[X_ZDR].attrs

        if attach_all_vars:
            if len(zdr_offset[zdr_off_name].values) > 1:
                ds = ds.assign(zdr_offset.sel(time=ds["time"], method="nearest"))
            else:
                zdr_offset_ = zdr_offset.map(lambda x: xr.full_like(ds["time"], x.values.item(), dtype=x.dtype)).copy()
                zdr_offset_ = zdr_offset_.assign_coords(ds.coords)
                ds = ds.assign(zdr_offset_)
        return ds

# We define a custom exception to stop the next nexted loops
class StopLoops(Exception):
    pass

def get_ZDR_offset_files(file, split, offsetdir, offsetfile):
    """
    Look for the paths of the ZDR offset file associated with file.
    Basically, gets the path:
        glob.glob( file.split(split)[0] + split + offsetdir + \
                      os.path.dirname(file.split(split)[1]) + "/" + offsetfile )[0]

    Parameter
    ---------
    file : str
        Path to the radar data file
    split : str
        String to separate file and reconstruct
    offsetdir : str
        Directory to the ZDR offset files
    offsetfile : str
        File name or wildcards used to get the ZDR offset file

    Return
    ---------
    """
    if "/VP/" in offsetdir and "/vol5minng01/" in file:
        elevnr = file.split("/vol5minng01/")[-1][0:2]
        file = edit_str(file, "/vol5minng01/"+elevnr, "/90gradstarng01/00")

    offsetfilepath = file.split(split)[0] + split + offsetdir + \
                                os.path.dirname(file.split(split)[1]) + "/" + offsetfile
    offsetfilelist = glob.glob( offsetfilepath )

    if len(offsetfilelist) == 0:
        raise FileNotFoundError(offsetfile+" not found in "+os.path.dirname(offsetfilepath))
    if len(offsetfilelist) == 1:
        return offsetfilelist[0]
    if len(offsetfilelist) > 1:
        warnings.warn("get_ZDR_offset_files: more than one file match the given pattern, returning only the first file")
        return offsetfilelist[0]


def load_best_ZDR_offset(ds, X_ZDR, zdr_off_paths={}, daily_zdr_off_paths={},
                         zdr_off_name="ZDR_offset", zdr_oc_name="ZDR_OC",
                         attach_all_vars=False,
                         daily_corr = True, variability_check = False, variability_thresh = 0.1,
                         first_offset_method_abs_priority = True,
                         mix_offset_variants = False, mix_daily_offset_variants = False,
                         mix_zdr_offsets = False, how_mix_zdr_offset = "count",
                         t_tolerance = 10,
                         abs_zdr_off_min_thresh = 0.,
                         X_RHO="RHOHV", min_height=200,
                         propagate_forward = False, fill_with_daily_offset = True,
                         ):
    """
    Load the best ZDR offset according to priority and certain conditions, then correct ZDR
    and attach it as a new variable in ds. Optionally attach also all variables in the
    offset file (like the offset value and quality derived quantities).

    Parameter
    ---------
    ds : xarray.Dataset
            Dataset with ZDR data.
    X_ZDR : str
            Name of the ZDR variable in ds.
    zdr_off_paths : dict of list
            Dictionary containing lists of paths to the ZDR offset files (one offset
            per timestep). Each key-value pair should contain the paths to ZDR offset
            files for a given ZDR offset correction method (more than one file means there
            are diferent variations of the same method). They keys themselves are
            not important but their order and the order inside each list are important
            to set the priority.
            Example: zdr_off_paths = {"VP": ["/path/to/VP/offset1/file.nc",
                                             "/path/to/VP/offset2/file.nc"],
                                      "QVP": ["/path/to/QVP/offset1/file.nc"]}
    daily_zdr_off_paths : dict of list
            Like zdr_off_paths but for daily offsets (one offset value per day).
            Actually, there is no temporal restriction, only that one value must
            be provided, so longer ds timeseries can also be provided. That said,
            this is meant to be used with daily files. One of zdr_off_paths or
            daily_zdr_off_paths must be provided.
    zdr_off_name : str
            Name of the ZDR offset variable in the offset data file.
    zdr_oc_name : str
            Name of the new offset-corrected ZDR variable in the output dataset.
    attach_all_vars : bool
            If True, attach all variables from the ZDR offset file in the output ds.
            Default is False (attachs only the offset-corrected ZDR).
    daily_corr : bool
            If True, correct only with daily_zdr_off_paths.
    variability_check : bool
            If True and daily_corr is True, check the variability (std) of the
            timestep-based offset and if it is lower than variability_thresh then
            correct with the daily offset, otherwise correct with the timestep-based offset.
    variability_thresh : float
            Threshold value of timestep-based ZDR offset variability to use if
            variability_check is True.
    first_offset_method_abs_priority : bool
            If True, give absolute priority to the offset from the first method in
            zdr_off_paths or daily_zdr_off_paths. That means, if a valid offset
            is found from the first method's files, then stop and return ZDR offset
            corrected with that value.
    mix_offset_variants : bool
            If True, when correcting with timestep offsets, use the variants to fill
            the NaN values according to priority (order in the dictionary).
    mix_daily_offset_variants : bool
            If True when correcting with daily offset, select the most appropriate offset
            variant based on how_mix_zdr_offset.
    mix_zdr_offsets : bool
            If True:
                When correcting with daily offset, select the most appropriate offset
                    based on how_mix_zdr_offset (unless first_offset_class_abs_priority is True).
                When correcting with timestep offsets, compare offset methods for
                    each timestep and select the best one according to on how_mix_zdr_offset.
                    The NaN values are filled with the next method's values.
    how_mix_zdr_offset : str
            How to choose between the different offsets if mix_daily_offset_variants is True
            or mix_zdr_offsets is True. Possible values are "count" or "neg_overcorr".
            "count" will choose the offset that has more data points in its calculation
            (there must be a variable zdr_off_name+"_datacount" in the loaded offset.
            "neg_overcorr" will choose the offset that generates less negative ZDR values.
    t_tolerance : float
            Time difference tolerance in minutes to align timestep-based offsets with ds.
    abs_zdr_off_min_thresh : float
            If abs_zdr_off_min_thresh > 0, check if offset corrected ZDR has more
            negative values than the original ZDR and if the absolute median offset
            is < abs_zdr_off_min_thresh, then undo the correction (set to 0 to avoid this step).
    X_RHO : str
            Name of the RHOHV variable in ds. Only relevant if how_mix_zdr_offset == "neg_overcorr"
            or abs_zdr_off_min_thresh > 0, to evaluate only precipitation pixels.
    min_height : float
            Minimum value of height to be considered. Only relevant if how_mix_zdr_offset == "neg_overcorr"
            or abs_zdr_off_min_thresh > 0, to evaluate only precipitation pixels.
    propagate_forward : bool
            If True and correcting with timestep offsets, fill the missing values
            by propagating forward in time (ffill).
    fill_with_daily_offset : bool
            If True and correcting with timestep offsets, fill the missing values
            with the daily offset (this is applied after propagate_forward).

    Return
    ------
    ds : xarray.Dataset
        Dataset with original data plus offset corrected ZDR

    """
    t_tolerance = t_tolerance*60E9 # change the time tolerance to nanoseconds

    # Process daily correction first
    if daily_corr or (daily_corr is False and fill_with_daily_offset):

        # Load all daily offsets
        daily_zdr_off = daily_zdr_off_paths.copy()

        for zdroff in daily_zdr_off_paths.keys():
            daily_zdr_off[zdroff] = []
            for zdroffv in daily_zdr_off_paths[zdroff]:
                try:
                    daily_zdr_off[zdroff].append( xr.open_mfdataset(zdroffv, compat='no_conflicts') )
                    if len(daily_zdr_off[zdroff][-1][zdr_off_name]) > 1:
                        raise TypeError("load_best_ZDR_offset: daily offset has more than one value: "+zdroffv)
                except:
                    warnings.warn("load_best_ZDR_offset: unable to load "+zdroffv)

        dzdroff0 = {}

        for zdroffn, zdroff in enumerate(daily_zdr_off.keys()):
            ini = 0
            for zdroff_ in daily_zdr_off[zdroff]:
                # Load the first available offset
                if ini == 0 :
                    dzdroff0[zdroff] = zdroff_.copy()
                    if dzdroff0[zdroff][zdr_off_name].notnull().all():
                        ini = 1
                        if mix_daily_offset_variants:
                            continue
                        else:
                            break

                # If mixing zdr offsets variants, select the appropriate offset based on the
                # selected condition
                if ( mix_daily_offset_variants and ini > 0 and zdroff_[zdr_off_name].notnull().all() ) :

                    # if zdroff not in dzdroff0:
                    #     dzdroff0[zdroff] = zdroff_.copy()
                    #     continue

                    if how_mix_zdr_offset == "neg_overcorr":
                        # calculate the count of negative values after each correction
                        neg_count_ds_0 = ( load_ZDR_offset(ds, X_ZDR, dzdroff0[zdroff],
                                                         zdr_off_name=zdr_off_name,
                                                         zdr_oc_name=zdr_oc_name,
                                                         attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum().compute()

                        neg_count_ds_ = ( load_ZDR_offset(ds, X_ZDR, zdroff_,
                                                         zdr_off_name=zdr_off_name,
                                                         zdr_oc_name=zdr_oc_name,
                                                         attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum().compute()

                        if neg_count_ds_0.values > neg_count_ds_.values:
                            # continue with the correction with less negative values
                            dzdroff0[zdroff] = zdroff_.copy()

                    elif how_mix_zdr_offset == "count":
                        if zdr_off_name+"_datacount" in dzdroff0[zdroff] and zdr_off_name+"_datacount" in zdroff_:
                            # Choose the offset that has the most data points in its calculation
                            if zdroff_[zdr_off_name+"_datacount"].values > dzdroff0[zdroff][zdr_off_name+"_datacount"].values:
                                # continue with the correction with more data points
                                dzdroff0[zdroff] = zdroff_.copy()
                        else:
                            print("how_mix_zdr_offset == 'count' not possible, "+zdr_off_name+"_datacount not present in all offset datasets.")

            # If the first class should have absolute priority, then exit the loops
            if first_offset_method_abs_priority and zdroffn==0 and ini > 0:
                raise StopLoops

            # If mix_zdr_offsets is False, break the loop
            if mix_zdr_offsets is False and ini>0:
                break

        # If mix_zdr_offsets, compare between different offset methods
        if mix_zdr_offsets and len(dzdroff0) > 1 :
            for zdroffn, zdroff in enumerate(dzdroff0.keys()):
                if zdroffn == 0:
                    dfinal = dzdroff0[zdroff].copy()
                    continue

                if how_mix_zdr_offset == "neg_overcorr":
                    # calculate the count of negative values after each correction
                    neg_count_ds_0 = ( load_ZDR_offset(ds, X_ZDR, dfinal,
                                                     zdr_off_name=zdr_off_name,
                                                     zdr_oc_name=zdr_oc_name,
                                                     attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum().compute()

                    neg_count_ds_ = ( load_ZDR_offset(ds, X_ZDR, dzdroff0[zdroff],
                                                     zdr_off_name=zdr_off_name,
                                                     zdr_oc_name=zdr_oc_name,
                                                     attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum().compute()

                    if neg_count_ds_0.values > neg_count_ds_.values:
                        # continue with the correction with less negative values
                        dfinal = dzdroff0[zdroff].copy()

                elif how_mix_zdr_offset == "count":
                    if zdr_off_name+"_datacount" in dzdroff0[zdroff] and zdr_off_name+"_datacount" in dfinal:
                        # Choose the offset that has the most data points in its calculation
                        if dzdroff0[zdroff][zdr_off_name+"_datacount"].values > dfinal[zdr_off_name+"_datacount"].values:
                            # continue with the correction with more data points
                            dfinal = dzdroff0[zdroff].copy()
                    else:
                        print("how_mix_zdr_offset == 'count' not possible, "+zdr_off_name+"_datacount not present in all offset datasets.")
        # Else, just load the first offset in order of priority
        else:
            for zdroffn, zdroff in enumerate(dzdroff0.keys()):
                dfinal = dzdroff0[zdroff].copy()
                break

        if daily_corr:
            # Check  if the final offset overcorrects more than the given threshold
            if abs_zdr_off_min_thresh > 0. and variability_check is False:
                # calculate the count of negative values before and after correction
                neg_count_ds = (ds[X_ZDR].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum().compute()
                neg_count_ds_oc = (load_ZDR_offset(ds, X_ZDR, dfinal,
                                                 zdr_off_name=zdr_off_name,
                                                 zdr_oc_name=zdr_oc_name,
                                                 attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum().compute()

                if neg_count_ds_oc > neg_count_ds.values and dfinal[zdr_off_name] < abs_zdr_off_min_thresh:
                    # if the correction introduces more negative values and
                    # the offset is lower than abs_zdr_off_min_thresh, then do not correct
                    ds[zdr_oc_name] = ds[X_ZDR]
                    return ds
            # Otherwise just return with the current offset
            elif variability_check is False:
                return load_ZDR_offset(ds, X_ZDR, dfinal,
                                                 zdr_off_name=zdr_off_name,
                                                 zdr_oc_name=zdr_oc_name,
                                                 attach_all_vars=attach_all_vars)

    # Process timestep correction
    if variability_check or daily_corr is False:

        # Load all timestep offsets
        zdr_off = zdr_off_paths.copy()

        for zdroff in zdr_off_paths.keys():
            zdr_off[zdroff] = []
            for zdroffv in zdr_off_paths[zdroff]:
                try:
                    zdr_off[zdroff].append( xr.open_mfdataset(zdroffv, compat='no_conflicts').sel(time=ds.time, method="nearest", tolerance=t_tolerance).assign_coords(time=ds.time) )
                except:
                    warnings.warn("load_best_ZDR_offset: unable to load "+zdroffv)

        zdroff0 = {}
        # Get first valid offset series for each class and fill NaN with variants if mix_offset_variants is True
        for zdroffn, zdroff in enumerate(zdr_off.keys()):
            ini = 0
            for zdroff_ in zdr_off[zdroff]:
                # Load the first available offset
                if ini == 0 :
                    zdroff0[zdroff] = zdroff_.copy()
                    if zdroff0[zdroff][zdr_off_name].notnull().any():
                        ini = 1
                        continue

                # If mixing zdr offset variants, fill missing values with the different variants
                if ini>0 and mix_offset_variants:
                    zdroff0[zdroff] = zdroff0[zdroff].where(zdroff0[zdroff][zdr_off_name].notnull(), zdroff_.copy()).copy()

            # If the first class should have absolute priority, then exit the loops
            if ini>0 and first_offset_method_abs_priority and zdroffn==0:
                break

        # Get dimensions to reduce (other than time)
        dims_wotime = [kk for kk in ds.dims if kk != "time"]

        # If mix_zdr_offsets is True, merge offset methods based on the selected condition
        ini = 0
        for zdroffn, zdroff in enumerate(zdroff0.keys()):
            if ini == 0:
                final = zdroff0[zdroff].copy()
                ini = 1
                if mix_zdr_offsets is not True:
                    # if not mixing offset methods, break here
                    break
            else:
                if how_mix_zdr_offset == "neg_overcorr":
                    # calculate the count of negative values after each correction
                    neg_count_ds_final = ( load_ZDR_offset(ds, X_ZDR, final,
                                                     zdr_off_name=zdr_off_name,
                                                     zdr_oc_name=zdr_oc_name,
                                                     attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum(dims_wotime).compute()

                    neg_count_ds_ = ( load_ZDR_offset(ds, X_ZDR, zdroff0[zdroff],
                                                     zdr_off_name=zdr_off_name,
                                                     zdr_oc_name=zdr_oc_name,
                                                     attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum(dims_wotime).compute()

                    # Are there less negatives in the first correction than in the new one?
                    neg_count_final_cond = neg_count_ds_final < neg_count_ds_
                    # Retain first correction where the condition is True, otherwise use the new correction
                    final = final.where(neg_count_final_cond, zdroff0[zdroff].copy()).copy()

                elif how_mix_zdr_offset == "count":
                    if zdr_off_name+"_datacount" in final and zdr_off_name+"_datacount" in zdroff0[zdroff]:
                        # Choose the offset that has the most data points in its calculation
                        final = final.where(final[zdr_off_name+"_datacount"] > zdroff0[zdroff][zdr_off_name+"_datacount"],
                                            zdroff0[zdroff]).copy()
                    else:
                        print("how_mix_zdr_offset == 'count' not possible, "+zdr_off_name+"_datacount not present in all offset datasets.")

                # Finally, fill the last NaN values with the alternative-method offset
                final = final.where(final[zdr_off_name].notnull(), zdroff0[zdroff]).copy()

        # Check if the final offset overcorrects more than the given threshold
        if abs_zdr_off_min_thresh > 0.:
            # calculate the count of negative values before and after correction
            neg_count_ds = (ds[X_ZDR].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum(dims_wotime).compute()
            neg_count_ds_oc = (load_ZDR_offset(ds, X_ZDR, final,
                                             zdr_off_name=zdr_off_name,
                                             zdr_oc_name=zdr_oc_name,
                                             attach_all_vars=False)[zdr_oc_name].where((ds[X_RHO]>0.99) * (ds["z"]>min_height)) < 0).sum(dims_wotime).compute()
            neg_count_final_cond = (neg_count_ds_oc > neg_count_ds) * (final[zdr_off_name] < abs_zdr_off_min_thresh)

            # if the correction introduces more negative values and
            # the offset is lower than abs_zdr_off_min_thresh, then do not correct
            final = final.where(~neg_count_final_cond)

        if propagate_forward:
            final = final.ffill("time")
        if fill_with_daily_offset:
            # we need to expand the daily offset into the shape of the timestep offset
            dfinal_ = dfinal.map(lambda x: xr.full_like(final[x.name], x.values.item()))
            dfinal_ = dfinal_.assign_coords(final.coords)
            final = final.fillna(dfinal_)

        if variability_check and daily_corr:
            if final[zdr_off_name].std("time") > variability_thresh:
                return load_ZDR_offset(ds, X_ZDR, final,
                                                 zdr_off_name=zdr_off_name,
                                                 zdr_oc_name=zdr_oc_name,
                                                 attach_all_vars=attach_all_vars)
            else:
                return load_ZDR_offset(ds, X_ZDR, dfinal,
                                                 zdr_off_name=zdr_off_name,
                                                 zdr_oc_name=zdr_oc_name,
                                                 attach_all_vars=attach_all_vars)


        else:
            return load_ZDR_offset(ds, X_ZDR, final,
                                             zdr_off_name=zdr_off_name,
                                             zdr_oc_name=zdr_oc_name,
                                             attach_all_vars=attach_all_vars)



def load_corrected_RHOHV(ds, rho_nc_path, rho_nc_name="RHOHV_NC"):
    """
    Load noise corrected RHOHV and attach it to ds.

    Parameter
    ---------
    ds : xarray.Dataset or xarray.Dataarray
            Dataset
    rho_nc_path : str
            Location of the file or path with wildcards
    rho_nc_name : str
            Name of the RHOHV variable in the corrected data file

    Return
    ------
    ds : xarray.Dataset
        Dataset with original data plus noise corrected RHOHV
    """

    rho_nc = xr.open_mfdataset(rho_nc_path, compat='no_conflicts')

    if rho_nc[rho_nc_name].notnull().any():

        # create RHOHV_NC variable
        ds = ds.assign(rho_nc)
        ds[rho_nc_name].attrs["noise correction level"] = rho_nc.attrs["noise correction level"]

        return ds
    else:
        warnings.warn("load_corrected_RHOHV: "+rho_nc_name+" in the provided file has no valid values!")
        return ds

#### QVPs
def compute_qvp(ds, min_thresh = {"RHOHV":0.7, "TH":0, "ZDR":-1} , output_count=False):
    """
    Computes QVP by doing the azimuthal median from the values of an
    xarray Dataset, thresholded by min_thresh.

    Parameter
    ---------
    ds : xarray.Dataset
            Dataset
    min_thresh : dict
            dictionary where the keys are variable names and the values are
            the minimum values of each variable, for thresholding.
    output_count : bool
            If True, output a second dataset with the counts of valid values that
            went into the QVP calculation.
    Return
    ------
    ds_qvp : xarray.Dataset
        Dataset with the thresholded data reduced to a QVP with dim z (and time if available)
    ds_qvp_count : xarray.Dataset, optional
        Dataset with the counts of valid values that went into the QVP calculation.
    """
    # Georeference if not
    if "z" not in ds:
        ds = ds.pipe(wrl.georef.georeference)

    # Create a combined filter mask for all conditions in the dictionary
    combined_mask = None
    for var_name, threshold in min_thresh.items():
        if var_name in ds:
            if ds[var_name].count().compute() == 0:
                # if all values are NaN, skip this variable
                continue
            condition = ds[var_name] > threshold
            if combined_mask is None:
                combined_mask = condition.compute()
            else:
                combined_mask &= condition.compute()

    ds_qvp = ds.where(combined_mask).median("azimuth", keep_attrs=True)

    # assign coord z
    ds_qvp = ds_qvp.assign_coords({"z": ds["z"].median("azimuth", keep_attrs=True)})

    try:
        ds_qvp = ds_qvp.swap_dims({"range":"z"}) # swap range dimension for height
    except ValueError:
        warnings.warn("compute_qvp: Unable to swap range and z dimensions")

    if output_count:
        ds_qvp_count = ds.where(combined_mask).count("azimuth", keep_attrs=True)

        # assign coord z
        ds_qvp_count = ds_qvp_count.assign_coords({"z": ds["z"].median("azimuth", keep_attrs=True)})

        try:
            ds_qvp_count = ds_qvp_count.swap_dims({"range":"z"}) # swap range dimension for height
        except ValueError:
            None
        return ds_qvp, ds_qvp_count

    else:
        return ds_qvp

def compute_rdqvp(ds, min_thresh = {"RHOHV":0.7, "TH":0, "ZDR":-1}, max_range=50000. ):
    """
    Computes range-defined QVP by doing the azimuthal median from the values of an
    xarray Dataset with several elevations (radar volume), thresholded by min_thresh.
    This simple version only considers data inside the defined range and does not
    use any weighting outside the range, it just ignores it.

    Parameter
    ---------
    ds : xarray.Dataset
            Dataset with several elevations (radar volume)
    min_thresh : dict
            dictionary where the keys are variable names and the values are
            the minimum values of each variable, for thresholding.
    max_range : float
            Maximum ground range within wich to consider values. This is the
            ground distance to the radar and not the range along the ray.

    Return
    ------
    ds_qvp : xarray.Dataset
        Dataset with the thresholded data reduced to a QVP with dim z (and time if available)

    Reference
    ------
    Tobin, D. M., and M. R. Kumjian, 2017: Polarimetric Radar and Surface-Based Precipitation-Type Observations of Ice Pellet to Freezing Rain Transitions. Wea. Forecasting, 32, 2065–2082
    https://doi.org/10.1175/WAF-D-17-0054.1
    """
    qvps=[]
    qvps_count=[]
    qvps_highres=[]
    qvps_highres_count=[]
    ds_close = ds.where(ds["gr"]<max_range)
    min_z = ds_close["z"].min().values
    max_z = ds_close["z"].max().values

    # call compute_qvp for each elevation
    for sfa in ds_close["sweep_fixed_angle"]:
        qvp, count = compute_qvp(ds_close.sel(sweep_fixed_angle=sfa), min_thresh=min_thresh, output_count=True)
        qvps.append(qvp.copy(deep=True))
        qvps_count.append(count.fillna(0).copy(deep=True))

    # interpolate to higher res z
    new_z = np.linspace(min_z, max_z, round((max_z-min_z)/2) )

    for qvp in qvps:
        qvps_highres.append( qvp.interp(z=new_z) )

    for count in qvps_count:
        qvps_highres_count.append( count.interp(z=new_z) )

    # merge qvps into one dataset
    qvps_highres = xr.concat(qvps_highres, dim="sweep_fixed_angle", join="outer", coords="different", compat='equals').chunk(dict(sweep_fixed_angle=-1))
    qvps_highres_count = xr.concat(qvps_highres_count, dim="sweep_fixed_angle", join="outer", coords="different", compat='equals').chunk(dict(sweep_fixed_angle=-1))

    # weighted median of all elevs
    ds_qvp = qvps_highres.weighted(qvps_highres_count["DBZH"].fillna(0)).quantile(q=0.5, dim="sweep_fixed_angle")

    return ds_qvp

#### Entropy calculation
def Entropy_timesteps_over_azimuth_different_vars_schneller(ds, n_az=360, zhlin="zhlin", zdrlin="zdrlin", rhohvnc="RHOHV_NC", kdp="KDP_ML_corrected"):

    '''
    From Tobias Scharbach

    Function to calculate the Efficiency (Normalized Entropy) according to information theory,
    to estimate the homogenity from a sector PPi or the whole 360° PPi
    for each timestep. Values over 0.8 are considered stratiform.

    The dataset should have zhlin and zdrlin which are the linear form of ZH and ZDR, i.e. only positive values
    (not in DB, use wradlib.trafo.idecibel to transform from DBZ to linear)


    Parameter
    ---------
    ds : xarray.DataArray
        array with PPI data.

    n_az : int
        number of azimuth values.

    Keyword Arguments
    -----------------
    zhlin : str
        Name of the ZH linear variable

    zdrlin : str
        Name of the ZDR linear variable

    rhohvnc : str
        Name of the RHOHV noise corrected variable

    kdp : str
        Name of the KDP variable. Melting layer corrected KDP is better.

    Return
    ------
    entropy_all_xr : xarray.DataArray
        DataArray with entropy values for the four input variables

    ######### Example how to calculate the min over the entropy calculated over the polarimetric variables
    Entropy = Entropy_timesteps_over_azimuth_different_vars_schneller(ds)

    strati = xr.concat((Entropy.entropy_zdrlin, Entropy.entropy_Z, Entropy.entropy_RHOHV, Entropy.entropy_KDP),"entropy", join="outer", coords="different")

    min_trst_strati = strati.min("entropy")
    ds["min_entropy"] = min_trst_strati

    '''
    Variable_List_new_zhlin = (ds[zhlin]/(ds[zhlin].sum(("azimuth"),skipna=True)))
    entropy_zhlin = - ((Variable_List_new_zhlin * np.log10(Variable_List_new_zhlin)).sum("azimuth"))/np.log10(n_az)
    entropy_zhlin = entropy_zhlin.rename("entropy_Z")

    Variable_List_new_zdrlin = (ds[zdrlin]/(ds[zdrlin].sum(("azimuth"),skipna=True)))
    entropy_zdrlin = - ((Variable_List_new_zdrlin * np.log10(Variable_List_new_zdrlin)).sum("azimuth"))/np.log10(n_az)
    entropy_zdrlin = entropy_zdrlin.rename("entropy_zdrlin")


    Variable_List_new_RHOHV = (ds[rhohvnc]/(ds[rhohvnc].sum(("azimuth"),skipna=True)))
    entropy_RHOHV = - ((Variable_List_new_RHOHV * np.log10(Variable_List_new_RHOHV)).sum("azimuth"))/np.log10(n_az)
    entropy_RHOHV = entropy_RHOHV.rename("entropy_RHOHV")


    Variable_List_new_KDP = (ds[kdp]/(ds[kdp].sum(("azimuth"),skipna=True)))
    entropy_KDP = - ((Variable_List_new_KDP * np.log10(Variable_List_new_KDP)).sum("azimuth"))/np.log10(n_az)
    entropy_KDP = entropy_KDP.rename("entropy_KDP")



    entropy_all_xr = xr.merge([entropy_zhlin, entropy_zdrlin, entropy_RHOHV, entropy_KDP ], compat='no_conflicts')

    return entropy_all_xr

def calculate_pseudo_entropy(ds, dim='azimuth', var_names=["zhlin", "zdrlin", "RHOHV_NC", "KDP_ML_corrected"], n_lowest=30):

    '''
    Function to calculate the Efficiency (Normalized Entropy) according to information theory.
    This implementation differs from the original formulation in that the probabilities of
    each value are replaced by the values normalized by the sum of all values.
    Useful to estimate the homogenity from a sector PPi or the whole 360° PPi
    for each timestep. Values over 0.8 or 0.85 could be considered stratiform.

    The dataset should have zhlin and zdrlin which are the linear form of ZH and ZDR, i.e. only positive values
    (not in DB, use wradlib.trafo.idecibel to transform from DBZ to linear)

    Parameter
    ---------
    ds : xarray.DataArray
        array with PPI data.

    dim : str
        dimension over which to perform the operation

    var_names : list
        list of variable names over which to perform the operation

    n_lowest : int
        minimum amount of non-nan values for returning non-nan entropy

    Return
    ------
    entropy_all_xr : xarray.Dataset
        Dataset with (pseudo-)entropy values for the input variables

    ######### Example how to calculate the min over the entropy calculated over the polarimetric variables
    Entropy = calculate_pseudo_entropy(ds)

    strati = xr.concat((Entropy.entropy_zhlin, Entropy.entropy_zdrlin, Entropy.entropy_RHOHV, Entropy.entropy_KDP),"entropy")

    min_trst_strati = strati.min("entropy")
    ds["min_entropy"] = min_trst_strati

    '''
    def calc_pseudo_entropy(da):
        # This function calculates the pseudo entropy for the input data along dim
        da_normed = da / da.sum(dim, skipna=True)
        pseudo_entropy = -((da_normed * np.log10(da_normed)).sum(dim)) \
                         / np.log10(da_normed[dim].size)
        pseudo_entropy = pseudo_entropy.where(~(da==0.).all(dim), other=1.).where(da.count(dim=dim) >= n_lowest)
        return pseudo_entropy

    pseudo_entropy_list = []
    for vv in var_names:
        pseudo_entropy_list.append( calc_pseudo_entropy(ds[vv]).rename("entropy_"+vv) )

    return xr.merge(pseudo_entropy_list, compat='no_conflicts')

def calculate_binned_normalized_entropy(ds, dim='azimuth', var_names=["zhlin", "zdrlin", "RHOHV_NC", "KDP_ML_corrected"],
                                        n_lowest=30, bins=50, remove_empty_bins=False):

    '''
    Function to calculate the Efficiency (Normalized Entropy) according to information theory
    based on a binning of the input data. Useful to estimate the homogenity from a sector PPi
    or the whole 360° PPi for each timestep. Values over 0.8 could be considered stratiform.

    The dataset should have zhlin and zdrlin which are the linear form of ZH and ZDR, i.e. only positive values
    (not in DB, use wradlib.trafo.idecibel to transform from DBZ to linear)

    Parameter
    ---------
    ds : xarray.DataArray
        array with PPI data.

    dim : str
        dimension over which to perform the operation

    var_names : list
        list of variable names over which to perform the operation

    n_lowest : int
        minimum amount of non-nan values for returning non-nan entropy

    bins : int, str
        number of bins to use for binning the data or the method used to automatically calculate
        the optimal bin width as defined by numpy.histogram_bin_edges. The probabilities of each bin
        are estimated and the normalized entropy is calculated based on those probabilities

    Return
    ------
    entropy_all_xr : xarray.Dataset
        Dataset with entropy values for the input variables

    ######### Example how to calculate the min over the entropy calculated over the polarimetric variables
    Entropy = calculate_normalized_entropy(ds)

    strati = xr.concat((Entropy.entropy_zhlin, Entropy.entropy_zdrlin, Entropy.entropy_RHOHV, Entropy.entropy_KDP),"entropy")

    min_trst_strati = strati.min("entropy")
    ds["min_entropy"] = min_trst_strati

    '''

    def calc_entropy_slices(da_slice, n_valid_values=n_lowest, bins=bins):
        if np.isfinite(da_slice).sum() < n_valid_values:
            # return xr.DataArray(np.array(np.nan), name="entropy_"+da_slice.name)
            return np.array(np.nan)
        elif np.all(da_slice == 0.):
            # return xr.DataArray(np.array(1.), name="entropy_"+da_slice.name)
            return np.array(1.)
        else:
            # This function calculates the normalized entropy for the whole input data (meant to be used in 1D slices)

            # calculate the bins manually because xhistogram does not automatically compute bins for dask arrays
            # bins_array = np.histogram_bin_edges(da_slice, bins=bins, range=(float(da_slice.min()), float(da_slice.max())))

            # calculate the histogram and the probabilities
            hist = np.histogram(da_slice, bins=bins, range=(float(np.nanmin(da_slice)), float(np.nanmax(da_slice))))
            probs = hist[0]/hist[0].sum()

            # Calculate normalized entropy
            if remove_empty_bins:
                norm_entropy = - (probs*np.log10(probs+1e-15)).sum()/np.log10(np.where(probs>0, 1, 0).sum())
            else:
                norm_entropy = - (probs*np.log10(probs+1e-15)).sum()/np.log10(len(probs))

            # return norm_entropy.rename("entropy_"+da_slice.name)
            return norm_entropy

    norm_entropy_list = []
    for vv in var_names:
        norm_entropy_list.append( xr.apply_ufunc(calc_entropy_slices,
                                                 ds[vv],
                                                 input_core_dims=[[dim]],
                                                 vectorize=True,
                                                 dask="parallelized",
                                                 output_dtypes=[float],
                                                 on_missing_core_dim="copy",
                                                 dask_gufunc_kwargs={"allow_rechunk":True}
                                                 ).rename("entropy_"+vv) )

    return xr.merge(norm_entropy_list, compat='no_conflicts')

def calculate_std(ds, dim='azimuth', var_names=["zhlin", "zdrlin", "RHOHV_NC", "KDP_ML_corrected"], n_lowest=30, normlims=None):

    '''
    Function to calculate the standard deviation in a given dimension after
    normalizing the variables. Can be used to estimate the homogenity from a
    sector PPi or the whole 360° PPi for each timestep.

    Parameter
    ---------
    ds : xarray.DataArray
        array with PPI data.

    dim : str
        dimension over which to perform the operation

    var_names : list
        list of variable names over which to perform the operation

    n_lowest : int
        minimum amount of non-nan values for returning non-nan results

    normlims : list, array, tuple
        Iterable with the minimum and maximum values to use for normalization. If None,
        the minimum and maximum of ds are used.

    Return
    ------
    std : xarray.Dataset
        Dataset with std values for the input variables along the given dimension

    '''
    try:
        def calc_std_slices(da_slice):
            return np.nanstd((da_slice-normlims[0])/(normlims[1]-normlims[0]))
    except TypeError:
        def calc_std_slices(da_slice):
            return np.nanstd((da_slice-np.nanmin(da_slice))/(np.nanmax(da_slice)-np.nanmin(da_slice)))

    norm_std_list = []
    for vv in var_names:
        norm_std_list.append( xr.apply_ufunc(calc_std_slices,
                                                 ds[vv],
                                                 input_core_dims=[[dim]],
                                                 vectorize=True,
                                                 dask="parallelized",
                                                 output_dtypes=[float],
                                                 on_missing_core_dim="copy",
                                                 dask_gufunc_kwargs={"allow_rechunk":True}
                                                 ).rename("std_"+vv) )

    return xr.merge(norm_std_list, compat='no_conflicts')


#### Melting Layer after Wolfensberger et al 2016 but refined for PHIDP correction using Silke's style from Trömel 2019 and Giangrande refinement

def normalise(da, dim):
    damin = da.min(dim=dim, skipna=True, keep_attrs=True)
    damax = da.max(dim=dim, skipna=True, keep_attrs=True)
    da = (da - damin) / (damax - damin)
    return da


def sobel(da, dim):
    axis = da.get_axis_num(dim)
    func = lambda x, y: ndimage.sobel(x, y)
    return xr.apply_ufunc(func, da, axis, dask='parallelized')


def ml_normalise(ds, moments=dict(DBZH=(10., 60.), RHOHV=(0.65, 1.)), dim='height'):
    assign = {}
    for m, span in moments.items():
        v = ds[m]
        v = v.where((v >= span[0]) & (v <= span[1]))
        v = v.pipe(normalise, dim=dim)
        assign.update({f'{m}_norm': v})
    return xr.Dataset(assign)


def ml_clean(ds, zh, dim='height'):
    # removing profiles with too few data (>93% of array is nan)
    good = ds[zh+"_norm"].count(dim=dim) / ds[zh+"_norm"].sizes[dim] * 100
    return ds.where(good > 7)


def ml_combine(ds, zh, rho, dim='height'):
    comb = (1 - ds[rho+"_norm"]) * ds[zh+"_norm"]
    return comb


def ml_gradient(ds, dim='height', ywin=None):
    assign = {}
    for m in ds.data_vars:
        # step 3 sobel filter
        dy = ds[m].pipe(sobel, dim)
        # step 3 smoothing
        # currently smoothes only in y-direction (height)
        dy = dy.rolling({dim: ywin}, center=True).mean()
        assign.update({f'{m}_dy': dy})
    return ds.assign(assign)


def ml_noise_reduction(ds, dim='height', thres=0.02):
    assign = {}
    for m in ds.data_vars:
        if '_dy' in m:
            dy = ds[m].where((ds[m] > thres) | (ds[m] < -thres))
            assign.update({f"{m}": dy})
    return ds.assign(assign)



def ml_height_bottom_new(ds, moment='comb_dy', dim='height', skipna=True, drop=True):

    hgt = ds[moment].idxmax(dim=dim, skipna=skipna, fill_value=np.nan).load()


    ds = ds.assign(dict(
                        mlh_bottom=hgt))
    return ds


def ml_height_top_new(ds, moment='comb_dy', dim='height',skipna=True, drop=True):#, max_height=3000): 2000 für 16.11.2014

    hgt = ds[moment].idxmin(dim=dim, skipna=skipna, fill_value=np.nan).load()

    ds = ds.assign(dict(
                    mlh_top=hgt))
    return ds




def melting_layer_qvp_X_new(ds, moments=dict(DBZH=(10., 60.), RHOHV=(0.65, 1.), PHIDP=(-90.,-70.)), dim='height',
                            thres=0.02, xwin=5, ywin=5, fmlh=0.3, min_h=600, max_h=5000, rhohv_thresh_gia=(0.97, 1),
                            grad_thresh=0.0001, all_data=False, clowres=False):
    '''
    Function to detect the melting layer based on wolfensberger et al 2016 (https://doi.org/10.1002/qj.2672)
    refined by T. Scharbach. Giangrande refinement is also calculated and included in separate variables.

    Parameter
    ---------
    ds : xarray.DataArray
        array with QVP data.

    Keyword Arguments
    -----------------
    moments : dict
        Dictionary with values for normalization of every moment.

    dim : str
        Name of the height dimension.

    thres : float
        Threshold for noise reduction in the gradients of the normalized smoothed variables. Only values over thres are kept.

    xwin : int
        Window size for rolling median smoothing

    ywin : int
        Window size for rolling mean smoothing

    fmlh : float
        Tolerance value for melting layer height limits, above and below +-(1 +- flmh) from
        calculated median top and bottom, respectively.

    min_h : int, float
        Minimum height of usable data within the polarimetric profiles, in m. This is relative to
        sea level and not relative to the altitude of the radar (in accordance to the "z" coordinate
        from wradlib.georef.georeference). The default is 600.

    max_h: int, float
        Maximum height of usable data within the polarimetric profiles, in m. Analogous to min_h.
        This basically sets an upper limit for the melting layer detection.

    rhohv_thresh_gia : tuple or list
        Thresholds for filtering RHOHV in Giangrande refinement. Only data between the provided
        thresholds is used for the refinement.

    grad_thresh : float
        Threshold for filtering RHOHV gradient after Giangrande refinement. RHOHV gradient in dim
        must be lower than this threshold to qualify as ML top or bottom. To ignore this condition just
        set the value of grad_thresh to an unreasonably high value (e.g. grad_thresh=1).

    all_data : bool
        If True, include all normalized moments in the output dataset. If False, only output
        melting layer height values. Default is False.

    clowres : bool
        If True, use an adaptation for low resolution data (e.g. 1 km range resolution in DWD's C-band). Default is False.

    Return
    ------
    ds : xarray.DataArray
        DataArray with input data plus variables for ML top and bottom and also normalized and derived variables.
    '''
    zh = [k for k in moments if ("zh" in k.lower()) or ("th" in k.lower())][0]
    rho = [k for k in moments if "rho" in k.lower()][0]
    phi = [k for k in moments if "phi" in k.lower()][0]

    # step 1: Filter values below min_h and normalize
    ds0 = ml_normalise(ds.where(ds[dim]>min_h).where(ds[dim]<max_h), moments=moments, dim=dim)

    # step 1a
    # removing profiles with too few data (>93% of array is nan)
    good = ml_clean(ds0, zh, dim=dim)

    # step 2
    comb = ml_combine(good, zh, rho, dim=dim).fillna(0.) # 07/11/23: added fillna(0.) for cases where the filtering removes one of the ML gradients
    ds0 = ds0.assign(dict(comb=comb))

    # step 3 (and 8)
    ds0 = ml_gradient(ds0, dim=dim, ywin=ywin)

    # step 4
    ds1 = ml_noise_reduction(ds0, dim=dim, thres=thres)
    #display(ds1)

    # step 5
    ds2 = ml_height_bottom_new(ds1, dim=dim, drop=False)
    ds2 = ml_height_top_new(ds2, dim=dim, drop=False)
    #!!! TO DO: add a filter in ml_height_top_new so that the preselected ML top must be
    # above the ML bottom. I would have to check that the mlh_bottom exists and carefully
    # deal with the NaNs. I cannot just filter ds2 in this line or it will broadcast the
    # ML heights to the z coord.

    # step 6
    while xwin >1: # try: in case there are few timesteps reduce xwin until it is possible to compute
        try:
            med_mlh_bot = ds2.mlh_bottom.rolling(time=xwin, min_periods=xwin//2, center=True).median(skipna=True)     #min_periods=xwin//2
            med_mlh_top = ds2.mlh_top.rolling(time=xwin, min_periods=xwin//2, center=True).median(skipna=True)        # min_periods=xwin//2
            break
        except ValueError:
            xwin-=2

    if xwin == 1:
        med_mlh_bot = np.nan
        med_mlh_top = np.nan

    # step 7 (step 5 again)
    above = (1 + fmlh) * med_mlh_top
    below = (1 - fmlh) * med_mlh_bot
    ds3 = ds1.where((ds1[dim] >= below) & (ds1[dim] <= above), drop=False)
    ds3 = ml_height_bottom_new(ds3, dim=dim, drop=False)
    ds3 = ml_height_top_new(ds3, dim=dim, drop=False)

    # ds3.mlh_bottom and ds3.ml_bottom derived according Wolfensberger et. al.

    # step 8 already done at step 3

    # step 9

    # ml top refinement
    # cut below ml_top
    ds4 = ds0.where((ds0[dim] > ds3.mlh_top))# & (ds0[dim] < above))
    # cut above first local maxima (via differentiation and difference of signs)
    ########## rechunk, weil plötzlich nicht mehr geht, warum auch immer naja, neue Version????
    ds4 = ds4.chunk(-1)
    p4 = np.sign(ds4[zh+"_norm_dy"].differentiate(dim)).diff(dim).idxmin(dim, skipna=True)
    ds5 = ds4.where(ds4[dim] < p4)
    ds5 = ml_height_top_new(ds5, moment=phi+"_norm", dim=dim, drop=False)

    # ds5.mlh_top,ds5.ml_top, derived according Wolfensberger et. al. but used PHIDP_norm instead of DBZH_norm

    # ml bottom refinement
    ds6 = ds0.where((ds0[dim] < ds3.mlh_bottom) & (ds0[dim] > below))
    # cut below first local maxima (via differentiation and difference of signs)
    ds6 = ds6.chunk(-1)
    p4a = np.sign(ds6[phi+"_norm_dy"].differentiate(dim)).diff(dim).sortby(dim, ascending=False).idxmin(dim, skipna=True)

    if clowres is not True:
        ds7 = ds6.where(ds6[dim] > p4a)

    #idx = ds7[phi+"_norm"].argmin(dim=dim, skipna=True)
    #idx[np.isnan(idx)] = 0
    if clowres:
        hgt = ds6[phi+"_norm"].idxmin(dim=dim, skipna=True, fill_value=np.nan)
        # Julian Giles modification: instead of taking the mean, calculate the bottom height again
        # hgt = ml_height_bottom_new(ds6, moment=phi+"_norm", dim=dim, drop=False)["mlh_bottom"]
    else:
        hgt = ds7[phi+"_norm"].idxmin(dim=dim, skipna=True, fill_value=np.nan)
    #hgt = ds7.isel({dim: idx.load()}, drop=False)[dim]
    #for i in range(0,len(idx)):
    #    if idx[i].values == 0:
    #        hgt[idx].values = np.nan
    if clowres:
        ds7 = ds6.assign(dict(
                              mlh_bottom=hgt))
    else:
        ds7 = ds7.assign(dict(
                              mlh_bottom=hgt))
    # ds7.mlh_bottom ds7.ml_bottom, derived similar to Wolfensberger et. al. but for bottom
    # uses PHIDP_norm

    # assign variables and coords
    ds = ds.assign_coords(dict(height_ml=ds5.mlh_top,

                        height_ml_bottom=ds7.mlh_bottom,

                       ),
                  )

    if all_data is True:
        ds = ds.assign({"comb": ds0.comb,
                        rho+"_norm": ds0[rho+"_norm"],
                        zh+"_norm": ds0[zh+"_norm"],
                        phi+"_norm": ds0[phi+"_norm"],
                        "comb_dy": ds0.comb_dy,
                        rho+"_norm_dy": ds0[rho+"_norm_dy"],
                        zh+"_norm_dy": ds0[zh+"_norm_dy"],
                        phi+"_norm_dy": ds0[phi+"_norm_dy"],
                       })

    ds = ds.assign_coords({dim+'_idx': ([dim], np.arange(len(ds[dim])))})

    ## Giangrande refinment (included in this function on 16.10.23)
    # get data iside the currently detected ML
    cut_above = ds.where(ds[dim]<ds.height_ml)
    cut_above = cut_above.where(ds[dim]>ds.height_ml_bottom)
    #test_above = cut_above.where((cut_above.rho >=0.7)&(cut_above.rho <0.98))

    # get the heights with min RHOHV
    min_height_ML = cut_above[rho].idxmin(dim=dim)

    # cut the data below and above the previous value
    new_cut_below_min_ML = ds.where(ds[dim] > min_height_ML)
    new_cut_above_min_ML = ds.where(ds[dim] < min_height_ML)

    # Filter out values outside some RHOHV range
    new_cut_below_min_ML_filter = new_cut_below_min_ML[rho].where((new_cut_below_min_ML[rho]>=rhohv_thresh_gia[0])&(new_cut_below_min_ML[rho]<=rhohv_thresh_gia[1]))
    new_cut_above_min_ML_filter = new_cut_above_min_ML[rho].where((new_cut_above_min_ML[rho]>=rhohv_thresh_gia[0])&(new_cut_above_min_ML[rho]<=rhohv_thresh_gia[1]))

    # J. Giles refinement
    # Add condition that the absolute gradient of the RHOHV profile must be below certain threshold (like 0.0001)
    ds_grad = abs(ds[rho].differentiate(dim)) < grad_thresh

    # ML TOP Giangrande+Giles refinement

    notnull = new_cut_below_min_ML_filter.notnull() # this replaces nan for False and the rest for True
    first_valid_height_after_ml = notnull.where(notnull).where(ds_grad).idxmax(dim=dim) # get the first True value, i.e. first valid value

    # ML BOTTOM Giangrande+Giles refinement
    # For this one, we need to flip the coordinate so that it is actually selecting the last valid index
    notnull = new_cut_above_min_ML_filter.notnull() # this replaces nan for False and the rest for True
    last_valid_height = notnull.where(notnull).isel({dim:slice(None, None, -1)}).where(ds_grad).idxmax(dim=dim) # get the first True value, i.e. first valid value (flipped)

    # assign new values
    ds = ds.assign_coords(height_ml_new_gia = (first_valid_height_after_ml.dims,
                                               first_valid_height_after_ml.data))
    ds = ds.assign_coords(height_ml_bottom_new_gia = (last_valid_height.dims,
                                                      last_valid_height.data))

    return ds



'''
################# Example usage of melting layer detection and PHIDP processing
X_ZH = "DBTH"
X_ZDR = "UZDR"
X_RHOHV = "RHOHV"
X_PHIDP = "PHIDP"

######### Processing PHIDP for BoXPol

phi = ds[X_PHIDP].where((ds[X_RHOHV+"_NC"]>=0.9) & (ds[X_ZH+"_OC"]>=0))
start_range, off = phi.pipe(phase_offset, rng=3000)

fix_range = 750
phi_fix = ds[X_PHIDP].copy()
off_fix = off.broadcast_like(phi_fix)
phi_fix = phi_fix.where(phi_fix.range >= start_range + fix_range).fillna(off_fix) - off

window = 11
window2 = None
phi_median = phi_fix.pipe(xr_rolling, window, window2=window2, method='median', skipna=True, min_periods=3)
phi_masked = phi_median.where((ds[X_RHOHV+"_NC"] >= 0.95) & (ds[X_ZH+"_OC"] >= 0.))

dr = phi_masked.range.diff('range').median('range').values / 1000.

winlen = 31 # windowlen
min_periods = 3 # min number of vaid bins
kdp = kdp_from_phidp(phi_masked, winlen, min_periods=3)
kdp1 = kdp.interpolate_na(dim='range')

winlen = 31
phidp = phidp_from_kdp(kdp1, winlen)

assign = {X_PHIDP+"_OC_SMOOTH": phi_median.assign_attrs(ds[X_PHIDP].attrs),
  X_PHIDP+"_OC_MASKED": phi_masked.assign_attrs(ds[X_PHIDP].attrs),
  "KDP_CONV": kdp.assign_attrs(ds.KDP.attrs),
  "PHI_CONV": phidp.assign_attrs(ds[X_PHIDP].attrs),

  X_PHIDP+"_OFFSET": off.assign_attrs(ds[X_PHIDP].attrs),
  X_PHIDP+"_OC": phi_fix.assign_attrs(ds[X_PHIDP].attrs)}

ds = ds.assign(assign)
ds_qvp_ra = ds.median("azimuth")

moments={X_ZH+"_OC": (10., 60.), X_RHOHV+"_NC": (0.65, 1.), X_PHIDP+"_OC": (-0.5, 360)}
dim = 'height'
thres = 0.02
limit = None
xwin = 5
ywin = 5
fmlh = 0.3

ml_qvp = melting_layer_qvp_X_new(ds_qvp_ra, moments=moments,
         dim=dim, thres=thres, xwin=xwin, ywin=ywin, fmlh=fmlh, all_data=True)

ds_qvp_ra = ds_qvp_ra.assign_coords({'height_ml': ml_qvp.mlh_top})
ds_qvp_ra = ds_qvp_ra.assign_coords({'height_ml_bottom': ml_qvp.mlh_bottom})

ml_qvp = ml_qvp.where(ml_qvp.mlh_top<10000)
nan = np.isnan(ds_plus_entropy.PHIDP_OC_MASKED)
phi2 = ds_plus_entropy["PHIDP_OC_MASKED"].where((ds_plus_entropy.z < ml_qvp.mlh_bottom) | (ds_plus_entropy.z > ml_qvp.mlh_top))#.interpolate_na(dim='range',dask_gufunc_kwargs = "allow_rechunk")

phi2 = phi2.interpolate_na(dim='range', method=interpolation_method_ML)
phi2 = xr.where(nan, np.nan, phi2)

dr = phi2.range.diff('range').median('range').values / 1000.
print("range res [km]:", dr)
# winlen in gates
# todo window length in m
winlen = 31
min_periods = 3
kdp_ml = kdp_from_phidp(phi2, winlen, min_periods=3)
ds = ds.assign({"KDP_ML_corrected": (["time", "azimuth", "range"], kdp_ml.values, ml_qvp.KDP.attrs)})
ds["KDP_ML_corrected"] = ds.KDP_ML_corrected.where((ds.KDP_ML_corrected >= 0.01) & (ds.KDP_ML_corrected <= 3)) #### maybe you dont need this filtering here

ds = ds.assign_coords({'height': ds.z})

ds = ds.assign_coords({'height_ml': ml_qvp.mlh_top})
ds = ds.assign_coords({'height_ml_bottom': ml_qvp.mlh_bottom})


#################### Giagrande refinment
cut_above = ds_qvp_ra.where(ds_qvp_ra.height<ds_qvp_ra.height_ml)
cut_above = cut_above.where(ds_qvp_ra.height>ds_qvp_ra.height_ml_bottom)
#test_above = cut_above.where((cut_above.rho >=0.7)&(cut_above.rho <0.98))

min_height_ML = cut_above.rho.idxmin(dim="height")

new_cut_below_min_ML = ds_qvp_ra.where(ds_qvp_ra.height > min_height_ML)
new_cut_above_min_ML = ds_qvp_ra.where(ds_qvp_ra.height < min_height_ML)

new_cut_below_min_ML_filter = new_cut_below_min_ML.rho.where((new_cut_below_min_ML.rho>=0.97)&(new_cut_below_min_ML.rho<=1))
new_cut_above_min_ML_filter = new_cut_above_min_ML.rho.where((new_cut_above_min_ML.rho>=0.97)&(new_cut_above_min_ML.rho<=1))


import pandas as pd
######### ML TOP Giagrande refinement
panda_below_min = new_cut_below_min_ML_filter.to_pandas()
first_valid_height_after_ml = pd.DataFrame(panda_below_min).apply(pd.Series.first_valid_index)
first_valid_height_after_ml = first_valid_height_after_ml.to_xarray()
######### ML BOTTOM Giagrande refinement
panda_above_min = new_cut_above_min_ML_filter.to_pandas()

last_valid_height = pd.DataFrame(panda_above_min).apply(pd.Series.last_valid_index)

last_valid_height = last_valid_height.to_xarray()

ds_qvp_ra = ds_qvp_ra.assign_coords(height_ml_new_gia = ("time",first_valid_height_after_ml.data))
ds_qvp_ra = ds_qvp_ra.assign_coords(height_ml_bottom_new_gia = ("time", last_valid_height.data))


ds = ds.assign_coords(height_ml_new_gia = ("time",first_valid_height_after_ml.data))
ds = ds.assign_coords(height_ml_bottom_new_gia = ("time", last_valid_height.data))
'''


#################################### CFADs

def hist2d(ax, PX, PY, binsx=[], binsy=[], mode='rel_all', whole_x_range=True, cb_mode=True,
           mq="median", mq_color="black", mq_lw=2, qq=0.2, qq_color="black", qq_lw=2,
           cmap='turbo', smooth_out=False, binsx_out=[],
           colsteps=10, mini=0, fsize=13, fcolor='black', mincounts=500, cblim=[0,26],
           N=False, N_color="cornflowerblue", N_xlim=None,
           cborientation="horizontal", shading='gouraud', **kwargs):
    """
    Plots the 2-dimensional distribution of two Parameters
    # Input:
    # ------
    PX = Parameter x-axis
    PY = Parameter y-axis
    binsx = [start, stop, step]
    binsy = [start, stop, step]
    mode = 'rel_all', 'abs' or 'rel_y'
            rel_all : Relative Dist. to all pixels (this is not working ATM)
            rel_y   : Relative Dist. to y-axis.
            abs     : Absolute Dist.
    whole_x_range: use the whole range of values in the x coordinate? if False, only values inside the limits of binsx will be considered
                in the calculations and the counting of valid values; which can lead to different results depending how the bin ranges are defined.
    smooth_out : If True, calculates the hist2d according to binsx and then interpolates the result to binsx_out.
                This is useful if the input data has low resolution and close to that of the desired bins, which
                produces a histogram with alternating bands of low or high values, depending on binsx. If using this
                option, binsx should respresent the bins that best fit the data, producing an hist2d without
                visual glitches; and binsx_out should be the desired output bins (but not too different from binsx).
                If the visual artifacts continue, a better approach may be to round the data and select binsx
                so that bands of zero values are generated, which will then be filled by the interpolation.
    binsx_out : Desired output bins for the x dimension if smooth_out is True.
    cb_mode : plot colorbar?
    mq = Middle line to plot. Can be "median" or "mean"
    mq_color = Color for the middle line. Default is "black"
    mq_lw = Line with for the middle line
    qq = percentile [0-1]. Calculates and plots the qq and 1-qq percentiles.
    qq_color = Color for the percentile lines. Default is "black"
    qq_lw = Line with for the percentile lines
    mincounts: minimum sample number to plot
    N: plot sample size?
    N_color: Color for the sample size line plot. Default is "cornflowerblue".
    N_xlim: if not None, tuple of range values to set the x limits of the sample size plot.
    cborientation: orientation of the colorbar, "horizontal" or "vertical"
    shading: shading argument for matplotlib pcolormesh. Should be 'nearest' (no interpolation) or 'gouraud' (interpolated).
    kwargs: additional arguments for matplotlib pcolormesh

    # Output
    # ------
    Plot of 2-dimensional distribution
    """


    import matplotlib
    from matplotlib import pyplot as plt
    from mpl_toolkits.axes_grid1 import make_axes_locatable
    import numpy as np
    import xarray

    # Flatten the arrays
    if type(PX) == xr.core.dataarray.DataArray:
        PX_flat = PX.values.flatten()
    elif type(PX) == np.ndarray:
        PX_flat = PX.flatten()
    else:
        raise TypeError("PX should be xarray.core.dataarray.DataArray or numpy.ndarray")

    if type(PY) == xr.core.dataarray.DataArray:
        PY_flat = PY.values.flatten()
    elif type(PY) == np.ndarray:
        PY_flat = PY.flatten()
    else:
        raise TypeError("PY should be xarray.core.dataarray.DataArray or numpy.ndarray")


    matplotlib.rc('axes',edgecolor='black')

    # discret cmap
    cmap = plt.cm.get_cmap(cmap, colsteps+1).copy()
    colors = list(cmap(np.arange(colsteps+1)))
    cmap = matplotlib.colors.ListedColormap(colors[:-1], "cfad")
    # set over-color to last color of list
    cmap.set_over(colors[-1])
    cmap.set_under("#FFFFFF00")

    # Define bins arange
    bins_px = np.arange(binsx[0], binsx[1], binsx[2])
    bins_py = np.arange(binsy[0], binsy[1], binsy[2])

    # Hist 2d
    if whole_x_range:
        # to consider the whole range of values in x, we extend the bins array by adding bins to -inf and inf
        # at the edges and computing the histogram with those bins into account. Then, we discard the extreme values
        bins_px_ext = np.append(np.append(bins_px[::-1], -np.inf)[::-1], np.inf).copy()
        H_ext, xe_ext, ye = np.histogram2d(PX_flat, PY_flat, bins = (bins_px_ext, bins_py))
        H = H_ext[1:-1,:].copy()
        xe = xe_ext[1:-1]
    else:
        H, xe, ye = np.histogram2d(PX_flat, PY_flat, bins = (bins_px, bins_py))
        H_ext = H.copy() # this is for the counting part of the overall sum

    # Calc mean x and y (for plotting with center-based index)
    mx =0.5*(xe[0:-1]+xe[1:len(xe)])
    my =0.5*(ye[0:-1]+ye[1:len(ye)])

    if smooth_out:
        bins_px2 = np.arange(binsx_out[0], binsx_out[1], binsx_out[2])
        mx2 =0.5*(bins_px2[0:-1]+bins_px2[1:])
        H_xr = xr.DataArray(H, coords={"mx":mx, "my":my})
        # H_xr_int = H_xr.interp(coords={"mx":mx2}) # deprecated
        # We discard points with zero, interpolate those with adjacent values and then interp everything to new grid
        H_xr_int = H_xr.where(H_xr>0).interpolate_na(dim="mx").interp(coords={"mx":mx2})
        H = H_xr_int.where(H_xr_int.notnull(), 0).values # replace nans by zeros
        mx=mx2
        xe=bins_px2
        if whole_x_range:
            # we need to put this new values from the new H into H_ext so the calculations below are correct
            H_ext = np.concatenate([np.expand_dims(H_ext[0,:], 0),H, np.expand_dims(H_ext[-1,:], 0)])
        else:
            H_ext = H.copy()

    # Calculate Percentil
    var_mean = []

    var_med = []
    var_qq1 = []
    var_qq2 = []
    var_count = []

    for i in bins_py[:-1]:
        if whole_x_range:
            PX_sub = PX_flat[(PY_flat>i)&(PY_flat<=i+binsy[2])]
        else:
            # Improved: get the subset of values in the range of bins_px and the specific range of bins_py
            # otherwise it will consider outliers that are not considered in histogram2d
            PX_sub = PX_flat[(PX_flat>bins_px[0])&(PX_flat<bins_px[-1])&(PY_flat>i)&(PY_flat<=i+binsy[2])]

        # for every bin in Y dimension, calculate statistics of values in X
        var_med.append(np.nanmedian(PX_sub))
        var_mean.append(np.nanmean(PX_sub))

        var_qq1.append(np.nanquantile(PX_sub, qq))
        var_qq2.append(np.nanquantile(PX_sub, 1-qq))
        #var_count.append(len(PX_flat[(PY_flat>i)&(PY_flat<=i+binsy[2])])) # this is counting all values per Y bin, including nans
        var_count.append(np.isfinite(PX_sub).sum()) # improved, counting only valid values (not nan, not inf)

    var_med = np.array(var_med)
    var_mean = np.array(var_mean)

    var_qq1 = np.array(var_qq1)
    var_qq2 = np.array(var_qq2)
    var_count = np.array(var_count)

    var_med[var_count<mincounts]=np.nan
    var_mean[var_count<mincounts]=np.nan

    var_qq1[var_count<mincounts]=np.nan
    var_qq2[var_count<mincounts]=np.nan


    # overall sum for relative distribution
    if mode=='rel_all':
        allsum = np.nansum(H_ext)
        allsum[var_count<mincounts]=np.nan
        relHa = H.T/allsum
    elif mode=='rel_y':
        allsum = np.nansum(H_ext, axis=0)
        allsum[var_count<mincounts]=np.nan
        relHa = (H/allsum).T # transpose so the y axis is temperature

    elif mode=='abs':
        relHa = H.T
    else:
        print('Wrong mode parameter used! Please use mode="rel_all", mode="abs" or mode="rel_y"!')

    RES = 100*relHa

    RES[RES<mini]=np.nan


    img = ax.pcolormesh(mx, my ,RES , cmap=cmap, vmin=cblim[0], vmax=cblim[1], shading=shading, **kwargs) #, shading="gouraud"

    if mq == "median":
        ax.plot(var_med, my, color=mq_color, lw=mq_lw)
        # ax.plot(var_med, my, color='black', lw=2, ls=(0, (5, 5)))
    elif mq == "mean":
        ax.plot(var_mean, my, color=mq_color, lw=mq_lw)
        # ax.plot(var_mean, my, color='black', lw=2, ls=(0, (5, 5)))

    ax.plot(var_qq1, my, color=qq_color, ls="-.", lw=qq_lw)
    # ax.plot(var_qq1, my, color='black', linestyle=(0, (1, 5)), lw=2)
    ax.plot(var_qq2, my, color=qq_color, ls="-.", lw=qq_lw)
    # ax.plot(var_qq2, my, color='black', linestyle=(0, (1, 5)), lw=2)

    # se the x limits in case the lines go off the pcolormesh
    ax.set_xlim(xe[0], xe[-1])

    ax.grid(color=fcolor, linestyle='-.', lw=0.5, alpha=0.9)

    ax.xaxis.label.set_color(fcolor)
    ax.tick_params(axis='both', colors=fcolor)

    if N==True:
        ax2 = ax.twiny()
        ax2.plot(var_count, my, color=N_color, linestyle='-', lw=2)
        if N_xlim is not None:
            ax2.set_xlim(N_xlim[0], N_xlim[1])
        ax2.xaxis.label.set_color(N_color)
        ax2.yaxis.label.set_color(N_color)
        ax2.tick_params(axis='both', colors=N_color)

        xticks = ax2.xaxis.get_major_ticks()
        xticks[0].label1.set_visible(False)
        xticks[-1].label1.set_visible(False)

    if cb_mode==True:
        '''
        if cborientation=="horizontal":
            cax = plt.axes([0.15, -0.05, 0.70, 0.03]) #Left, bottom, length, width
        if cborientation=="vertical":
            cax = plt.axes([0.95, 0.15, 0.03, 0.70]) #Left, bottom, length, width
        '''

        cb=plt.colorbar(img, cax=None, pad=0.05, ticks=np.linspace(cblim[0],cblim[1], colsteps+1), extend = "max", orientation=cborientation)

        if mode=='abs':
            cb.ax.set_title('#', color=fcolor)
        if mode!='abs':
            cb.ax.set_title('%', color=fcolor, fontsize=fsize)
        cb.ax.tick_params(labelsize=fsize, color=fcolor)
        cbar_yticks = plt.getp(cb.ax.axes, 'yticklabels')
        plt.setp(cbar_yticks, color=fcolor)



    return img



'''
# preprocessing

KDP_DGL_max_test = []




ZH = []
ZDR = []
KDP = []
RHO = []
TT = []
E = []
ML = []
valid_values = []
ZH_ML_max = []
ZDR_ML_max = []
RHO_ML_min = []
KDP_ML_mean = []
MLTH_ML = []
BETA = []

ZH_DGL = []
ZDR_DGL = []
RHO_DGL = []
KDP_DGL = []
ZH_DGL_09 = []
ZDR_DGL_09 = []
KDP_DGL_09 = []
KDP_DGL_max= []
RHO_DGL_min= []
ZH_DGL_max= []
ZDR_DGL_max= []
# ZH_snow_list= []
# ZDR_snow_list= []
# ZH_rain_list= []
# ZDR_rain_list= []
ZH_snow = []
ZDR_snow = []
ZH_rain = []
ZDR_rain = []
ZH_sfc = []
ZDR_sfc = []

Dm_ZDR_KDP_Z_max = []
Nt_ZDR_KDP_Z_max = []
Nt_ZDR_KDP_Z_max_log = []

IWC_ZDR_KDP_Z_max = []

Dm_ZDR_KDP_Z = []
Nt_ZDR_KDP_Z_log = []
Nt_ZDR_KDP_Z = []

IWC_ZDR_KDP_Z = []
Dm_ZDR_KDP_Z_DGL_09 = []
Nt_ZDR_KDP_Z_DGL_09 = []
IWC_ZDR_KDP_Z_DGL_09 = []
Dm_ZDR_KDP_Z_DGL = []
Nt_ZDR_KDP_Z_DGL = []
IWC_ZDR_KDP_Z_DGL = []
#.where(~np.isnan(ds.height_ml))
# .where(ds.height_ml>height_ml_bottom, drop=True)
for i in range(len(qvp_nc_files)):
    #print(qvp_nc_files[i])

    #try:
    ds = xr.open_dataset(qvp_nc_files[i], chunks='auto')
    ds = ds.swap_dims({"index_new":"time"})
    ml_height_thres = ~np.isnan(ds.height_ml_new_gia)
    ds_thrs = ds.where(ml_height_thres == True, drop=True)
    ml_bottom_thres = ~np.isnan(ds_thrs.height_ml_bottom_new_gia)
    ds_thrs = ds_thrs.where(ml_bottom_thres == True, drop=True)
    ds_thrs = ds_thrs.where(ds_thrs.height_ml_new_gia > ds_thrs.height_ml_bottom_new_gia)
    ds = ds_thrs
    ds["Nt_ZDR_KDP_Z_log"] = np.log10(ds.Nt_ZDR_KDP_Z/1000)
    ds["Nt_ZDR_KDP_Z"] = ds.Nt_ZDR_KDP_Z/1000

    ds_stat_ML = ds.where(ds.min_entropy>=0.8, drop=True)
    ds_stat_ML = ds_stat_ML.where((ds_stat_ML.height<ds_stat_ML.height_ml_new_gia) & (ds_stat_ML.height>ds_stat_ML.height_ml_bottom_new_gia))
    ds_stat_ML = ds_stat_ML.where((ds_stat_ML.min_entropy>=0.8)&(ds_stat_ML.DBTH_OC > 0 )&(ds_stat_ML.KDP_ML_corrected > 0.01)&(ds_stat_ML.RHOHV_NC > 0.7)&(ds_stat_ML.UZDR_OC > -1),  drop=True)

    ### ML statistics
    if ds_stat_ML.time.shape[0]!=0:
        ZH_ML_max.append(ds_stat_ML.DBTH_OC.max(dim="height").values.flatten())
        ZDR_ML_max.append(ds_stat_ML.UZDR_OC.max(dim="height").values.flatten())
        RHO_ML_min.append(ds_stat_ML.RHOHV_NC.min(dim="height").values.flatten())
        KDP_ML_mean.append(ds_stat_ML.KDP_ML_corrected.mean(dim="height").values.flatten())
        mlth_ML = ds_stat_ML.height_ml_new_gia - ds_stat_ML.height_ml_bottom_new_gia
        MLTH_ML.append(mlth_ML.values.flatten())

        ### Silke Style
        Gradient_silke = ds.where(ds.min_entropy>=0.8)
        Gradient_silke = Gradient_silke.where((Gradient_silke.min_entropy>=0.8)&(Gradient_silke.DBTH_OC > 0 )&(Gradient_silke.KDP_ML_corrected > 0.01)&(Gradient_silke.RHOHV_NC > 0.7)&(Gradient_silke.UZDR_OC > -1))

        DBTH_OC_gradient_Silke_ML = Gradient_silke.DBTH_OC.sel(height = Gradient_silke.height_ml_new, method="nearest")
        DBTH_OC_gradient_Silke_ML_plus_2_km = Gradient_silke.DBTH_OC.sel(height = DBTH_OC_gradient_Silke_ML.height+2000, method="nearest")
        DBTH_OC_gradient_Final = (DBTH_OC_gradient_Silke_ML_plus_2_km - DBTH_OC_gradient_Silke_ML)/2
        BETA.append(DBTH_OC_gradient_Final)

    ### DGL statistics
    ds_stat_DGL = ds.where((ds.temp_coord>=-20)&(ds.temp_coord<=-10), drop=True)
    ds_stat_DGL = ds_stat_DGL.where(ds_stat_DGL.min_entropy>=0.8, drop=True)
    ds_stat_DGL = ds_stat_DGL.where((ds_stat_DGL.min_entropy>=0.8)&(ds_stat_DGL.DBTH_OC > 0 )&(ds_stat_DGL.KDP_ML_corrected > 0.01)&(ds_stat_DGL.RHOHV_NC > 0.7)&(ds_stat_DGL.UZDR_OC > -1),  drop=True)

    if ds_stat_DGL.time.shape[0]!=0:
        ZH_DGL.append(ds_stat_DGL.DBTH_OC.values.flatten())
        ZDR_DGL.append(ds_stat_DGL.UZDR_OC.values.flatten())
        KDP_DGL_max.append(ds_stat_DGL.KDP_ML_corrected.max(dim="height").values.flatten())

        KDP_DGL_max_test.append(np.asarray(ds_stat_DGL.KDP_ML_corrected.max(dim="height").stack(dim=["time"]).data))

        RHO_DGL_min.append(ds_stat_DGL.RHOHV_NC.min(dim="height").values.flatten())
        ZH_DGL_max.append(ds_stat_DGL.DBTH_OC.max(dim="height").values.flatten())
        ZDR_DGL_max.append(ds_stat_DGL.UZDR_OC.max(dim="height").values.flatten())
        ZDR_DGL_09.append(ds_stat_DGL.UZDR_OC.quantile(0.9, dim="height").values.flatten())
        ZH_DGL_09.append(ds_stat_DGL.DBTH_OC.quantile(0.9, dim="height").values.flatten())

        RHO_DGL.append(ds_stat_DGL.RHOHV_NC.values.flatten())

        KDP_DGL.append(ds_stat_DGL.KDP_ML_corrected.values.flatten())
        KDP_DGL_09.append(ds_stat_DGL.KDP_ML_corrected.quantile(0.9, dim="height").values.flatten())


 #ds_stat_ML_list_KDP_ML_corrected.append(np.asarray(ds.KDP_ML_corrected.max(dim="height").stack(dim=["height","time"]).data))



    ### other statistics

    ds_other1 = ds.where(ds.min_entropy>=0.8)
    ds_other1 = ds_other1.where((ds_other1.min_entropy>=0.8)&(ds_other1.DBTH_OC > 0 )&(ds_other1.KDP_ML_corrected > 0.01)&(ds_other1.RHOHV_NC > 0.7)&(ds_other1.UZDR_OC > -1))
    ZH_sfc.append(ds_other1.DBTH_OC.swap_dims({"height":"range"}).isel(range = 7).values.flatten())
    ZDR_sfc.append(ds_other1.UZDR_OC.swap_dims({"height":"range"}).isel(range = 7).values.flatten())
#     ZH_snow = ds_other.DBTH_OC.sel(height = ds_other.height_ml_new, method="nearest")
#     ZDR_snow = ds_other.UZDR_OC.sel(height = ds_other.height_ml_new, method="nearest")
#     ZH_rain = ds_other.DBTH_OC.sel(height = ds_other.height_ml_bottom_new_gia, method="nearest")
#     ZDR_rain = ds_other.UZDR_OC.sel(height = ds_other.height_ml_bottom_new_gia, method="nearest")
#     ds_other = ds.where(ds.min_entropy>=0.8, drop=True)
#     ds_other = ds_other.where((ds_other.min_entropy>=0.8)&(ds_other.DBTH_OC > 0 )&(ds_other.KDP_ML_corrected > 0.001)&(ds_other.RHOHV_NC > 0.7)&(ds_other.UZDR_OC > -1),  drop=True)

    ZH_snow.append(ds_other1.DBTH_OC.sel(height = ds_other1.height_ml_new, method="nearest").values.flatten())
    ZDR_snow.append(ds_other1.UZDR_OC.sel(height = ds_other1.height_ml_new, method="nearest").values.flatten())
    ZH_rain.append(ds_other1.DBTH_OC.sel(height = ds_other1.height_ml_bottom_new_gia, method="nearest").values.flatten())
    ZDR_rain.append(ds_other1.UZDR_OC.sel(height = ds_other1.height_ml_bottom_new_gia, method="nearest").values.flatten())





    ### IWC, Nt, Dm statistics    hier ist weiteres Filtern eher nicht gut i would say
    ds_microphysical = ds.where(ds.min_entropy>=0.8, drop=True)
    ds_microphysical = ds_microphysical.where((ds_microphysical.temp_coord>=-20)&(ds_microphysical.temp_coord<=-10), drop=True)

    Dm_ZDR_KDP_Z_DGL_09.append(ds_microphysical.Dm_ZDR_KDP_Z.quantile(0.9, dim="height").values.flatten())
    Nt_ZDR_KDP_Z_DGL_09.append(ds_microphysical.Nt_ZDR_KDP_Z.quantile(0.9, dim="height").values.flatten())
    IWC_ZDR_KDP_Z_DGL_09.append(ds_microphysical.IWC_ZDR_KDP_Z.quantile(0.9, dim="height").values.flatten())

    Dm_ZDR_KDP_Z_DGL.append(ds_microphysical.Dm_ZDR_KDP_Z.values.flatten())
    Nt_ZDR_KDP_Z_DGL.append(ds_microphysical.Nt_ZDR_KDP_Z.values.flatten())
    IWC_ZDR_KDP_Z_DGL.append(ds_microphysical.IWC_ZDR_KDP_Z.values.flatten())

    Dm_ZDR_KDP_Z_max.append(ds_microphysical.Dm_ZDR_KDP_Z.max(dim="height").values.flatten())
    Nt_ZDR_KDP_Z_max_log.append(ds_microphysical.Nt_ZDR_KDP_Z_log.max(dim="height").values.flatten())
    Nt_ZDR_KDP_Z_max.append(ds_microphysical.Nt_ZDR_KDP_Z.max(dim="height").values.flatten())

    IWC_ZDR_KDP_Z_max.append(ds_microphysical.IWC_ZDR_KDP_Z.max(dim="height").values.flatten())


#     ZH_snow_list.append(np.asarray(ZH_snow.squeeze().stack(dim=["height","time"]).data))
#     ZDR_snow_list.append(np.asarray(ZDR_snow.squeeze().stack(dim=["height","time"]).data))
#     ZH_rain_list.append(np.asarray(ZH_rain.squeeze().stack(dim=["height","time"]).data))
#     ZDR_rain_list.append(np.asarray(ZDR_rain.squeeze().stack(dim=["height","time"]).data))



    ZH.append(np.asarray(ds.DBTH_OC.squeeze().stack(dim=["height","time"]).data))
    ZDR.append(np.asarray(ds.UZDR_OC.squeeze().stack(dim=["height","time"]).data))
    RHO.append(np.asarray(ds.RHOHV_NC.squeeze().stack(dim=["height","time"]).data))
    KDP.append(np.asarray(ds.KDP_ML_corrected.squeeze().stack(dim=["height","time"]).data))
    E.append(np.asarray(ds.min_entropy.squeeze().stack(dim=["height","time"]).data))
    valid_values.append(np.asarray(ds.valid_values_min_120.squeeze().stack(dim=["height","time"]).data))
    TT.append(np.asarray((ds.temp_coord).squeeze().stack(dim=["height","time"]).data))
    Dm_ZDR_KDP_Z.append(np.asarray(ds.Dm_ZDR_KDP_Z.squeeze().stack(dim=["height","time"]).data))
    Nt_ZDR_KDP_Z.append(np.asarray(ds.Nt_ZDR_KDP_Z.squeeze().stack(dim=["height","time"]).data))
    Nt_ZDR_KDP_Z_log.append(np.asarray(ds.Nt_ZDR_KDP_Z_log.squeeze().stack(dim=["height","time"]).data))

    IWC_ZDR_KDP_Z.append(np.asarray(ds.IWC_ZDR_KDP_Z.squeeze().stack(dim=["height","time"]).data))
#     ZH.append(ds.DBTH_OC.values.flatten())
#     ZDR.append(ds.UZDR_OC.values.flatten())
#     RHO.append(ds.RHOHV_NC.values.flatten())
#     KDP.append(ds.KDP_ML_corrected.values.flatten())
#     TT.append(ds.temp_coord.values.flatten())
#     E.append(ds.min_entropy.values.flatten())
    #except:
    #print('Error')


ZH = np.concatenate(ZH)
ZDR = np.concatenate(ZDR)
KDP = np.concatenate(KDP)
RHO = np.concatenate(RHO)
TT = np.concatenate(TT)
E = np.concatenate(E)
valid_values = np.concatenate(valid_values)

RHO_ML_min = np.concatenate(RHO_ML_min)
ZDR_ML_max = np.concatenate(ZDR_ML_max)
ZH_ML_max = np.concatenate(ZH_ML_max)
MLTH_ML = np.concatenate(MLTH_ML)
BETA = np.concatenate(BETA)
KDP_ML_mean = np.concatenate(KDP_ML_mean)

ZH_DGL = np.concatenate(ZH_DGL)
ZDR_DGL = np.concatenate(ZDR_DGL)
RHO_DGL = np.concatenate(RHO_DGL)
KDP_DGL = np.concatenate(KDP_DGL)
ZDR_DGL_09 = np.concatenate(ZDR_DGL_09)
KDP_DGL_09 = np.concatenate(KDP_DGL_09)


Dm_ZDR_KDP_Z_DGL_09= np.concatenate(Dm_ZDR_KDP_Z_DGL_09)
Nt_ZDR_KDP_Z_DGL_09= np.concatenate(Nt_ZDR_KDP_Z_DGL_09)
IWC_ZDR_KDP_Z_DGL_09= np.concatenate(IWC_ZDR_KDP_Z_DGL_09)
Dm_ZDR_KDP_Z_DGL= np.concatenate(Dm_ZDR_KDP_Z_DGL)
Nt_ZDR_KDP_Z_DGL= np.concatenate(Nt_ZDR_KDP_Z_DGL)
IWC_ZDR_KDP_Z_DGL= np.concatenate(IWC_ZDR_KDP_Z_DGL)

Dm_ZDR_KDP_Z_max= np.concatenate(Dm_ZDR_KDP_Z_max)
Nt_ZDR_KDP_Z_max= np.concatenate(Nt_ZDR_KDP_Z_max)
Nt_ZDR_KDP_Z_max_log= np.concatenate(Nt_ZDR_KDP_Z_max_log)

IWC_ZDR_KDP_Z_max= np.concatenate(IWC_ZDR_KDP_Z_max)

KDP_DGL_max_test = np.concatenate(KDP_DGL_max_test)


KDP_DGL_max= np.concatenate(KDP_DGL_max)
RHO_DGL_min= np.concatenate(RHO_DGL_min)
ZH_DGL_max= np.concatenate(ZH_DGL_max)
ZDR_DGL_max= np.concatenate(ZDR_DGL_max)

Dm_ZDR_KDP_Z = np.concatenate(Dm_ZDR_KDP_Z)
Nt_ZDR_KDP_Z = np.concatenate(Nt_ZDR_KDP_Z)
IWC_ZDR_KDP_Z = np.concatenate(IWC_ZDR_KDP_Z)
Nt_ZDR_KDP_Z_log = np.concatenate(Nt_ZDR_KDP_Z_log)

ZH_snow = np.concatenate(ZH_snow)
ZDR_snow = np.concatenate(ZDR_snow)
ZH_rain = np.concatenate(ZH_rain)
ZDR_rain = np.concatenate(ZDR_rain)
ZH_sfc = np.concatenate(ZH_sfc)
ZDR_sfc = np.concatenate(ZDR_sfc)




####### Plotting example how to use the function above


mask = (Dm_ZDR_KDP_Z>0) & (IWC_ZDR_KDP_Z>0) & (E>=0.8)& (TT<=0.5)  &(TT>=-20)

smask =  (Dm_syn>0.01) & (IWC_syn>0) &  (sE_retrievals>=0.8)& (sTMP_retrievals<=0.5)  &(sTMP_retrievals>=-20)& (~np.isnan(Nt_syn_log))
#smask =    (sE_retrievals>=0.8)#& (sTMP_retrievals<=0.5)  &(sTMP_retrievals>=-20)
# Remove Color for bins with th
mth = 0

# Temp bins
tb=1#0.7

# Min counts per Temp layer
mincounts=200

#Colorbar limits
cblim=[0,10]

fig, ax = plt.subplots(3, 2, sharey=True, figsize=(20,24))#, gridspec_kw={'width_ratios': [0.47,0.53]})
hist2d(ax[0,0], Dm_ZDR_KDP_Z[mask], TT[mask], binsx=[0,10,0.1], binsy=[ytlim,0.5,tb],
       mode='rel_y', qq=0.2,cb_mode=False,cmap=cm, colsteps=10, mini=mth,  fsize=30,
       mincounts=mincounts, cblim=cblim)
ax[0,0].set_ylim(0.5,ytlim)
ax[0,0].set_ylabel('Temperature [°C]', fontsize=30, color='black')
ax[0,0].set_xlabel("$D_{m}$ [$mm$]", fontsize=30, color='black')

ax[0,0].text(0.05, 0.95, 'a)', horizontalalignment='center', verticalalignment='center', color='black', fontsize=40, transform=ax[0,0].transAxes)
ax[0,0].set_title('Observations \n '+'N: '+str(len(Dm_ZDR_KDP_Z[mask])), fontsize=30, color='black', loc='left')


hist2d(ax[1,0], Nt_ZDR_KDP_Z_log[mask], TT[mask], binsx=[-2,2,0.1], binsy=[ytlim,0.5,tb],
       mode='rel_y', qq=0.2,cb_mode=False,cmap=cm, colsteps=10, mini=mth,  fsize=30,
       mincounts=mincounts, cblim=cblim)
ax[1,0].set_ylim(0.5,ytlim)
ax[1,0].set_ylabel('Temperature [°C]', fontsize=30, color='black')
ax[1,0].set_xlabel("$N_{t}$ [log$_{10}$($L^{-1}$)]", fontsize=30, color='black')
ax[1,0].xaxis.set_ticks(np.arange(-1.5, 2, 0.5))
ax[1,0].text(0.05, 0.95, 'c)', horizontalalignment='center', verticalalignment='center', color='black', fontsize=40, transform=ax[1,0].transAxes)

ax2 =hist2d(ax[2,0], IWC_ZDR_KDP_Z[mask], TT[mask],  binsx=[0,0.7,0.01], binsy=[ytlim,0.5,tb],
       mode='rel_y', qq=0.2,cb_mode=False,cmap=cm, colsteps=10, mini=mth,  fsize=30,
       mincounts=mincounts, cblim=cblim, N=True)
ax[2,0].set_ylim(0.5,ytlim)
ax[2,0].set_ylabel('Temperature [°C]', fontsize=30, color='black')
ax[2,0].set_xlabel("IWC [$g/m^3$]", fontsize=30, color='black')

ax2.set_xlim(200,95000)
ax[2,0].text(0.05, 0.95, 'e)', horizontalalignment='center', verticalalignment='center', color='black', fontsize=40, transform=ax[2,0].transAxes)


hist2d(ax[0,1], Dm_syn[smask], sTMP_retrievals[smask], binsx=[0,10,0.1], binsy=[ytlim,0.5,tb],
       mode='rel_y', qq=0.2,cb_mode=False,cmap=cm, colsteps=10,mini=mth,  fsize=30,
       mincounts=mincounts, cblim=cblim)
ax[0,1].set_ylim(0.5,ytlim)
ax[0,1].set_xlabel("$D_{m}$ [$mm$]", fontsize=30, color='black')

ax[0,1].text(0.05, 0.95, 'b)', horizontalalignment='center', verticalalignment='center', color='black', fontsize=40, transform=ax[0,1].transAxes)
ax[0,1].set_title('Simulations \n '+'N: '+str(len(Dm_syn[smask])), fontsize=30, color='black', loc='left')

hist2d(ax[1,1], Nt_syn_log[smask], sTMP_retrievals[smask], binsx=[-2,2,0.1], binsy=[ytlim,0.5,tb],
       mode='rel_y', qq=0.2,cb_mode=False,cmap=cm, colsteps=10, mini=mth,  fsize=30,
       mincounts=mincounts, cblim=cblim)
ax[1,1].set_ylim(0.5,ytlim)

ax[1,1].set_xlabel("$N_{t}$ [log$_{10}$($L^{-1}$)]", fontsize=30, color='black')
ax[1,1].xaxis.set_ticks(np.arange(-1.5, 2, 0.5))

ax[1,1].text(0.05, 0.95, 'd)', horizontalalignment='center', verticalalignment='center', color='black', fontsize=40, transform=ax[1,1].transAxes)

ax2 =hist2d(ax[2,1], IWC_syn[smask], sTMP_retrievals[smask], binsx=[0,0.7,0.01], binsy=[ytlim,0.5,tb],
       mode='rel_y', qq=0.2,cmap=cm, colsteps=10, mini=mth,  fsize=30,
       mincounts=mincounts, cblim=cblim, N=True)

ax[2,1].set_ylim(0.5,ytlim)
ax[2,1].text(0.05, 0.95, 'f)', horizontalalignment='center', verticalalignment='center', color='black', fontsize=40, transform=ax[2,1].transAxes)
legend = ax[2,1].legend(title ="Sample size", loc = "upper center", labelcolor = 'cornflowerblue', frameon=False,)
plt.setp(legend.get_title(), color='cornflowerblue',fontsize=30)
ax[2,1].set_xlabel("IWC [$g/m^3$]", fontsize=30, color='black')
ax2.set_xlim(200, 11500)
box1 = ax[0,0].get_position()
box2 = ax[1,0].get_position()
box3 = ax[2,0].get_position()
box4 = ax[0,1].get_position()
box5 = ax[1,1].get_position()
box6 = ax[2,1].get_position()


ax[0,0].set_position([box1.x0, box1.y0 + box1.height * 1, box1.width * 1.15, box1.height * 1])
ax[0,1].set_position([box4.x0, box4.y0 + box4.height * 1, box4.width* 1.15, box4.height * 1])

ax[1,0].set_position([box2.x0, box2.y0 + box2.height *1., box2.width* 1.15, box2.height * 1])
ax[1,1].set_position([box5.x0, box5.y0 + box5.height *1., box5.width* 1.15, box5.height * 1])

ax[2,0].set_position([box3.x0, box3.y0 + box3.height * 0.9, box3.width* 1.15, box3.height * 1])

ax[2,1].set_position([box6.x0, box6.y0 + box6.height * 0.9, box6.width* 1.15, box6.height * 1])


'''

#### Function to interpolate ERA5 to radar grid
def era5_to_radar_volume(radar_volume, site=None, path=None, convert_to_C=True,
                         variables=["temperature"], rename={"t":"TEMP"}, k_n=1,
                         pre_interpolate_z=False):
    """
    Function to interpolate ERA5 fields into the shape of radar_volume.

    Parameters
    ----------
    radar_volume : xarray Dataset
        Reference radar volume dataset to interpolate to.
    site : str, optional
        (Short) Name of the radar site to locate the data in the default folder:
        "/automount/ags/jgiles/ERA5/hourly/"
        Either site or path must be given.
    path : str, optional
        Path to the folder where ERA5 data can be found.
        Either site or path must be given.
    convert_to_C : bool
        If True (default), convert ERA5 temperature from K to C.
    variables : list
        List of variables to load (named as in the folders). By default load only temperature.
    rename : dict
        Dictionary to rename from dataset variable name to new names. Leave the
        dictionary empty for no renaming.
    k_n : int
        Number of neighbors to pass to the inverse_distance_weighting function.
        k=1 means nearest neighbors method.
    pre_interpolate_z : bool
        If True, linearly interpolate the vertical coordinate of ERA5 to higher resolution
        before the regridding, for smoother results. Default is False.

    Returns
    ----------
    era5_vol : xarray Dataset
        ERA5 fields interpolated into the shape of radar_volume
    """
    if path is None:
        # Set the default path if path is None
        try:
            era5_dir = "/automount/ags/jgiles/ERA5/hourly/"+site+"/pressure_level_vars/"
            if not os.path.exists(era5_dir):
                # if path does not exist, raise an error
                raise RuntimeError("folder for site="+site+" not found!")

        except TypeError:
            raise TypeError("If path is not provided, site must be provided!")
    elif type(path) is str:
        era5_dir = path
    else:
        raise TypeError("path must be type str!")

    # if time is not well defined, we try to get it from variable rtime
    if radar_volume["time"].isnull().any():
        try:
            radar_volume.coords["time"] = radar_volume.rtime.min(dim="azimuth", skipna=True).compute()
        except:
            raise KeyError("Dimension time has not valid values")

    # if some coord has dimension time, reduce using median
    for coord in ["latitude", "longitude", "altitude", "elevation"]:
        if coord in radar_volume.coords:
            if "time" in radar_volume[coord].dims:
                radar_volume.coords[coord] = radar_volume.coords[coord].median("time")

    # get times of the radar files
    startdt0 = dt.datetime.utcfromtimestamp(int(radar_volume.time[0].values)/1e9).date()
    enddt0 = dt.datetime.utcfromtimestamp(int(radar_volume.time[-1].values)/1e9).date() + dt.timedelta(hours=24)

    # transform the dates to datetimes
    startdt = dt.datetime.fromordinal(startdt0.toordinal())
    enddt = dt.datetime.fromordinal(enddt0.toordinal())

    # open ERA5 geopotental file
    try:
        era5_g = xr.open_mfdataset(reversed(sorted(glob.glob(era5_dir+"geopotential/*"+str(startdt.year)+"*"),
                                                   key=lambda file_name: int(file_name.split("/")[-1].split('_')[1]))),
                                   concat_dim="lvl", combine="nested", compat='no_conflicts')
    except ValueError:
        era5_g = xr.open_mfdataset(sorted(glob.glob(era5_dir+"geopotential/*"+str(startdt.year)+"*")), compat='no_conflicts').rename(
                        {"valid_time":"time", "pressure_level":"lvl"})

    # select the desired period and area and compute z coord
    dtslice0 = startdt.strftime('%Y-%m-%d %H')
    dtslice1 = enddt.strftime('%Y-%m-%d %H')
    era5_g = era5_g.loc[{"time":slice(dtslice0, dtslice1),
                         "longitude":slice(float(radar_volume.longitude)-1, float(radar_volume.longitude)+1),
                         "latitude":slice(float(radar_volume.latitude)+1, float(radar_volume.latitude)-1)}]

    earth_r = wrl.georef.projection.get_earth_radius(radar_volume.latitude.values)
    gravity = 9.80665
    z_coord = (earth_r*(era5_g.z/gravity)/(earth_r - era5_g.z/gravity)).compute()

    era5_fields = {}
    for vv in variables:
        try:
            era5_fields[vv] = xr.open_mfdataset(reversed(sorted(glob.glob(era5_dir+vv+"/*"+str(startdt.year)+"*"),
                                                       key=lambda file_name: int(file_name.split("/")[-1].split('_')[1]))),
                                       concat_dim="lvl", combine="nested", compat='no_conflicts')
        except ValueError:
            era5_fields[vv] = xr.open_mfdataset(sorted(glob.glob(era5_dir+vv+"/*"+str(startdt.year)+"*")), compat='no_conflicts').rename(
                        {"valid_time":"time", "pressure_level":"lvl"})

        # select time slice
        era5_fields[vv] = era5_fields[vv].loc[{"time":slice(dtslice0, dtslice1),
                         "longitude":slice(float(radar_volume.longitude)-1, float(radar_volume.longitude)+1),
                         "latitude":slice(float(radar_volume.latitude)+1, float(radar_volume.latitude)-1)}]


        # add z coord
        era5_fields[vv].coords["z"] = z_coord

        if convert_to_C and vv == "temperature":
            # convert from K to C
            temp_attrs = era5_fields[vv]["t"].attrs
            era5_fields[vv]["t"] = era5_fields[vv]["t"] -273.15
            temp_attrs["units"] = "C"
            era5_fields[vv]["t"].attrs = temp_attrs

        if pre_interpolate_z:
            era5_fields[vv] = interp_to_ht_parallel(era5_fields[vv].rename({"z":"height"}),
                                                    ht=np.arange(0,25000,100))\
                                                    .rename({"height":"z"})\
                .transpose(*tuple(dd if dd != "lvl" else "z" for dd in era5_fields[vv].dims )).compute()

            new_latitude = give_array(float(era5_fields[vv]["latitude"].min()),
                                      float(era5_fields[vv]["latitude"].max()),
                                      0.1)
            new_longitude = give_array(float(era5_fields[vv]["longitude"].min()),
                                      float(era5_fields[vv]["longitude"].max()),
                                      0.1)

            era5_fields[vv] = era5_fields[vv].interp({"latitude": new_latitude, "longitude": new_longitude})

    if pre_interpolate_z:
        lon_era5 = np.meshgrid(era5_fields[vv]["longitude"], era5_fields[vv]["latitude"])[0].flatten()
        lat_era5 = np.meshgrid(era5_fields[vv]["longitude"], era5_fields[vv]["latitude"])[1].flatten()
    else:
        lon_era5 = np.meshgrid(era5_g["longitude"], era5_g["latitude"])[0].flatten()
        lat_era5 = np.meshgrid(era5_g["longitude"], era5_g["latitude"])[1].flatten()
    # the vertical coordinates of ERA5 changes with time so we need to include
    # them in the function below for each timestep, and not here

    mod_x = lon_era5
    mod_y = lat_era5

    # ERA5 is already in WGS84, we need to georeference the radar volume to the same system
    proj_wgs = osr.SpatialReference()
    proj_wgs.ImportFromEPSG(4326)

    radar_volume = radar_volume.pipe(wrl.georef.georeference, crs=proj_wgs)
    rad_x, rad_y, alt = radar_volume.x.values, radar_volume.y.values, radar_volume.z

    trg = np.vstack((rad_x.flatten().ravel(),
                        rad_y.flatten().ravel(),
                        alt.values.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)

    def pyinterp_NN(data):
        if "time" in data["z"].coords:
            alt_era5 = np.vstack(data["z"].isel(time=0).T).T
        else:
            alt_era5 = np.vstack(data["z"].T).T
        if pre_interpolate_z:
            alt_era5 = np.repeat(alt_era5.T,len(mod_x), axis=1)

        src = np.vstack((np.repeat(mod_x[np.newaxis, :], alt_era5.shape[0], axis=0).ravel(),
                            np.repeat(mod_y[np.newaxis, :], alt_era5.shape[0], axis=0).ravel(),
                            alt_era5.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)

        try:
            mesh = pyinterp.RTree(ecef=False)
        except: # New pyinterp versions
            mesh = pyinterp.RTree3D(spheroid=pyinterp.core.geometry.geographic.Spheroid())
        if pre_interpolate_z:
            mesh.packing(src, data.isel(time=0).stack(stacked=['z', 'latitude', 'longitude']).values)
        else:
            mesh.packing(src, data.isel(time=0).stack(stacked=['lvl', 'latitude', 'longitude']).values)
        try:
            data_interp, neighbors = mesh.inverse_distance_weighting(trg, within=False, k=k_n, p=2) # k=1 is like nearest neighbors
        except: # New pyinterp versions
            # 1. Create the IDW configuration object
            # .with_k(k_n) replaces k=k_n
            # .with_p(2) replaces p=2
            # Note: 'within=False' is now handled by the default behavior
            # of the IDW config (it will search for 'k' neighbors regardless of bounds)
            idw_config = pyinterp.config.rtree.InverseDistanceWeighting().with_k(k_n).with_p(2)

            # 2. Call the method using the config object
            # coordinates must be the first positional argument, config must be the second
            data_interp, neighbors = mesh.inverse_distance_weighting(trg, config=idw_config)

        data_interp_reshape = data_interp.reshape(radar_volume["x"].shape)
        data_interp_reshape_xr = xr.DataArray(data_interp_reshape,
                                                coords=radar_volume["x"].coords,
                                                dims=radar_volume["x"].dims,
                                                name=data.name).expand_dims(dim={"time": data["time"]}, axis=0)
        return data_interp_reshape_xr

    # Define a function to process each variable and timestep
    def process_variable_time(var, func):
        """Apply a function to each timestep of a variable."""
        results = []
        for t in range(var.sizes['time']):
            result = func(var.isel(time=t).expand_dims("time"))
            results.append(result)

        # Combine the results along the time dimension
        return xr.concat(results, dim='time', join="outer", coords="different", compat='equals')

    # Wrapper to process all variables in the dataset
    def process_dataset(ds_dict, func):
        """Apply a function to all variables and timesteps in a dataset."""
        processed_vars = {}

        for var_name, ds in ds_dict.items():
            for vv_name, var_data in ds.data_vars.items():
                print(vv_name)
                processed_vars[vv_name] = process_variable_time(var_data, func).assign_attrs(var_data.attrs)

        # Combine all variables back into a dataset
        return xr.Dataset(processed_vars)

    # Apply the function
    start_time = time.time()
    print("Regridding ERA5 fields to radar volume...")
    era5_vol = process_dataset(era5_fields, pyinterp_NN)
    total_time = time.time() - start_time
    print(f"... took {total_time/60:.2f} minutes to run.")

    if len(rename) >0:
        era5_vol = era5_vol.rename(rename)

    return era5_vol

#### Function to attach the interpolated ERA5 fields into a dataset
def attach_ERA5_fields(radar_volume, site=None, path=None, convert_to_C=True,
                       variables=["temperature"], rename={"t":"TEMP"}, set_as_coords=False,
                       k_n=1, pre_interpolate_z=False):
    """
    Function to interpolate and attach data from ERA5 into radar_volume.

    Parameters
    ----------
    radar_volume : xarray Dataset
        Dataset to which to attach the ERA5 fields.
    site : str, optional
        (Short) Name of the radar site to locate the data in the default folder:
        "/automount/ags/jgiles/ERA5/hourly/"
        Either site or path must be given.
    path : str, optional
        Path to the folder where ERA5 data can be found.
        Either site or path must be given.
    convert_to_C : bool
        If True (default), convert ERA5 temperature from K to C.
    variables : list
        List of variables to load (named as in the folders). By default load only temperature.
    rename : dict
        Dictionary to rename from dataset variable name to new names. Leave the
        dictionary empty for no renaming.
    set_as_coords : bool
        If True, set the attach the ERA5 fields as coordinates instead of variables
    k_n : int
        Number of neighbors to pass to the inverse_distance_weighting function.
        k=1 means nearest neighbors method.
    pre_interpolate_z : bool
        If True, linearly interpolate the vertical coordinate of ERA5 to higher resolution
        before the regridding, for smoother results. Default is False.

    Returns
    ----------
    ds : xarray Dataset
        Original dataset with added ERA5 fields.
    """

    era5_vol = era5_to_radar_volume(radar_volume, site=site, path=path, convert_to_C=convert_to_C,
                             variables=variables, rename=rename, k_n=k_n, pre_interpolate_z=pre_interpolate_z)

    radar_volume_era5 = xr.merge((radar_volume, era5_vol.interp({"time": radar_volume["time"]}, method="linear")), compat='no_conflicts')
    if set_as_coords:
        radar_volume_era5 = radar_volume_era5.set_coords([vv for vv in era5_vol.data_vars])

    return radar_volume_era5

#### Function to load ERA5 temperature into a dataset
def interp_to_ht(ds, ht):
    """
    Interpolate 1D profile from ERA5 to higher resolution
    """
    ds = ds.swap_dims({"lvl":"height"})
    return ds.interp({"height": ht})

def interp_to_ht_parallel(ds, ht=np.arange(0,50000,50)):
    """
    Interpolate an ERA5 field to higher vertical resolution

    Parameters
    ----------
    ds : xarray.Dataset or xarray.Dataarray
        Dataset to interpolate.
    ht : numpy.array
        Array of height values to interpolate to.

    Returns
    ----------
    ds_interp : xarray.Dataset
        ds interpolated to new height coordinate.
    """
    # Interpolate to higher resolution

    interp_to_ht_partial = partial(interp_to_ht, ht=ht)

    results = []

    tasks = (ds.isel({"time":tt, "longitude":lon, "latitude":lat})
         for tt in range(len(ds.time))
         for lon in range(len(ds.longitude))
         for lat in range(len(ds.latitude)))

    with Pool() as P:
        # results = P.map( interp_to_ht_partial,
        #                 [ds.isel({"time":tt, "longitude":lon, "latitude":lat}) for tt in range(len(ds.time)) for lon in range(len(ds.longitude)) for lat in range(len(ds.latitude)) ] )
        results = P.map(interp_to_ht_partial, tasks)

    ds_interp = xr.combine_by_coords([ds.expand_dims(("time", "longitude", "latitude")) for ds in results], coords="different", compat="no_conflicts")

    # Fix Temperature below first measurement and above last one
    ds_interp = ds_interp.bfill(dim="height")
    ds_interp = ds_interp.ffill(dim="height")

    # Attempt to fill any missing timestep with adjacent data
    ds_interp = ds_interp.ffill(dim="time")
    ds_interp = ds_interp.bfill(dim="time")

    return ds_interp


def attach_ERA5_TEMP(ds, site=None, path=None, convert_to_C=True):
    """
    Function to attach temperature data from ERA5 as a new coordinate of ds. It
    interpolates the temperature profile from ERA5 levels to the ds heights. By
    default it is converted to degrees C.

    This function is deprecated because it only takes the lon/lat point closest
    to the radar site instead of interpolating the whole scanned area. It is
    kept for backwards compatibility. Use instead attach_ERA5_fields.

    Parameters
    ----------
    ds : xarray Dataset
        Dataset to which to attach the temperature coordinate as a function of height.
    site : str, optional
        (Short) Name of the radar site to locate the data in the default folder:
        "/automount/ags/jgiles/ERA5/hourly/"
        Either site or path must be given.
    path : str, optional
        Path to the folder where ERA5 temperature and geopotential data can be found.
        Either site or path must be given.
    convert_to_C : bool
        If True (default), convert ERA5 temperature from K to C.

    Returns
    ----------
    ds : xarray Dataset
        Original dataset with added TEMP coordinate
    """
    if path is None:
        # Set the default path if path is None
        try:
            era5_dir = "/automount/ags/jgiles/ERA5/hourly/"+site+"/pressure_level_vars/"
            if not os.path.exists(era5_dir):
                # if path does not exist, raise an error
                raise RuntimeError("folder for site="+site+" not found!")

        except TypeError:
            raise TypeError("If path is not provided, site must be provided!")
    elif type(path) is str:
        era5_dir = path
    else:
        raise TypeError("path must be type str!")

    # if time is not well defined, we try to get it from variable rtime
    if ds["time"].isnull().any():
        try:
            ds.coords["time"] = ds.rtime.min(dim="azimuth", skipna=True).compute()
        except:
            raise KeyError("Dimension time has not valid values")

    # if some coord has dimension time, reduce using median
    for coord in ["latitude", "longitude", "altitude", "elevation"]:
        if coord in ds.coords:
            if "time" in ds[coord].dims:
                ds.coords[coord] = ds.coords[coord].median("time")

    # We need the ds to be georeferenced in case it is not
    if "z" not in ds.coords:
        ds = ds.pipe(wrl.georef.georeference)

    # get times of the radar files
    startdt0 = dt.datetime.utcfromtimestamp(int(ds.time[0].values)/1e9).date()
    enddt0 = dt.datetime.utcfromtimestamp(int(ds.time[-1].values)/1e9).date() + dt.timedelta(hours=24)

    # transform the dates to datetimes
    startdt = dt.datetime.fromordinal(startdt0.toordinal())
    enddt = dt.datetime.fromordinal(enddt0.toordinal())

    # open ERA5 files
    try:
        era5_t = xr.open_mfdataset(reversed(sorted(glob.glob(era5_dir+"temperature/*"+str(startdt.year)+"*"),
                                                   key=lambda file_name: int(file_name.split("/")[-1].split('_')[1]))),
                                   concat_dim="lvl", combine="nested")
        era5_g = xr.open_mfdataset(reversed(sorted(glob.glob(era5_dir+"geopotential/*"+str(startdt.year)+"*"),
                                                   key=lambda file_name: int(file_name.split("/")[-1].split('_')[1]))),
                                   concat_dim="lvl", combine="nested")

    except:
        # first glob all files and then retain only the ones inside the period we want
        start_year_month = (startdt.year, startdt.month)
        end_year_month = (enddt.year, enddt.month)

        era5_t_files = glob.glob(era5_dir+"temperature/*all*")
        era5_t_files = [ file for file in era5_t_files
                if start_year_month <= tuple(map(int, file.split('_')[-1].split('.')[0].split('-'))) <= end_year_month
            ]

        era5_g_files = glob.glob(era5_dir+"geopotential/*all*")
        era5_g_files = [ file for file in era5_g_files
                if start_year_month <= tuple(map(int, file.split('_')[-1].split('.')[0].split('-'))) <= end_year_month
            ]

        era5_t = xr.open_mfdataset(era5_t_files, compat='no_conflicts').rename({"pressure_level": "lvl"})
        era5_g = xr.open_mfdataset(era5_g_files, compat='no_conflicts').rename({"pressure_level": "lvl"})

        if "valid_time" in era5_t:
            era5_t = era5_t.rename({"valid_time": "time"})
        if "valid_time" in era5_g:
            era5_g = era5_g.rename({"valid_time": "time"})

    # add altitude coord to temperature data
    earth_r = wrl.georef.projection.get_earth_radius(ds.latitude.values)
    gravity = 9.80665

    era5_t.coords["height"] = (earth_r*(era5_g.z/gravity)/(earth_r - era5_g.z/gravity)).compute()

    # Create time dimension and concatenate
    try: # this might fail because of the issue with the time dimension in elevations that some files have
        dtslice0 = startdt.strftime('%Y-%m-%d %H')
        dtslice1 = enddt.strftime('%Y-%m-%d %H')
        temperatures = era5_t["t"].loc[{"time":slice(dtslice0, dtslice1)}].sel({"latitude":ds["latitude"], "longitude":ds["longitude"]}, method="nearest")
        if convert_to_C:
            # convert from K to C
            temp_attrs = temperatures.attrs
            temperatures = temperatures -273.15
            temp_attrs["units"] = "C"
            temperatures.attrs = temp_attrs

        # Interpolate to higher resolution
        hmax = 25000.
        ht = np.arange(0., hmax, 100)


        interp_to_ht_partial = partial(interp_to_ht, ht=ht)

        results = []

        with Pool() as P:
            results = P.map( interp_to_ht_partial, [temperatures.isel(time=tt) for tt in range(len(temperatures.time)) ] )

        itemp_da = xr.concat(results, "time", join="outer", coords="different", compat='equals')

        # Fix Temperature below first measurement and above last one
        itemp_da = itemp_da.bfill(dim="height")
        itemp_da = itemp_da.ffill(dim="height")

        # Attempt to fill any missing timestep with adjacent data
        itemp_da = itemp_da.ffill(dim="time")
        itemp_da = itemp_da.bfill(dim="time")

        # Interpolate to dataset height and time, then add to dataset
        def merge_radar_profile(rds, cds):
            # cds = cds.interp({'height': rds.z}, method='linear')
            cds = cds.interp({'height': rds.z}, method='linear')
            cds = cds.interp({"time": rds.time}, method="linear")

            # Fill any missing values in z or range
            try:
                cds = cds.bfill(dim="z")
                cds = cds.ffill(dim="z")
            except ValueError:
                cds = cds.bfill(dim="range")
                cds = cds.ffill(dim="range")

            # Fill any missing values in time
            cds = cds.ffill(dim="time")
            cds = cds.bfill(dim="time")

            rds = rds.assign({"TEMP": cds})
            rds.TEMP.attrs["source"]="ERA5"
            return rds

        ds = ds.pipe(merge_radar_profile, itemp_da)

        ds.coords["TEMP"] = ds["TEMP"] # move TEMP from variable to coordinate
        return ds
    except ValueError:
        raise ValueError("!!!! ERROR: some issue when concatenating ERA5 data")

#### KDP delta bump correction in the ML
def KDP_ML_correction(ds, X_PHI="PHIDP_OC_MASKED", winlen=7, min_periods=2, mlt="height_ml_new_gia",
                      mlb="height_ml_bottom_new_gia", method="linear", top_tolerance=0, bottom_tolerance=0):
    '''
    Function to correct KDP in the melting layer due to PHIDP delta bump. KDP calculation
    uses Vulpiani et al 2012 method.

    Parameter
    ---------
    ds : xarray.DataArray
        array with PHIDP data as well as ML top and bottom heights. The array
        must be georreferenced with height coordinate named "z".

    Keyword Arguments
    -----------------
    X_PHI : str
        Name of the variable with PHIDP data. PHIDP should be offset corrected and masked for homogeneous values.
    winlen : int
        Size of window in range dimension for calculating KDP from PHIDP (Vulpiani method)
    min_periods : int
        minimum number of valid bins
    mlt : str
        Name of the variable/coordinate with melting layer top data.
    mlb : str
        Name of the variable/coordinate with melting layer bottom data.
    method : str
        Method to interpolating PHIDP in the melting layer. Default is "linear".
    top_tolerance : float
        Top tolerance for ML selection. top_tolerance is added to the values of mlt
    bottom_tolerance : float
        Bottom tolerance for ML selection. bottom_tolerance is substracted from the values of mlb


    Return
    ------
    ds : xarray.DataArray
        DataArray with input data plus KDP corrected in the melting layer.
    '''

    # PHIDP delta bump correction
    # get where PHIDP has nan values
    nan = np.isnan(ds[X_PHI])
    # get PHIDP outside the ML
    phi2 = ds[X_PHI].where( (ds.z < ( ds[mlb] - bottom_tolerance ) ) | (ds.z > ( ds[mlt] + top_tolerance ) ) | ds[mlt].isnull() )#.interpolate_na(dim='range',dask_gufunc_kwargs = "allow_rechunk")
    # interpolate PHIDP in ML
    phi2 = phi2.chunk(dict(range=-1)).interpolate_na(dim='range', method=method)
    # restore originally nan values
    phi2 = xr.where(nan, np.nan, phi2)

    # Derive KPD from the new PHIDP
    # dr = phi2.range.diff('range').median('range').values / 1000.
    # print("range res [km]:", dr)
    # winlen in gates
    # TODO: window length in m
    phidp_ml, kdp_ml = kdp_phidp_vulpiani(phi2, winlen, min_periods=min_periods)

    # assign to dataset
    ds = ds.assign({"KDP_ML_corrected": (["time", "azimuth", "range"],
                                         kdp_ml.values,
                                         KDP_attrs)})

    return ds


#### NOISE CORRECTION RHOHV
## From Veli


def noise_correction(ds, noise_level):
    """Calculate SNR, apply to RHOHV
    """
    # noise calculations
    snrh = ds.DBZH - 20 * np.log10(ds.range * 0.001) - noise_level - 0.033 * ds.range / 1000
    snrh = snrh.where(snrh >= 0).fillna(0)
    # attrs = wrl.io.xarray.moments_mapping['SNRH']
    attrs = xd.model.sweep_vars_mapping['SNRH'] # moved to xradar since wradlib 1.19
    attrs.pop('gamic', None)
    snrh = snrh.assign_attrs(attrs)
    rho = ds.RHOHV * (1. + 1. / 10. ** (snrh * 0.1))
    rho = rho.assign_attrs(ds.RHOHV.attrs)
    ds = ds.assign({'SNRH': snrh, 'RHOHV_NC': rho})
    ds = ds.assign_coords({'NOISE_LEVEL': noise_level})
    return ds


def noise_correction2(dbz, rho, noise_level):
    """
    Calculate SNR, apply to RHOHV
    Formula from Ryzhkov book page 187/203
    """
    # noise calculations
    snrh = dbz - 20 * np.log10(dbz.range * 0.001) - noise_level - 0.033 * dbz.range / 1000
    snrh = snrh.where(snrh >= 0).fillna(0)
    # attrs = wrl.io.xarray.moments_mapping['SNRH']
    attrs = xd.model.sweep_vars_mapping['SNRH'] # moved to xradar since wradlib 1.19
    attrs.pop('gamic', None)
    snrh = snrh.assign_attrs(attrs)
    snrh.name = "SNRH"
    rho_nc = rho * (1. + 1. / 10. ** (snrh * 0.1))
    rho_nc = rho_nc.assign_attrs(rho.attrs)
    rho_nc.name = "RHOHV_NC"
    return snrh, rho_nc

def calculate_noise_level(dbz, rho, noise=(-40, -20, 1), rho_bins=(0.9, 1.1, 0.005), snr_bins=(5., 30., .1)):
    """
    This functions calculates the noise levels and noise corrections for RHOHV, for a range of noise values.
    It returns a list of signal-to-noise and corrected rhohv arrays, as well as histograms involed in the calculations,
    a list of standard deviations for every result and the noise value with the minimum std.
    The final noise correction should be chosen based on the rn value (minumum std)

    The default noise range is based on BoXPol data, it may be good to extend it a bit for C-Band.

    The final noise level (rn) should be used with noise_correction2 one more time to get the final result.
    It may happen that the correction is too strong and we get some RHOHV values over 1. We should
    check this for some days of data and if that is the case, then select a noise level that is slightly less (about 2% less)
    """
    noise = np.arange(*noise)
    rho_bins = np.arange(*rho_bins)
    snr_bins = np.arange(*snr_bins)
    corr = [noise_correction2(dbz, rho, n) for n in noise]
    #with ProgressBar():
    #    corr = dask.compute(*corr)
    # hist = [dask.delayed(histogram)(rho0, snr0, bins=[rho_bins, snr_bins], block_size=rho.time.size) for snr0, rho0 in corr]
    hist = [histogram(rho0, snr0, bins=[rho_bins, snr_bins], block_size=rho.time.size) for snr0, rho0 in corr]
    # with ProgressBar():
    #     hist = dask.compute(*hist)
    std = [np.std(r.idxmax('RHOHV_NC_bin')).values for r in hist]
    rn = noise[np.argmin(std)]
    return corr, hist, std, rn



def hist_2d(A,B, bins1=35, bins2=35, mini=1, maxi=None, cmap='jet', colsteps=30, alpha=1, mode='absolute', fsize=15, colbar=True):
    """
    # Histogram 2d Quicklooks
    # ------------------------

    Plotting 2d Histogramm of two varibles

    # Input
    # -----

    A,B          ::: Variables
    bins1, bins2 ::: x, y bins
    mini, maxi   ::: min and max
    cmap         ::: colormap
    colsteps     ::: number of cmap steps
    alpha        ::: transperency
    fsize        ::: fontsize
    mode         ::: hist mode


    # Output
    # ------

    2D Histogramm Plot


    ::: Hist mode:::
    absolute ::: absolute numbers
    relative ::: relative numbers
    relative_with_y ::: relative numbers of y levels

    """
    from matplotlib.colors import LogNorm

    # discret cmap
    cmap = plt.cm.get_cmap(cmap, colsteps)

    # mask array
    m=~np.isnan(A) & ~np.isnan(B)

    if mode=='absolute':

        plt.hist2d(A[m], B[m], bins=(bins1, bins2), cmap=cmap, norm=LogNorm( vmin=mini, vmax=maxi), alpha=alpha)
        if colbar==True:
          cb = plt.colorbar(shrink=1, pad=0.01)
          cb.set_label('number of samples', fontsize=fsize)
          cb.ax.tick_params(labelsize=fsize)
        plt.xticks(fontsize=fsize)
        plt.yticks(fontsize=fsize)

    if mode=='relative':
        H, xe, ye = np.histogram2d(A[m], B[m], bins=(bins1, bins2))
        xm = (xe[0:-1]+ xe[1:len(xe)])/2
        ym = (ye[0:-1]+ ye[1:len(ye)])/2
        nsum = np.nansum(H)
        plt.pcolormesh(xm, ym, 100*(H.T/nsum),  cmap=cmap, norm=LogNorm( vmin=mini, vmax=maxi), alpha=alpha)
        if colbar==True:
          cb = plt.colorbar(shrink=1, pad=0.01)
          cb.set_label('%', fontsize=fsize)
          cb.ax.tick_params(labelsize=fsize)
        plt.xticks(fontsize=fsize)
        plt.yticks(fontsize=fsize)

    if mode=='relative_with_y':
        H, xe, ye = np.histogram2d(A[m], B[m], bins=(bins1, bins2))
        xm = (xe[0:-1]+ xe[1:len(xe)])/2
        ym = (ye[0:-1]+ ye[1:len(ye)])/2
        nsum = np.nansum(H, axis=0)
        plt.pcolormesh(xm, ym, 100*(H/nsum).T,  cmap=cmap, norm=LogNorm( vmin=mini, vmax=maxi), alpha=alpha)
        if colbar==True:
          cb = plt.colorbar(shrink=1, pad=0.01)
          cb.set_label('%', fontsize=fsize)
          cb.ax.tick_params(labelsize=fsize)
        plt.xticks(fontsize=fsize)
        plt.yticks(fontsize=fsize)

#### Calculate phase offset
def phase_offset_old(phioff, rng=3000.): # I do not remember why I wrote this function with differences to the one below (original from radarmet)
    """Calculate Phase offset.

    Parameter
    ---------
    phioff : xarray.DataArray
        differential phase array

    Keyword Arguments
    -----------------
    rng : float
        range in m to calculate system phase offset

    Return
    ------
    xarray.Dataset
        Dataset with variables PHIDP_OFFSET, start_range and stop_range
    """
    range_step = np.diff(phioff.range)[0]
    nprec = int(rng / range_step)
    if not nprec % 2:
        nprec += 1

    # create binary array
    phib = xr.where(np.isnan(phioff), 0, 1)

    # take nprec range bins and calculate sum
    phib_sum = phib.rolling(range=nprec, center=True).sum(skipna=True)

    # get start range of first N consecutive precip bins
    start_range = phib_sum.idxmax(dim="range") - nprec // 2 * np.diff(phib_sum.range)[0]
    # get range of first non-nan value per ray
    #start_range = (~np.isnan(phioff)).idxmax(dim='range', skipna=True)
    # add range
    stop_range = start_range + rng
    # get phase values in specified range
    off = phioff.where((phioff.range >= start_range) & (phioff.range <= stop_range),
                       drop=True)
    # calculate nan median over range
    off = off.median(dim='range', skipna=True)
    return xr.Dataset(dict(PHIDP_OFFSET=off,
                           start_range=start_range,
                           stop_range=stop_range))


def phase_offset(phioff, method=None, rng=3000.0, npix=None, **kwargs):
    """Calculate Phase offset.

    Parameter
    ---------
    phioff : xarray.DataArray
        differential phase DataArray

    Keyword Arguments
    -----------------
    method : str
        aggregation method, defaults to 'median'
    rng : float
        range in m to calculate system phase offset
    kwargs: additional keyword arguments to pass to the rolling sum

    Return
    ------
    phidp_offset : xarray.Dataset
        Dataset with PhiDP offset and start/stop ranges
    """
    range_step = np.diff(phioff.range)[0]
    nprec = int(rng / range_step)
    if not nprec % 2:
        nprec += 1

    if npix is None:
        npix = nprec // 2 + 1

    # create binary array
    phib = xr.where(np.isnan(phioff), 0, 1)

    # take nprec range bins and calculate sum
    phib_sum = phib.rolling(range=nprec, **kwargs).sum(skipna=True)

    # find at least N pixels in
    # phib_sum_N = phib_sum.where(phib_sum >= npix)
    phib_sum_N = xr.where(phib_sum <= npix, phib_sum, npix).where(phib)

    # get start range of first N consecutive precip bins
    start_range = (
        phib_sum_N.idxmax(dim="range") - nprec // 2 * np.diff(phib_sum.range)[0]
    )
    start_range = xr.where(start_range < 0, 0, start_range)

    # get stop range
    stop_range = start_range + rng
    # get phase values in specified range
    off = phioff.where(
        (phioff.range >= start_range) & (phioff.range <= stop_range), drop=False
    )
    # calculate nan median over range
    if method is None:
        method = "median"
    func = getattr(off, method)
    off_func = func(dim="range", skipna=True)

    return xr.Dataset(
        dict(
            PHIDP_OFFSET=off_func,
            start_range=start_range,
            stop_range=stop_range,
            phib_sum=phib_sum,
            phib=phib,
        )
    )


#### PHIDP processing
def phidp_from_kdp(da, winlen):
    """Derive PHIDP from KDP.

    Parameter
    ---------
    da : xarray.DataArray
        array with specific differential phase data
    winlen : int
        size of window in range dimension

    Return
    ------
    phi : xarray.DataArray
        DataArray with differential phase values
    """
    dr = da.range.diff('range').median('range').values / 1000.
    print("range res [km]:", dr)
    print("processing window [km]:", dr * winlen)
    return xr.apply_ufunc(scipy.integrate.cumulative_trapezoid,
                          da,
                          input_core_dims=[["range"]],
                          output_core_dims=[["range"]],
                          dask='parallelized',
                          kwargs=dict(dx=dr, initial=0.0, axis=-1),
                          dask_gufunc_kwargs={"allow_rechunk":True}
                          ) * 2

def phidp_offset_detection(ds, phidp="PHIDP", rhohv="RHOHV", dbzh="DBZH", rhohvmin=0.9,
                           dbzhmin=0., dphid_inithresh=10, min_height=0., rng=3000., azmedian=False, **kwargs):
    r"""
    Calculate the offset on PHIDP. Wrapper around phase_offset.

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with PHIDP, RHOHV and DBZH.
    phidp : str
        Name of the variable for PHIDP data in ds.
    rhohv : str
        Name of the variable for RHOHV data in ds.
    dbzh : str
        Name of the variable for DBZH data in ds.
    rhohvmin : float
        Minimum value for filtering RHOHV.
    dbzhmin : float
        Minimum value for filtering DBZH.
    dphid_inithresh : float
        Threshold value for filtering out initial high variability of PHIDP. Initial
        (first 4) bins are masked out if their azimuthal-median range-differentiate
        values are higher than dphid_inithresh in module.
    min_height : float
        Minimum height for filtering the z coordinate.
    rng : float
        range in m to calculate system phase offset.
    azmedian : bool, int
        If True, compute the median in the azimuth dimension to reduce the offset
        to a single value per PPI. Default is False. Alternatively, an integer
        can be passed to compute a rolling median of window size azmedian over
        the azimuth dimension to smooth out the resulting offsets. Possible NaN
        values are filled with the median over all azimuths.
    kwargs: additional keyword arguments to pass to the rolling sum in phase_offset.

    Returns
    ----------
    ds_offset : xarray Dataset
        xarray Dataset with the detected offset and related satatistics.

    """
    # filter
    diff_filter0 = abs(ds[phidp].median("azimuth").differentiate("range")*1000) < dphid_inithresh
    diff_filter1 = ds['range'] >= ds['range'][4]
    diff_filter = diff_filter0 | diff_filter1
    phi = ds[phidp].where((ds[rhohv]>=rhohvmin) & (ds[dbzh]>=dbzhmin) & (ds["z"]>min_height) & diff_filter )
    # calculate offset
    phidp_offset = phi.pipe(phase_offset, rng=rng, **kwargs)
    # reduce to one value per PPI
    if azmedian is True:
        # if azmedian is True, take the median of all azimuths
        phidp_offset["PHIDP_OFFSET"] = phidp_offset["PHIDP_OFFSET"].compute().median("azimuth")
    elif type(azmedian) is int:
        # if azmedian is an integer, run a rolling median over azimuth with window size azmedian
        if azmedian & 1: # azmedian is odd
            pass
        else: # if azmedian is even, add 1
            azmedian = azmedian +1
        azwindow = azmedian
        azhalfwindow = int(azwindow/2) # we need to pad the edges of the array with "wrap" so the median wraps around
        azthirdwindow = int(azwindow/3) # at least a third of azwindow must ve valid values
        phidp_offset["PHIDP_OFFSET"] = phidp_offset["PHIDP_OFFSET"].compute().pad({"azimuth":azhalfwindow}, mode="wrap")\
                .rolling(azimuth=azwindow, center=True, min_periods=azthirdwindow)\
                .median("azimuth", skipna=True).isel(azimuth=slice(azhalfwindow, -azhalfwindow))\
                .fillna(phidp_offset["PHIDP_OFFSET"].compute().median("azimuth")) # fill remaining NaN with the median of all

    return phidp_offset

def phidp_offset_correction(ds, X_PHI="UPHIDP", X_RHO="RHOHV", X_DBZH="DBZH", X_Zm="Zm",
                     rhohvmin=0.9, dbzhmin=-20., zm_max=35, min_height=0,
                     additional_thresholds=None,
                     window=7, window_time = 7,
                     fix_range=500., rng=None, rng_min=3000.,
                     fillna=False, clean_invalid=False, azmedian=False, tolerance=(0,0)):
    r"""
    Calculate PHIDP offset and attach results to the input dataset.

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with PHIDP, RHOHV, DBZH and z (height) coord.
    X_PHI : str
        Name of the variable for PHIDP data in ds.
    X_RHO : str
        Name of the variable for RHOHV data in ds.
    X_DBZH : str
        Name of the variable for DBZH data in ds.
    X_Zm : str
        Name of the variable for Zm data in ds (near-field reflectivity for wet radome detection).
    rhohvmin : float
        Minimum value for filtering RHOHV.
    dbzhmin : float
        Minimum value for filtering DBZH.
    zm_max : float
        Maximum value for filtering Zm (removing wet radome effects).
    min_height : float
        Minimum height for filtering the z coordinate.
    additional_thresholds : None, list of dict
        List with two dictionaries with additional data quality min max thresholds, to be
        passed on to apply_min_max_thresh(). If None, no thresholds are applied.
    fix_range : int
        Minimum range from where to consider PHIDP values.
    window : int
        Number of range bins used in calculating rng in case rng=None.
    window_time : int
        Number of time steps for PHIDP rolling median (median filter).
    rng : float
        Range in m to calculate system phase offset. If None (default), it
        will be calculated according to window. It should be large enough to
        allow sufficient data for offset identification (a value around 3000
        is usually enough)
    rng_min : float
        Minimum value of rng. If the value of rng (either passed by the user
        or calculated automatically) is lower than rng_min, then rng_min will be
        used instead.
    azmedian : bool, int
        Passed to phidp_offset_detection. Default is False.
    fillna : bool, float
        If True, fill non valid values (na) in the end result with zero. If float,
        fill the non valid values with fillna. Default is False (do not fill na).
    clean_invalid : bool
        If True, only output corrected phase for pixels with range beyond start_range + fix_range.
        start_range is the range of the first bin with the necessary consecutive valid bins from
        phase_offset(). Default is False (apply the offset to all ds[X_PHI]).
    tolerance : tuple
        If the phase offset lies between the values in tolerance, then no offset correction
        is applied. clean_invalid and fillna are still applied.

    Returns
    ----------
    ds : xarray Dataset
        xarray Dataset with the original data and offset corrected PHIDP.

    """
    # apply additional thresholds
    if additional_thresholds is not None:
        try:
            ds1 = apply_min_max_thresh(ds, additional_thresholds[0], additional_thresholds[1], skipfullna=True)
        except:
            warnings.warn("phidp_processing : additional_thresholds must be a list with two dictionaries, no thresholds were applied")
            ds1 = ds.copy()

    # Calculate range for offset calculation if rng is None
    if rng is None:
        rng = ds[X_PHI].range.diff("range").median().values * window

    if rng < rng_min:
        rng = rng_min

    # Calculate phase offset
    phidp_offset = phidp_offset_detection(ds1, phidp=X_PHI, rhohv=X_RHO, dbzh=X_DBZH, rhohvmin=rhohvmin,
                                          dbzhmin=dbzhmin, min_height=min_height, rng=rng, azmedian=azmedian,
                                          min_periods=3)

    off = phidp_offset["PHIDP_OFFSET"]
    tolerance_cond = ( off<=tolerance[0] ) + ( off>tolerance[1] )
    off = off.where(tolerance_cond)
    start_range = phidp_offset["start_range"].fillna(0)

    # Clean wet radome steps
    if X_Zm in ds:
        off = off.where(ds[X_Zm] < zm_max)
    else:
        warnings.warn(X_Zm+" not found in ds, wet radome effect not removed!")

    # Register NaN locations and fill them with global median
    valid_mask = off.notnull()
    off = off.fillna(off.median(dim='time', skipna=True))

    # Apply rolling median filter
    off = off.compute().rolling(time=window_time, center=True).median()

    # Bring back NaNs
    off = off.where(valid_mask)

    # Interpolate and extrapolate
    off = off.interpolate_na(dim='time', method='linear').bfill(dim='time').ffill(dim='time')

    # apply offset
    if clean_invalid:
        phi_fix = ds[X_PHI].copy().where(ds[X_PHI]["range"] >= start_range + fix_range)
    else:
        phi_fix = ds[X_PHI].copy()

    if fillna is True:
        off_fix = off.broadcast_like(phi_fix)
        phi_fix = phi_fix.fillna(off_fix) - off
    elif fillna is False:
        phi_fix = phi_fix - off
    elif isinstance(fillna, int) or isinstance(fillna, float):
        phi_fix = phi_fix.fillna(fillna) - off

    assign = {X_PHI+"_OFFSET": off.assign_attrs(ds[X_PHI].attrs),
              X_PHI+"_OC": phi_fix.assign_attrs(ds[X_PHI].attrs)}

    return ds.assign(assign)

def phidp_processing(ds, X_PHI="UPHIDP", X_RHO="RHOHV", X_DBZH="DBZH", X_Zm="Zm",
                     rhohvmin=0.9, dbzhmin=-20., zm_max=35, min_height=0,
                     additional_thresholds=None,
                     window=7, window2 = None, window_time = 7,
                     gaussian_smoothing=True, gauss_rng=5, gauss_az=3,
                     fix_range=500., rng=None, rng_min=3000.,
                     fillna=False, clean_invalid=False, azmedian=False, tolerance=(0,0)):
    r"""
    Calculate basic PHIDP processing including thresholding, smoothing and
    offset correction. Attach results to the input dataset.

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with PHIDP, RHOHV, DBZH and z (height) coord.
    X_PHI : str
        Name of the variable for PHIDP data in ds.
    X_RHO : str
        Name of the variable for RHOHV data in ds.
    X_DBZH : str
        Name of the variable for DBZH data in ds.
    X_Zm : str
        Name of the variable for Zm data in ds (near-field reflectivity for wet radome detection).
    rhohvmin : float
        Minimum value for filtering RHOHV.
    dbzhmin : float
        Minimum value for filtering DBZH.
    zm_max : float
        Maximum value for filtering Zm (removing wet radome effects).
    min_height : float
        Minimum height for filtering the z coordinate.
    additional_thresholds : None, list of dict
        List with two dictionaries with additional data quality min max thresholds, to be
        passed on to apply_min_max_thresh(). If None, no thresholds are applied.
    window : int
        Number of range bins for PHIDP rolling median (median filter).
    window2 : int
        Number of azimuth bins for PHIDP rolling median (median filter).
    window_time : int
        Number of time steps for PHIDP rolling median (median filter).
    gaussian_smoothing : bool
        If True, perform additional gaussian smoothing after median smoothing.
    gauss_rng : int
        Number of range bins for PHIDP Gaussian smoothing.
    gauss_az : int
        Number of azimuth bins for PHIDP Gaussian smoothing.
    fix_range : int
        Minimum range from where to consider PHIDP values.
    rng : float
        Range in m to calculate system phase offset. If None (default), it
        will be calculated according to window. It should be large enough to
        allow sufficient data for offset identification (a value around 3000
        is usually enough)
    rng_min : float
        Minimum value of rng. If the value of rng (either passed by the user
        or calculated automatically) is lower than rng_min, then rng_min will be
        used instead.
    azmedian : bool, int
        Passed to phidp_offset_detection. Default is False.
    fillna : bool, float
        If True, fill non valid values (na) in the end result with zero. If float,
        fill the non valid values with fillna. Default is False (do not fill na).
    clean_invalid : bool
        If True, only output corrected phase for pixels with range beyond start_range + fix_range.
        start_range is the range of the first bin with the necessary consecutive valid bins from
        phase_offset(). Default is False (apply the offset to all ds[X_PHI]).
    tolerance : tuple
        If the phase offset lies between the values in tolerance, then no offset correction
        is applied. clean_invalid and fillna are still applied.

    Returns
    ----------
    ds : xarray Dataset
        xarray Dataset with the original data and processed PHIDP.

    """
    # apply additional thresholds
    if additional_thresholds is not None:
        try:
            ds1 = apply_min_max_thresh(ds, additional_thresholds[0], additional_thresholds[1], skipfullna=True)
        except:
            warnings.warn("phidp_processing : additional_thresholds must be a list with two dictionaries, no thresholds were applied")
            ds1 = ds.copy()

    # smooth range dim
    phi_median = ds1[X_PHI].where((ds1[X_RHO]>=rhohvmin) & (ds1[X_DBZH]>=dbzhmin) & (ds1["z"]>min_height) & (ds1["range"]>fix_range) ).pipe(xr_rolling, window, window2=window2, method='median', min_periods=window//2+1, skipna=True)

    # Apply additional smoothing
    if gaussian_smoothing:
        gkern = gauss_kernel(gauss_az, gauss_rng)
        smooth_partial = partial(smooth_data, kernel=gkern)
        phiclean = xr.apply_ufunc(smooth_partial, phi_median.compute(),
                                  input_core_dims=[["azimuth","range"]], output_core_dims=[["azimuth","range"]],
                                  vectorize=True)
    else:
        phiclean = phi_median

    # Calculate range for offset calculation if rng is None
    if rng is None:
        rng = ds1[X_PHI].range.diff("range").median().values * window

    if rng < rng_min:
        rng = rng_min

    # Calculate phase offset
    phidp_offset = phidp_offset_detection(ds1.assign({X_PHI: phiclean}), phidp=X_PHI, rhohv=X_RHO, dbzh=X_DBZH, rhohvmin=rhohvmin,
                                          dbzhmin=dbzhmin, min_height=min_height, rng=rng, azmedian=azmedian,
                                          min_periods=3)

    off = phidp_offset["PHIDP_OFFSET"]
    tolerance_cond = ( off<=tolerance[0] ) + ( off>tolerance[1] )
    off = off.where(tolerance_cond)
    start_range = phidp_offset["start_range"].fillna(0)

    # Clean wet radome steps
    if X_Zm in ds:
        off = off.where(ds[X_Zm] < zm_max)
    else:
        warnings.warn(X_Zm+" not found in ds, wet radome effect not removed!")

    # Register NaN locations and fill them with global median
    valid_mask = off.notnull()
    off = off.fillna(off.median(dim='time', skipna=True))

    # Apply rolling median filter
    off = off.compute().rolling(time=window_time, center=True).median()

    # Bring back NaNs
    off = off.where(valid_mask)

    # Interpolate and extrapolate
    off = off.interpolate_na(dim='time', method='linear').bfill(dim='time').ffill(dim='time')

    # apply offset
    if clean_invalid:
        phi_fix = ds[X_PHI].copy().where(ds[X_PHI]["range"] >= start_range + fix_range)
        phiclean = phiclean.where(ds[X_PHI]["range"] >= start_range + fix_range)
    else:
        phi_fix = ds[X_PHI].copy()
        phiclean = phiclean.copy()

    if fillna is True:
        off_fix = off.broadcast_like(phi_fix)
        phi_fix = phi_fix.fillna(off_fix) - off
        phiclean = phiclean.fillna(off_fix) - off
    elif fillna is False:
        phi_fix = phi_fix - off
        phiclean = phiclean - off
    elif isinstance(fillna, int) or isinstance(fillna, float):
        phi_fix = phi_fix.fillna(fillna) - off
        phiclean = phiclean.fillna(fillna) - off

    # assign results
    assign = {X_PHI+"_OC_SMOOTH": phiclean.assign_attrs(ds[X_PHI].attrs),
              X_PHI+"_OFFSET": off.assign_attrs(ds[X_PHI].attrs),
              X_PHI+"_OC": phi_fix.assign_attrs(ds[X_PHI].attrs)}

    return ds.assign(assign)

def count_and_filter_segments(da, min_length=7):
    # Identify valid values (not NaN)
    valid_mask = ~np.isnan(da)

    # Find the indices where the valid_mask changes
    changes = np.diff(valid_mask.astype(int))

    # Get start and end indices of segments
    start_indices = np.where(changes == 1)[0] + 1
    end_indices = np.where(changes == -1)[0] + 1

    # Adjust for segments that start or end at the edges
    if valid_mask[0]:
        start_indices = np.insert(start_indices, 0, 0)
    if valid_mask[-1]:
        end_indices = np.append(end_indices, len(valid_mask))

    # Calculate segment lengths
    segment_lengths = end_indices - start_indices

    # Create a mask for segments longer than min_length
    long_segment_mask = np.zeros_like(valid_mask, dtype=bool)
    for start, length in zip(start_indices, segment_lengths):
        if length >= min_length:
            long_segment_mask[start:start + length] = True

    # Apply the mask to the original DataArray
    try:
        filtered_da = da.where(xr.DataArray(long_segment_mask, dims=["range"]), drop=False)
    except:
        filtered_da = np.where(long_segment_mask, da, np.nan)

    return filtered_da

def phidp_processing_ryzhkov(ds, X_PHI="UPHIDP", X_RHO="RHOHV", X_DBZH="DBZH", rhohvmin=0.9,
                     dbzhmin=-20., min_height=0, window=3, window2 = None, window3=7, fix_range=500., rng=None, rng_min=3000.,
                     fillna=False, clean_invalid=False, azmedian=False, tolerance=(0,0)):
    r"""
    Calculate basic PHIDP processing including thresholding, smoothing and
    offset correction like A. Ryzhkov does for NEXRAD. Attach results to the input dataset.

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with PHIDP, RHOHV, DBZH and z (height) coord.
    X_PHI : str
        Name of the variable for PHIDP data in ds.
    X_RHO : str
        Name of the variable for RHOHV data in ds.
    X_DBZH : str
        Name of the variable for DBZH data in ds.
    rhohvmin : float
        Minimum value for filtering RHOHV.
    dbzhmin : float
        Minimum value for filtering DBZH.
    min_height : float
        Minimum height for filtering the z coordinate.
    window : int
        Number of range bins for PHIDP rolling median (median filter).
    window2 : int
        Number of azimuth bins for PHIDP rolling median (median filter).
    window3 : int
        Number of range bins for PHIDP valid window size and rolling mean.
    fix_range : int
        Minimum range from where to consider PHIDP values.
    rng : float
        Range in m to calculate system phase offset. If None (default), it
        will be calculated according to window. It should be large enough to
        allow sufficient data for offset identification (a value around 3000
        is usually enough)
    rng_min : float
        Minimum value of rng. If the value of rng (either passed by the user
        or calculated automatically) is lower than rng_min, then rng_min will be
        used instead.
    azmedian : bool, int
        Passed to phidp_offset_detection. Default is False.
    fillna : bool, float
        If True, fill non valid values (na) in the end result with zero. If float,
        fill the non valid values with fillna. Default is False (do not fill na).
    clean_invalid : bool
        If True, only output corrected phase for pixels with range beyond start_range + fix_range.
        start_range is the range of the first bin with the necessary consecutive valid bins from
        phase_offset(). Default is False (apply the offset to all ds[X_PHI]).
    tolerance : tuple
        If the phase offset lies between the values in tolerance, then no offset correction
        is applied. clean_invalid and fillna are still applied.

    Returns
    ----------
    ds : xarray Dataset
        xarray Dataset with the original data and processed PHIDP.

    """

    # smooth range dim
    phi_median = ds[X_PHI].where((ds[X_RHO]>=rhohvmin)).pipe(xr_rolling, window, window2=window2, method='median', min_periods=window//2+1, skipna=True)

    # select only the segments of PHIDP that have enough valid values
    phimed_clean = xr.apply_ufunc(count_and_filter_segments, phi_median.compute(), kwargs=dict(min_length=window3),
                              input_core_dims=[["range"]], output_core_dims=[["range"]],
                              vectorize=True)

    # calculate PHIDP for the good intervals with a running average

    phi_mean = phimed_clean.rolling(range=window3, min_periods=window3//2+1, center=True).mean(skipna=True)

    # fill in the gaps with linear interpolation

    phi_mean_interp = phi_mean.interpolate_na(dim="range", method="linear")

    # fill the edges

    phi_mean_interp_fill = phi_mean_interp.bfill("range").ffill("range")

    # Calculate range for offset calculation if rng is None
    if rng is None:
        rng = ds[X_PHI].range.diff("range").median().values * window

    if rng < rng_min:
        rng = rng_min

    # Calculate phase offset
    phidp_offset = phidp_offset_detection(ds.assign({X_PHI: phi_mean_interp_fill}), phidp=X_PHI, rhohv=X_RHO, dbzh=X_DBZH, rhohvmin=rhohvmin,
                                          dbzhmin=dbzhmin, min_height=min_height, rng=rng, azmedian=azmedian,
                                          min_periods=3)

    off = phidp_offset["PHIDP_OFFSET"]
    tolerance_cond = ( off<=tolerance[0] ) + ( off>tolerance[1] )
    off = off.where(tolerance_cond, other=0)
    start_range = phidp_offset["start_range"].fillna(0)

    # apply offset
    if clean_invalid:
        phi_fix = ds[X_PHI].copy().where(ds[X_PHI]["range"] >= start_range + fix_range)
        phi_mean_interp_fill = phi_mean_interp_fill.where(ds[X_PHI]["range"] >= start_range + fix_range)
    else:
        phi_fix = ds[X_PHI].copy()
        phi_mean_interp_fill = phi_mean_interp_fill.copy()

    if fillna is True:
        off_fix = off.broadcast_like(phi_fix)
        phi_fix = phi_fix.fillna(off_fix) - off
        phi_mean_interp_fill = phi_mean_interp_fill.fillna(off_fix) - off
    elif fillna is False:
        phi_fix = phi_fix - off
        phi_mean_interp_fill = phi_mean_interp_fill - off
    elif isinstance(fillna, int) or isinstance(fillna, float):
        phi_fix = phi_fix.fillna(fillna) - off
        phi_mean_interp_fill = phi_mean_interp_fill.fillna(fillna) - off

    # assign results
    assign = {X_PHI+"_OC_SMOOTH": phi_mean_interp_fill.assign_attrs(ds[X_PHI].attrs),
              X_PHI+"_OFFSET": off.assign_attrs(ds[X_PHI].attrs),
              X_PHI+"_OC": phi_fix.assign_attrs(ds[X_PHI].attrs)}

    return ds.assign(assign)

#### KDP derivation from PHIDP

def kdp_from_phidp(ds, winlen, X_PHI=None, min_periods=2):
    """Derive KDP from PHIDP (based on convolution filter).

    Parameter
    ---------
    da : xarray.DataArray
        array with differential phase data
    winlen : int
        size of window in range dimension

    Keyword Arguments
    -----------------
    X_PHI : str
        name of variable for differential phase in case ds is a Dataset.
    min_periods : int
        minimum number of valid bins

    Return
    ------
    ds : xarray.Dataset
        Dataset with differential phase values and specific differential phase; or
    phidp, kdp : xarray.DataArray
        DataArrays with differential phase values (PHI_CONV) and specific differential phase (KDP_CONV)
    """
    if type(ds) is xr.DataArray:

        dr = ds.range.diff('range').median('range').values / 1000.
        print("range res [km]:", dr)
        print("processing window [km]:", dr * winlen)
        return xr.apply_ufunc(wrl.dp.kdp_from_phidp,
                              ds,
                              input_core_dims=[["range"]],
                              output_core_dims=[["range"]],
                              dask='parallelized',
                              kwargs=dict(winlen=winlen, dr=dr,
                                          min_periods=min_periods),
                              dask_gufunc_kwargs=dict(allow_rechunk=True),
                              )

    elif type(ds) is xr.Dataset:
        dr = ds.range.diff('range').median('range').values / 1000.
        print("range res [km]:", dr)
        print("processing window [km]:", dr * winlen)
        kdp = xr.apply_ufunc(wrl.dp.kdp_from_phidp,
                              ds[X_PHI],
                              input_core_dims=[["range"]],
                              output_core_dims=[["range"]],
                              dask='parallelized',
                              kwargs=dict(winlen=winlen, dr=dr,
                                          min_periods=min_periods),
                              dask_gufunc_kwargs=dict(allow_rechunk=True),
                              )

        assign = {
                  "KDP_CONV": kdp.assign_attrs(KDP_attrs),
                  }
        return ds.assign(assign)


def kdp_phidp_vulpiani(ds, winlen, X_PHI=None, min_periods=2):
    """Derive KDP from PHIDP (based on Vulpiani).

    Parameter
    ---------
    da : xarray.DataArray
        array with differential phase data
    winlen : int
        size of window in range dimension

    Keyword Arguments
    -----------------
    X_PHI : str
        name of variable for differential phase in case ds is a Dataset.
    min_periods : int
        minimum number of valid bins

    Return
    ------
    ds : xarray.Dataset
        Dataset with differential phase values and specific differential phase or
    phidp, kdp : xarray.DataArray
        DataArrays with differential phase values (PHI_CONV) and specific differential phase (KDP_CONV)
    """
    if type(ds) is xr.DataArray:

        dr = ds.range.diff('range').median('range').values / 1000.
        print("range res [km]:", dr)
        print("processing window [km]:", dr * winlen)
        return xr.apply_ufunc(wrl.dp.phidp_kdp_vulpiani,
                              ds,
                              input_core_dims=[["range"]],
                              output_core_dims=[["range"], ["range"]],
                              dask='parallelized',
                              kwargs=dict(winlen=winlen, dr=dr,
                                          min_periods=min_periods),
                              dask_gufunc_kwargs=dict(allow_rechunk=True),
                              )

    elif type(ds) is xr.Dataset:
        dr = ds.range.diff('range').median('range').values / 1000.
        print("range res [km]:", dr)
        print("processing window [km]:", dr * winlen)
        phidp, kdp = xr.apply_ufunc(wrl.dp.phidp_kdp_vulpiani,
                              ds[X_PHI],
                              input_core_dims=[["range"]],
                              output_core_dims=[["range"], ["range"]],
                              dask='parallelized',
                              kwargs=dict(winlen=winlen, dr=dr,
                                          min_periods=min_periods),
                              dask_gufunc_kwargs=dict(allow_rechunk=True),
                              )

        assign = {
                  "KDP_CONV": kdp.assign_attrs(KDP_attrs),
                  "PHI_CONV": phidp.assign_attrs(ds[X_PHI].attrs),
                  }
        return ds.assign(assign)

#### KDP angle dependency correction
def kdp_elevdep(kdp, angle):
    """
    For a given value of KDP at the given elevation angle, returns the estimated value at elevation angle 0.
    """
    return 2*kdp / (1 + np.cos(2*np.deg2rad(angle)))

def kdp_elev_corr(ds, angle, kdp=["KDP"]):
    """
    Returns ds with elevation-angle corrected KDP variables. Uses the elevation-
    dependency equation (9) from Schneebeli et al. (2013) and approximates the correction
    taking KDP=1 as reference.

    ds : xarray Dataset
        Dataset with KDP.
    angle : float
        Elevation angle of ds.
    kdp : list of str
        List with the name of KDP variables to correct. If a variable is not found,
        returns without correction and raises a warning.

    Returns
    -------
    ds : xarray Dataset
        Same as ds with elevation-angle corrected KDP variables named like KDP_EC.

    References
    -------
    Schneebeli, M., N. Dawes, M. Lehning, and A. Berne (2013) High-Resolution Vertical
        Profiles of X-Band Polarimetric Radar Observables during Snowfall in the Swiss
        Alps. J. Appl. Meteor. Climatol., 52, 378–394, https://doi.org/10.1175/JAMC-D-12-015.1.
    """
    ds1 = ds.copy()

    corr_factor = kdp_elevdep(1, angle)

    for kdpn in kdp:
        if kdpn not in ds.data_vars:
            warnings.warn("kdp_elev_corr: "+kdpn+" not present in ds, no correction was applied")
        else:
            ds1 = ds1.assign({kdpn+"_EC": (ds[kdpn]*corr_factor).assign_attrs(ds[kdpn].attrs)})

    return ds1


#### ZDR angle dependency correction
def zdr_elevdep(zdr0, angle):
    """
    For a given value of ZDR at elevation angle 0, returns the estimated value at the given elevation angle.
    """
    return wrl.trafo.decibel(wrl.trafo.idecibel(zdr0)/((wrl.trafo.idecibel(zdr0)**0.5*np.sin(np.deg2rad(angle))**2 + np.cos(np.deg2rad(angle))**2)**2))

def zdr_elev_corr(ds, angle, zdr=["ZDR"]):
    """
    Returns ds with elevation-angle corrected ZDR variables. Uses the elevation-
    dependency equation 28 from Rhyzkov et al. (2005) and approximates the correction
    taking ZDR_0=1 as reference.

    ds : xarray Dataset
        Dataset with ZDR.
    angle : float
        Elevation angle of ds.
    zdr : list of str
        List with the name of ZDR variables to correct. If a variable is not found,
        returns without correction and raises a warning.

    Returns
    -------
    ds : xarray Dataset
        Same as ds with elevation-angle corrected ZDR variables named like ZDR_EC.

    References
    -------
    Ryzhkov, A. V., S. E. Giangrande, V. M. Melnikov, and T. J. Schuur, 2005:
        Calibration Issues of Dual-Polarization Radar Measurements. J. Atmos.
        Oceanic Technol., 22, 1138–1155, https://doi.org/10.1175/JTECH1772.1.

    """
    ds1 = ds.copy()

    corr_factor = zdr_elevdep(1, angle)

    for zdrn in zdr:
        if zdrn not in ds.data_vars:
            warnings.warn("zdr_elev_corr: "+zdrn+" not present in ds, no correction was applied")
        else:
            ds1 = ds1.assign({zdrn+"_EC": (ds[zdrn]/corr_factor).assign_attrs(ds[zdrn].attrs)})

    return ds1

#### Calculate depolarization ratio
def calc_depolarization(da, zdr="ZDR_OC", rho="RHOHV_NC"):
    # Wrapper around wrl.dp.depolarization
    return xr.apply_ufunc(wrl.dp.depolarization,
                          da[zdr], da[rho].where(da[rho]<1),
                        dask='parallelized',
    )

#### Calibration of ZDR with light-rain consistency
from matplotlib import pyplot as plt

def zhzdr_lr_consistency_old(ZH, ZDR, RHO, TMP, rhohv_th=0.99, tmp_th=5, plot_correction=True):
    """
    ZH-ZDR Consistency in light rain, for ZDR calibration
    AR p.155-156

    """
    zdr_zh_20 = np.nanmedian(ZDR[(ZH>=19)&(ZH<21)&(RHO>rhohv_th)&(TMP>tmp_th)])
    zdr_zh_22 = np.nanmedian(ZDR[(ZH>=21)&(ZH<23)&(RHO>rhohv_th)&(TMP>tmp_th)])
    zdr_zh_24 = np.nanmedian(ZDR[(ZH>=23)&(ZH<25)&(RHO>rhohv_th)&(TMP>tmp_th)])
    zdr_zh_26 = np.nanmedian(ZDR[(ZH>=25)&(ZH<27)&(RHO>rhohv_th)&(TMP>tmp_th)])
    zdr_zh_28 = np.nanmedian(ZDR[(ZH>=27)&(ZH<29)&(RHO>rhohv_th)&(TMP>tmp_th)])
    zdr_zh_30 = np.nanmedian(ZDR[(ZH>=29)&(ZH<31)&(RHO>rhohv_th)&(TMP>tmp_th)])

    zdroffset = np.nansum([zdr_zh_20-.23, zdr_zh_22-.27, zdr_zh_24-.33, zdr_zh_26-.40, zdr_zh_28-.48, zdr_zh_30-.56])/6.

    if plot_correction:
        mask = (RHO>rhohv_th)&(TMP>tmp_th)
        plt.figure(figsize=(8,3))
        plt.subplot(1,2,1)
        hist_2d(ZH[mask], ZDR[mask], bins1=np.arange(0,40,1), bins2=np.arange(-1,3,.1))
        plt.plot([20,22,24,26,28,30],[.23, .27, .33, .40, .48, .56], color='black')
        plt.title('Non-calibrated $Z_{DR}$')
        plt.xlabel(r'$Z_H$', fontsize=15)
        plt.ylabel(r'$Z_{DR}$', fontsize=15)
        plt.grid(which='both', color='black', linestyle=':', alpha=0.5)

        plt.subplot(1,2,2)
        hist_2d(ZH[mask], ZDR[mask]-zdroffset, bins1=np.arange(0,40,1), bins2=np.arange(-1,3,.1))
        plt.plot([20,22,24,26,28,30],[.23, .27, .33, .40, .48, .56], color='black')
        plt.title('Calibrated $Z_{DR}$')
        plt.xlabel(r'$Z_H$', fontsize=15)
        plt.ylabel(r'$Z_{DR}$', fontsize=15)
        plt.grid(which='both', color='black', linestyle=':', alpha=0.5)
        plt.legend(title=r'$\Delta Z_{DR}$: '+str(np.round(zdroffset,3))+'dB')

        plt.tight_layout()
        plt.show()

    return zdroffset

def zhzdr_lr_consistency(ds, zdr="ZDR", dbzh="DBZH", rhohv="RHOHV", rhvmin=0.99, min_h=500, min_count=30, band="C",
                         mlbottom=None, temp=None, timemode="step", plot_correction=False, plot_timestep=0,
                         binszh=np.arange(0,40,1), binszdr=np.arange(-1,3,.1)):
    """
    Improved function for
    ZH-ZDR Consistency in light rain, for ZDR calibration
    Ryzhkov and Zrnic p.155-156

    For ZDR calibration: SNR> 20-25 and attenuation should be insignificant (Ryzhkov and Zrnic p. 156)

    ds : xarray Dataset
        Dataset with ZDR, DBZH and RHOHV.
    zdr : str
        Name of the variable in ds for differential reflectivity data. Default is "ZDR".
    dbzh : str
        Name of the variable in ds for horizontal reflectivity data (in dB). Default is "DBZH".
    rhohv : str
        Name of the variable in ds for cross-correlation coefficient data. Default is "RHOHV".
    mlbottom : str, int or float
        If str: name of the ML bottom variable in ds. If None, it is assumed to
        be "height_ml_bottom_new_gia" or "height_ml_bottom" (in that order).
        If int or float: we assume the ML bottom is not available and we take the given
        int value as the temperature level from which to consider radar bins.
        Only gates below the melting layer bottom (i.e. the rain
        region below the melting layer) are included in the method.
    temp : str, optional
        Name of the temperature variable in ds. Only necessary if mlbottom is int.
        If None is given and mlbottom is int or float, the default name "TEMP" is used.
    rhvmin : float, optional
        Threshold on :math:`\rho_{HV}` (unitless) related to light rain.
        The default is 0.99.
    min_h : float, optional
        Minimum height of usable data within the polarimetric profiles, in m. This is relative to
        sea level and not relative to the altitude of the radar (in accordance to the "z" coordinate
        from wradlib.georef.georeference). The default is 500.
    min_count : int, optional
        Minimum count of valid values in each reflectivity interval for the calculation to be valid.
    band : str, list
        Frequency band to select the reference values according to Ryzhkov and Zrnic. Possible
        values are: "S", "C" or "X". Alternatively, a custom list with 6 reference values
        can be passed and will be used instead. E.g.: band=[.23, .27, .32, .38, .46, .55]
    timemode : str
        How to calculate the offset in case a time dimension is found. "step" calculates one offset
        per timestep. "all" calculates one offset for the whole ds. Default is "step"
    plot_correction : bool
        If True, plot the histogram showing the uncorrected vs corrected data. Default is False.
    plot_timestep : int
        In case timemode="step" and plot_correction=True, plot_timestep defines the time index to
        be plotted. By default the first timestep (index=0) is plotted.
    binszh, binszdr : ZH and ZDR bins to pass to the 2d histogram plotting function. Only used if
        plot_correction=True.

    Returns
    ----------
    zdroffset : xarray Dataset
        xarray Dataset with the detected offset and the count of valid values used for the calculation.
    """

    # Set the climatological values according to the book for each band for 20<Zh<30
    clim_values = {
        "S": [.23, .27, .32, .38, .46, .55],
        "C": [.23, .27, .33, .40, .48, .56],
        "X": [.23, .28, .33, .41, .49, .58]
        }

    if type(band) is str:
        ref_vals = clim_values[band]
    elif type(band) is list:
        ref_vals = band
    else:
        raise ValueError("Keyword argument 'band' is not str nor list.")

    # We need the ds to be georeferenced in case it is not
    if "z" not in ds.coords:
        ds = ds.pipe(wrl.georef.georeference)

    if mlbottom is None:
        try:
            ml_bottom = ds["z"] < ds["height_ml_bottom_new_gia"]
        except KeyError:
            try:
                ml_bottom = ds["z"] < ds["height_ml_bottom"]
            except KeyError:
                raise KeyError("Melting layer bottom not found in ds. Provide melting layer bottom or temperature level.")
            except:
                raise RuntimeError("Something went wrong when looking for ML variable")
        except:
            raise RuntimeError("Something went wrong when looking for ML variable")
    elif type(mlbottom) is str:
        ml_bottom = ds["z"] < ds[mlbottom]
    elif type(mlbottom) in [float, int]:
        if type(temp) is str:
            ml_bottom = ds[temp] > mlbottom
        elif temp is None:
            try:
                ml_bottom = ds["TEMP"] > mlbottom
            except KeyError:
                raise KeyError("temp is not given and could not be found by default")
        else:
            raise TypeError("temp must be str or None")
    else:
        raise TypeError("mlbottom must be str, int or None")

    # filter data below ML and above min_h
    ds_fil = ds.where(ml_bottom)
    ds_fil = ds_fil.where(ds["z"]>min_h)

    # Define a function to filter zdr by dbzh and rhohv
    def where_dbzh_rhohv(data, db0, db1, rhv=rhvmin):
        return (data[zdr].where((data[dbzh]>=db0)&(data[dbzh]<db1)&(data[rhohv]>rhv)))

    if "time" in ds and timemode=="step":
        # Get dimensions to reduce (other than time)
        dims_wotime = [kk for kk in ds_fil.dims]
        while "time" in dims_wotime:
            dims_wotime.remove("time")

        zdr_zh_20 = where_dbzh_rhohv(ds_fil, 19, 21).compute().median(dim=dims_wotime)
        zdr_zh_22 = where_dbzh_rhohv(ds_fil, 21, 23).compute().median(dim=dims_wotime)
        zdr_zh_24 = where_dbzh_rhohv(ds_fil, 23, 25).compute().median(dim=dims_wotime)
        zdr_zh_26 = where_dbzh_rhohv(ds_fil, 25, 27).compute().median(dim=dims_wotime)
        zdr_zh_28 = where_dbzh_rhohv(ds_fil, 27, 29).compute().median(dim=dims_wotime)
        zdr_zh_30 = where_dbzh_rhohv(ds_fil, 29, 31).compute().median(dim=dims_wotime)

        # check that there are sufficient values in each interval (at least 30)
        zdr_zh_20 = zdr_zh_20.where(where_dbzh_rhohv(ds_fil, 19, 21).count(dim=dims_wotime)>=min_count)
        zdr_zh_22 = zdr_zh_22.where(where_dbzh_rhohv(ds_fil, 21, 23).count(dim=dims_wotime)>=min_count)
        zdr_zh_24 = zdr_zh_24.where(where_dbzh_rhohv(ds_fil, 23, 25).count(dim=dims_wotime)>=min_count)
        zdr_zh_26 = zdr_zh_26.where(where_dbzh_rhohv(ds_fil, 25, 27).count(dim=dims_wotime)>=min_count)
        zdr_zh_28 = zdr_zh_28.where(where_dbzh_rhohv(ds_fil, 27, 29).count(dim=dims_wotime)>=min_count)
        zdr_zh_30 = zdr_zh_30.where(where_dbzh_rhohv(ds_fil, 29, 31).count(dim=dims_wotime)>=min_count)

        zdroffset = xr.concat([zdr_zh_20-ref_vals[0], zdr_zh_22-ref_vals[1], zdr_zh_24-ref_vals[2], zdr_zh_26-ref_vals[3], zdr_zh_28-ref_vals[4], zdr_zh_30-ref_vals[5]], dim='dataarrays', join="outer", coords="different", compat='equals').mean(dim='dataarrays', skipna=False, keep_attrs=True)

        # get also data quality vars
        zdr_max = where_dbzh_rhohv(ds_fil, 19, 31).max(dim=dims_wotime)
        zdr_min = where_dbzh_rhohv(ds_fil, 19, 31).min(dim=dims_wotime)
        zdr_std = where_dbzh_rhohv(ds_fil, 19, 31).std(dim=dims_wotime)
        zdr_sem = ( zdr_std / where_dbzh_rhohv(ds_fil, 19, 31).count(dim=dims_wotime)**(1/2) )
        zdr_offset_datacount = where_dbzh_rhohv(ds_fil, 19, 31).count(dim=dims_wotime)

        # drop ML coordinates if present
        for coord in zdroffset.coords:
            if "_ml" in coord:
                zdroffset = zdroffset.drop_vars(coord)
                zdr_max = zdr_max.drop_vars(coord)
                zdr_min = zdr_min.drop_vars(coord)
                zdr_std = zdr_std.drop_vars(coord)
                zdr_sem = zdr_sem.drop_vars(coord)
                zdr_offset_datacount = zdr_offset_datacount.drop_vars(coord)

    else:
        zdr_zh_20 = where_dbzh_rhohv(ds_fil, 19, 21).compute().median()
        zdr_zh_22 = where_dbzh_rhohv(ds_fil, 21, 23).compute().median()
        zdr_zh_24 = where_dbzh_rhohv(ds_fil, 23, 25).compute().median()
        zdr_zh_26 = where_dbzh_rhohv(ds_fil, 25, 27).compute().median()
        zdr_zh_28 = where_dbzh_rhohv(ds_fil, 27, 29).compute().median()
        zdr_zh_30 = where_dbzh_rhohv(ds_fil, 29, 31).compute().median()

        # check that there are sufficient values in each interval (at least 30)
        if where_dbzh_rhohv(ds_fil, 19, 21).count()<min_count:
            zdr_zh_20 = zdr_zh_20*np.nan
        if where_dbzh_rhohv(ds_fil, 21, 23).count()<min_count:
            zdr_zh_22 = zdr_zh_22*np.nan
        if where_dbzh_rhohv(ds_fil, 23, 25).count()<min_count:
            zdr_zh_24 = zdr_zh_24*np.nan
        if where_dbzh_rhohv(ds_fil, 25, 27).count()<min_count:
            zdr_zh_26 = zdr_zh_26*np.nan
        if where_dbzh_rhohv(ds_fil, 27, 29).count()<min_count:
            zdr_zh_28 = zdr_zh_28*np.nan
        if where_dbzh_rhohv(ds_fil, 29, 31).count()<min_count:
            zdr_zh_30 = zdr_zh_30*np.nan

        zdroffset = xr.concat([zdr_zh_20-ref_vals[0], zdr_zh_22-ref_vals[1], zdr_zh_24-ref_vals[2], zdr_zh_26-ref_vals[3], zdr_zh_28-ref_vals[4], zdr_zh_30-ref_vals[5]], dim='dataarrays', combine_attrs="override", join="outer", coords="different", compat='equals').mean(dim='dataarrays', skipna=False, keep_attrs=True)

        # get also data quality vars
        zdr_max = where_dbzh_rhohv(ds_fil, 19, 31).max()
        zdr_min = where_dbzh_rhohv(ds_fil, 19, 31).min()
        zdr_std = where_dbzh_rhohv(ds_fil, 19, 31).std()
        zdr_sem = ( zdr_std / where_dbzh_rhohv(ds_fil, 19, 31).count()**(1/2) )
        zdr_offset_datacount = where_dbzh_rhohv(ds_fil, 19, 31).count()

        # restore time dim if present
        if "time" in ds:
            zdroffset = zdroffset.expand_dims("time")
            zdroffset["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord
            zdr_max = zdr_max.expand_dims("time")
            zdr_max["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord
            zdr_min = zdr_min.expand_dims("time")
            zdr_min["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord
            zdr_std = zdr_std.expand_dims("time")
            zdr_std["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord
            zdr_sem = zdr_sem.expand_dims("time")
            zdr_sem["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord
            zdr_offset_datacount = zdr_offset_datacount.expand_dims("time")
            zdr_offset_datacount["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord

    # restore attrs
    zdroffset.attrs = ds_fil[zdr].attrs
    zdroffset.attrs["long_name"] = "ZDR offset from light rain consistency method"
    zdroffset.attrs["standard_name"] = "ZDR_offset_from_light_rain_consistency_method"

    zdr_max.attrs["long_name"] = "ZDR max from offset calculation"
    zdr_max.attrs["standard_name"] = "ZDR_max_from_offset_calculation"

    zdr_min.attrs["long_name"] = "ZDR min from offset calculation"
    zdr_min.attrs["standard_name"] = "ZDR_min_from_offset_calculation"

    zdr_std.attrs["long_name"] = "ZDR standard deviation from offset calculation"
    zdr_std.attrs["standard_name"] = "ZDR_std_from_offset_calculation"

    zdr_sem.attrs["long_name"] = "ZDR standard error of the mean from offset calculation"
    zdr_sem.attrs["standard_name"] = "ZDR_sem_from_offset_calculation"

    zdr_offset_datacount.attrs["long_name"] = "Count of values (bins) used for the ZDR offset calculation"
    zdr_offset_datacount.attrs["standard_name"] = "count_of_values_zdr_offset"

    if plot_correction:
        try:
            mask = ds_fil[rhohv]>rhvmin
            plt.figure(figsize=(8,3))
            plt.subplot(1,2,1)
            if "time" in ds and timemode=="step":
                hist_2d(ds_fil[dbzh].where(mask)[plot_timestep].values, ds_fil[zdr].where(mask)[plot_timestep].values, bins1=binszh, bins2=binszdr)
            else:
                hist_2d(ds_fil[dbzh].where(mask).values, ds_fil[zdr].where(mask).values, bins1=binszh, bins2=binszdr)
            plt.plot([20,22,24,26,28,30],[.23, .27, .33, .40, .48, .56], color='black')
            plt.title('Non-calibrated $Z_{DR}$')
            plt.xlabel(r'$Z_H$', fontsize=15)
            plt.ylabel(r'$Z_{DR}$', fontsize=15)
            plt.grid(which='both', color='black', linestyle=':', alpha=0.5)

            plt.subplot(1,2,2)
            if "time" in ds and timemode=="step":
                hist_2d(ds_fil[dbzh].where(mask)[plot_timestep].values, ds_fil[zdr].where(mask)[plot_timestep].values-zdroffset[plot_timestep].values, bins1=binszh, bins2=binszdr)
            else:
                hist_2d(ds_fil[dbzh].where(mask).values, ds_fil[zdr].where(mask).values-zdroffset.values, bins1=binszh, bins2=binszdr)
            plt.plot([20,22,24,26,28,30],[.23, .27, .33, .40, .48, .56], color='black')
            plt.title('Calibrated $Z_{DR}$')
            plt.xlabel(r'$Z_H$', fontsize=15)
            plt.ylabel(r'$Z_{DR}$', fontsize=15)
            plt.grid(which='both', color='black', linestyle=':', alpha=0.5)
            if "time" in ds and timemode=="step":
                plt.legend(title=r'$\Delta Z_{DR}$: '+str(np.round(zdroffset.values[plot_timestep],3))+'dB')
            else:
                plt.legend(title=r'$\Delta Z_{DR}$: '+str(np.round(zdroffset.values,3))+'dB')

            plt.tight_layout()
            plt.show()
        except ValueError:
            print("No plotting: No light rain detected with current settings")

    # change name of the array
    zdroffset.name="ZDR_offset"

    # promote to Dataset
    zdroffset = zdroffset.to_dataset().assign({
        "ZDR_max_from_offset": zdr_max,
        "ZDR_min_from_offset": zdr_min,
        "ZDR_std_from_offset": zdr_std,
        "ZDR_sem_from_offset": zdr_sem,
        "ZDR_offset_datacount": zdr_offset_datacount
        })

    return zdroffset



#### ZDR calibration from VPs. Adapted from Daniel Sanchez-Rivas (TowerPy) to xarray
def zdr_offset_detection_vps(ds, zdr="ZDR", dbzh="DBZH", rhohv="RHOHV", mode="median",
                        mlbottom=None, temp=None, min_h=1000, zhmin=5,
                        zhmax=30, rhvmin=0.98, minbins=10, azmed=False, timemode="step"):
    r"""
    Calculate the offset on :math:`Z_{DR}` using vertical profiles. Only gates
    below the melting layer bottom (i.e. the rain region below the melting layer)
    or below the given temperature level are included in the method.

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with the vertical scan. ZDR, DBZH and RHOHV are needed. Dimensions
        should include "azimuth" and "range"
    zdr : str
        Name of the variable in ds for differential reflectivity data. Default is "ZDR".
    dbzh : str
        Name of the variable in ds for horizontal reflectivity data (in dB). Default is "DBZH".
    rhohv : str
        Name of the variable in ds for cross-correlation coefficient data. Default is "RHOHV".
    mode : str
        Method for calculating the offset from the distribution of ZDR values in light rain.
        Can be either "median" or "mean". Default is "median".
    mlbottom : str, int or float
        If str: name of the ML bottom variable in ds. If None, it is assumed to
        be "height_ml_bottom_new_gia" or "height_ml_bottom" (in that order).
        If int or float: we assume the ML bottom is not available and we take the given
        int value as the temperature level from which to consider radar bins.
        Only gates below the melting layer bottom (i.e. the rain
        region below the melting layer) are included in the method.
    temp : str, optional
        Name of the temperature variable in ds. Only necessary if mlbottom is int.
        If None is given and mlbottom is int or float, the default name "TEMP" is used.
    min_h : float, optional
        Minimum height of usable data within the polarimetric profiles, in m. This is relative to
        sea level and not relative to the altitude of the radar (in accordance to the "z" coordinate
        from wradlib.georef.georeference). The default is 1000.
    zhmin : float, optional
        Threshold on :math:`Z_{H}` (in dBZ) related to light rain.
        The default is 5.
    zhmax : float, optional
        Threshold on :math:`Z_{H}` (in dBZ) related to light rain.
        The default is 30.
    rhvmin : float, optional
        Threshold on :math:`\rho_{HV}` (unitless) related to light rain.
        The default is 0.98.
    minbins : float, optional
        Minimum number of consecutive :math:`Z_{DR}` bins related to light rain. This should
        vary according to range resolution. The default is 10.
    azmed : bool
        If True, perform azimuthal median after filtering values and before offset calculation. Default is False
    timemode : str
        How to calculate the offset in case a time dimension is found. "step" calculates one offset
        per timestep. "all" calculates one offset for the whole ds. Default is "step"

    Returns
    ----------
    ds_offset : xarray Dataset
        xarray Dataset with the detected offset and related satatistics.

    Notes
    -----
    1. Based on the method described in [1]_ and [2]_
    2. Adapted from Daniel Sanchez-Rivas (TowerPy) [3] to xarray by Julian Giles.

    References
    ----------
    .. [1] Gorgucci, E., Scarchilli, G., and Chandrasekar, V. (1999),
        A procedure to calibrate multiparameter weather radar using
        properties of the rain medium, IEEE T. Geosci. Remote, 37, 269–276,
        https://doi.org/10.1109/36.739161
    .. [2] Sanchez-Rivas, D. and Rico-Ramirez, M. A. (2022): "Calibration
        of radar differential reflectivity using quasi-vertical profiles",
        Atmos. Meas. Tech., 15, 503–520,
        https://doi.org/10.5194/amt-15-503-2022
    .. [3] Sanchez-Rivas, D., and Rico-Ramirez, M. A. (2023). Towerpy:
        An open-source toolbox for processing polarimetric weather radar data.
        Environmental Modelling & Software, 167, 105746.
        https://doi.org/10.1016/j.envsoft.2023.105746
    """

    # We need the ds to be georeferenced in case it is not
    if "z" not in ds.coords:
        ds = ds.pipe(wrl.georef.georeference)

    if mlbottom is None:
        try:
            ml_bottom = ds["z"] < ds["height_ml_bottom_new_gia"]
        except KeyError:
            try:
                ml_bottom = ds["z"] < ds["height_ml_bottom"]
            except KeyError:
                raise KeyError("Melting layer bottom not found in ds. Provide melting layer bottom or temperature level.")
            except:
                raise RuntimeError("Something went wrong when looking for ML variable")
        except:
            raise RuntimeError("Something went wrong when looking for ML variable")
    elif type(mlbottom) is str:
        ml_bottom = ds["z"] < ds[mlbottom]
    elif type(mlbottom) in [float, int]:
        if type(temp) is str:
            ml_bottom = ds[temp] > mlbottom
        elif temp is None:
            try:
                ml_bottom = ds["TEMP"] > mlbottom
            except KeyError:
                raise KeyError("temp is not given and could not be found by default")
        else:
            raise TypeError("temp must be str or None")
    else:
        raise TypeError("mlbottom must be str, int or None")

    # get ZDR data and filter values below ML and above min_h
    ds_zdr = ds[zdr]
    ds_zdr = ds_zdr.where(ml_bottom)
    ds_zdr = ds_zdr.where(ds["z"]>min_h)

    # Filter according to DBZH and RHOHV limits
    ds_zdr = ds_zdr.where(ds[dbzh]>zhmin).where(ds[dbzh]<zhmax).where(ds[rhohv]>rhvmin)

    # Azimuth median before computing?
    if azmed:
        if "azimuth" in ds_zdr.dims:
            ds_zdr_med = ds_zdr.median("azimuth")
        else:
            raise KeyError("azimuth not found in dataset dimensions")
    else:
        ds_zdr_med = ds_zdr

    if "time" in ds and timemode=="step":
        # Get dimensions to reduce (other than time)
        dims_wotime = [kk for kk in ds_zdr_med.dims]
        while "time" in dims_wotime:
            dims_wotime.remove("time")

        # same as before but with ds_zdr, in case the azimuth has already been taken off (for the data count)
        dims_full_wotime = [kk for kk in ds_zdr.dims]
        while "time" in dims_full_wotime:
            dims_full_wotime.remove("time")

        # Filter according to the minimum number of bins limit
        ds_zdr_med_ready = ds_zdr_med.where(n_longest_consecutive(ds_zdr_med, dim="range").compute() > minbins)

        # Calculate offset and others
        if mode=="median":
            zdr_offset = ds_zdr_med_ready.median(dim=dims_wotime).assign_attrs(
                {"long_name":"ZDR offset from vertical profile (median)",
                 "standard_name":"ZDR_offset_from_vertical_profile",
                 "units": "dB"}
                )
        elif mode=="mean":
            zdr_offset = ds_zdr_med_ready.mean(dim=dims_wotime).assign_attrs(
                {"long_name":"ZDR offset from vertical profile (mean)",
                 "standard_name":"ZDR_offset_from_vertical_profile",
                 "units": "dB"}
                )
        else:
            raise KeyError("mode must be either 'median' or 'mean'")

        zdr_max = ds_zdr_med_ready.max(dim=dims_wotime).assign_attrs(
            {"long_name":"ZDR max from offset calculation",
             "standard_name":"ZDR_max_from_offset_calculation"}
            )
        zdr_min = ds_zdr_med_ready.min(dim=dims_wotime).assign_attrs(
            {"long_name":"ZDR min from offset calculation",
             "standard_name":"ZDR_min_from_offset_calculation"}
            )
        zdr_std = ds_zdr_med_ready.std(dim=dims_wotime).assign_attrs(
            {"long_name":"ZDR standard deviation from offset calculation",
             "standard_name":"ZDR_std_from_offset_calculation"}
            )
        zdr_sem = ( zdr_std / ds_zdr_med_ready.count(dim=dims_wotime)**(1/2) ).assign_attrs(
            {"long_name":"ZDR standard error of the mean from offset calculation",
             "standard_name":"ZDR_sem_from_offset_calculation"}
            )
        zdr_offset_datacount = ds_zdr.where(ds_zdr_med_ready.notnull().any(dims_wotime)).count(dim=dims_full_wotime).assign_attrs(
            {"long_name":"Count of values (bins) used for the ZDR offset calculation",
             "standard_name":"count_of_values_zdr_offset"}
            )


    else:
        # Filter according to the minimum number of bins limit
        ds_zdr_med_ready = ds_zdr_med.where(n_longest_consecutive(ds_zdr_med, dim="range").compute() > minbins)

        # Calculate offset and others
        if mode=="median":
            zdr_offset = ds_zdr_med_ready.compute().median().assign_attrs(
                {"long_name":"ZDR offset from vertical profile (median)",
                 "standard_name":"ZDR_offset_from_vertical_profile",
                 "units": "dB"}
                )
        elif mode=="mean":
            zdr_offset = ds_zdr_med_ready.compute().mean().assign_attrs(
                {"long_name":"ZDR offset from vertical profile (mean)",
                 "standard_name":"ZDR_offset_from_vertical_profile",
                 "units": "dB"}
                )
        else:
            raise KeyError("mode must be either 'median' or 'mean'")

        zdr_max = ds_zdr_med_ready.compute().max().assign_attrs(
            {"long_name":"ZDR max from offset calculation",
             "standard_name":"ZDR_max_from_offset_calculation"}
            )
        zdr_min = ds_zdr_med_ready.compute().min().assign_attrs(
            {"long_name":"ZDR min from offset calculation",
             "standard_name":"ZDR_min_from_offset_calculation"}
            )
        zdr_std = ds_zdr_med_ready.compute().std().assign_attrs(
            {"long_name":"ZDR standard deviation from offset calculation",
             "standard_name":"ZDR_std_from_offset_calculation"}
            )
        zdr_sem = ( zdr_std / ds_zdr_med_ready.compute().count()**(1/2) ).assign_attrs(
            {"long_name":"ZDR standard error of the mean from offset calculation",
             "standard_name":"ZDR_sem_from_offset_calculation"}
            )
        zdr_offset_datacount = ds_zdr.where(ds_zdr_med_ready.notnull()).count().assign_attrs(
            {"long_name":"Count of values (bins) used for the ZDR offset calculation",
             "standard_name":"count_of_values_zdr_offset"}
            )

    # Merge results in a dataset
    ds_offset = xr.Dataset({"ZDR_offset": zdr_offset,
                            "ZDR_max_from_offset": zdr_max,
                            "ZDR_min_from_offset": zdr_min,
                            "ZDR_std_from_offset": zdr_std,
                            "ZDR_sem_from_offset": zdr_sem,
                            "ZDR_offset_datacount": zdr_offset_datacount}
                           )

    # restore time dim if present
    if "time" in ds and "time" not in ds_offset:
        ds_offset = ds_offset.expand_dims("time")
        ds_offset["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord

    # drop ML coordinates if present
    for coord in ds_offset.coords:
        if "_ml" in coord:
            ds_offset = ds_offset.drop_vars(coord)


    return ds_offset


### ZDR calibration from QVPs. Adapted from Daniel Sanchez-Rivas (TowerPy) to xarray
def zdr_offset_detection_qvps(ds, zdr="ZDR", dbzh="DBZH", rhohv="RHOHV", mode="median",
                        mlbottom=None, temp=None, zdr_0=0.182, min_h=1000, zhmin=0,
                        zhmax=20, rhvmin=0.98, minbins=10, azmed=True, timemode="step"):
    r"""
    Calculate the offset on :math:`Z_{DR}` using QVPs, acoording to [1]_.  Only gates
    below the melting layer bottom (i.e. the rain region below the melting layer)
    or below the given temperature level are included in the method.

    For ZDR calibration: SNR> 20-25 and attenuation should be insignificant (Ryzhkov and Zrnic p. 156)

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with the vertical scan. ZDR, DBZH and RHOHV are needed. Dimensions
        should include "azimuth" and "range"
    zdr : str
        Name of the variable in ds for differential reflectivity data. Default is "ZDR".
    dbzh : str
        Name of the variable in ds for horizontal reflectivity data (in dB). Default is "DBZH".
    rhohv : str
        Name of the variable in ds for cross-correlation coefficient data. Default is "RHOHV".
    mode : str
        Method for calculating the offset from the distribution of ZDR values in light rain.
        Can be either "median" or "mean". Default is "median".
    mlbottom : str, int or float
        If str: name of the ML bottom variable in ds. If None, it is assumed to
        be "height_ml_bottom_new_gia" or "height_ml_bottom" (in that order).
        If int or float: we assume the ML bottom is not available and we take the given
        int value as the temperature level from which to consider radar bins.
        Only gates below the melting layer bottom (i.e. the rain
        region below the melting layer) are included in the method.
    temp : str, optional
        Name of the temperature variable in ds. Only necessary if mlbottom is int.
        If None is given and mlbottom is int or float, the default name "TEMP" is used.
    zdr_0 : float, optional
        Intrinsic value of :math:`Z_{DR}` in light rain at ground level.
        Defaults to 0.182.
    min_h : float, optional
        Minimum height of usable data within the polarimetric profiles, in m. This is relative to
        sea level and not relative to the altitude of the radar (in accordance to the "z" coordinate
        from wradlib.georef.georeference). The default is 1000.
    zhmin : float, optional
        Threshold on :math:`Z_{H}` (in dBZ) related to light rain.
        The default is 0.
    zhmax : float, optional
        Threshold on :math:`Z_{H}` (in dBZ) related to light rain.
        The default is 20.
    rhvmin : float, optional
        Threshold on :math:`\rho_{HV}` (unitless) related to light rain.
        The default is 0.98.
    minbins : float, optional
        Minimum number of consecutive :math:`Z_{DR}` bins related to light rain. This should
        vary according to range resolution. The default is 10.
    azmed : bool
        If True, perform azimuthal median after filtering values and before offset calculation.
        Default is True (QVP-like)
    timemode : str
        How to calculate the offset in case a time dimension is found. "step" calculates one offset
        per timestep. "all" calculates one offset for the whole ds. Default is "step"

    Returns
    ----------
    ds_offset : xarray Dataset
        xarray Dataset with the detected offset and related satatistics.

    Notes
    -----
    1. Based on the method described in [1]
    2. Adapted from Daniel Sanchez-Rivas (TowerPy) [2] to xarray by Julian Giles.

    References
    ----------
    .. [1] Sanchez-Rivas, D. and Rico-Ramirez, M. A. (2022): "Calibration
        of radar differential reflectivity using quasi-vertical profiles",
        Atmos. Meas. Tech., 15, 503–520,
        https://doi.org/10.5194/amt-15-503-2022
    .. [2] Sanchez-Rivas, D., and Rico-Ramirez, M. A. (2023). Towerpy:
        An open-source toolbox for processing polarimetric weather radar data.
        Environmental Modelling & Software, 167, 105746.
        https://doi.org/10.1016/j.envsoft.2023.105746
    """
    # We need the ds to be georeferenced in case it is not
    if "z" not in ds.coords:
        ds = ds.pipe(wrl.georef.georeference)

    if mlbottom is None:
        try:
            ml_bottom = ds["z"] < ds["height_ml_bottom_new_gia"]
        except KeyError:
            try:
                ml_bottom = ds["z"] < ds["height_ml_bottom"]
            except KeyError:
                raise KeyError("Melting layer bottom not found in ds. Provide melting layer bottom or temperature level.")
            except:
                raise RuntimeError("Something went wrong when looking for ML variable")
        except:
            raise RuntimeError("Something went wrong when looking for ML variable")
    elif type(mlbottom) is str:
        ml_bottom = ds["z"] < ds[mlbottom]
    elif type(mlbottom) in [float, int]:
        if type(temp) is str:
            ml_bottom = ds[temp] > mlbottom
        elif temp is None:
            try:
                ml_bottom = ds["TEMP"] > mlbottom
            except KeyError:
                raise KeyError("temp is not given and could not be found by default")
        else:
            raise TypeError("temp must be str or None")
    else:
        raise TypeError("mlbottom must be str, int or None")


    # Azimuth median before computing (QVP-based)?
    if azmed:
        if "azimuth" in ds.dims:
            ds_qvp = compute_qvp(ds.where(ml_bottom).where(ds["z"]>min_h),
                                 min_thresh = {rhohv:0.7, dbzh:0, "SNRH":10,"SNRHC":10, "SQIH":0.5})
            ds_zdr_med = ds_qvp[zdr].where(ds_qvp[dbzh]>zhmin).where(ds_qvp[dbzh]<zhmax).where(ds_qvp[rhohv]>rhvmin)

            # only for the count of valid values, we need this
            ds_zdr = ds[zdr].where(ml_bottom).where(ds["z"]>min_h).where(ds[dbzh]>zhmin).where(ds[dbzh]<zhmax).where(ds[rhohv]>rhvmin)
        else:
            raise KeyError("azimuth not found in dataset dimensions")
    else:
        # get ZDR data and filter values below ML and above min_h
        ds_zdr = ds[zdr]
        ds_zdr = ds_zdr.where(ml_bottom)
        ds_zdr = ds_zdr.where(ds["z"]>min_h)

        # Filter according to DBZH and RHOHV limits
        ds_zdr = ds_zdr.where(ds[dbzh]>zhmin).where(ds[dbzh]<zhmax).where(ds[rhohv]>rhvmin)
        ds_zdr_med = ds_zdr

    if "time" in ds and timemode=="step":
        # Get dimensions to reduce (other than time)
        dims_wotime = [kk for kk in ds_zdr_med.dims]
        while "time" in dims_wotime:
            dims_wotime.remove("time")

        # same as before but with ds_zdr, in case the azimuth has already been taken off (for the data count)
        dims_full_wotime = [kk for kk in ds_zdr.dims]
        while "time" in dims_full_wotime:
            dims_full_wotime.remove("time")

        # Filter according to the minimum number of bins limit
        if "range" in ds_zdr_med.dims:
            ds_zdr_med_ready = ds_zdr_med.where(n_longest_consecutive(ds_zdr_med, dim="range").compute() > minbins)
        elif "z" in ds_zdr_med.dims:
            ds_zdr_med_ready = ds_zdr_med.where(n_longest_consecutive(ds_zdr_med, dim="z").compute() > minbins)
        else:
            warnings.warn("zdr_offset_detection_qvps: Condition for minbins could not be checked, ignored (is range or z a dimension?)")

        # Calculate offset and others
        if mode=="median":
            zdr_offset = (ds_zdr_med_ready.median(dim=dims_wotime) - zdr_0).assign_attrs(
                {"long_name":"ZDR offset from QVP method (median)",
                 "standard_name":"ZDR_offset_from_qvp",
                 "units": "dB"}
                )
        elif mode=="mean":
            zdr_offset = (ds_zdr_med_ready.mean(dim=dims_wotime) - zdr_0).assign_attrs(
                {"long_name":"ZDR offset from QVP method (mean)",
                 "standard_name":"ZDR_offset_from_qvp",
                 "units": "dB"}
                )
        else:
            raise KeyError("mode must be either 'median' or 'mean'")

        zdr_max = ds_zdr_med_ready.max(dim=dims_wotime).assign_attrs(
            {"long_name":"ZDR max from offset calculation",
             "standard_name":"ZDR_max_from_offset_calculation"}
            )
        zdr_min = ds_zdr_med_ready.min(dim=dims_wotime).assign_attrs(
            {"long_name":"ZDR min from offset calculation",
             "standard_name":"ZDR_min_from_offset_calculation"}
            )
        zdr_std = ds_zdr_med_ready.std(dim=dims_wotime).assign_attrs(
            {"long_name":"ZDR standard deviation from offset calculation",
             "standard_name":"ZDR_std_from_offset_calculation"}
            )
        zdr_sem = ( zdr_std / ds_zdr_med_ready.count(dim=dims_wotime)**(1/2) ).assign_attrs(
            {"long_name":"ZDR standard error of the mean from offset calculation",
             "standard_name":"ZDR_sem_from_offset_calculation"}
            )
        zdr_offset_datacount = ds_zdr.where(ds_zdr_med_ready.notnull().any(dims_wotime)).count(dim=dims_full_wotime).assign_attrs(
            {"long_name":"Count of values (bins) used for the ZDR offset calculation",
             "standard_name":"count_of_values_zdr_offset"}
            )

    else:
        # Filter according to the minimum number of bins limit
        if "range" in ds_zdr_med.dims:
            ds_zdr_med_ready = ds_zdr_med.where(n_longest_consecutive(ds_zdr_med, dim="range").compute() > minbins)
        elif "z" in ds_zdr_med.dims:
            ds_zdr_med_ready = ds_zdr_med.where(n_longest_consecutive(ds_zdr_med, dim="z").compute() > minbins)
        else:
            warnings.warn("zdr_offset_detection_qvps: Condition for minbins could not be checked, ignored (is range or z a dimension?)")

        # Calculate offset and others
        if mode=="median":
            zdr_offset = ds_zdr_med_ready.compute().median().assign_attrs(
                {"long_name":"ZDR offset from QVP method (median)",
                 "standard_name":"ZDR_offset_from_qvp",
                 "units": "dB"}
                ) - zdr_0
        elif mode=="mean":
            zdr_offset = ds_zdr_med_ready.compute().mean().assign_attrs(
                {"long_name":"ZDR offset from QVP method (mean)",
                 "standard_name":"ZDR_offset_from_qvp",
                 "units": "dB"}
                ) - zdr_0
        else:
            raise KeyError("mode must be either 'median' or 'mean'")

        zdr_max = ds_zdr_med_ready.compute().max().assign_attrs(
            {"long_name":"ZDR max from offset calculation",
             "standard_name":"ZDR_max_from_offset_calculation"}
            )
        zdr_min = ds_zdr_med_ready.compute().min().assign_attrs(
            {"long_name":"ZDR min from offset calculation",
             "standard_name":"ZDR_min_from_offset_calculation"}
            )
        zdr_std = ds_zdr_med_ready.compute().std().assign_attrs(
            {"long_name":"ZDR standard deviation from offset calculation",
             "standard_name":"ZDR_std_from_offset_calculation"}
            )
        zdr_sem = ( zdr_std / ds_zdr_med_ready.compute().count()**(1/2) ).assign_attrs(
            {"long_name":"ZDR standard error of the mean from offset calculation",
             "standard_name":"ZDR_sem_from_offset_calculation"}
            )
        zdr_offset_datacount = ds_zdr.where(ds_zdr_med_ready.notnull()).count().assign_attrs(
            {"long_name":"Count of values (bins) used for the ZDR offset calculation",
             "standard_name":"count_of_values_zdr_offset"}
            )

    # Merge results in a dataset
    ds_offset = xr.Dataset({"ZDR_offset": zdr_offset,
                            "ZDR_max_from_offset": zdr_max,
                            "ZDR_min_from_offset": zdr_min,
                            "ZDR_std_from_offset": zdr_std,
                            "ZDR_sem_from_offset": zdr_sem,
                            "ZDR_offset_datacount": zdr_offset_datacount}
                           )

    # restore time dim if present
    if "time" in ds and "time" not in ds_offset:
        ds_offset = ds_offset.expand_dims("time")
        ds_offset["time"] = np.atleast_1d(ds.coords["time"][0]) # put the first time value as coord

    # drop ML coordinates if present
    for coord in ds_offset.coords:
        if "_ml" in coord:
            ds_offset = ds_offset.drop_vars(coord)


    return ds_offset


#### Wet radome correction

def zdr_wr_offset_zm_cuadratic(Zm, a=-0.00022, b=0.00032, max_zm=32.5):
    r"""
    Corrects higher ZDR values due to wet radome based on a reference cuadratic fit.

    Parameters
    ----------
    Zm : Median reflectivity values in a 1.5 km radius around the radar (or
         whatever other reflectivity value was used to derive the reference fit).
        It must be free of NaNs (set them to zero before).
    a : linear coefficient of the fit
    b : quadratic coefficient of the fit
    max_zm : maximum value of Zm until where the correction is valid.

    Returns
    ----------
    value for correction: ZDR_WRcorrected = ZDR - zdr_wr_offset_zm_cuadratic(Zm)
    """

    Zm_ = Zm.fillna(0).where(Zm.fillna(0)<max_zm, other=max_zm)

    return a*Zm_ + b*Zm_**2


#### Attenuation correction

def attenuation_corr_linear(ds, alpha = 0.08, beta = 0.02, alphaml = 0.08, betaml = 0.02,
                            dbzh = "DBZH", zdr = "ZDR", phidp = "UPHIDP_OC",
                            phidp_min = 0, phidp_max = 200,
                            ML_bot = "height_ml_bottom_new_gia", ML_top = "height_ml_new_gia",
                            temp = "TEMP", temp_mlbot = 3, temp_mltop = 0, z_mlbot = 2000, dz_ml = 500,
                            interpolate_deltabump = True ):
    r'''

    Corrects attenuation in ZH and ZDR.
    Below the melting layer bottom:
    ZH_corr_below = ZH + alpha*PHIDP
    ZDR_corr_below = ZDR + beta*PHIDP

    In the melting layer:
    ZH_corr_in = ZH_corr_below + alphaml*ΔPHIDP_ML
    ZDR_corr_in = ZDR_corr_below + betaml*ΔPHIDP_ML

    Above the ML: the last correction values in the ML are propagated

    Reference values from Ryzhkov and Zrnic book 2019 Table 6.4
    X band:
    alpha = 0.28; beta = 0.05 #dB/deg

    C band:
    alpha = 0.08; beta = 0.02 #dB/deg

    S band:
    alpha = 0.02; beta = 0.004 #dB/deg

    For BoXPol and JuXPol:
    alpha = 0.25

    From https://doi.org/10.1002/qj.3366 (X-band):
    alpha = 0.276
    beta = 0.032
    alphaml = 0.6 (thus 2.17 times the value below ML)
    betaml = 0.06 (thus 1.875 times the value below ML)

    Parameters
    ----------
    ds : xarray Dataset
        Dataset with ZH and/or ZDR.
    alpha : float
        alpha value for the linear attenuation correction (in liquid phase)
    beta : float
        beta value for the linear attenuation correction (in liquid phase)
    alphaml : float
        Multiplier value for the linear attenuation correction in the ML and above
    betaml : float
        Multiplier value for the linear attenuation correction in the ML and above
    dbzh : str
        Name(s) of the variable(s) with ZH to correct. A list of strings can be used to pass more than one name.
    zdr : str
        Name(s) of the variable(s) with ZDR to correct. A list of strings can be used to pass more than one name.
    phidp : str
        Name of the variable with PHIDP data. A list of strings can be used to pass more
        than one name, but only the first valid name is used.
    phidp_min : float
        Minimum value of PHIDP to consider. Lower values are capped.
    phidp_max : float
        Maximum value of PHIDP to consider. Higher values are capped.
    ML_bot : str
        Name of the variable with melting layer bottom height information. A list of
        strings can be used to pass more than one name, but only the first valid name is used.
    ML_top : str
        Name of the variable with melting layer top height information. A list of
        strings can be used to pass more than one name, but only the first valid name is used.
    temp : str
        Name of the variable with temperature information. A list of
        strings can be used to pass more than one name, but only the first valid name is used.
        Temperature data is used to estimate the ML bottom/top only where ML_bot/ML_top are not valid.
    temp_mlbot : float
        Value of the temperature level to use as ML bottom.
    temp_mltop : float
        Value of the temperature level to use as ML top.
    z_mlbot : float
        Height value to use as ML bottom. This is only used where ML_bot and temp_mlbot are not valid.
    dz_ml : float
        ML thickness value. This is only used where ML_top and temp_mltop are not valid.
    interpolate_deltabump : bool
        If True (default), interpolate phidp within the ML to avoid the typical delta bump signature.

    Returns
    ----------
    ds : xarray Dataset
        Dataset with the original variables plus their attenuation corrected versions

    '''
    # first check that ds is georeferenced
    if "z" not in ds:
        ds = ds.pipe(wrl.georef.georeference)

    # check if we have range dim (PPI) or z dim (QVP)
    if "range" in ds.dims:
        rdim = "range"
    else:
        rdim = "z"

    # check that phidp variable exists in ds (necessary condition)
    if isinstance(phidp, str):
        phidp = [phidp]
    for phidpn in phidp:
        if phidpn in ds:
            phidp = phidpn
            ds_phidp = ds[phidp].clip(min=phidp_min, max=phidp_max, keep_attrs=True)
            break
    if not isinstance(phidp, str):
        raise KeyError("phidp definition is not in the dataset")

    # filter below ML
    if isinstance(ML_bot, str):
        ML_bot = [ML_bot]

    cond_belowML = xr.full_like(ds_phidp, np.nan) # dummy empty array
    for ML_botn in ML_bot:
        if ML_botn in ds:
            ML_bot = ML_botn
            cond_belowML = (ds["z"]<ds[ML_bot]).where(ds[ML_bot].notnull())
            break

    # filter below temp_mlbot
    if isinstance(temp, str):
        temp = [temp]

    cond_below_temp_mlbot = xr.full_like(ds_phidp, np.nan) # dummy empty array
    for tempn in temp:
        if tempn in ds:
            temp = tempn
            cond_below_temp_mlbot = (ds[temp]>temp_mlbot).where(ds[temp].notnull())
            break

    # filter below z_mlbot
    cond_below_z_mlbot = ds["z"]<z_mlbot

    # combine conditions
    cond_below_comb = cond_belowML.fillna(cond_below_temp_mlbot).fillna(cond_below_z_mlbot)


    #### filter above and inside ML
    # start with the opposite of cond_below_comb
    cond_inabove = (cond_below_comb==0).where(cond_below_comb.notnull())

    # filter above ML
    if isinstance(ML_top, str):
        ML_top = [ML_top]

    cond_aboveML = xr.full_like(ds_phidp, np.nan) # dummy empty array
    for ML_topn in ML_top:
        if ML_topn in ds:
            ML_top = ML_topn
            cond_aboveML = (ds["z"]>ds[ML_top]).where(ds[ML_top].notnull())
            break

    # filter above temp_mltop
    if isinstance(temp, str):
        temp = [temp]

    cond_above_temp_mltop = xr.full_like(ds_phidp, np.nan) # dummy empty array
    for tempn in temp:
        if tempn in ds:
            temp = tempn
            cond_above_temp_mltop = (ds[temp]<temp_mltop).where(ds[temp].notnull())
            # ds_belowltemp = ds.where(ds[temp]>temp_mlbot)
            break

    # filter above cond_below_comb + dz_ml
    cond_above_dz_ml0 = xr.full_like(ds_phidp, 1.).where(ds_phidp.notnull())*ds["z"] # expand z through time
    cond_above_dz_ml1 = cond_above_dz_ml0.where(cond_inabove) # take only z that is above the ML bottom
    cond_above_dz_ml2 = cond_above_dz_ml1.min(rdim)+dz_ml # get the min z value per ray and add + dz_ml
    cond_above_dz_ml = cond_above_dz_ml0 >= cond_above_dz_ml2 # take only z values above cond_above_dz_ml2

    # combine conditions
    cond_above_comb = cond_aboveML.fillna(cond_above_temp_mltop).fillna(cond_above_dz_ml)

    # get condition for in ML
    cond_in = (cond_above_comb==0).where(cond_above_comb.notnull()) * (cond_below_comb==0).where(cond_below_comb.notnull())

    #### Interpolate the delta bump
    if interpolate_deltabump:
        ds_phidp = ds_phidp.where(cond_in==0).where(ds_phidp.notnull()).interpolate_na(rdim)

    #### Apply the conditions
    ds_phidp_below = ds_phidp.where(cond_below_comb)
    ds_phidp_in = ds_phidp.where(cond_in)

    # Make the correction

    if isinstance(dbzh, str): # check dbzh
        dbzh = [dbzh]
    for dbzhn in dbzh:
        if dbzhn in ds:
            # dbzh_corr = (alpha*ds_phidp_below).fillna(alphaml*ds_phidp_in).ffill(rdim).fillna(0.)
            dbzh_corr = (alpha*ds_phidp_below.ffill(rdim) + alphaml*(ds_phidp_in.ffill(rdim)-ds_phidp_below.ffill(rdim)).fillna(0.) ).fillna(0.)
            ds[dbzhn+"_AC"] = (ds[dbzhn] + dbzh_corr).assign_attrs(ds[dbzhn].attrs)

    if isinstance(zdr, str): # check zdr
        zdr = [zdr]
    for zdrn in zdr:
        if zdrn in ds:
            # zdr_corr = (beta*ds_phidp_below).fillna(betaml*ds_phidp_in).ffill(rdim).fillna(0.)
            zdr_corr = (beta*ds_phidp_below.ffill(rdim) + betaml*(ds_phidp_in.ffill(rdim)-ds_phidp_below.ffill(rdim)).fillna(0.) ).fillna(0.)
            ds[zdrn+"_AC"] = (ds[zdrn] + zdr_corr).assign_attrs(ds[zdrn].attrs)

    return ds

def attenuation_corr_zphi(swp0 , alpha = 0.08, beta = 0.02,
                          X_DBZH="DBZH", X_ZDR="ZDR", X_PHI="UPHIDP_OC_MASKED"):
    '''
    ZPHI method for attenuation correction.

    Parameters:
        * swp0(xarray.Dataset): single sweep (PPI for a single timestep) of radar data,
                                must contain DBZH, corrected smoothed and masked PHIDP,
                                RHOHV noise corrected and optionally ZDR
        * alpha(float): alpha value for X or C band, default value is for C band
        * beta(float): beta value for X or C band, default value is for C band
        * X_DBZH(str): name of reflectivity variable
        * X_ZDR(str): name of differential reflectivity variable
        * X_PHI(str): name of differential phase

    Returns:
    ds : xarray Dataset
        Dataset with the original variables plus:
        * ah_fast(numpy.array): Attenuation (horizontal)
        * phical(numpy.array): PHIDP calculated from attenuation
        * cphase(xarray.Dataset): Corrected PHIDP
        * attenuation corrected DBZH
        * attenuation corrected ZDR

    ZH_corr = ZH + alpha*PHIDP
    ZDR_corr = ZDR + beta*PHIDP

    X band:
    alpha = 0.28; beta = 0.05 #dB/deg

    C band:
    alpha = 0.08; beta = 0.02 #dB/deg

    For BoXPol and JuXPol:
    alpha = 0.25
    '''

    swp_msk = swp0.copy()
    dr_m = swp0.range.diff('range').median()
    dr_km = dr_m / 1000.

    cphase = phase_zphi(swp_msk[X_PHI], rng=1000.)
    #cphase.first.plot(label="first")
    #cphase.last.plot(label="last")
    dphi = cphase.last - cphase.first
    dphi = dphi.where(dphi>=0).fillna(0)

    alphax = alpha
    betax = beta
    bx = 0.78 # Average value representative of X or C band, see https://doi.org/10.1175/1520-0426(2000)017<0332:TRPAAT>2.0.CO;2
    # need to expand alphax to dphi-shape
    fdphi = 10 ** (0.1 * bx * alphax * dphi) - 1

    zhraw = swp0[X_DBZH].where((swp0.range > cphase.start_range) & (swp0.range < cphase.stop_range))

    zax = zhraw.pipe(wrl.trafo.idecibel).fillna(0)

    za = zax ** bx

    # set masked to zero for integration
    za_zero = za.fillna(0)

    iza_x = za_zero.copy( data= 0.46 * bx * cumulative_trapezoid(za_zero.values, axis=za_zero.dims.index("range"),
                                             initial=0, dx=dr_km.values) )
    iza = iza_x.max("range") - iza_x

    # we need some np.newaxis voodoo here, to get the correct dimensions (this version is for an array of alphax)
    #iza_fdphi = iza[np.newaxis, ...] / fdphi[..., np.newaxis]
    #iza_first = np.array([iza_fdphi[:, ray, first[ray]]
    #                      for ray in range(za.shape[0])])

    iza_fdphi = iza / fdphi

    iza_first = iza_fdphi.isel(range=cphase.first_idx.astype(int).compute())

    ah_fast = ( za / (iza_first + iza) ).compute().fillna(0)

    phical = ah_fast.copy( data= 2 * cumulative_trapezoid(ah_fast/alphax, axis=ah_fast.dims.index("range"),
                                                          dx=dr_km.values, initial=0) )

    # Assign variables and return

    return swp_msk.assign({
            "AH" : ah_fast.assign_attrs(
                {"long_name":"Attenuation (horizontal) from ZPHI method",
                 "standard_name":"AH"}),
            "PHIDP_ZPHI" : phical.assign_attrs(
                {"long_name":"PHIDP calculated from AH (ZPHI method)",
                 "standard_name":"PHIDP_ZPHI"}),
            X_DBZH+"_AC" : (swp0[X_DBZH]+alphax*phical).assign_attrs(
                {"long_name":"Attenuation corrected reflectivity (ZPHI method)",
                 "standard_name": X_DBZH+"_AC",
                 "alpha": alphax}),
            X_ZDR+"_AC" : (swp0[X_ZDR]+betax*phical).assign_attrs(
                {"long_name":"Attenuation corrected differential reflectivity (ZPHI method)",
                 "standard_name": X_ZDR+"_AC",
                 "beta": betax}),
        })


def phase_zphi(phi, rng=1000.):
    range_step = np.diff(phi.range)[0]
    nprec = int(rng / range_step)
    if nprec % 2:
        nprec += 1

    # create binary array
    phib = xr.where(np.isnan(phi), 0, 1)

    # take nprec range bins and calculate sum
    phib_sum = phib.rolling(range=nprec, center=True).sum(skipna=True)

    offset = nprec // 2 * phib_sum.range.diff("range")[0]
    offset_idx = xr.ones_like(offset) * (nprec // 2)
    start_range = (phib_sum.idxmax(dim="range") - offset).compute()
    start_range_idx = phib_sum.argmax(dim="range") - offset_idx
    stop_range = (phib_sum.sel(range=slice(None, None, -1)).idxmax(dim="range") - offset).compute()
    stop_range_idx = len(phib_sum.range) - (phib_sum.sel(range=slice(None, None, -1)).argmax(dim="range") - offset_idx) - 2
    # get phase values in specified range
    first = phi.where((phi.range >= start_range) & (phi.range <= start_range + rng),
                       drop=True).quantile(0.05, dim='range', skipna=True).broadcast_like(phib_sum).drop_vars(["quantile"])
    last = phi.where((phi.range >= stop_range - rng) & (phi.range <= stop_range),
                       drop=True).quantile(0.95, dim='range', skipna=True).broadcast_like(phib_sum).drop_vars(["quantile"])


    # return xr.Dataset(dict(phib=phib_sum,
    #                        offset=offset,
    #                        offset_idx=offset_idx,
    #                        start_range=start_range,
    #                        stop_range=stop_range,
    #                        first=first,
    #                        first_idx=start_range_idx,
    #                        last=last,
    #                        last_idx=stop_range_idx,
    #                       ))

    return xr.merge([phib_sum.rename("phib"),
                           offset.rename("offset"),
                           offset_idx.rename("offset_idx"),
                           start_range.rename("start_range"),
                           stop_range.rename("stop_range"),
                           first.rename("first"),
                           start_range_idx.rename("first_idx"),
                           last.rename("last"),
                           stop_range_idx.rename("last_idx"),
                          ], compat='no_conflicts')

#### Microphysical retrievals

def calc_microphys_retrievals(ds, Lambda = 53.1, mu=0.33,
                              X_DBZH="DBZH", X_ZDR="ZDR", X_KDP="KDP", X_TEMP="TEMP",
                              X_AH="AH", X_PHI="UPHIDP_OC_MASKED"):
    """
    Calculate microphysical retrievals based on a collection of formulas. See references below.
    The retrievals are calculated for the whole range of values, the user is
    responsible for checking the range of validity of each retrieval and filtering
    accordingly.

    Parameter
    ---------
    ds : xarray.Dataset
        Dataset with all variables needed for retrievals calculation.

    Keyword Arguments
    -----------------
    Lambda : float
        Radar wavelength in mm. For C-band Lambda≈53.1.
        Reference values: PRO: 53.138, ANK: 53.1, AFY: 53.3, GZT: 53.3, HTY: 53.3, SVS:53.3
        However, not all retrievals are wavelength-adjusted, check references.
    mu : float
        Shape factor of the gamma size distribution, for D0 to Dm conversion using
        Dm = (4 + µ) / (3.67 + µ) D0.
        µ is typically between -1 and 1
    X_DBZH : str
        Name of the variable with DBZH data.
    X_ZDR : str
        Name of the variable with ZDR data.
    X_KDP : str
        Name of the variable with KDP data.
    X_TEMP : str
        Name of the variable with temperature data.
    X_AH : str (optional)
        Name of the variable with specific attenuation data.
        Used for LWC (4) from Reimann et al 2021 eq 3.10
    X_PHI : str (optional)
        Name of the variable with differential phase.
        Used for hybrid LWC from Reimann et al 2021

    References
    ----------
    Ice water content:
        1) iwc_zh_t_hogan2006 = 10 ** (0.06 X_DBZH - 0.0197 TEMP - 1.7) (Empirical from Hogan et al. 2006 Table 2)
        2) iwc_zh_t_hogan2006_model = 10**(0.06 * ds[X_DBZH] - 0.0212*ds[X_TEMP] - 1.92) # model from Hogan et al 2006 eq 14
        3) iwc_zh_t_hogan2006_combined = xr.where(ds[X_TEMP]<=-15, # combination of the two previous retrievals based on a temperature thresholds suggested by Blanke et al. 2023
                                                   iwc_zh_t_hogan2006,
                                                   iwc_zh_t_hogan2006_model)

        4) iwc_zdr_zh_kdp_carlin2021 = xr.where(ds[X_ZDR]>=0.4,  (Carlin et al. 2021 eqs 4b and 5b)
                                                4*10**(-3)*( ds[X_KDP]*Lambda/( 1-wrl.trafo.idecibel(ds[X_ZDR])**-1 ) ),
                                                0.033 * ( ds[X_KDP]*Lambda )**0.67 * wrl.trafo.idecibel(ds[X_DBZH])**0.33 )

    Liquid water content:
        1) lwc_zh_zdr_reimann2021 = 10**(0.058*ds[X_DBZH] - 0.118*ds[X_ZDR] - 2.36) (Reimann et al. 2021 eq 3.7; adjusted for Germany)
        2) lwc_zh_zdr_rhyzkov2022 = 1.38*10**(-3) *10**(0.1*ds[X_DBZH] - 2.43*ds[X_ZDR] + 1.12*ds[X_ZDR]**2 - 0.176*ds[X_ZDR]**3 ) # used in S band, Ryzhkov 2022 PROM presentation https://www2.meteo.uni-bonn.de/spp2115/lib/exe/fetch.php?media=internal:uploads:all_hands_schneeferner_july2022:ryzhkov.pdf
        3) lwc_kdp_reimann2021 = 10**(0.568*np.log10(ds[X_KDP]) + 0.06) # Reimann et al 2021 eq 3.13 (adjusted for Germany)
        4) lwc_ah_reimann2021 = 10**(-0.1415*np.log10(ds[X_AH])**2 + 0.209*np.log10(ds[X_AH]) + 0.46) # Reimann et al 2021 eq 3.10 (adjusted for Germany)
        5) lwc_hybrid_reimann2021 =
                        lwc_zh_zdr_reimann2021 for ΔPHIDP < 5 degrees,
                        lwc_ah_reimann2021 for ΔPHIDP > 5 degrees and Z < 45 dBZ, and
                        lwc_hybrid_reimann2021 for ΔPHIDP > 5 degrees and Z > 45 dBZ .


    Mean volume diameter in ice:
        1) Dm_ice_zh_matrosov2019 = 1.055*wrl.trafo.idecibel(ds[X_DBZH])**0.271 # Matrosov et al. (2019) Fig 10 (S band)
        2) Dm_ice_zh_kdp_carlin2021 = 0.67*( wrl.trafo.idecibel(ds[X_DBZH])/(ds[X_KDP]*Lambda) )**(1/3) # Ryzhkov and Zrnic (2019) eq 11.45. Idk exactly where does the 0.67 approximation comes from, Blanke et al. 2023 eq 10 and Carlin et al 2021 eq 5a cite Bukovčić et al. (2018, 2020) but those two references do not show this formula.
        3) Dm_ice_zdp_kdp_carlin2021 = -0.1 + 2*( (wrl.trafo.idecibel(ds[X_DBZH])*(1-wrl.trafo.idecibel(ds[X_ZDR])**-1 ) ) / (ds[X_KDP]*Lambda) )**(1/2) # Ryzhkov and Zrnic (2019). Zdp = Z(1-ZDR**-1) from Carlin et al 2021
        4) Dm_hybrid_blanke2023 = xr.where(ds[X_TEMP]<=-15, # combination of 1) and 2) retrievals based on a temperature thresholds suggested by Blanke et al. 2023
                                                   Dm_ice_zdp_kdp_carlin2021,
                                                   Dm_ice_zh_matrosov2019)

    Mean volume diameter in liquid (D0 is automatically converted to Dm):
        1) Dm_rain_zdr = 0.3015*ds[X_ZDR]**3 - 1.2087*ds[X_ZDR]**2 + 1.9068*ds[X_ZDR] + 0.5090 # (for rain but tuned for Germany X-band, JuYu Chen (reference missing), Zdr in dB, Dm in mm)
        2) D0_rain_zdr_hu2022 = 0.171*ds[X_ZDR]**3 - 0.725*ds[X_ZDR]**2 + 1.48*ds[X_ZDR] + 0.717 # (D0 from Hu and Ryzhkov 2022 eq 2, used in S band data but could work for C band) [mm]
        3) D0_rain_zdr_bringi2009 = xr.where(ds[X_ZDR]<1.25, # D0 from Bringi et al 2009 (C-band) eq. 1 [mm]
                                    0.0203*ds[X_ZDR]**4 - 0.1488*ds[X_ZDR]**3 + 0.2209*ds[X_ZDR]**2 + 0.5571*ds[X_ZDR] + 0.801,
                                    0.0355*ds[X_ZDR]**3 - 0.3021*ds[X_ZDR]**2 + 1.0556*ds[X_ZDR] + 0.6844
                                    ).where(ds[X_ZDR]>=-0.5)

    Number concentration of particles in ice (in log units [log(1/L)]):
        1) Nt_ice_iwc_zh_t_hu2022 = (3.39 + 2*np.log10(iwc_zh_t_hogan2006) - 0.1*ds[X_DBZH]) # (Hu and Ryzhkov 2022 eq. 10, [log(1/L)] using IWC from Hogan et al. 2006
        2) Nt_ice_iwc_zh_t_carlin2021 = (3.69 + 2*np.log10(iwc_zh_t_hogan2006) - 0.1*ds[X_DBZH]) # Carlin et al 2021 eq. 7 using IWC from Hogan et al. 2006; originally in [log(1/m3)], transformed units here to [log(1/L)] by subtracting 3
        3) Nt_ice_iwc_zh_t_combined_hu2022 = (3.39 + 2*np.log10(iwc_zh_t_hogan2006_combined) - 0.1*ds[X_DBZH]) # (Hu and Ryzhkov 2022 eq. 10, [log(1/L)] using combined IWC from Hogan et al. 2006
        4) Nt_ice_iwc_zh_t_combined_carlin2021 = (3.69 + 2*np.log10(iwc_zh_t_hogan2006_combined) - 0.1*ds[X_DBZH]) # Carlin et al 2021 eq. 7 using combined IWC from Hogan et al. 2006; originally in [log(1/m3)], transformed units here to [log(1/L)] by subtracting 3
        5) Nt_ice_iwc_zdr_zh_kdp_hu2022 = (3.39 + 2*np.log10(iwc_zdr_zh_kdp_carlin2021) - 0.1*ds[X_DBZH]) # (Hu and Ryzhkov 2022 eq. 10, [log(1/L)] using IWC from Carlin et al. 2021
        6) Nt_ice_iwc_zdr_zh_kdp_carlin2021 = (3.69 + 2*np.log10(iwc_zdr_zh_kdp_carlin2021) - 0.1*ds[X_DBZH]) # Carlin et al 2021 eq. 7 using IWC from Carlin et al. 2021; originally in [log(1/m3)], transformed units here to [log(1/L)] by subtracting 3

    Number concentration of particles in liquid (in log units [log(1/L)]):
        1) Nt_rain_zh_zdr_rhyzkov2020 = ( -2.37 + 0.1*ds[X_DBZH] - 2.89*ds[X_ZDR] + 1.28*ds[X_ZDR]**2 - 0.213*ds[X_ZDR]**3 )# Ryzhkov et al. 2020 eq. 11 [log(1/L)] (I assume this is for Sband)

    Blanke et al. 2023: https://doi.org/10.5194/amt-16-2089-2023
    Bringi et al. 2009: https://doi.org/10.1175/2009JTECHA1258.1
    Carlin et al. 2021: https://doi.org/10.1175/JAMC-D-21-0038.1
    Hogan et al. 2006: https://doi.org/10.1175/JAM2340.1
    Hu and Rhyzkov 2022: https://doi.org/10.1029/2021JD035498
    Matrosov et al. 2019: https://cscenter.co.jp/icrm2019/program/data/abstracts/Session11A-02_2.pdf
    Reimann et al. 2021: http://dx.doi.org/10.1127/metz/2021/1072
    Ryzhkov 2022: https://www2.meteo.uni-bonn.de/spp2115/lib/exe/fetch.php?media=internal:uploads:all_hands_schneeferner_july2022:ryzhkov.pdf
    Ryzhkov and Zrnic 2019: https://link.springer.com/book/10.1007/978-3-030-05093-1
    Rhyzkov et al. 2020: https://doi.org/10.3390/atmos11040362
    """

    # LWC
    lwc_zh_zdr_reimann2021 = 10**(0.058*ds[X_DBZH] - 0.118*ds[X_ZDR] - 2.36) # Reimann et al 2021 eq 3.7 (adjusted for Germany)
    lwc_zh_zdr_rhyzkov2022 = 1.38*10**(-3) *10**(0.1*ds[X_DBZH] - 2.43*ds[X_ZDR] + 1.12*ds[X_ZDR]**2 - 0.176*ds[X_ZDR]**3 ) # used in S band, Ryzhkov 2022 PROM presentation https://www2.meteo.uni-bonn.de/spp2115/lib/exe/fetch.php?media=internal:uploads:all_hands_schneeferner_july2022:ryzhkov.pdf
    lwc_kdp_reimann2021 = 10**(0.568*np.log10(ds[X_KDP]) + 0.06) # Reimann et al 2021 eq 3.13 (adjusted for Germany)
    if X_AH in ds.data_vars:
        lwc_ah_reimann2021 = 10**(-0.1415*np.log10(ds[X_AH])**2 + 0.209*np.log10(ds[X_AH]) + 0.46) # Reimann et al 2021 eq 3.10 (adjusted for Germany)
    if X_PHI in ds.data_vars and X_AH in ds.data_vars:
        lwc_hybrid_reimann2021 = xr.where(ds[X_PHI]<=5,
                                          lwc_zh_zdr_reimann2021,
                                          lwc_ah_reimann2021).where(
                                              ds[X_DBZH]<=45, other=lwc_kdp_reimann2021)

    # IWC (Collected from Blanke et al 2023)
    iwc_zh_t_hogan2006 = 10**(0.06 * ds[X_DBZH] - 0.0197*ds[X_TEMP] - 1.7) # empirical from Hogan et al 2006 Table 2
    iwc_zh_t_hogan2006_model = 10**(0.06 * ds[X_DBZH] - 0.0212*ds[X_TEMP] - 1.92) # model from Hogan et al 2006 eq 14
    iwc_zh_t_hogan2006_combined = xr.where(ds[X_TEMP]<=-15, # combination of the two previous retrievals based on a temperature thresholds suggested by Blanke et al. 2023
                                           iwc_zh_t_hogan2006,
                                           iwc_zh_t_hogan2006_model)

    iwc_zdr_zh_kdp_carlin2021 = xr.where(ds[X_ZDR]>=0.4, # Carlin et al 2021 eqs 4b and 5b
                                         4*10**(-3)*( ds[X_KDP]*Lambda/( 1-wrl.trafo.idecibel(ds[X_ZDR])**-1 ) ),
                                         0.033 * ( ds[X_KDP]*Lambda )**0.67 * wrl.trafo.idecibel(ds[X_DBZH])**0.33 )

    # Dm (ice collected from Blanke et al 2023)
    Dm_ice_zh_matrosov2019 = 1.055*wrl.trafo.idecibel(ds[X_DBZH])**0.271 # Matrosov et al. (2019) Fig 10 (S band)
    Dm_ice_zh_kdp_carlin2021 = 0.67*( wrl.trafo.idecibel(ds[X_DBZH])/(ds[X_KDP]*Lambda) )**(1/3) # Ryzhkov and Zrnic (2019) eq 11.45. Idk exactly where does the 0.67 approximation comes from, Blanke et al. 2023 eq 10 and Carlin et al 2021 eq 5a cite Bukovčić et al. (2018, 2020) but those two references do not show this formula.
    Dm_ice_zdp_kdp_carlin2021 = -0.1 + 2*( (wrl.trafo.idecibel(ds[X_DBZH])*(1-wrl.trafo.idecibel(ds[X_ZDR])**-1 ) ) / (ds[X_KDP]*Lambda) )**(1/2) # Ryzhkov and Zrnic (2019). Zdp = Z(1-ZDR**-1) from Carlin et al 2021
    Dm_hybrid_blanke2023 = xr.where(ds[X_TEMP]<=-15, # combination of 1) and 2) retrievals based on a temperature thresholds suggested by Blanke et al. 2023
                                               Dm_ice_zdp_kdp_carlin2021,
                                               Dm_ice_zh_matrosov2019)

    Dm_rain_zdr_chen = 0.3015*ds[X_ZDR]**3 - 1.2087*ds[X_ZDR]**2 + 1.9068*ds[X_ZDR] + 0.5090 # (for rain but tuned for Germany X-band, JuYu Chen, Zdr in dB, Dm in mm)

    D0_rain_zdr_hu2022 = 0.171*ds[X_ZDR]**3 - 0.725*ds[X_ZDR]**2 + 1.48*ds[X_ZDR] + 0.717 # (D0 from Hu and Ryzhkov 2022 eq 2, used in S band data but could work for C band) [mm]
    D0_rain_zdr_bringi2009 = xr.where(ds[X_ZDR]<1.25, # D0 from Bringi et al 2009 (C-band) eq. 1 [mm]
                            0.0203*ds[X_ZDR]**4 - 0.1488*ds[X_ZDR]**3 + 0.2209*ds[X_ZDR]**2 + 0.5571*ds[X_ZDR] + 0.801,
                            0.0355*ds[X_ZDR]**3 - 0.3021*ds[X_ZDR]**2 + 1.0556*ds[X_ZDR] + 0.6844
                            ).where(ds[X_ZDR]>=-0.5)
    Dm_rain_zdr_hu2022 = D0_rain_zdr_hu2022 * (4+mu)/(3.67+mu) # conversion from D0 to Dm according to eq 4 of Hu and Ryzhkov 2022.
    Dm_rain_zdr_bringi2009 = D0_rain_zdr_bringi2009 * (4+mu)/(3.67+mu)

    # log(Nt)
    Nt_ice_iwc_zh_t_hu2022 = (3.39 + 2*np.log10(iwc_zh_t_hogan2006) - 0.1*ds[X_DBZH]) # (Hu and Ryzhkov 2022 eq. 10, [log(1/L)] using IWC from Hogan et al. 2006
    Nt_ice_iwc_zh_t_carlin2021 = (3.69 + 2*np.log10(iwc_zh_t_hogan2006) - 0.1*ds[X_DBZH]) # Carlin et al 2021 eq. 7 using IWC from Hogan et al. 2006; originally in [log(1/m3)], transformed units here to [log(1/L)] by subtracting 3

    Nt_ice_iwc_zh_t_combined_hu2022 = (3.39 + 2*np.log10(iwc_zh_t_hogan2006_combined) - 0.1*ds[X_DBZH]) # (Hu and Ryzhkov 2022 eq. 10, [log(1/L)] using combined IWC from Hogan et al. 2006
    Nt_ice_iwc_zh_t_combined_carlin2021 = (3.69 + 2*np.log10(iwc_zh_t_hogan2006_combined) - 0.1*ds[X_DBZH]) # Carlin et al 2021 eq. 7 using combined IWC from Hogan et al. 2006; originally in [log(1/m3)], transformed units here to [log(1/L)] by subtracting 3

    Nt_ice_iwc_zdr_zh_kdp_hu2022 = (3.39 + 2*np.log10(iwc_zdr_zh_kdp_carlin2021) - 0.1*ds[X_DBZH]) # (Hu and Ryzhkov 2022 eq. 10, [log(1/L)] using IWC from Carlin et al. 2021
    Nt_ice_iwc_zdr_zh_kdp_carlin2021 = (3.69 + 2*np.log10(iwc_zdr_zh_kdp_carlin2021) - 0.1*ds[X_DBZH]) # Carlin et al 2021 eq. 7 using IWC from Carlin et al. 2021; originally in [log(1/m3)], transformed units here to [log(1/L)] by subtracting 3

    Nt_rain_zh_zdr_rhyzkov2020 = ( -2.37 + 0.1*ds[X_DBZH] - 2.89*ds[X_ZDR] + 1.28*ds[X_ZDR]**2 - 0.213*ds[X_ZDR]**3 )# Ryzhkov et al. 2020 eq. 11 [log(1/L)] (I assume this is for Sband)

    # Put everything together
    retrievals = xr.Dataset({"lwc_zh_zdr_reimann2021":lwc_zh_zdr_reimann2021.assign_attrs(
                                name="liquid water content",
                                units="g/m³",
                                description="LWC from Reimann et al. 2021 eq 3.7 (http://dx.doi.org/10.1127/metz/2021/1072)"),
                            "lwc_zh_zdr_rhyzkov2022":lwc_zh_zdr_rhyzkov2022.assign_attrs(
                                name="liquid water content",
                                units="g/m³",
                                description="LWC from Ryzhkov 2022 PROM presentation (https://www2.meteo.uni-bonn.de/spp2115/lib/exe/fetch.php?media=internal:uploads:all_hands_schneeferner_july2022:ryzhkov.pdf)"),
                            "lwc_kdp_reimann2021": lwc_kdp_reimann2021.assign_attrs(
                                name="liquid water content",
                                units="g/m³",
                                description="LWC from Reimann et al. 2021 eq 3.13 (http://dx.doi.org/10.1127/metz/2021/1072)"),
                            "iwc_zh_t_hogan2006": iwc_zh_t_hogan2006.assign_attrs(
                                name="ice water content",
                                units="g/m³",
                                description="Empirical IWC from Hogan et al. 2006 Table 2 (https://doi.org/10.1175/JAM2340.1)"),
                            "iwc_zh_t_hogan2006_model": iwc_zh_t_hogan2006_model.assign_attrs(
                                name="ice water content",
                                units="g/m³",
                                description="Model IWC from Hogan et al. 2006 eq 14 (https://doi.org/10.1175/JAM2340.1)"),
                            "iwc_zh_t_hogan2006_combined": iwc_zh_t_hogan2006_combined.assign_attrs(
                                name="ice water content",
                                units="g/m³",
                                description="Combined IWC from Hogan et al. 2006 as suggested by Blanke et al 2023 (https://doi.org/10.1175/JAM2340.1, https://doi.org/10.5194/amt-16-2089-2023)"),
                            "iwc_zdr_zh_kdp_carlin2021": iwc_zdr_zh_kdp_carlin2021.assign_attrs(
                                name="ice water content",
                                units="g/m³",
                                description="IWC from Carlin et al. 2021 eqs 4b and 5b (https://doi.org/10.1175/JAMC-D-21-0038.1)"),
                            "Dm_ice_zh_matrosov2019": Dm_ice_zh_matrosov2019.assign_attrs(
                                name="mean volume diameter in ice",
                                units="mm",
                                description="Dm from Matrosov et al. 2019 (https://cscenter.co.jp/icrm2019/program/data/abstracts/Session11A-02_2.pdf)"),
                            "Dm_ice_zh_kdp_carlin2021": Dm_ice_zh_kdp_carlin2021.assign_attrs(
                                name="mean volume diameter in ice",
                                units="mm",
                                description="Dm from Carlin et al. 2021 eq 5a (https://doi.org/10.1175/JAMC-D-21-0038.1)"),
                            "Dm_ice_zdp_kdp_carlin2021": Dm_ice_zdp_kdp_carlin2021.assign_attrs(
                                name="mean volume diameter in ice",
                                units="mm",
                                description="Dm from Carlin et al. 2021 eq 4a (https://doi.org/10.1175/JAMC-D-21-0038.1)"),
                            "Dm_hybrid_blanke2023": Dm_hybrid_blanke2023.assign_attrs(
                                name="mean volume diameter in ice",
                                units="mm",
                                description="Hybrid Dm from Matrosov et al. 2019 and Carlin et al. 2021 as suggested by Blanke et al 2023 (https://doi.org/10.5194/amt-16-2089-2023)"),
                            "Dm_rain_zdr_chen": Dm_rain_zdr_chen.assign_attrs(
                                name="mean volume diameter in liquid",
                                units="mm",
                                description="Dm from JuYu Chen (reference missing)"),
                            "Dm_rain_zdr_hu2022": Dm_rain_zdr_hu2022.assign_attrs(
                                name="mean volume diameter in liquid",
                                units="mm",
                                description="Dm from Hu and Ryzhkov 2022 eq 2 (https://doi.org/10.1029/2021JD035498)"),
                            "Dm_rain_zdr_bringi2009": Dm_rain_zdr_bringi2009.assign_attrs(
                                name="mean volume diameter in liquid",
                                units="mm",
                                description="Dm from Bringi et al 2009 (C-band) eq. 1 [mm] (https://doi.org/10.1175/2009JTECHA1258.1)"),
                            "Nt_ice_iwc_zh_t_hu2022": Nt_ice_iwc_zh_t_hu2022.assign_attrs(
                                name="Number concentration of frozen particles",
                                units="log(1/L)",
                                description="Nt from Hu and Ryzhkov 2022 eq. 10 (https://doi.org/10.1029/2021JD035498) using IWC from Hogan et al. 2006 (https://doi.org/10.1175/JAM2340.1)"),
                            "Nt_ice_iwc_zh_t_carlin2021": Nt_ice_iwc_zh_t_carlin2021.assign_attrs(
                                name="Number concentration of frozen particles",
                                units="log(1/L)",
                                description="Nt from from Carlin et al. 2021 eq 7 (https://doi.org/10.1175/JAMC-D-21-0038.1) using IWC from Hogan et al. 2006 (https://doi.org/10.1175/JAM2340.1)"),
                            "Nt_ice_iwc_zh_t_combined_hu2022": Nt_ice_iwc_zh_t_combined_hu2022.assign_attrs(
                                name="Number concentration of frozen particles",
                                units="log(1/L)",
                                description="Nt from Hu and Ryzhkov 2022 eq. 10 (https://doi.org/10.1029/2021JD035498) using combined IWC from Hogan et al. 2006 (https://doi.org/10.1175/JAM2340.1)"),
                            "Nt_ice_iwc_zh_t_combined_carlin2021": Nt_ice_iwc_zh_t_combined_carlin2021.assign_attrs(
                                name="Number concentration of frozen particles",
                                units="log(1/L)",
                                description="Nt from from Carlin et al. 2021 eq 7 (https://doi.org/10.1175/JAMC-D-21-0038.1) using combined IWC from Hogan et al. 2006 (https://doi.org/10.1175/JAM2340.1)"),
                            "Nt_ice_iwc_zdr_zh_kdp_hu2022": Nt_ice_iwc_zdr_zh_kdp_hu2022.assign_attrs(
                                name="Number concentration of frozen particles",
                                units="log(1/L)",
                                description="Nt from Hu and Ryzhkov 2022 eq. 10 (https://doi.org/10.1029/2021JD035498) using IWC from Carlin et al. 2021 (https://doi.org/10.1175/JAMC-D-21-0038.1)"),
                            "Nt_ice_iwc_zdr_zh_kdp_carlin2021": Nt_ice_iwc_zdr_zh_kdp_carlin2021.assign_attrs(
                                name="Number concentration of frozen particles",
                                units="log(1/L)",
                                description="Nt from from Carlin et al. 2021 eq 7 (https://doi.org/10.1175/JAMC-D-21-0038.1) using IWC from Carlin et al. 2021 (https://doi.org/10.1175/JAMC-D-21-0038.1)"),
                            "Nt_rain_zh_zdr_rhyzkov2020": Nt_rain_zh_zdr_rhyzkov2020.assign_attrs(
                                name="Number concentration of liquid particles",
                                units="log(1/L)",
                                description="Nt from from Rhyzkov et al. 2020 eq 11(https://doi.org/10.3390/atmos11040362)"),
                            })

    if X_AH in ds.data_vars:
        retrievals = retrievals.assign({"lwc_ah_reimann2021": lwc_ah_reimann2021.assign_attrs(
                                name="liquid water content",
                                units="g/m³",
                                description="LWC from Reimann et al. 2021 eq 3.10 (http://dx.doi.org/10.1127/metz/2021/1072)"),
            })
    if X_PHI in ds.data_vars and X_AH in ds.data_vars:
        retrievals = retrievals.assign({"lwc_hybrid_reimann2021": lwc_hybrid_reimann2021.assign_attrs(
                                name="liquid water content",
                                units="g/m³",
                                description="Hybrid LWC from Reimann et al. 2021 (http://dx.doi.org/10.1127/metz/2021/1072)"),
            })

    return retrievals

#### Full variables correction, melting layer detection, KDP derivation, entropy calculation and QVP derivation for a PPI

"""
## Example usage of the full pipeline

For an example of the full workflow see plot_ppis_qvps_etc.py
"""

#### Volume matching two radars

def get_common_projection(*datasets):
    """
    Return a common OSR SpatialReference object for multiple radar datasets.

    Chooses UTM if all radars lie in the same UTM zone,
    otherwise falls back to an Azimuthal Equidistant (AEQD)
    projection centered between them.

    Parameters
    ----------
    *datasets : xarray.Dataset
        Radar datasets, each containing `latitude` and `longitude`
        (either as scalar, 1D, or 2D coordinates).

    Returns
    -------
    proj : osr.SpatialReference
        Common spatial reference to use with wradlib.georeference().
    """
    if len(datasets) < 2:
        raise ValueError("Provide at least two radar datasets.")

    def get_latlon(ds):
        """Extract representative latitude and longitude from dataset."""
        lat = ds['latitude']
        lon = ds['longitude']
        # Reduce to scalar if necessary
        if hasattr(lat, "values"):
            lat = np.nanmean(lat.values)
            lon = np.nanmean(lon.values)
        return float(lat), float(lon)

    # Collect all radar positions
    lats, lons = zip(*(get_latlon(ds) for ds in datasets))
    lats = np.array(lats)
    lons = np.array(lons)

    # Determine UTM zone for each
    def utm_zone(lat, lon):
        zone = int(np.floor((lon + 180) / 6) + 1)
        hemisphere = "north" if lat >= 0 else "south"
        epsg = 32600 + zone if hemisphere == "north" else 32700 + zone
        return zone, epsg, hemisphere

    zones, epsgs, hemispheres = zip(*(utm_zone(lat, lon) for lat, lon in zip(lats, lons)))

    # Check if all radars are in the same UTM zone & hemisphere
    same_zone = len(set(zones)) == 1 and len(set(hemispheres)) == 1

    if same_zone:
        # All in the same UTM zone
        zone = zones[0]
        hemisphere = hemispheres[0]
        epsg = epsgs[0]
        proj = osr.SpatialReference()
        proj.ImportFromEPSG(epsg)
        print(f"Using UTM zone {zone} ({hemisphere}), EPSG:{epsg}")
    else:
        # Different zones → use AEQD centered at mean location
        proj = osr.SpatialReference()
        proj.SetAE(
            np.mean(lats),
            np.mean(lons),
            0,0
        )
        proj.SetWellKnownGeogCS("WGS84")
        print(f"Using Azimuthal Equidistant projection centered at "
              f"({np.mean(lats):.2f}°, {np.mean(lons):.2f}°)")

    return proj

def match_timesteps(ds1, ds2, has_time1=None, has_time2=None, tolerance_time=None):
    """
    Find nearest neighbor matches in time dimension, if there is no time dimension
    returns [(0, 0)].
    """
    matched_timesteps = []

    if has_time1 is None:
        has_time1 = ('time' in ds1.dims) and ds1.sizes.get('time', 0) > 1
    if has_time2 is None:
        has_time2 = ('time' in ds2.dims) and ds2.sizes.get('time', 0) > 1

    if has_time1 and has_time2 and (tolerance_time is not None):
        # get representative times
        t1 = ds1['time'].values
        t2 = ds2['time'].values

        # convert to integer seconds since epoch
        t1s = np.array([np.datetime64(tt, 's').astype('int64') for tt in t1])
        t2s = np.array([np.datetime64(tt, 's').astype('int64') for tt in t2])

        # Build pairwise absolute time difference matrix
        # shape: (len(t1), len(t2))
        diff_matrix = np.abs(t1s[:, None] - t2s[None, :])

        # Forward nearest (ds1 → ds2)
        nearest_j = np.argmin(diff_matrix, axis=1)
        nearest_dist_1 = diff_matrix[np.arange(len(t1s)), nearest_j]

        # Backward nearest (ds2 → ds1)
        nearest_i = np.argmin(diff_matrix, axis=0)
        #nearest_dist_2 = diff_matrix[nearest_i, np.arange(len(t2s))]

        for i, j in enumerate(nearest_j):
            # Check mutual nearest condition
            if nearest_i[j] == i:
                # Check tolerance condition
                if nearest_dist_1[i] <= tolerance_time:
                    matched_timesteps.append((i, int(j)))
    else:
        # fallback / simpler matching rules
        if has_time1 and not has_time2:
            matched_timesteps = [(i, 0) for i in range(ds1.sizes['time'])]
        elif has_time2 and not has_time1:
            matched_timesteps = [(0, j) for j in range(ds2.sizes['time'])]
        elif has_time1 and has_time2 and (tolerance_time is None):
            # match by index up to min length
            n = min(ds1.sizes['time'], ds2.sizes['time'])
            matched_timesteps = [(i, i) for i in range(n)]
        else:
            # neither has meaningful time -> single pair
            matched_timesteps = [(0, 0)]

    return matched_timesteps

def find_radar_overlap(ds1, ds2, tolerance=1000.0, tolerance_time=None):
    """
    Finds neighbors bins for two radar xarray Datasets based on 3D (x,y,z)
    distance and optional time tolerance. Uses scipy.spatial.KDTree to look for
    overlapping points. Returns masks in the shape of ds1 and ds2 to identify neighbors and
    flattened indeces to select the neighbor pairs, per timestep.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        Must contain coordinates/variables 'x', 'y', 'z' in a common coordinate system
        in meters with shape (azimuth, range) or (time, azimuth, range). 'azimuth'
        and 'range' coords must exist.
    tolerance : float
        Spatial tolerance in meters for looking for neighbors.
    tolerance_time : float or None
        Temporal tolerance in seconds. If None, time is ignored (volumes matched
        by index or single-volume logic).

    Returns
    -------
    mask1, mask2 : xarray.DataArray (dtype=bool)
        Masks have dims ('time','azimuth','range') if the corresponding dataset
        has a time dimension (len>1); otherwise dims ('azimuth','range').
        True = overlapping bin (within tolerance to at least one bin of the other radar).
    idx_1_flat, idx_2_flat: np.array or list
        Contain the indeces of the neighbouring points from the flattened arrays, for
        each timestep. np.array if there is no time dimension or if the matching is
        the same for all timesteps, otherwise list of np.arrays.
    matched_timesteps: list
        List with matched time indices. In case any dataset has no time dimension
        or the time dimension is of size 1, the index for that dataset will be zero.

    Notes
    -----
    If the x,y,z coordinates are static in time in both datasets the computation
    of overlapping points is done only once and then propagated, resulting in
    great time savings. If the x,y,z coordinates are not static but they change
    only a few times, it is recommended to subdivide the datasets into timespans
    with static coordinates and process them separately.

    Example
    -------
    proj = get_common_projection(ds1, ds2)
    ds1 = wrl.georef.georeference(ds1, crs=proj)
    ds2 = wrl.georef.georeference(ds2, crs=proj)
    mask1, mask2, idx_1_flat, idx_2_flat, matched_timesteps = find_radar_overlap(ds1, ds2, tolerance_time=60*4)

    """
    # --- basic checks ---
    for c in ('x', 'y', 'z'):
        if c not in ds1.coords and c not in ds1:
            raise ValueError(f"Coordinate '{c}' missing from ds1")
        if c not in ds2.coords and c not in ds2:
            raise ValueError(f"Coordinate '{c}' missing from ds2")

    static1 = all(is_static(ds1, c) for c in ('x', 'y', 'z'))
    static2 = all(is_static(ds2, c) for c in ('x', 'y', 'z'))

    has_time1 = ('time' in ds1.dims) and ds1.sizes.get('time', 0) > 1
    has_time2 = ('time' in ds2.dims) and ds2.sizes.get('time', 0) > 1

    # --- determine matched time pairs ---
    matched_timesteps = match_timesteps(ds1, ds2, has_time1=has_time1, has_time2=has_time2, tolerance_time=tolerance_time)

    if len(matched_timesteps) == 0:
        warnings.warn("No matched time pairs found within tolerance_time. Returning all-False masks.")

    # Initialize masks

    mask1 = make_mask_template(ds1)
    mask2 = make_mask_template(ds2)

    # caches for static coords / already computed coord slices
    coords_cache = {}

    def get_coords(ds, coord_name, t_index):
        key = (id(ds), coord_name, None if ('time' not in ds[coord_name].dims) else int(t_index))
        if key in coords_cache:
            return coords_cache[key]
        arr2d = coord_slice(ds, coord_name, int(t_index))
        coords_cache[key] = arr2d
        return arr2d

    # --- compute pairwise spatial overlap for a single i1,i2 pair ---
    def compute_pair_mask(ds1, ds2, i1, i2):
        # -------------------------
        # 1) Build flattened coordinate arrays (Nx3, Mx3)
        # -------------------------
        x1 = get_coords(ds1, 'x', i1)
        y1 = get_coords(ds1, 'y', i1)
        z1 = get_coords(ds1, 'z', i1)

        x2 = get_coords(ds2, 'x', i2)
        y2 = get_coords(ds2, 'y', i2)
        z2 = get_coords(ds2, 'z', i2)

        shape1 = x1.shape
        shape2 = x2.shape

        coords_1 = np.column_stack([x1.ravel(),
                                    y1.ravel(),
                                    z1.ravel()])
        coords_2 = np.column_stack([x2.ravel(),
                                    y2.ravel(),
                                    z2.ravel()])

        # -------------------------
        # 2) Remove invalid points (NaNs/inf) but keep mapping to original indices
        # -------------------------
        def _valid_mask(coords):
            return np.isfinite(coords).all(axis=1)

        valid_1 = _valid_mask(coords_1)
        valid_2 = _valid_mask(coords_2)

        coords_1_valid = coords_1[valid_1]
        coords_2_valid = coords_2[valid_2]

        # Keep index maps back to flattened original arrays
        indices_1_orig = np.nonzero(valid_1)[0]   # length N1_valid
        indices_2_orig = np.nonzero(valid_2)[0]   # length N2_valid

        # -------------------------
        # 3) KD-trees and Radius search instead
        # -------------------------

        tree_2 = KDTree(coords_2_valid)
        # For each point in ds1_valid, get list of ds2_valid neighbors within tolerance
        neighbors_list = tree_2.query_ball_point(coords_1_valid, r=tolerance)

        # -------------------------
        # 4) Build all matching pairs
        # -------------------------

        matched_idx_1_valid = []
        matched_idx_2_valid = []

        for i1_valid, neighs in enumerate(neighbors_list):
            for j2_valid in neighs:
                matched_idx_1_valid.append(i1_valid)
                matched_idx_2_valid.append(j2_valid)

        matched_idx_1_valid = np.array(matched_idx_1_valid, dtype=int)
        matched_idx_2_valid = np.array(matched_idx_2_valid, dtype=int)

        # -------------------------
        # 5) Map back to original flattened indices (and then to (azimuth,range)
        # -------------------------
        matched_1_flat = indices_1_orig[matched_idx_1_valid]  # indices into ds1.ravel() ordering
        matched_2_flat = indices_2_orig[matched_idx_2_valid]  # indices into ds2.ravel() ordering

        # Build (azimuth, range) tuples:
        matched_1_az, matched_1_rg = np.unravel_index(matched_1_flat, shape1)
        matched_2_az, matched_2_rg = np.unravel_index(matched_2_flat, shape2)

        # -------------------------
        # 6) Generate masks
        # -------------------------
        mask1 = np.zeros(shape1, dtype=bool)
        mask2 = np.zeros(shape2, dtype=bool)

        mask1[matched_1_az, matched_1_rg] = True
        mask2[matched_2_az, matched_2_rg] = True

        return mask1, mask2, matched_1_flat, matched_2_flat

    # --- loop matched pairs and assemble masks (use OR accumulation where needed) ---
    if static1 and static2:
        mask_once_1, mask_once_2, matched_1_flat, matched_2_flat = compute_pair_mask(ds1, ds2, 0, 0)

        mask1[:] = mask_once_1
        if has_time1:
            idx_1_flat = np.vstack([matched_1_flat]*len(mask1.time))
        else:
            idx_1_flat = matched_1_flat

        mask2[:] = mask_once_2
        if has_time2:
            idx_2_flat = np.vstack([matched_2_flat]*len(mask2.time))
        else:
            idx_2_flat = matched_2_flat
    else:
        idx_1_flat = []
        idx_2_flat = []
        for (i1, i2) in matched_timesteps:
            m1pair, m2pair, m1pair_nn, m2pair_nn = compute_pair_mask(ds1, ds2, i1, i2)

            # assign/accumulate into mask1
            if ('time' in mask1.dims) and mask1.sizes.get('time', 0) > 1:
                # i1 is a time index in ds1 (if ds1 has time), otherwise i1 is 0 (no-op)
                mask1.values[int(i1), :, :] |= m1pair
                idx_1_flat.append(m1pair_nn)
            else:
                # no time dim on mask1: OR the pair result (so any match at any paired time is kept)
                mask1.values[:, :] |= m1pair
                idx_1_flat.append(m1pair_nn)

            # assign/accumulate into mask2
            if ('time' in mask2.dims) and mask2.sizes.get('time', 0) > 1:
                mask2.values[int(i2), :, :] |= m2pair
                idx_2_flat.append(m2pair_nn)
            else:
                mask2.values[:, :] |= m2pair
                idx_2_flat.append(m2pair_nn)

    return mask1, mask2, idx_1_flat, idx_2_flat, matched_timesteps

def refine_radar_overlap(
    ds1,
    ds2,
    mask1,
    mask2,
    matched_timesteps,
    var_name="DBZH",
    tolerance=1000.0,
    tolerance_time=None,
    z_tolerance=None,
):
    """
    Refine two geometric overlap masks so that a bin is kept only if it has at
    least one matched neighbour in the other dataset with finite var_name value.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        Radar datasets (must contain coords 'x','y','z' and variable `var_name`).
    mask1, mask2 : xarray.DataArray or None
        Geometric overlap masks returned by `find_radar_overlap`.
    matched_timesteps: list
        List with matched time indices as returned from find_radar_overlap.
    var_name : str
        Variable name to test for NaN (e.g., "DBZH").
    tolerance : float
        Spatial tolerance in meters used when deciding neighbours (should match the
        tolerance used to produce the geometric masks).
    tolerance_time : float or None
        Temporal tolerance in seconds (used to pair volumes). If None, pairing is
        done by index (or single-volume rules).
    z_tolerance : float or None
        Tolerance in the z coordinate. If a pair of points is separated by more than
        z_tolerance in the vertical, they are removed.

    Returns
    -------
    new_mask1, new_mask2 : xarray.DataArray (bool)
        Refined masks with same dims & coords as input masks (or masks produced
        by find_radar_overlap). True = keep (has at least one valid match).
    idx_1_flat_ref, idx_2_flat_ref: np.array or list
        Analogous to idx_1_flat and idx_2_flat from find_radar_overlap but
        with pairs containing non-valid values removed.
    """

    # ---- basic checks ----
    for c in ('x', 'y', 'z'):
        if c not in ds1.coords and c not in ds1:
            raise ValueError(f"Coordinate '{c}' missing from ds1")
        if c not in ds2.coords and c not in ds2:
            raise ValueError(f"Coordinate '{c}' missing from ds2")
    if var_name not in ds1.data_vars:
        raise ValueError(f"{var_name} not found in ds1")
    if var_name not in ds2.data_vars:
        raise ValueError(f"{var_name} not found in ds2")

    # ---- helpers to safely extract 2D coordinate arrays (azimuth, range) ----

    def var_slice(ds, var, time_index):
        arr = ds[var]
        if 'time' in arr.dims and arr.sizes.get('time', 0) >= 1:
            return arr.isel(time=time_index).values
        return arr.values

    if len(matched_timesteps) == 0:
        warnings.warn("No matched time pairs found within tolerance_time. Returning all-False masks.")
        return mask1.copy(), mask2.copy()

    # ---- prepare output masks (copies, keep dims/coords) ----
    new_mask1 = mask1.copy()
    new_mask2 = mask2.copy()

    idx_1_flat_ref = []
    idx_2_flat_ref = []

    # We'll accumulate "keep" results per time (or across pairs for no-time dims)
    # For mask with time dim: keep_map shape = mask.values shape (time,az,rg)
    # For mask without time dim: keep_map_flat shape = (az*rg,)
    if 'time' in mask1.dims and mask1.sizes.get('time', 0) > 1:
        keep1 = np.zeros_like(mask1.values, dtype=bool)
    else:
        keep1_flat = np.zeros(mask1.values.size, dtype=bool)

    if 'time' in mask2.dims and mask2.sizes.get('time', 0) > 1:
        keep2 = np.zeros_like(mask2.values, dtype=bool)
    else:
        keep2_flat = np.zeros(mask2.values.size, dtype=bool)

    # ---- main loop over matched time pairs ----
    for (i1, i2) in matched_timesteps:
        # get 2D coords for this pair
        x1 = coord_slice(ds1, 'x', i1)
        y1 = coord_slice(ds1, 'y', i1)
        z1 = coord_slice(ds1, 'z', i1)

        x2 = coord_slice(ds2, 'x', i2)
        y2 = coord_slice(ds2, 'y', i2)
        z2 = coord_slice(ds2, 'z', i2)

        # shapes and flat arrays
        shape1 = x1.shape
        shape2 = x2.shape
        n1 = shape1[0] * shape1[1]
        n2 = shape2[0] * shape2[1]

        pts1 = np.vstack((x1.ravel(), y1.ravel(), z1.ravel())).T
        pts2 = np.vstack((x2.ravel(), y2.ravel(), z2.ravel())).T

        coords1_finite = np.all(np.isfinite(pts1), axis=1)
        coords2_finite = np.all(np.isfinite(pts2), axis=1)

        # get geometric mask flattened for this time
        if ('time' in mask1.dims) and mask1.sizes.get('time', 0) > 1:
            mask1_flat = mask1.isel(time=i1).values.ravel()
        else:
            mask1_flat = mask1.values.ravel()

        if ('time' in mask2.dims) and mask2.sizes.get('time', 0) > 1:
            mask2_flat = mask2.isel(time=i2).values.ravel()
        else:
            mask2_flat = mask2.values.ravel()

        # candidate indices: those geometric-overlap bins that also have finite coords
        cand1 = np.nonzero(mask1_flat & coords1_finite)[0]
        cand2 = np.nonzero(mask2_flat & coords2_finite)[0]

        if cand1.size == 0 or cand2.size == 0:
            # nothing to do for this pair (but do not zero masks; keep default False in keep maps)
            continue

        pts1_c = pts1[cand1]
        pts2_c = pts2[cand2]

        # build KDTree on pts2_c (candidates only)
        tree2 = KDTree(pts2_c)
        neighbours = tree2.query_ball_point(pts1_c, r=tolerance, workers=-1)

        # if no neighbour relationships at all, skip
        total_pairs = sum(len(n) for n in neighbours)
        if total_pairs == 0:
            continue

        # build flattened pair list: rows = idx in [0..M-1] referencing cand1, cols = idx in [0..K-1] referencing cand2
        lens = np.array([len(n) for n in neighbours], dtype=int)
        row_idx = np.repeat(np.arange(len(neighbours)), lens)
        col_idx = np.concatenate([np.array(n, dtype=int) for n in neighbours])  # indices into pts2_c

        # var_name flattened arrays for candidates
        db1_flat = var_slice(ds1, var_name, i1).ravel()
        db2_flat = var_slice(ds2, var_name, i2).ravel()

        db1_c = db1_flat[cand1]
        db2_c = db2_flat[cand2]

        db1_valid = np.isfinite(db1_c)
        db2_valid = np.isfinite(db2_c)

        M = len(cand1)
        K = len(cand2)

        # compute per-candidate keep flags:
        # - keep1[k] = any(neighbouring db2 candidate is finite)
        # - keep2[j] = any(neighbouring db1 candidate is finite)
        keep1_c = np.zeros(M, dtype=bool)
        keep2_c = np.zeros(K, dtype=bool)

        # use vectorized accumulation:
        if row_idx.size > 0:
            # Legacy version
            # # For keep1: map db2_valid[col_idx] to rows -> any per row
            # np.logical_or.at(keep1_c, row_idx, db2_valid[col_idx])
            # # For keep2: map db1_valid[row_idx] to cols -> any per col
            # np.logical_or.at(keep2_c, col_idx, db1_valid[row_idx])

            # Pairwise variable validity
            pair_valid = db1_valid[row_idx] & db2_valid[col_idx]

            # Optional vertical filtering
            if z_tolerance is not None:
                z1_flat = z1.ravel()
                z2_flat = z2.ravel()

                z1_c = z1_flat[cand1]
                z2_c = z2_flat[cand2]

                delta_z = np.abs(z1_c[row_idx] - z2_c[col_idx])
                pair_valid &= (delta_z <= z_tolerance)

            # ---- collect valid pairs ----
            valid_rows = row_idx[pair_valid]
            valid_cols = col_idx[pair_valid]

            # Map back to original flat indices
            final_idx1 = cand1[valid_rows]
            final_idx2 = cand2[valid_cols]

            # Store with time info
            idx_1_flat_ref.append(final_idx1)
            idx_2_flat_ref.append(final_idx2)

            # Accumulate valid pairs into per-bin flags
            np.logical_or.at(keep1_c, row_idx, pair_valid)
            np.logical_or.at(keep2_c, col_idx, pair_valid)
        # Note: rows with no neighbours remain False (they have no valid partner)

        # accumulate into global keep maps
        if ('time' in mask1.dims) and mask1.sizes.get('time', 0) > 1:
            # update the 2D slice of keep1 for time i1
            view = keep1[int(i1)].ravel()
            view[cand1] |= keep1_c.copy()
        else:
            keep1_flat[cand1] |= keep1_c.copy()

        if ('time' in mask2.dims) and mask2.sizes.get('time', 0) > 1:
            view2 = keep2[int(i2)].ravel()
            view2[cand2] |= keep2_c.copy()
        else:
            keep2_flat[cand2] |= keep2_c.copy()

    # ---- apply accumulated keep maps to original masks ----
    if ('time' in mask1.dims) and mask1.sizes.get('time', 0) > 1:
        # keep1 is array shaped (time,az,rg)
        # ensure we only change True->False where keep1 is False
        new_mask1.values = new_mask1.values & keep1
    else:
        # reshape keep1_flat to (az,rg)
        shape1 = mask1.values.shape
        if keep1_flat.size != mask1.values.size:
            raise RuntimeError("Internal shape mismatch for mask1")
        new_mask1.values = new_mask1.values & keep1_flat.reshape(shape1)

    if ('time' in mask2.dims) and mask2.sizes.get('time', 0) > 1:
        new_mask2.values = new_mask2.values & keep2
    else:
        shape2 = mask2.values.shape
        if keep2_flat.size != mask2.values.size:
            raise RuntimeError("Internal shape mismatch for mask2")
        new_mask2.values = new_mask2.values & keep2_flat.reshape(shape2)

    return new_mask1, new_mask2, idx_1_flat_ref, idx_2_flat_ref

def return_value_pairs(ds1, ds2, idx_1, idx_2, matched_timesteps, var_name):
    """
    Takes two datasets and the output from find_radar_overlap or
    refine_radar_overlap and returns the identified value pairs
    from variable var_name.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        The same ds1 and ds2 that were used in find_radar_overlap
        or refine_radar_overlap
    idx_1, idx_2 : np.array or list
        Arrays containing the indeces of the selected values in the flattened arrays
        (per timestep).
    matched_timesteps: list
        List with matched time indices.
    var_name: str
        Name of the variable of ds1 and ds2 from which values are requested

    Returns
    -------
    ds1_values, ds2_values:
        Arrays with the flattened selected values for each timestep

    """
    # Check if ds1 and ds2 have time dimension
    has_time1 = ('time' in ds1.dims) and ds1.sizes.get('time', 0) > 1
    has_time2 = ('time' in ds2.dims) and ds2.sizes.get('time', 0) > 1

    ds1_ = ds1.expand_dims("time") if not has_time1 else ds1
    ds2_ = ds2.expand_dims("time") if not has_time2 else ds2

    # Create template arrays to save the results
    if type(idx_1) is list:
        idx_1_maxlen = np.nanmax(np.array([len(idx) for idx in idx_1]))
    else:
        idx_1_maxlen = idx_1.shape[-1]
    if type(idx_2) is list:
        idx_2_maxlen = np.nanmax(np.array([len(idx) for idx in idx_2]))
    else:
        idx_2_maxlen = idx_2.shape[-1]

    ds1_values = np.full(( len(matched_timesteps), idx_1_maxlen ), np.nan)
    ds2_values = np.full(( len(matched_timesteps), idx_2_maxlen ), np.nan)

    if ds1_[var_name].dims == ds1_["DBZH"].dims:
        ds1_vals = ds1_[var_name].values
    else: # broadcast to DBZH dims if necessary
        ds1_vals = ds1_[var_name].broadcast_like(ds1_["DBZH"]).values
    if ds2_[var_name].dims == ds2_["DBZH"].dims:
        ds2_vals = ds2_[var_name].values
    else: # broadcast to DBZH dims if necessary
        ds2_vals = ds2_[var_name].broadcast_like(ds2_["DBZH"]).values

    for ix, (i1, i2) in enumerate(matched_timesteps):
        ds1_vals_ = ds1_vals[i1].ravel()[idx_1[ix]]
        ds1_values[ix, :len(ds1_vals_)] = ds1_vals_
        ds2_vals_ = ds2_vals[i2].ravel()[idx_2[ix]]
        ds2_values[ix, :len(ds2_vals_)] = ds2_vals_

    return ds1_values, ds2_values

# helpers to safely extract a (azimuth,range) numpy array of a coordinate
def coord_slice(ds, coord, time_index):
    arr = ds[coord]
    if 'time' in arr.dims and arr.sizes.get('time', 0) > 0:
        # if time dimension exists but has length 1, isel works fine and returns 2D
        if arr.sizes.get('time', 0) >= 1:
            return arr.isel(time=time_index).values
    # no time dim -> return the 2D array
    return arr.values

# detect whether ds coordinates vary with time (static geometry optimization)
def is_static(ds, coord):
    arr = ds[coord]
    if 'time' not in arr.dims:
        return True
    if arr.sizes.get('time', 0) <= 1:
        return True
    # compare the first time-slice to the rest
    first = arr.isel(time=0).values
    # compare each slice (using allclose for floats). If very large, this will compute arrays.
    for t in range(arr.sizes['time']):
        if not np.allclose(arr.isel(time=t).values, first, atol=1e-6, rtol=1e-6):
            return False
    return True

# prepare empty masks with correct dims & coords
def make_mask_template(ds):
    if 'time' in ds.dims and ds.sizes.get('time', 0) > 1:
        coords = {'time': ds['time'], 'azimuth': ds['azimuth'], 'range': ds['range']}
        dims = ('time', 'azimuth', 'range')
        shape = (ds.sizes['time'], ds.sizes['azimuth'], ds.sizes['range'])
    else:
        coords = {'azimuth': ds['azimuth'], 'range': ds['range']}
        dims = ('azimuth', 'range')
        shape = (ds.sizes['azimuth'], ds.sizes['range'])
    return xr.DataArray(np.zeros(shape, dtype=bool), coords=coords, dims=dims)

def find_radar_overlap_unique_NN_pairs(ds1, ds2, tolerance=1000.0, tolerance_time=None):
    """
    Finds mutual nearest neighbors bins for two radar xarray Datasets based on 3D (x,y,z)
    distance and optional time tolerance. That is, looks for the nearest neighbors pairs
    between ds1 and ds2, where the distance between the bins is the closest both ways and
    it is shorter than tolerance. Uses scipy.spatial.KDTree.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        Must contain coordinates/variables 'x', 'y', 'z' in a common coordinate system
        in meters with shape (azimuth, range) or (time, azimuth, range). 'azimuth'
        and 'range' coords must exist.
    tolerance : float
        Spatial tolerance in meters for looking for neighbors.
    tolerance_time : float or None
        Temporal tolerance in seconds. If None, time is ignored (volumes matched
        by index or single-volume logic).

    Returns
    -------
    mask1, mask2 : xarray.DataArray (dtype=bool)
        Masks have dims ('time','azimuth','range') if the corresponding dataset
        has a time dimension (len>1); otherwise dims ('azimuth','range').
        True = matching bin (nearest neighbor and closer than tolerance).
    idx_1, idx_2: xarray.DataArray (dtype=float)
        Analogous to mask1, mask2 but containing the order of the selected values
        in the flattened array (per timestep). This is meant to extract the values
        from the (azimuth, range) array into a 1D array and compare them as pairs.
    matched_timesteps: list
        List with matched time indices. In case any dataset has no time dimension
        or the time dimension is of size 1, the index for that dataset will be zero.

    Notes
    -----
    If the x,y,z coordinates are static in time in both datasets the computation
    of overlapping points is done only once and then propagated, resulting in
    great time savings. If the x,y,z coordinates are not static but they change
    only a few times, it is recommended to subdivide the datasets into timespans
    with static coordinates and process them separately.

    Example
    -------
    proj = get_common_projection(ds1, ds2)
    ds1 = wrl.georef.georeference(ds1, crs=proj)
    ds2 = wrl.georef.georeference(ds2, crs=proj)
    mask1, mask2, idx1, idx2, matched_timesteps = utils.find_radar_overlap_unique_NN_pairs(
                                                                        ds1, ds2,
                                                                        tolerance=500.,
                                                                        tolerance_time=60*4)

    """
    # --- basic checks ---
    for c in ('x', 'y', 'z'):
        if c not in ds1.coords and c not in ds1:
            raise ValueError(f"Coordinate '{c}' missing from ds1")
        if c not in ds2.coords and c not in ds2:
            raise ValueError(f"Coordinate '{c}' missing from ds2")

    static1 = all(is_static(ds1, c) for c in ('x', 'y', 'z'))
    static2 = all(is_static(ds2, c) for c in ('x', 'y', 'z'))

    has_time1 = ('time' in ds1.dims) and ds1.sizes.get('time', 0) > 1
    has_time2 = ('time' in ds2.dims) and ds2.sizes.get('time', 0) > 1

    # --- determine matched time pairs ---
    matched_timesteps = match_timesteps(ds1, ds2, has_time1=has_time1, has_time2=has_time2, tolerance_time=tolerance_time)

    if len(matched_timesteps) == 0:
        warnings.warn("No matched time pairs found within tolerance_time. Returning all-False masks.")

    # Initialize masks
    mask1 = make_mask_template(ds1)
    mask2 = make_mask_template(ds2)
    idx_1 = mask1.astype(float)*np.nan
    idx_2 = mask2.astype(float)*np.nan

    # caches for static coords / already computed coord slices
    coords_cache = {}

    def get_coords(ds, coord_name, t_index):
        key = (id(ds), coord_name, None if ('time' not in ds[coord_name].dims) else int(t_index))
        if key in coords_cache:
            return coords_cache[key]
        arr2d = coord_slice(ds, coord_name, int(t_index))
        coords_cache[key] = arr2d
        return arr2d

    # --- compute pairwise spatial overlap for a single i1,i2 pair ---
    def compute_pair_mask(ds1, ds2, i1, i2):
        # -------------------------
        # 1) Build flattened coordinate arrays (Nx3, Mx3)
        # -------------------------
        x1 = get_coords(ds1, 'x', i1)
        y1 = get_coords(ds1, 'y', i1)
        z1 = get_coords(ds1, 'z', i1)

        x2 = get_coords(ds2, 'x', i2)
        y2 = get_coords(ds2, 'y', i2)
        z2 = get_coords(ds2, 'z', i2)

        shape1 = x1.shape
        shape2 = x2.shape

        coords_1 = np.column_stack([x1.ravel(),
                                    y1.ravel(),
                                    z1.ravel()])
        coords_2 = np.column_stack([x2.ravel(),
                                    y2.ravel(),
                                    z2.ravel()])

        # -------------------------
        # 2) Remove invalid points (NaNs/inf) but keep mapping to original indices
        # -------------------------
        def _valid_mask(coords):
            return np.isfinite(coords).all(axis=1)

        valid_1 = _valid_mask(coords_1)
        valid_2 = _valid_mask(coords_2)

        coords_1_valid = coords_1[valid_1]
        coords_2_valid = coords_2[valid_2]

        # Keep index maps back to flattened original arrays
        indices_1_orig = np.nonzero(valid_1)[0]   # length N1_valid
        indices_2_orig = np.nonzero(valid_2)[0]   # length N2_valid

        # -------------------------
        # 3) KD-trees and nearest neighbor queries
        # -------------------------

        tree_2 = KDTree(coords_2_valid)
        d_12, idx_2_for_1_valid = tree_2.query(coords_1_valid, k=1, workers=-1)   # for every 1 -> index in coords_2_valid

        tree_1 = KDTree(coords_1_valid)
        d_21, idx_1_for_2_valid = tree_1.query(coords_2_valid, k=1, workers=-1)   # for every 2 -> index in coords_1_valid

        # -------------------------
        # 4) Find mutual pairs (use indices in the VALID arrays)
        # -------------------------

        # For 1 index i (in coords_1_valid), its nearest 2 is j = idx_2_for_1_valid[i].
        # We want those i such that idx_1_for_2_valid[j] == i
        idx_2_for_1_valid = np.asarray(idx_2_for_1_valid, dtype=np.int64)[idx_2_for_1_valid<len(d_21)]
        idx_1_for_2_valid = np.asarray(idx_1_for_2_valid, dtype=np.int64)[idx_1_for_2_valid<len(d_12)]

        # boolean mask over 1-valid indices
        mutual_mask_valid_1 = idx_1_for_2_valid[idx_2_for_1_valid] == np.arange(len(coords_1_valid))

        # Get valid indices (in coords_1_valid and coords_2_valid)
        matched_idx_1_valid = np.nonzero(mutual_mask_valid_1)[0]       # indices into coords_1_valid
        matched_idx_2_valid = idx_2_for_1_valid[matched_idx_1_valid]   # corresponding indices into coords_2_valid

        # distances for mutual pairs
        matched_distances = d_12[matched_idx_1_valid]

        # Reduce according to tolerance
        matched_idx_1_valid = matched_idx_1_valid[matched_distances <= tolerance]
        matched_idx_2_valid = matched_idx_2_valid[matched_distances <= tolerance]
        # matched_distances = matched_distances[matched_distances <= tolerance]

        # -------------------------
        # 5) Map back to original flattened indices (and then to (azimuth,range)
        # -------------------------
        matched_1_flat = indices_1_orig[matched_idx_1_valid]  # indices into ds1.ravel() ordering
        matched_2_flat = indices_2_orig[matched_idx_2_valid]  # indices into ds2.ravel() ordering

        # Build (azimuth, range) tuples:
        matched_1_az, matched_1_rg = np.unravel_index(matched_1_flat, shape1)
        matched_2_az, matched_2_rg = np.unravel_index(matched_2_flat, shape2)

        # -------------------------
        # 6) Generate masks
        # -------------------------
        mask1 = np.zeros(shape1, dtype=bool)
        mask2 = np.zeros(shape2, dtype=bool)

        mask1[matched_1_az, matched_1_rg] = True
        mask2[matched_2_az, matched_2_rg] = True

        # -------------------------
        # 7) Generate arrays of matched flattened indeces
        # -------------------------
        idx_1 = np.zeros(shape1, dtype=float)*np.nan
        idx_2 = np.zeros(shape2, dtype=float)*np.nan

        idx_1[matched_1_az, matched_1_rg] = np.arange(len(matched_1_flat)) # matched_1_flat
        idx_2[matched_2_az, matched_2_rg] = np.arange(len(matched_2_flat)) # matched_2_flat

        return mask1, mask2, idx_1, idx_2

    # --- loop matched pairs and assemble masks (use OR accumulation where needed) ---
    if static1 and static2:
        mask_once_1, mask_once_2, idx_once_1, idx_once_2 = compute_pair_mask(ds1, ds2, 0, 0)

        mask1[:] = mask_once_1
        idx_1[:] = idx_once_1

        mask2[:] = mask_once_2
        idx_2[:] = idx_once_2
    else:
        for (i1, i2) in matched_timesteps:
            m1pair, m2pair, idx1pair, idx2pair = compute_pair_mask(ds1, ds2, i1, i2)

            # assign/accumulate into mask1
            if ('time' in mask1.dims) and mask1.sizes.get('time', 0) > 1:
                # i1 is a time index in ds1 (if ds1 has time), otherwise i1 is 0 (no-op)
                mask1.values[int(i1), :, :] |= m1pair
                idx_1.values[int(i1), :, :] = idx1pair
            else:
                # no time dim on mask1: OR the pair result (so any match at any paired time is kept)
                mask1.values[:, :] |= m1pair
                idx_1.values[:, :] = idx1pair

            # assign/accumulate into mask2
            if ('time' in mask2.dims) and mask2.sizes.get('time', 0) > 1:
                mask2.values[int(i2), :, :] |= m2pair
                idx_2.values[int(i2), :, :] = idx2pair
            else:
                mask2.values[:, :] |= m2pair
                idx_2.values[:, :] = idx2pair

    return mask1, mask2, idx_1, idx_2, matched_timesteps

# Numpy based function to compute pairwise spatial overlap for a single i1,i2 pair ---
def refine_pair_mask(arr1, arr2, idx_1, idx_2, z1, z2, z_tolerance):
    # The arrays need to be passed with a variable and timestep selected, only with
    # azimuth and range dimensions
    # -------------------------
    # Refine by removing pairs with NaN var_name
    # -------------------------
    shape_1 = z1.shape              # (azimuth_1, range_2)
    shape_2 = z2.shape              # (azimuth_1, range_2)

    ds1_flat = arr1.flatten()
    ds2_flat = arr2.flatten()

    # this will extract the order in which the values should be paired
    idx_1_flat_order = idx_1.flatten()
    idx_2_flat_order = idx_2.flatten()

    # Find valid (finite) pair indices
    valid_1 = np.isfinite(idx_1_flat_order)
    valid_2 = np.isfinite(idx_2_flat_order)

    # Extract pair indices
    pair_idx_1 = idx_1_flat_order[valid_1].astype(int)
    pair_idx_2 = idx_2_flat_order[valid_2].astype(int)

    # Sort by pair index to get consistent order
    order_1 = np.argsort(pair_idx_1)
    order_2 = np.argsort(pair_idx_2)

    # Flattened positions of arr1/arr2 matched bins (in consistent order)
    idx_1_flat = np.nonzero(valid_1)[0][order_1]
    idx_2_flat = np.nonzero(valid_2)[0][order_2]

    # --- extract pairs ---
    ds1_p = ds1_flat[idx_1_flat]
    ds2_p = ds2_flat[idx_2_flat]

    # --- drop pairs where either value is NaN ---
    valid_pairs = np.isfinite(ds1_p) & np.isfinite(ds2_p)

    if z_tolerance is not None:
        # in this case drop pairs that are separated more than z_tolerance in the vertical
        z1_flat = z1.flatten()
        z2_flat = z2.flatten()

        z1_p = z1_flat[idx_1_flat]
        z2_p = z2_flat[idx_2_flat]

        delta_z = abs(z1_p - z2_p)

        valid_pairs = valid_pairs & (delta_z <= z_tolerance)

    idx_1_flat = idx_1_flat[valid_pairs]
    idx_2_flat = idx_2_flat[valid_pairs]

    # Put results into final arrays
    matched_1_az, matched_1_rg = np.unravel_index(idx_1_flat, shape_1)
    matched_2_az, matched_2_rg = np.unravel_index(idx_2_flat, shape_2)

    mask1_ref = np.zeros(shape_1, dtype=bool)
    mask2_ref = np.zeros(shape_2, dtype=bool)
    idx_1_ref = np.full(shape_1, np.nan, dtype=float)
    idx_2_ref = np.full(shape_2, np.nan, dtype=float)

    mask1_ref[matched_1_az, matched_1_rg] = True
    mask2_ref[matched_2_az, matched_2_rg] = True
    idx_1_ref[matched_1_az, matched_1_rg] = np.arange(len(idx_1_flat)) # idx_1_flat
    idx_2_ref[matched_2_az, matched_2_rg] = np.arange(len(idx_2_flat)) # idx_2_flat

    return mask1_ref, mask2_ref, idx_1_ref, idx_2_ref

# Define a wrapper function to process faster in parallel
from concurrent.futures import ProcessPoolExecutor, as_completed
from tqdm import tqdm
def refine_pair_mask_wrapper(args):
    """Worker-safe wrapper that uses pre-extracted numpy arrays."""
    arr1, arr2, idx_1, idx_2, i1, i2, z1, z2, z_tolerance = args
    # Call refine_pair_mask
    m1pair, m2pair, idx1pair, idx2pair = refine_pair_mask(
        arr1, arr2, idx_1, idx_2, z1, z2, z_tolerance
    )
    return (i1, i2, m1pair, m2pair, idx1pair, idx2pair)


def refine_radar_overlap_unique_NN_pairs(ds1, ds2, idx_1, idx_2, matched_timesteps, var_name, tolerance_time=None, z_tolerance=None):
    """
    Refines the masks and indices-order from find_radar_overlap_unique_NN_pairs
    to keep only value-pairs where var_name is a valid value in both datasets, for
    each matched timestep. That is, checks for validity of both values for each
    value-pair and discards those that have any missing value or non-finite value.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        Must contain coordinates/variables 'x', 'y', 'z' in a common coordinate system
        in meters with shape (azimuth, range) or (time, azimuth, range). 'azimuth'
        and 'range' coords must exist.
    idx_1, idx_2 : xarray.Dataset
        Arrays containing the indeces of the selected values in the flattened array
        (per timestep). It should be the output of find_radar_overlap_unique_NN_pairs
    matched_timesteps: list
        List with matched time indices as returned from find_radar_overlap_unique_NN_pairs.
    var_name: str
        Name of the variable of ds1 and ds2 to use to filter out non valid values.
    tolerance_time : float or None
        Temporal tolerance in seconds. If None, time is ignored (volumes matched
        by index or single-volume logic).
    z_tolerance : float or None
        Tolerance in the z coordinate. If a pair of points is separated by more than
        z_tolerance in the vertical, they are removed.

    Returns
    -------
    mask1_ref, mask2_ref : xarray.DataArray (dtype=bool)
        Analogous to mask1 and mask2 from find_radar_overlap_unique_NN_pairs but
        with pairs containing non-valid values removed.
    idx_1_ref, idx_2_ref: xarray.DataArray (dtype=float)
        Analogous to idx_1 and idx_2 from find_radar_overlap_unique_NN_pairs but
        with pairs containing non-valid values removed.

    """
    # --- basic checks ---
    for c in ('x', 'y', 'z'):
        if c not in ds1.coords and c not in ds1:
            raise ValueError(f"Coordinate '{c}' missing from ds1")
        if c not in ds2.coords and c not in ds2:
            raise ValueError(f"Coordinate '{c}' missing from ds2")

    if len(matched_timesteps) == 0:
        warnings.warn("No matched time pairs found within tolerance_time. Returning all-False masks.")

    # Initialize masks
    mask1_ref = make_mask_template(ds1)
    mask2_ref = make_mask_template(ds2)
    idx_1_ref = mask1_ref.astype(float)*np.nan
    idx_2_ref = mask2_ref.astype(float)*np.nan

    # caches for static coords / already computed coord slices
    coords_cache = {}

    def get_coords(ds, coord_name, t_index):
        key = (id(ds), coord_name, None if ('time' not in ds[coord_name].dims) else int(t_index))
        if key in coords_cache:
            return coords_cache[key]
        arr2d = coord_slice(ds, coord_name, int(t_index))
        coords_cache[key] = arr2d
        return arr2d

    # --- loop matched pairs and assemble masks (use OR accumulation where needed) ---
    # Pre-extract minimal arrays for each pair
    print("Extracting necessary values")

    # Preload the full variable arrays into memory (NumPy)
    arr1_all = ds1[var_name].values  # entire 3D array
    arr2_all = ds2[var_name].values

    tasks = []
    for (i1, i2) in matched_timesteps:
        arr1 = arr1_all[i1] if "time" in ds1.dims else arr1_all
        arr2 = arr2_all[i2] if "time" in ds2.dims else arr2_all
        idx1 = idx_1.isel(time=i1).values if "time" in idx_1.dims else idx_1.values
        idx2 = idx_2.isel(time=i2).values if "time" in idx_2.dims else idx_2.values
        z1 = get_coords(ds1, "z", i1)
        z2 = get_coords(ds2, "z", i2)
        tasks.append((arr1, arr2, idx1, idx2, i1, i2, z1, z2, z_tolerance))

    # Run in parallel
    print("Running calculations in parallel")
    results = []
    with ProcessPoolExecutor(max_workers=os.cpu_count() - 1) as executor:
        futures = [executor.submit(refine_pair_mask_wrapper, t) for t in tasks]
        for f in tqdm(as_completed(futures), total=len(futures), desc="Refining pairs"):
            results.append(f.result())

    for (i1, i2, m1pair, m2pair, idx1pair, idx2pair) in results:
        # assign/accumulate into mask1_ref
        if ('time' in mask1_ref.dims) and mask1_ref.sizes.get('time', 0) > 1:
            # i1 is a time index in ds1 (if ds1 has time), otherwise i1 is 0 (no-op)
            mask1_ref.values[int(i1), :, :] |= m1pair
            idx_1_ref.values[int(i1), :, :] = idx1pair
        else:
            # no time dim on mask1_ref: OR the pair result (so any match at any paired time is kept)
            mask1_ref.values[:, :] |= m1pair
            idx_1_ref.values[:, :] = idx1pair

        # assign/accumulate into mask2_ref
        if ('time' in mask2_ref.dims) and mask2_ref.sizes.get('time', 0) > 1:
            mask2_ref.values[int(i2), :, :] |= m2pair
            idx_2_ref.values[int(i2), :, :] = idx2pair
        else:
            mask2_ref.values[:, :] |= m2pair
            idx_2_ref.values[:, :] = idx2pair

    return mask1_ref, mask2_ref, idx_1_ref, idx_2_ref

def extract_unique_pairs(args):
    """Helper worker to extract unique NN value pairs for a 2D array."""
    ds1_m_arr, ds2_m_arr, idx_1_arr, idx_2_arr, n = args

    # Flatten slices for this time pair
    ds1_flat = ds1_m_arr.flatten()
    ds2_flat = ds2_m_arr.flatten()
    idx_1_flat_ = idx_1_arr.flatten()
    idx_2_flat_ = idx_2_arr.flatten()

    valid_1 = np.isfinite(idx_1_flat_)
    valid_2 = np.isfinite(idx_2_flat_)

    idx_1_flat = idx_1_flat_[valid_1].astype(int)
    idx_2_flat = idx_2_flat_[valid_2].astype(int)

    # Sort by pair index for consistent order
    order_1 = np.argsort(idx_1_flat)
    order_2 = np.argsort(idx_2_flat)

    # Flattened positions of ds1/ds2 matched bins (in consistent order)
    idx_1_flat_ordered = np.nonzero(valid_1)[0][order_1]
    idx_2_flat_ordered = np.nonzero(valid_2)[0][order_2]

    ds1_values_ = ds1_flat[idx_1_flat_ordered]
    ds2_values_ = ds2_flat[idx_2_flat_ordered]

    return (n, ds1_values_, ds2_values_)

def return_unique_NN_value_pairs(ds1, ds2, mask1, mask2, idx_1, idx_2, matched_timesteps, var_name):
    """
    Takes two datasets and the output from find_radar_overlap_unique_NN_pairs or
    refine_radar_overlap_unique_NN_pairs and returns the identified value pairs
    from variable var_name.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        The same ds1 and ds2 that were used in find_radar_overlap_unique_NN_pairs
        or refine_radar_overlap_unique_NN_pairs
    mask1, mask2: xarray.Dataset
        Arrays containing the masks of the selected values
    idx_1, idx_2 : xarray.Dataset
        Arrays containing the indeces of the selected values in the flattened array
        (per timestep).
    matched_timesteps: list
        List with matched time indices.
    var_name: str
        Name of the variable of ds1 and ds2 from which values are requested

    Returns
    -------
    ds1_values, ds2_values:
        Arrays with the flattened selected values for each timestep

    """
    # Check if ds1 and ds2 have time dimension
    has_time1 = ('time' in ds1.dims) and ds1.sizes.get('time', 0) > 1
    has_time2 = ('time' in ds2.dims) and ds2.sizes.get('time', 0) > 1

    # expand dims if needed
    ds1_ = ds1.expand_dims("time") if not has_time1 else ds1
    ds2_ = ds2.expand_dims("time") if not has_time2 else ds2
    mask1_ = mask1.expand_dims("time") if not has_time1 else mask1
    mask2_ = mask2.expand_dims("time") if not has_time2 else mask2
    idx_1_ = idx_1.expand_dims("time") if not has_time1 else idx_1
    idx_2_ = idx_2.expand_dims("time") if not has_time2 else idx_2

    # Apply the masks
    if ds1_[var_name].dims == ds1_["DBZH"].dims:
        ds1_m_arr = ds1_[var_name].where(mask1_).values
    else: # broadcast to DBZH dims if necessary
        ds1_m_arr = ds1_[var_name].broadcast_like(ds1_["DBZH"]).where(mask1_).values
    if ds2_[var_name].dims == ds2_["DBZH"].dims:
        ds2_m_arr = ds2_[var_name].where(mask2_).values
    else:
        ds2_m_arr = ds2_[var_name].broadcast_like(ds2_["DBZH"]).where(mask2_).values

    idx_1_arr = idx_1_.values
    idx_2_arr = idx_2_.values

    # Create template arrays to save the results
    ds1_values = np.full(( len(matched_timesteps), int(idx_1_.max().values+1) ), np.nan)
    ds2_values = np.full(( len(matched_timesteps), int(idx_2_.max().values+1) ), np.nan)

    # Build argument list
    tasks = [
        (ds1_m_arr[i1], ds2_m_arr[i2], idx_1_arr[i1], idx_2_arr[i2], n)
        for n, (i1, i2) in enumerate(matched_timesteps)
    ]

    # Run in parallel
    results = []
    with ProcessPoolExecutor(max_workers=os.cpu_count() - 1) as executor:
        futures = [executor.submit(extract_unique_pairs, t) for t in tasks]
        for f in tqdm(as_completed(futures), total=len(futures), desc="Extracting unique pairs"):
            results.append(f.result())

    # Loop matched time pairs and assemble results
    for n, ds1_values_, ds2_values_ in results:
        ds1_values[n, :len(ds1_values_)] = ds1_values_
        ds2_values[n, :len(ds2_values_)] = ds2_values_

    return ds1_values, ds2_values

#!!! I tried to remove loops and make the functions more efficient and faster but
# so far they are not really faster and they fill up the memory. The issue seems
# to be when extracting all variables even before the call to extract_unique_pairs_faster
def extract_unique_pairs_faster(args):
    """Helper worker to extract unique NN value pairs for stacked variable arrays."""
    ds1_m_stack, ds2_m_stack, idx_1_arr, idx_2_arr, n, var_names = args
    n_vars = ds1_m_stack.shape[0]

    # Flatten indices once
    idx_1_flat_ = idx_1_arr.flatten()
    idx_2_flat_ = idx_2_arr.flatten()

    valid_1 = np.isfinite(idx_1_flat_)
    valid_2 = np.isfinite(idx_2_flat_)

    idx_1_flat = idx_1_flat_[valid_1].astype(int)
    idx_2_flat = idx_2_flat_[valid_2].astype(int)

    # Sort by pair index for consistent order
    order_1 = np.argsort(idx_1_flat)
    order_2 = np.argsort(idx_2_flat)

    # Flattened positions of ds1/ds2 matched bins (in consistent order)
    idx_1_flat_ordered = np.nonzero(valid_1)[0][order_1]
    idx_2_flat_ordered = np.nonzero(valid_2)[0][order_2]

    # Vectorized extraction for all variables
    ds1_values_dict = {}
    ds2_values_dict = {}

    # Flatten entire 3D stack: shape (n_vars, ny*nx)
    ds1_flat = ds1_m_stack.reshape(n_vars, -1)
    ds2_flat = ds2_m_stack.reshape(n_vars, -1)

    # Index once for all variables using advanced indexing
    ds1_values_sel = ds1_flat[:, idx_1_flat_ordered]
    ds2_values_sel = ds2_flat[:, idx_2_flat_ordered]

    # Store back as dicts per variable name
    for vi, vname in enumerate(var_names):
        ds1_values_dict[vname] = ds1_values_sel[vi]
        ds2_values_dict[vname] = ds2_values_sel[vi]

    return (n, ds1_values_dict, ds2_values_dict)

def return_unique_NN_value_pairs_faster(ds1, ds2, mask1, mask2, idx_1, idx_2, matched_timesteps, var_names):
    """
    Takes two datasets and the output from find_radar_overlap_unique_NN_pairs or
    refine_radar_overlap_unique_NN_pairs and returns the identified value pairs
    from variables var_names.

    Parameters
    ----------
    ds1, ds2 : xarray.Dataset
        The same ds1 and ds2 that were used in find_radar_overlap_unique_NN_pairs
        or refine_radar_overlap_unique_NN_pairs
    mask1, mask2: xarray.Dataset
        Arrays containing the masks of the selected values
    idx_1, idx_2 : xarray.Dataset
        Arrays containing the indeces of the selected values in the flattened array
        (per timestep).
    matched_timesteps: list
        List with matched time indices.
    var_names: list
        List of names of the variables of ds1 and ds2 from which values are requested

    Returns
    -------
    ds1_values, ds2_values:
        Arrays with the flattened selected values for each timestep

    """
    # If var_names is a str, conver to list
    if type(var_names) is str:
        var_names = [var_names]

    # Check if ds1 and ds2 have time dimension
    has_time1 = ('time' in ds1.dims) and ds1.sizes.get('time', 0) > 1
    has_time2 = ('time' in ds2.dims) and ds2.sizes.get('time', 0) > 1

    # expand dims if needed
    ds1_ = ds1.expand_dims("time") if not has_time1 else ds1
    ds2_ = ds2.expand_dims("time") if not has_time2 else ds2
    mask1_ = mask1.expand_dims("time") if not has_time1 else mask1
    mask2_ = mask2.expand_dims("time") if not has_time2 else mask2
    idx_1_ = idx_1.expand_dims("time") if not has_time1 else idx_1
    idx_2_ = idx_2.expand_dims("time") if not has_time2 else idx_2

    # Apply the masks (once for all variables)
    ds1_m_arrs = [ds1_[v].where(mask1_).values for v in var_names]
    ds2_m_arrs = [ds2_[v].where(mask2_).values for v in var_names]
    idx_1_arr = idx_1_.values
    idx_2_arr = idx_2_.values

    # Create template arrays to save the results
    max_len1 = int(idx_1_.max().values + 1)
    max_len2 = int(idx_2_.max().values + 1)
    nt = len(matched_timesteps)

    ds1_values_dict = {v: np.full((nt, max_len1), np.nan) for v in var_names}
    ds2_values_dict = {v: np.full((nt, max_len2), np.nan) for v in var_names}

    # Build argument list with stacked arrays
    tasks = []
    for n, (i1, i2) in enumerate(matched_timesteps):
        ds1_stack = np.stack([arr[i1] for arr in ds1_m_arrs], axis=0)
        ds2_stack = np.stack([arr[i2] for arr in ds2_m_arrs], axis=0)
        tasks.append((ds1_stack, ds2_stack, idx_1_arr[i1], idx_2_arr[i2], n, var_names))

    # Run in parallel
    results = []
    with ProcessPoolExecutor(max_workers=os.cpu_count() - 1) as executor:
        futures = [executor.submit(extract_unique_pairs_faster, t) for t in tasks]
        for f in tqdm(as_completed(futures), total=len(futures), desc="Extracting unique pairs"):
            results.append(f.result())

    # Assemble results
    indices, arrs1, arrs2 = zip(*results)

    for v in var_names:
        padded_ds1 = np.vstack([
            np.pad(a[v], (0, max_len1 - len(a[v])), constant_values=np.nan)
            for a in arrs1
        ])
        padded_ds2 = np.vstack([
            np.pad(a[v], (0, max_len2 - len(a[v])), constant_values=np.nan)
            for a in arrs2
        ])

        ds1_values_dict[v][np.array(indices)] = padded_ds1.copy()
        ds2_values_dict[v][np.array(indices)] = padded_ds2.copy()

    return ds1_values_dict, ds2_values_dict

def compute_crossing_angle_cartesian(ds, R1, R2):
    """
    Compute true beam crossing angle at each grid point
    using already georeferenced Cartesian coordinates.

    Parameters
    ----------
    ds : xarray.Dataset
        Dataset containing x, y, z coordinates
    R1 : tuple (x1, y1, z1)
        Radar 1 position in same Cartesian system
    R2 : tuple (x2, y2, z2)
        Radar 2 position in same Cartesian system

    Returns
    -------
    alpha : DataArray
        Beam crossing angle in degrees

    Example
    -------
    compute_crossing_angle_cartesian(dsx, (dsx.x[:,0].mean(), dsx.y[:,0].mean(), dsx.z[:,0].mean()), (dsy.x[:,0].mean(), dsy.y[:,0].mean(), dsy.z[:,0].mean()))
    """

    x = ds["x"]
    y = ds["y"]
    z = ds["z"]

    # Vector from radar 1 to grid point
    r1x = x - R1[0]
    r1y = y - R1[1]
    r1z = z - R1[2]

    # Vector from radar 2 to grid point
    r2x = x - R2[0]
    r2y = y - R2[1]
    r2z = z - R2[2]

    # Magnitudes
    mag1 = np.sqrt(r1x**2 + r1y**2 + r1z**2)
    mag2 = np.sqrt(r2x**2 + r2y**2 + r2z**2)

    # Unit vectors
    u1x = r1x / mag1
    u1y = r1y / mag1
    u1z = r1z / mag1

    u2x = r2x / mag2
    u2y = r2y / mag2
    u2z = r2z / mag2

    # Dot product
    cosang = u1x*u2x + u1y*u2y + u1z*u2z
    cosang = xr.apply_ufunc(np.clip, cosang, -1.0, 1.0)

    alpha = xr.apply_ufunc(np.arccos, cosang)
    alpha = np.rad2deg(alpha)

    alpha.name = "beam_crossing_angle"
    alpha.attrs["units"] = "degrees"

    return alpha

#### Plotting helping functions

def get_discrete_cmap(ticks, colors, bad="white", over=None, under=None):
    """Create discrete colormap.

    Parameters
    ----------
    ticks : int | sequence
        number of ticks or sequence of ticks
    colors : colormap | sequence
        colormap or sequence of colors
    bad : color
    over : color
    under : colors

    Returns
    -------
    matplotlib.colors.ListedColormap
    """
    ticks = ticks if isinstance(ticks, int) else len(ticks)
    if isinstance(colors, (str, mpl.colors.Colormap)):
        cmap = mpl.cm.get_cmap(colors)
        colors = cmap(np.linspace(0, 1, ticks + 1))
    cmap = mpl.colors.ListedColormap(colors[1:-1])
    if over is None:
        over = colors[-1]
    if under is None:
        under = colors[0]
    cmap.set_under(under)
    cmap.set_over(over)
    cmap.set_bad(color=bad)
    return cmap


def get_discrete_norm(ticks, cmap, clip=False, extend=None):
    """Return discrete boundary norm.

    Parameters
    ----------
    ticks : sequence
        sequence of ticks
    cmap : colormap or number of colors
        If number of colors, then it is directly passed to mpl.colors.BoundaryNorm. If
        colormap, then the number of colors is inferred.

    Keyword Arguments from matplotlib.colors.BoundaryNorm
    ----------
    clip : bool, optional
        If clip is ``True``, out of range values are mapped to 0 if they
        are below ``boundaries[0]`` or mapped to ``ncolors - 1`` if they
        are above ``boundaries[-1]``.

        If clip is ``False``, out of range values are mapped to -1 if
        they are below ``boundaries[0]`` or mapped to *ncolors* if they are
        above ``boundaries[-1]``. These are then converted to valid indices
        by `Colormap.__call__`.

    extend : {None, 'neither', 'both', 'min', 'max'}, default: 'both'
        Extend the number of bins to include one or both of the
        regions beyond the boundaries.  For example, if ``extend``
        is 'min', then the color to which the region between the first
        pair of boundaries is mapped will be distinct from the first
        color in the colormap, and by default a
        `~matplotlib.colorbar.Colorbar` will be drawn with
        the triangle extension on the left or lower end. If extend is None,
        it is inferred from ticks and cmap.

    Returns
    -------
    matplotlib.colors.BoundaryNorm
    """
    if type(cmap) is int:
        ncols = cmap
        # set ncols
        if extend is None:
            raise KeyError("If cmap is the number of colors, then extend must be set explicitly (None not possible)")

    else:
        try:
            if type(cmap) is str:
                cmap0 = mpl.colormaps.get_cmap(cmap)
                cmap = mpl.colors.ListedColormap(cmap0(np.linspace(0, 1, len(ticks))), N=len(ticks)+1)
            # try to infer if over and under color values are set (different than the extreme colormap values)
            has_over = False
            has_under = False
            ncols = cmap.N
            if (cmap.get_over() != cmap.colors[-1]).all():
                has_over = True
                ncols = ncols + 1
            if (cmap.get_under() != cmap.colors[0]).all():
                has_under = True
                ncols = ncols + 1

            if extend is None:
                # set extend
                if has_over:
                    extend = "max"
                    if has_under:
                        extend="both"
                elif has_under:
                    extend = "min"
                else:
                    extend = "neither"

        except:
            raise ValueError("Something went wrong when building the discrete norm")

    return mpl.colors.BoundaryNorm(ticks, ncols, clip=clip, extend=extend)


#### Operations with cartesian grid
# Taken from https://gist.github.com/dennissergeev/60bf7b03443f1b2c8eb96ce0b1880150#file-xgrid_utils-py

EARTH_RADIUS = 6371000.0  # m


def _guess_bounds(points, bound_position=0.5):
    """
    Guess bounds of grid cells.

    Simplified function from iris.coord.Coord.

    Parameters
    ----------
    points: numpy.array
        Array of grid points of shape (N,).
    bound_position: float, optional
        Bounds offset relative to the grid cell centre.

    Returns
    -------
    Array of shape (N, 2).
    """
    diffs = np.diff(points)
    diffs = np.insert(diffs, 0, diffs[0])
    diffs = np.append(diffs, diffs[-1])

    min_bounds = points - diffs[:-1] * bound_position
    max_bounds = points + diffs[1:] * (1 - bound_position)

    return np.array([min_bounds, max_bounds]).transpose()


def _quadrant_area(radian_lat_bounds, radian_lon_bounds, radius_of_earth):
    """
    Calculate spherical segment areas.

    Taken from SciTools iris library.

    Area weights are calculated for each lat/lon cell as:
        .. math::
            r^2 (lon_1 - lon_0) ( sin(lat_1) - sin(lat_0))

    The resulting array will have a shape of
    *(radian_lat_bounds.shape[0], radian_lon_bounds.shape[0])*
    The calculations are done at 64 bit precision and the returned array
    will be of type numpy.float64.

    Parameters
    ----------
    radian_lat_bounds: numpy.array
        Array of latitude bounds (radians) of shape (M, 2)
    radian_lon_bounds: numpy.array
        Array of longitude bounds (radians) of shape (N, 2)
    radius_of_earth: float
        Radius of the Earth (currently assumed spherical)

    Returns
    -------
    Array of grid cell areas of shape (M, N).
    """
    # ensure pairs of bounds
    if (
        radian_lat_bounds.shape[-1] != 2
        or radian_lon_bounds.shape[-1] != 2
        or radian_lat_bounds.ndim != 2
        or radian_lon_bounds.ndim != 2
    ):
        raise ValueError("Bounds must be [n,2] array")

    # fill in a new array of areas
    radius_sqr = radius_of_earth ** 2
    radian_lat_64 = radian_lat_bounds.astype(np.float64)
    radian_lon_64 = radian_lon_bounds.astype(np.float64)

    ylen = np.sin(radian_lat_64[:, 1]) - np.sin(radian_lat_64[:, 0])
    xlen = radian_lon_64[:, 1] - radian_lon_64[:, 0]
    areas = radius_sqr * np.outer(ylen, xlen)

    # we use abs because backwards bounds (min > max) give negative areas.
    return np.abs(areas)


def grid_cell_areas(lon1d, lat1d, radius=EARTH_RADIUS):
    """
    Calculate grid cell areas given 1D arrays of longitudes and latitudes
    for a planet with the given radius.
    Only works well with regular lat/ lon grids. For irregular or rotated
    grids it is not appropriate.

    Parameters
    ----------
    lon1d: numpy.array
        Array of longitude points [degrees] of shape (M,)
    lat1d: numpy.array
        Array of latitude points [degrees] of shape (M,)
    radius: float, optional
        Radius of the planet [metres] (currently assumed spherical)

    Returns
    -------
    Array of grid cell areas [metres**2] of shape (M, N).
    """
    lon_bounds_radian = np.deg2rad(_guess_bounds(lon1d))
    lat_bounds_radian = np.deg2rad(_guess_bounds(lat1d))
    area = _quadrant_area(lat_bounds_radian, lon_bounds_radian, radius)
    return area


def calc_spatial_mean(
    xr_da, lon_name="longitude", lat_name="latitude", radius=EARTH_RADIUS
):
    """
    Calculate spatial mean of xr_da with grid cell weighting.
    Only works well with regular lat/ lon grids. For irregular or rotated
    grids it is not appropriate.

    Parameters
    ----------
    xr_da: xarray.DataArray or xarray.Dataset
        Data to average
    lon_name: str, optional
        Name of x-coordinate
    lat_name: str, optional
        Name of y-coordinate
    radius: float
        Radius of the planet [metres], currently assumed spherical (not important anyway)

    Returns
    -------
    Spatially averaged xarray.DataArray.
    """
    lon = xr_da[lon_name].values
    lat = xr_da[lat_name].values

    area_weights = grid_cell_areas(lon, lat, radius=radius)

    if type(xr_da) is xr.Dataset:
        return xr_da.weighted(xr.DataArray(area_weights, coords=xr_da[[lat_name,lon_name]].coords)).mean(dim=[lon_name, lat_name])
    else: # if not dataset, we need to convert it to dataset first
        return xr_da.weighted(xr.DataArray(area_weights, coords=xr_da.to_dataset(name="")[[lat_name,lon_name]].coords)).mean(dim=[lon_name, lat_name])

def calc_spatial_integral(
    xr_da, lon_name="longitude", lat_name="latitude", radius=EARTH_RADIUS
):
    """
    Calculate spatial integral of xr_da with grid cell weighting.
    Only works well with regular lat/ lon grids. For irregular or rotated
    grids it is not appropriate.

    Parameters
    ----------
    xr_da: xarray.DataArray or xarray.Dataset
        Data to sum
    lon_name: str, optional
        Name of x-coordinate
    lat_name: str, optional
        Name of y-coordinate
    radius: float
        Radius of the planet [metres], currently assumed spherical (not important anyway)

    Returns
    -------
    Spatially averaged xarray.DataArray.
    """
    lon = xr_da[lon_name].values
    lat = xr_da[lat_name].values

    area_weights = grid_cell_areas(lon, lat, radius=radius)

    if type(xr_da) is xr.Dataset:
        return xr_da.weighted(xr.DataArray(area_weights, coords=xr_da[[lat_name,lon_name]].coords)).sum(dim=[lon_name, lat_name])
    else: # if not dataset, we need to convert it to dataset first
        return xr_da.weighted(xr.DataArray(area_weights, coords=xr_da.to_dataset(name="")[[lat_name,lon_name]].coords)).sum(dim=[lon_name, lat_name])

def get_regionmask(regionname):
    """
    Returns a mask for the desired region using regionemask and Natural Earth data.

    Parameters
    ----------
    regionname: str or list
        Name or list of names of the region(s). Can be a country of region name or "land" for a global land-ocean mask.

    Returns
    -------
    mask: regionmask.Regions
        Desired mask.
    """
    if regionname == "land":
        mask = rm.defined_regions.natural_earth_v5_1_2.land_10
        return mask
    else:
        try:
            rmcountries = rm.defined_regions.natural_earth_v5_1_2.countries_10
            mask = rmcountries[[regionname]]
            return mask
        except TypeError:
            rmcountries = rm.defined_regions.natural_earth_v5_1_2.countries_10
            mask = rmcountries[regionname]
            return mask
        except KeyError:
            raise KeyError("Desired region "+regionname+" is not available.")

#### Functions to load and compute fields from EMVORADO and ICON
# Some functions are adapted from Julian Steinheuer:
# https://github.com/JSteinheuer/RADAR_toolbox/blob/master/SET_SYN_RADAR.py
# https://github.com/JSteinheuer/RADAR_toolbox/blob/master/PROCESS_SYN_RADAR.py
def load_emvorado_to_radar_volume(path_or_data, rename=False):
    """
    Load and reorganize EMVORADO output into a xarray.Dataset in the same flavor as DWD data.
    Optimized for EMVORADO output with one file per timestep containing all elevations and variables.
    WARNING: The resulting volume has its elevations ordered from lower to higher and
            not according to the scan strategy

    Parameters
    ----------
    path_or_data : str or nested sequence of paths or xarray.Dataset
        – Either a string glob in the form "path/to/my/files/*.nc" or an
        explicit list of files to open. Paths can be given as strings or
        as pathlib Paths. Feeds into xarray.open_mfdataset. Alternatively,
        already-loaded data in the form of an xarray.Dataset can be passed.
    rename : bool. If True, then rename the variables to DWD-like naming.

    Returns
    -------
    data_vol : xarray.Dataset

    """
    if type(path_or_data) is xr.Dataset:
        data_emvorado_xr = path_or_data
    else:
        data_emvorado_xr = xr.open_mfdataset(path_or_data, concat_dim="time", combine="nested", compat='no_conflicts')

    try:
        data = data_emvorado_xr.rename_dims({"n_range": "range", "n_azimuth": "azimuth"})
    except ValueError:
        data = data_emvorado_xr

    # we make the coordinate arrays
    if "time" in data.dims and "time" not in data.coords:
        range_coord = np.array([ np.arange(rs, rr*rb+rs, rr) for rr, rs, rb in
                               zip(data.range_resolution[0], data.range_start[0], data.n_range_bins[0]) ])[0]
        azimuth_coord = np.array([ np.arange(azs, azr*azb+azs, azr) for azr, azs, azb in
                               zip(data.azimuthal_resolution[0], data.azimuth_start[0], data.azimuth.shape*np.ones_like(data.records)) ])[0]

        # create time coordinate
        time_coord = xr.DataArray( [
                    dt.datetime(int(yy), int(mm), int(dd),
                                      int(hh), int(mn), int(ss))
                    for yy,mm,dd,hh,mn,ss in

                                    zip( data.year.isel(records=0),
                                    data.month.isel(records=0),
                                    data.day.isel(records=0),
                                    data.hour.isel(records=0),
                                    data.minute.isel(records=0),
                                    data.second.isel(records=0),
                                    )
                    ], dims=["time"] )

    elif "time" not in data.coords:
        range_coord = np.array([ np.arange(rs, rr*rb+rs, rr) for rr, rs, rb in
                               zip(data.range_resolution, data.range_start, data.n_range_bins) ])[0]
        azimuth_coord = np.array([ np.arange(azs, azr*azb+azs, azr) for azr, azs, azb in
                               zip(data.azimuthal_resolution, data.azimuth_start, data.azimuth.shape*np.ones_like(data.records)) ])[0]

        # create time coordinate
        time_coord = xr.DataArray( [
                    dt.datetime(int(yy), int(mm), int(dd),
                                      int(hh), int(mn), int(ss))
                    for yy,mm,dd,hh,mn,ss in

                                    zip( data.year,
                                    data.month,
                                    data.day,
                                    data.hour,
                                    data.minute,
                                    data.second
                                    )
                    ], dims=["time"] )[0]

    # add coordinates for range, azimuth, time, latitude, longitude, altitude, elevation, sweep_mode
    try:
        data.coords["range"] = ( ( "range"), range_coord)
    except NameError: pass
    try:
        data.coords["azimuth"] = ( ( "azimuth"), azimuth_coord)
    except NameError: pass
    try:
        data.coords["time"] = time_coord
    except NameError: pass
    data.coords["latitude"] = float( data["station_latitude"].values.flatten()[0] )
    data.coords["longitude"] = float( data["station_longitude"].values.flatten()[0] )
    try:
        data.coords["altitude"] = float([ss for ss in data.attrs["Data_description"].split(" ") if "radar_alt_msl_mod" in ss][0].split("=")[1])
    except KeyError:
        data.coords["altitude"] = float( data["station_height"].values.flatten()[0] )
    if "elevation" not in data.coords:
        if "time" in data['ray_elevation'].dims:
            data.coords["elevation"] = data["ray_elevation"].mean(("azimuth", "time"))
        else:
            data.coords["ray_elevation"] = data["ray_elevation"].mean("azimuth")
    data.coords["sweep_mode"] = 'azimuth_surveillance'

    # move some variables to attributes
    vars_to_attrs = ["station_name", "country_ID", "station_ID_national",
                     "station_longitude", "station_height",
                     "station_latitude", "range_resolution", "azimuthal_resolution",
                     "range_start", "azimuth_start", "extended_nyquist",
                     "high_nyquist", "dualPRF_ratio", "range_gate_length",
                     "n_ranges_averaged", "n_pulses_averaged", "DATE", "TIME",
                     "year", "month", "day", "hour", "minute", "second",
                     "ppi_azimuth", "ppi_elevation", "n_range_bins"
                     ]
    for vta in vars_to_attrs:
        try:
            data.attrs[vta] = data[vta]
        except KeyError:
            pass

    # add attribute "fixed_angle"
    try:
        # if one timestep
        data.attrs["fixed_angle"] = float(data.attrs["ppi_elevation"])
    except TypeError:
        # if multiple timesteps
        data.attrs["fixed_angle"] = float(data.attrs["ppi_elevation"].values.flatten()[0])
    except KeyError:
        data.attrs["fixed_angle"] = float(data["elevation"].values.flatten()[0])

    # drop variables that were moved to attrs
    data = data.drop_vars(vars_to_attrs, errors="ignore")

    # for each remaining variable add "long_name" and "units" attribute
    for vv in data.data_vars.keys():
        try:
            data[vv].attrs["long_name"] = data[vv].attrs["Description"]
        except:
            print("no long_name attribute in "+vv)

        try:
            data[vv].attrs["units"] = data[vv].attrs["Unit"]
        except:
            print("no long_name attribute in "+vv)

    if rename:
        return data.rename({k: rename_vars_emvorado_dwd[k] for k in rename_vars_emvorado_dwd.keys() if k in data.data_vars or k in data.dims})
    else:
        return data

# Dictionary to rename EMVORADO vars to DWD-like vars
rename_vars_emvorado_dwd = {
    "ahsim":"AH",
    "ahpisim":"AHPI",
    "adpsim":"ADP",
    "adppisim":"ADPPI",
    "zdrsim":"ZDR",
    "rhvsim":"RHOHV",
    "kdpsim":"KDP",
    "phidpsim":"PHIDP",
    "zrsim":"DBZH",
    "vrsim":"VRADH",
    "records": "sweep_fixed_angle"
    }


def load_icon(files, file_z=None):
    """
    Load ICON data and transform the time coordinate to datetime format. In
    case the vertical axis is provided in a separate file (file_z), load it and
    attach it to the dataset.

    Parameters
    ----------
    files : str or nested sequence of paths
        Either a string glob in the form "path/to/my/files/*.nc" or an
        explicit list of files to open. Paths can be given as strings or
        as pathlib Paths. Feeds into xarray.open_mfdataset.
    file_z : str or nested sequence of paths
        Like 'file' but for the vertical coordinate.

    Returns
    -------
    data_vol : xarray.Dataset
    """

    icon_field = xr.open_mfdataset(files, compat='no_conflicts')

    if file_z is not None:
        icon_field_z = xr.open_dataset(file_z)

        if "time" in icon_field_z.dims:
            icon_field_z = icon_field_z.isel(time=0)

        # We need to flip the "height" and "height_2" dimension names because
        # of a naming issue when transforming to netcdf
        rename_heights = {}
        if "height" in icon_field_z.dims:
            rename_heights["height"] = "height_2"
        if "height_2" in icon_field_z.dims:
            rename_heights["height_2"] = "height"

        icon_field_z = icon_field_z.rename(rename_heights)

        if "z_ifc" in icon_field_z:
            icon_field["z_ifc"] = icon_field_z["z_ifc"]
        if "z_mc" in icon_field_z:
            icon_field["z_mc"] = icon_field_z["z_mc"]

    # Convert time dimension if necessary
    if icon_field.time.dtype==np.float64:
        # Separate the date and fractional day
        date_part = icon_field.time.astype(int)  # Extract the integer part as YYYYMMDD
        fractional_day = icon_field.time.values - date_part  # Extract the fractional part

        # Convert the date part to datetime
        date_part_datetime = pd.to_datetime(date_part.astype(str), format="%Y%m%d")

        # Add the fractional day converted to timedelta
        corrected_time = date_part_datetime + pd.to_timedelta(fractional_day * 24, unit="h")

        # Assign the corrected time back to the dataset
        icon_field['time'] = xr.DataArray(corrected_time, dims="time")

    return icon_field

def icon_to_radar_volume_old(icon_field, radar_volume):
    """
    Function to interpolate variable fields from ICON output into the
    shape of radar_volume using nearest neighbors.

    Parameters
    ----------
    radar_volume : xarray.Dataset
        Dataset with volume data
    icon_field : xarray.Dataset
        ICON fields.

    Returns
    -------
    icon_vol : xarray.Dataset
        ICON fields interpolated into the shape of radar_volume.
    """

    sitecoords = [float(radar_volume.longitude),
                  float(radar_volume.latitude),
                  float(radar_volume.altitude)]

    # proj_wgs84 = wrl.georef.epsg_to_osr(4326)

    # I have to shift the ranges:
    # wrl.georef.spherical_to_centroids: The ranges are assumed to define the exterior
    # boundaries of the range bins (thus they must be positive). The angles are assumed
    # to describe the pointing direction fo the main beam lobe.
    # cent_coords = wrl.georef.spherical_to_centroids(radar_volume["range"] + radar_volume["range"].diff("range").mean().values/2,
    #                                                 radar_volume["azimuth"],
    #                                                 radar_volume["elevation"],
    #                                                 sitecoords,
    #                                                 crs=proj_wgs84)

    # lon = xr.ones_like(radar_volume["x"])*cent_coords[:,:,:,0]
    # lat = xr.ones_like(radar_volume["x"])*cent_coords[:,:,:,1]
    # alt = xr.ones_like(radar_volume["x"])*cent_coords[:,:,:,2]

    # radar_volume = radar_volume.assign_coords({"lon": lon,
    #                                            "lat": lat,
    #                                            "alt": alt})

    xyz, proj_aeqd = wrl.georef.spherical_to_centroids(radar_volume["range"] + radar_volume["range"].diff("range").mean().values/2,
                                                   radar_volume["azimuth"],
                                                   radar_volume["elevation"],
                                                   sitecoords,
                                                   )

    if "x" not in radar_volume.coords:
        radar_volume = wrl.georef.georeference(radar_volume)

    lon_icon = np.rad2deg(icon_field["clon"])
    lat_icon = np.rad2deg(icon_field["clat"])
    alt_icon_hl = icon_field["z_ifc"]
    if "z_mc" in icon_field:
        alt_icon = icon_field["z_mc"]
    else: # if z_mc is not in the output then calculated based on z_ifc
        alt_icon = (icon_field["z_ifc"] + icon_field["z_ifc"].shift(height_2=-1))[:-1]/2 # transform from half levels to levels
        alt_icon = alt_icon.rename({"height_2": "height"})

    # reproject icon into radar grid
    proj_wgs = osr.SpatialReference()
    proj_wgs.ImportFromEPSG(4326)

    # proj_stereo = wrl.georef.create_osr("dwd-radolan")
    # mod_x, mod_y = wrl.georef.reproject(lon_icon.values,
    #                                     lat_icon.values,
    #                                     trg_crs=proj_stereo,
    #                                     src_crs =proj_wgs)
    # rad_x, rad_y = wrl.georef.reproject(lon.values,
    #                                     lat.values,
    #                                     trg_crs=proj_stereo,
    #                                     src_crs=proj_wgs)

    mod_x, mod_y = wrl.georef.reproject(lon_icon.values,
                                        lat_icon.values,
                                        trg_crs=proj_aeqd,
                                        src_crs =proj_wgs)
    rad_x, rad_y, alt = radar_volume.x.values, radar_volume.y.values, radar_volume.z


    # x y version
    # only those model data that are in radar domain + bordering volume
    outer_x = max(0.3 * (rad_x.max() - rad_x.min()), 1)
    outer_y = max(0.3 * (rad_y.max() - rad_y.min()), 1)
    lower_z = 50
    upper_z = 2000

    mask = ((mod_x >= rad_x.min() - outer_x) & (
            mod_x <= rad_x.max() + outer_x) & (
                   mod_y >= rad_y.min() - outer_y) & (
                   mod_y <= rad_y.max() + outer_y) & (
                   alt_icon >= alt.min() - lower_z) & (
                   alt_icon <= alt.max() + upper_z)).compute()
    mask_hl = ((mod_x >= rad_x.min() - outer_x) & (
            mod_x <= rad_x.max() + outer_x) & (
                   mod_y >= rad_y.min() - outer_y) & (
                   mod_y <= rad_y.max() + outer_y) & (
                   alt_icon_hl >= alt.min() - lower_z) & (
                   alt_icon_hl <= alt.max() + upper_z)).compute()

    mod_x_hl = mod_x[mask_hl[0]].copy() # make copy because we will modify them below
    mod_y_hl = mod_y[mask_hl[0]].copy()
    alt_icon_hl = alt_icon_hl.where(mask_hl, other=False, drop=True)

    mod_x = mod_x[mask[0]]
    mod_y = mod_y[mask[0]]
    alt_icon = alt_icon.where(mask, other=False, drop=True)

    src = np.vstack((np.repeat(mod_x[np.newaxis, :], alt_icon.shape[0], axis=0).ravel(),
                     np.repeat(mod_y[np.newaxis, :], alt_icon.shape[0], axis=0).ravel(),
                     alt_icon.values.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)
    src_hl = np.vstack((np.repeat(mod_x_hl[np.newaxis, :], alt_icon_hl.shape[0], axis=0).ravel(),
                     np.repeat(mod_y_hl[np.newaxis, :], alt_icon_hl.shape[0], axis=0).ravel(),
                     alt_icon_hl.values.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)
    trg = np.vstack((rad_x.flatten().ravel(),
                     rad_y.flatten().ravel(),
                     alt.values.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)

    # interpolate with pyinterp (only way I was able to compute this quickly)
    # use nearest neighborhs (inverse_distance_weighting with k=1)
    # I also tried different configurations of dask delayed, futures and map that
    # either crashed because of filled memory or were too slow.
    # Using dask.bag with map worked when creating the bags with appropriate size,
    # but it is not faster than just looping over timesteps
    # I also tried xarray.map_blocks but it only works for the first timestep, when
    # trying to compute other timesteps there is an error.
    # I did not try with multiprocessing, it could work.
    vars_to_compute = []
    vars_to_compute_hl = []
    for vv in icon_field.data_vars:
        if vv not in ["z_ifc", "z_mc"]:
            if "height" in icon_field[vv].dims and "ncells" in icon_field[vv].dims:
                vars_to_compute.append(vv)
            if "height_2" in icon_field[vv].dims and "ncells" in icon_field[vv].dims:
                vars_to_compute_hl.append(vv)

    # Define a reggriding function for one variable and one timestep. The time
    # dimension must be present (only first timestep is computed)
    def pyinterp_NN(data):
        mesh = pyinterp.RTree(ecef=True)
        mesh.packing(src, data.isel(time=0).where(mask, drop=True).stack(stacked=['height', 'ncells']))
        data_interp, neighbors = mesh.inverse_distance_weighting(trg, within=False, k=1) # k=1 is like nearest neighbors
        data_interp_reshape = data_interp.reshape(radar_volume["x"].shape)
        data_interp_reshape_xr = xr.DataArray(data_interp_reshape,
                                              coords=radar_volume["x"].coords,
                                              dims=radar_volume["x"].dims,
                                              name="data_interp_shape").expand_dims(dim={"time": data["time"]}, axis=0)
        return data_interp_reshape_xr

    def pyinterp_NN_hl(data):
        mesh = pyinterp.RTree(ecef=True)
        mesh.packing(src_hl, data.isel(time=0).where(mask_hl, drop=True).stack(stacked=['height_2', 'ncells']))
        data_interp, neighbors = mesh.inverse_distance_weighting(trg, within=False, k=1) # k=1 is like nearest neighbors
        data_interp_reshape = data_interp.reshape(radar_volume["x"].shape)
        data_interp_reshape_xr = xr.DataArray(data_interp_reshape,
                                              coords=radar_volume["x"].coords,
                                              dims=radar_volume["x"].dims,
                                              name="data_interp_shape").expand_dims(dim={"time": data["time"]}, axis=0)
        return data_interp_reshape_xr

    # Define a function to process each variable and timestep
    def process_variable_time(var, func):
        """Apply a function to each timestep of a variable."""
        results = []
        for t in range(var.sizes['time']):
            result = func(var.isel(time=t).expand_dims("time"))
            results.append(result)

        # Combine the results along the time dimension
        return xr.concat(results, dim='time', join="outer", coords="different", compat='equals')

    # Wrapper to process all variables in the dataset
    def process_dataset(ds, func):
        """Apply a function to all variables and timesteps in a dataset."""
        processed_vars = {}

        for var_name, var_data in ds.data_vars.items():
            print(var_name)
            processed_vars[var_name] = process_variable_time(var_data, func).assign_attrs(ds[var_name].attrs)

        # Combine all variables back into a dataset
        return xr.Dataset(processed_vars)

    # Apply the function to icon_field
    start_time = time.time()
    print("Regridding ICON fields to radar volume...")
    icon_vol = process_dataset(icon_field[vars_to_compute], pyinterp_NN)
    icon_vol_hl = process_dataset(icon_field[vars_to_compute_hl], pyinterp_NN_hl)
    total_time = time.time() - start_time
    print(f"... took {total_time/60:.2f} minutes to run.")
    # Regridding took 14.92 minutes to run for temp, u, v
    # Regridding took 4.58 minutes to run for temp

    return xr.merge([icon_vol, icon_vol_hl], compat='no_conflicts')

def icon_to_radar_volume(icon_field, radar_volume):
    """
    Function to interpolate variable fields from ICON output into the
    shape of radar_volume using nearest neighbors. Handles both rotated
    (2D coords) and regular (1D coords) grids.

    Parameters
    ----------
    radar_volume : xarray.Dataset
        Dataset with volume data
    icon_field : xarray.Dataset
        ICON fields.

    Returns
    -------
    icon_vol : xarray.Dataset
        ICON fields interpolated into the shape of radar_volume.
    """

    try:
        lon_icon = np.rad2deg(icon_field["clon"])
        lat_icon = np.rad2deg(icon_field["clat"])
    except KeyError:
        lon_icon = icon_field["lon"]
        lat_icon = icon_field["lat"]
    except:
        raise KeyError("!!! ERROR: Not able to extract lon and lat from icon_field !!!")

    alt_icon_hl = icon_field["z_ifc"]
    if "z_mc" in icon_field:
        alt_icon = icon_field["z_mc"]
    else: # if z_mc is not in the output then calculated based on z_ifc
        alt_icon = (icon_field["z_ifc"] + icon_field["z_ifc"].shift(height_2=-1))[:-1]/2 # transform from half levels to levels
        alt_icon = alt_icon.rename({"height_2":"height"})

    mod_x = lon_icon.values
    mod_y = lat_icon.values

    # Make mod_x and mod_y 2D if they are 1D (Standard Lat/Lon grid) ---
    if mod_x.ndim == 1 and mod_y.ndim == 1:
        mod_x, mod_y = np.meshgrid(mod_x, mod_y)

    # ICON is already in WGS84, we need to georeference the radar volume to the same system
    proj_wgs = osr.SpatialReference()
    proj_wgs.ImportFromEPSG(4326)

    radar_volume = wrl.georef.georeference(radar_volume, crs=proj_wgs)

    rad_x, rad_y, alt = radar_volume.x.values, radar_volume.y.values, radar_volume.z

    # x y version
    # only those model data that are in radar domain + bordering volume
    outer_x = 0.5
    outer_y = 0.5
    lower_z = 50
    upper_z = 2000

    mask = ((mod_x >= rad_x.min() - outer_x) & (
            mod_x <= rad_x.max() + outer_x) & (
                   mod_y >= rad_y.min() - outer_y) & (
                   mod_y <= rad_y.max() + outer_y) & (
                   alt_icon >= alt.min() - lower_z) & (
                   alt_icon <= alt.max() + upper_z)).compute()
    mask_hl = ((mod_x >= rad_x.min() - outer_x) & (
            mod_x <= rad_x.max() + outer_x) & (
                   mod_y >= rad_y.min() - outer_y) & (
                   mod_y <= rad_y.max() + outer_y) & (
                   alt_icon_hl >= alt.min() - lower_z) & (
                   alt_icon_hl <= alt.max() + upper_z)).compute()

    alt_icon_z = alt_icon.shape[0]
    alt_icon_hl_z = alt_icon_hl.shape[0]

    mod_x_masked = np.repeat(mod_x[np.newaxis, :], alt_icon_z, axis=0)[mask]
    mod_y_masked = np.repeat(mod_y[np.newaxis, :], alt_icon_z, axis=0)[mask]
    alt_icon_masked = alt_icon.values[mask]

    mod_x_hl_masked = np.repeat(mod_x[np.newaxis, :], alt_icon_hl_z, axis=0)[mask_hl].copy() # make copy because we will modify them below
    mod_y_hl_masked = np.repeat(mod_y[np.newaxis, :], alt_icon_hl_z, axis=0)[mask_hl].copy() # make copy because we will modify them below
    alt_icon_hl = alt_icon_hl.values[mask_hl]


    src = np.vstack((mod_x_masked,
                     mod_y_masked,
                     alt_icon_masked  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)
    src_hl = np.vstack((mod_x_hl_masked,
                     mod_y_hl_masked,
                     alt_icon_hl.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)

    trg = np.vstack((rad_x.flatten().ravel(),
                     rad_y.flatten().ravel(),
                     alt.values.ravel()  )).T # divide alt by 1000 if x and y are in km (depends on projection chosen)

    # interpolate with pyinterp (only way I was able to compute this quickly)
    # use nearest neighborhs (inverse_distance_weighting with k=1)
    # I also tried different configurations of dask delayed, futures and map that
    # either crashed because of filled memory or were too slow.
    # Using dask.bag with map worked when creating the bags with appropriate size,
    # but it is not faster than just looping over timesteps
    # I also tried xarray.map_blocks but it only works for the first timestep, when
    # trying to compute other timesteps there is an error.
    # I did not try with multiprocessing, it could work.
    vars_to_compute = []
    vars_to_compute_hl = []
    for vv in icon_field.data_vars:
        if vv not in ["z_ifc", "z_mc"]:
            has_spatial_dims = ("ncells" in icon_field[vv].dims or "x" in icon_field[vv].dims or "lon" in icon_field[vv].dims)
            if "height" in icon_field[vv].dims and has_spatial_dims:
                vars_to_compute.append(vv)
            if "height_2" in icon_field[vv].dims and has_spatial_dims:
                vars_to_compute_hl.append(vv)

    if "ncells" in icon_field.dims:
        dims3D = ['height', 'ncells']
        dims3D_h2 = ['height_2', 'ncells']
    elif "x" in icon_field.dims:
        dims3D = ['height', 'y', 'x']
        dims3D_h2 = ['height_2', 'y', 'x']
    elif "lon" in icon_field.dims:
        dims3D = ['height', 'lat', 'lon']
        dims3D_h2 = ['height_2', 'lat', 'lon']

    # Define the nearest neighbors indices

    # Create the configuration object for k=1 and within=False
    query_config = pyinterp.config.rtree.Query().with_k(1)

    if len(vars_to_compute) > 0:
        # Create an array of row indices to pack as the "values"
        indices_array = np.arange(len(src), dtype=np.float64)

        mesh = pyinterp.RTree3D(spheroid=pyinterp.core.geometry.geographic.Spheroid())
        mesh.packing(src, indices_array)

        # .query() replaces .value() and returns (distances, values).
        # Because we packed indices_array, 'values' contains the nearest neighbor indices!
        # Note: 'within=False' is now handled by the default behavior
        distances, nearest_indices = mesh.query(trg, config=query_config)

        # Flatten and cast back to integers for numpy array slicing
        indices = nearest_indices.flatten().astype(int)

    if len(vars_to_compute_hl) > 0:
        # Repeat the same direct-index packing for the half-levels
        indices_array_hl = np.arange(len(src_hl), dtype=np.float64)

        mesh_hl = pyinterp.RTree3D(spheroid=pyinterp.core.geometry.geographic.Spheroid())
        mesh_hl.packing(src_hl, indices_array_hl)

        distances_hl, nearest_indices_hl = mesh_hl.query(trg, config=query_config)

        indices_hl = nearest_indices_hl.flatten().astype(int)

    # Define functions to select the indices
    def pyinterp_NN(data):
        data_interp = data[:, indices]
        return data_interp

    def pyinterp_NN_hl(data):
        data_interp = data[:, indices_hl]
        return data_interp

    # Define a function to process all timesteps from one variable
    def process_variable_time(var, func):
        """Apply a function to all timestep of a variable."""

        result = func(var)

        data_interp_reshape = result.values.reshape((-1, *radar_volume["x"].shape))
        data_interp_reshape_xr =  xr.DataArray(data_interp_reshape,
                                              coords={"time":var["time"], **radar_volume["x"].coords},
                                              dims=("time", *radar_volume["x"].dims),
                                              name=var.name)
        return data_interp_reshape_xr

    # Wrapper to process all variables in the dataset
    def process_dataset(ds, func):
        """Apply a function to all variables and timesteps in a dataset."""
        processed_vars = {}

        for var_name, var_data in ds.data_vars.items():
            print(var_name)
            processed_vars[var_name] = process_variable_time(var_data, func).assign_attrs(ds[var_name].attrs)

        # Combine all variables back into a dataset
        return xr.Dataset(processed_vars)

    # Apply the function to icon_field
    start_time = time.time()
    print("Regridding ICON fields to radar volume...")
    if len(vars_to_compute) == 0 and len(vars_to_compute_hl) == 0:
        raise ValueError("ERROR: icon_field has no appropriate variables to regrid")
    if len(vars_to_compute) > 0:
        icon_field_stacked = icon_field[vars_to_compute].assign_coords(mask=mask).where(mask, drop=True).stack(stacked=dims3D)
        icon_vol = process_dataset(icon_field_stacked.where(icon_field_stacked.mask.fillna(False), drop=True), pyinterp_NN)
    if len(vars_to_compute_hl) > 0:
        icon_field_stacked_hl = icon_field[vars_to_compute_hl].assign_coords(mask_hl=mask_hl).where(mask_hl, drop=True).stack(stacked=dims3D_h2)
        icon_vol_hl = process_dataset(icon_field_stacked_hl.where(icon_field_stacked_hl.mask_hl.fillna(False), drop=True), pyinterp_NN)
    total_time = time.time() - start_time
    print(f"... took {total_time/60:.2f} minutes to run.")
    # Regridding took 14.92 minutes to run for temp, u, v
    # Regridding took 4.58 minutes to run for temp

    if len(vars_to_compute) > 0 and len(vars_to_compute_hl) > 0:
        return xr.merge([icon_vol, icon_vol_hl], compat='no_conflicts')
    elif len(vars_to_compute) > 0 :
        return icon_vol
    elif len(vars_to_compute_hl) > 0 :
        return icon_vol_hl


# ICON / EMVORADO specific stuff, code adapted from Jana Mendrok (DWD)

def icon_hydromets(mom=2, which='all', add_emvo=False):
    '''
    Preparing dict with ICON 2mom or 1mom microphysics (original PSD- and m-D-parameters)

    Parameters
    ----------
    mom : int
        If 1, then use the 1-mom scheme parameters. If 2, then use the 2-mom scheme parameters.
    which : list or str
        List of hydrometeor names to prepare. If "all", then return all default hydrometeors
        according to 1- or 2-mom scheme.
    add_emvo : bool
        If True, add EMVORADO Dmin and Dmax parameters to the 2-mom dict.

    Returns
    -------
    icon_vol : xarray.Dataset
        Dictionary with ICON 2-mom or 1-mom microphysical parameters.

    '''
    hydromets = {}

    a_w = 1e3 * np.pi/6.

    if not mom in [1,2]:
      raise TypeError("ERROR icon_hydromets: Wrong 'mom' value. Needs to be 1 or 2.")

    if isinstance(which,str):
      if which=='all':
        whichlist=['cloud','rain','ice','snow','graupel']
        if mom>1:
          whichlist.append('hail')
      else:
        whichlist=[which]
    elif isinstance(which,list):
      whichlist=which
    else:
      raise TypeError("ERROR icon_hydromets: Wrong 'which' type. Needs to be either list or string.")

    if mom>1:
      for item in whichlist:
        if item=='cloud':
          hydromets[item] = \
            seifert2general({'nu': 1.0, 'mu': 1.0, 'xmax': 2.6e-10, 'xmin': 4.2e-15, 'a': 1.24e-01, 'b': 0.333333})
        elif item=='rain.pre2023':
          hydromets[item] = \
            seifert2general({'nu': 0.0, 'mu': 0.333333, 'xmax': 3.0e-6, 'xmin': 2.6e-10, 'a': 1.24e-01, 'b': 0.333333})
          if add_emvo:
            hydromets[item].update({'Dmin': 50.0e-6, 'Dmax': 10.0e-3})
        elif item=='rain':
          hydromets[item] = \
            seifert2general({'nu': 1.0, 'mu': 0.333333, 'xmax': 6.50e-05, 'xmin': 2.6e-10, 'a': 1.24e-01, 'b': 0.333333})
          if add_emvo:
            hydromets[item].update({'Dmin': 50.0e-6, 'Dmax': 10.0e-3})
        elif item=='ice':
          hydromets[item] = \
            seifert2general({'nu': 0.0, 'mu': 0.333333, 'xmax': 1.0e-5, 'xmin': 1.0e-12, 'a': 0.835, 'b': 0.39})
          if add_emvo:
            hydromets[item].update({'Dmin': 5.0e-6, 'Dmax': 10.0e-3})
        elif item=='snow':
          hydromets[item] = \
            seifert2general({'nu': 0.0, 'mu': 0.5, 'xmax': 2.0e-5, 'xmin': 1.0e-10, 'a': 5.13, 'b': 0.5})
          if add_emvo:
            hydromets[item].update({'Dmin': 50.0e-6, 'Dmax': 50.0e-3})
        elif item=='graupel':
          hydromets[item] = \
            seifert2general({'nu': 1.0, 'mu': 0.333333, 'xmax': 5.3e-4, 'xmin': 4.19e-9, 'a': 1.42e-1, 'b': 0.314})
          if add_emvo:
            hydromets[item].update({'Dmin': 10.0e-6, 'Dmax': 30.0e-3})
        elif item=='hail':
          hydromets[item] = \
            seifert2general({'nu': 1.0, 'mu': 0.333333, 'xmax': 5.0e-3, 'xmin': 2.6e-9, 'a': 0.1366, 'b': 0.333333})
          if add_emvo:
            hydromets[item].update({'Dmin': 50.0e-6, 'Dmax': 100.0e-3})
        else:
          warnings.warn("WARNING icon_hydromets: Unknown entry in 'which' (%s)." %item)
    else:
      for item in whichlist:
        if item=='cloud':
          hydromets[item] = {'nu': 3.0, 'mu': 3.0, 'n0': 1.0, 'a': a_w, 'b': 3.0}
        elif item=='rain':
          hm = {'nu': 1.0, 'mu': 0.5, 'a': a_w, 'b': 3.0}
          hm['n0'] = 8e6 * np.exp(3.2*hm['mu']) * (1e-2)**(-hm['mu'])
          hydromets[item] = hm
        elif item=='ice':
          hydromets[item] = {'nu': 3.0, 'mu': 20.0, 'n0': 1.0, 'a': 130.0, 'b': 3.0}
        elif item=='snow':
          hydromets[item] = {'nu': 1.0, 'mu': 0.0, 'n0': 1.0, 'a': 0.038, 'b': 2.0}
        elif item=='graupel':
          hydromets[item] = {'nu': 1.0, 'mu': 0.0, 'n0': 4e6, 'a': 169.6, 'b': 3.1}
        else:
          warnings.warn("WARNING icon_hydromets: Unknown entry in 'which' (%s)." %item)
    return hydromets

def seifert2general(hymet_seif):
    """
    Convert original ICON (mass-based, Seifert notation) to Dmax-based,
    "general" notation micro-physical parameters.
    (in = COSMO/ICON) N(m) = N0 * m^nu_x * exp(-lam*m^mu_x)
                      D(m) = a * m^b
    (out = EMVORADO)  N(D) = N0 * D^mu_D * exp(-lam*D^nu_D)
                      m(D) = a * D^b   [ -> D = (m/a)^(1/b) ]
    """
    hymet_gen = {}
    hymet_gen['mu'] = (1.0 / hymet_seif['b']) * (hymet_seif['nu'] + 1.0) - 1.0
    hymet_gen['nu'] = (1.0 / hymet_seif['b']) * hymet_seif['mu']
    hymet_gen['xmax'] = hymet_seif['xmax']
    hymet_gen['xmin'] = hymet_seif['xmin']
    hymet_gen['a'] = (1.0 / hymet_seif['a']) ** (1.0 / hymet_seif['b'])
    hymet_gen['b'] = 1.0 / hymet_seif['b']
    return hymet_gen


def adjust_icon_fields(infields, hymets=icon_hydromets(), spec2dens=1, mom=2):
    """
    Take hydrometeor fields with qx and qnx, convert them to mass/number
    densities (from specific mass/number contents to densities) if necessary
    (spec2dens=1), and adjust qn to meet ICON min/max bounds of mean
    hydrometeor masses.
    Required input:
        Hydrometeor qx and qnx (all 6), qv (water vapor content), temp
        (temperature), pres (pressure).
    Output:
        volume specific qx, qnx.
    """
    r_d = 287.05  # dry air gas constant
    r_v = 461.51  # water vapor gas constant
    q = {}
    qn = {}

    hmdict = {"cloud": "c",
              "rain": "r",
              "ice": "i",
              "snow": "s",
              "graupel": "g",
              "hail": "h",
              }

    for hmname in hmdict.keys():
        try:
            q[hmname] = infields["q"+hmdict[hmname]]
        except:
            warnings.warn("q"+hmdict[hmname]+" not present in input icon field")
            pass
        if mom>1:
            try:
                qn[hmname] = infields["qn"+hmdict[hmname]]
            except:
                warnings.warn("qn"+hmdict[hmname]+" not present in input icon field")
                pass

    qv = infields['qv']
    t = infields['temp']
    p = infields['pres']
    for hmn, hmkey in enumerate(q.keys()):
        if hmn==0:
            qx = q[hmkey].copy()
        else:
            qx += q[hmkey]

    rvd_m_o = r_v / r_d - 1.0

    if spec2dens:
        rho = p / (r_d * t * (1.0 + rvd_m_o * qv - qx))
        for key in q:
            q[key] = q[key] * rho
        for key in qn:
            qn[key] = qn[key] * rho

    for key in q:
        if key in qn:
            x = q[key] / (qn[key] + 1e-38)
            x = x.where(x > hymets[key]['xmin'], other= hymets[key]['xmin'])
            x = x.where(x < hymets[key]['xmax'], other= hymets[key]['xmax'])
            qn[key] = q[key] / x.copy()
            q[key] = q[key].where(q[key] > 1e-7, other=0.)
            qn[key] = qn[key].where(q[key] > 1e-7, other=1.) # for numeric stability.
        else:
            q[key] = q[key].where(q[key] > 1e-7, other=0.)

    return q, qn


# MGD parameter and PSD-moments calculations
def gfct(x):
    """
    Gamma function (as implemented and used in EMVORADO)
    """
    c1 = 76.18009173
    c2 = -86.50532033
    c3 = 24.01409822
    c4 = -1.231739516
    c5 = 0.120858003e-2
    c6 = -0.536382e-5
    stp = 2.50662827465

    tmp = x + 4.5
    p = stp * (1.0 + c1 / x + c2 / (x + 1.0) + c3 / (x + 2.0) +
               c4 / (x + 3.0) + c5 / (x + 4.0) + c6 / (x + 5.0))
    g_fct = p * np.exp((x - 0.5) * np.log(tmp) - tmp)
    return g_fct

def calc_n0_snow(qs, t, ageos):
    '''
    Snow n0 from temperature-dependent parametrization by Field05
    '''
    n0 = xr.zeros_like(qs) + 1e9

    quasi_zero = 1e-20
    T0C_fwo = 273.15
    zn0s1 = 13.5 * 5.65e5
    zn0s2 = -0.107
    mma = [5.065339, -0.062659, -3.032362, 0.029469, -0.000285, \
           0.312550,  0.000204,  0.003199, 0.000000, -0.015952]
    mmb = [0.476221, -0.015896,  0.165977, 0.007468, -0.000141, \
           0.060366,  0.000079,  0.000594, 0.000000, -0.003577]

    ztc = t.where(qs>=quasi_zero) - T0C_fwo
    ztc = ztc.where(ztc.fillna(-40.) >= -40., other = -40.).where(ztc.fillna(0.) <= 0., other = 0.) #!!! Added .fillna() otherwise the NaN values will be replaced
    ztc2 = ztc**2
    ztc3 = ztc**3

    nn  = 3
    nn2 = nn**2
    nn3 = nn**3

    hlp = mma[0]    +mma[1]*ztc    +mma[2]*nn     +mma[3]*ztc*nn+mma[4]*ztc2 \
        + mma[5]*nn2+mma[6]*ztc2*nn+mma[7]*ztc*nn2+mma[8]*ztc3  +mma[9]*nn3

    alf = 10.0**hlp

    bet = mmb[0]    +mmb[1]*ztc    +mmb[2]*nn     +mmb[3]*ztc*nn+mmb[4]*ztc2 \
        + mmb[5]*nn2+mmb[6]*ztc2*nn+mmb[7]*ztc*nn2+mmb[8]*ztc3  +mmb[9]*nn3

    m2s = qs.where(qs >= quasi_zero) / ageos
    m3s = alf*np.exp(bet*np.log(m2s))
    hlp = zn0s1*np.exp(zn0s2*ztc)
    zn0s = 13.50 * m2s**4 / m3s**3
    zn0s = np.maximum(zn0s,0.5*hlp)
    zn0s = np.minimum(zn0s,1e2*hlp)
    zn0s = np.minimum(zn0s,1e9)
    n0_s = np.maximum(zn0s,8e5)
    n0 = n0.where(qs < quasi_zero, other=n0_s) #!!! should this be n0_s or zn0s? (Jana uses  zn0s but then why is n0_s calculated?)
    return n0

def nice_mono_1mom(t,q):
    '''
    '''
    znimax_Thom  = 250.0e3
    tmelt        = 273.15

    #qn = N.zeros_like(q)
    #qn[q>0.0] = N.minimum(5.0 * N.exp(0.304*N.maximum(tmelt-t[q>0.0],0.0)), znimax_Thom)
    qn = np.minimum(5.0 * np.exp(0.304*np.maximum(tmelt-t,0.0)), znimax_Thom)
    return qn

def mgdparams_1mom(q, hymets=icon_hydromets(mom=1), t=None, qn_out=False):
    '''
    Derive non-constant MGD-PSD parameter lam (mu & nu & N0 set constant from
      ICON microphysics)
    '''
    mgd={}
    if ('snow' in q.keys()) or ('ice' in q.keys()):
      assert(t is not None), \
        "Model field 'temperature' required for mgd parameters of classes 'ice' and 'snow', but is missing"
    for key in ['ice','snow']:
      if key in q.keys():
        assert(t.shape==q[key].shape), \
          "Shape of model field 'temperature' inconsistent with field 'q' of class '%s'" %key
    for key in q:
        if key!='ice':
            # initialize
            mgd[key] = {}
            mgd[key]['mu']  = hymets[key]['mu']
            mgd[key]['nu']  = hymets[key]['nu']
            mgd[key]['n0']  = xr.zeros_like(q[key])
            # n0 of snow according to temperature-dependent parametrization by Field05
            if key=='snow':
                mgd[key]['n0'] = mgd[key]['n0'].where(q[key].fillna(0.)<=0., other = calc_n0_snow(q[key].where(q[key]>0.),
                                                                                      t.where(q[key]>0.),
                                                                                      hymets[key]['a']) )
            else:
                mgd[key]['n0'] = mgd[key]['n0'].where(q[key].fillna(0.)<=0., other = hymets[key]['n0'] )

            mgd[key]['lam'] = xr.ones_like(q[key])

            # precalc auxiliary parameters
            tmp2 = (mgd[key]['mu'] + hymets[key]['b'] + 1.0) / mgd[key]['nu']

            # calculate for valid (q)
            #!!! Added .fillna() to retain NaNs
            mgd[key]['lam'] = mgd[key]['lam'].where(q[key].fillna(0.) <= 0., other= ( \
                                           ( hymets[key]['a'] * mgd[key]['n0'].where(q[key]>0.) * gfct(tmp2) ) / \
                                           ( q[key].where(q[key]>0.) * mgd[key]['nu'] ) \
                                         )**(1.0/tmp2) )
        else:
            # Predict qn_ice dependent on temperature, then mimic a monodisperse size
            # distribution around a mean mass of q_i/n_i by using 2-mom mgd method and
            # very large values for ice['mu'] and ice['nu']
            qn = {'ice': nice_mono_1mom(t, q['ice'])}
            mgd['ice'] = mgdparams({'ice': q['ice']}, qn, {'ice': hymets['ice']})['ice']

    if qn_out:
        qn={}
        for key in q:
            tmp1 = (mgd[key]['mu'] + 1.0) / mgd[key]['nu']
            qn[key] = xr.ones_like(q[key]).where(q[key].fillna(0.) <= 0., other= #!!! not sure this is correct
                                                             mgd[key]['n0'].where(q[key]>0.) * gfct(tmp1) / \
                                                            (mgd[key]['n0'].where(q[key]>0.) * mgd[key]['lam']**tmp1)
                                                            )

        return mgd, qn
    else:
        return mgd

def mgdparams(q, qn, hymets=icon_hydromets()):
    """
    Derive non-constant MGD-PSD parameters N0 and lam (mu & nu set constant
    from ICON microphysics)
    """
    mgd = {}
    for key in q:
        # initialize
        mgd[key] = {}
        mgd[key]['mu']  = hymets[key]['mu']
        mgd[key]['nu']  = hymets[key]['nu']
        mgd[key]['n0']  = xr.zeros_like(q[key])
        mgd[key]['lam'] = xr.ones_like(q[key])

        # precalc auxiliary parameters
        tmp1 = (mgd[key]['mu'] + 1.0) / mgd[key]['nu']
        tmp2 = (mgd[key]['mu'] + hymets[key]['b'] + 1.0) / mgd[key]['nu']
        tmp3 = mgd[key]['nu'] / hymets[key]['b']
        gfct_tmp1 = gfct(tmp1)
        gfct_tmp2 = gfct(tmp2)
        tmp4 = hymets[key]['a'] * gfct_tmp2
        tmp5 = mgd[key]['nu'] / gfct_tmp1

        # calculate for valid (q,qn)
        mgd[key]['lam'] = mgd[key]['lam'].where( q[key].fillna(0.) <= 0., other=
                                               (
                                                ( tmp4 * qn[key].where(q[key] > 0.) ) /
                                                ( q[key].where(q[key] > 0.) * gfct_tmp1 )
                                               ) ** tmp3 )

        mgd[key]['n0'] = mgd[key]['n0'].where( q[key].fillna(0.) <= 0., other=
                                               qn[key].where(q[key] > 0.) * tmp5 * \
                                               mgd[key]['lam'].where(q[key] > 0.)** tmp1 )

    return mgd


def calc_moments(mgd, k=[0, 3, 4], hymets=icon_hydromets(), adjust=0):
    """
    Calculate (fields of) (Dmax-based) PSD moments from given constant (mu,nu)
    and qx/qnx derived fields of variable (N0,lam) MGD-parameters.
    Usage:
      k: list of moments to be computed
      adjust: Flag whether to zero out (all) k moments if one of them is 0.
            Beside for qx=0, mom[k]=0 might occur due to number accuracy
            limitations. So, to avoid different moments contributing
            differently to multi-PSD statistics, zero all remaining if one of
            them has number issues.
    """
    Mk = {}
    for key in mgd:
        Mk[key] = {}
        for kk in k:
            c1 = (hymets[key]['mu'] + kk + 1) / hymets[key]['nu']
            c2 = gfct(c1) / hymets[key]['nu']

            # initialize Mk[kk]
            Mk[key][kk] = xr.zeros_like(mgd[key]['n0'])

            # calculate Mk[kk] only if q, ie n0, is non-zero
            Mk[key][kk] = Mk[key][kk].where( mgd[key]['n0'].fillna(0.) <= 0., other=
                                                c2 * mgd[key]['n0'].where(mgd[key]['n0'] > 0.) / \
                                                mgd[key]['lam'].where(mgd[key]['n0'] > 0.) ** c1 )

        if adjust:
            for kk in k:
                for ik in k:
                    Mk[key][kk] = Mk[key][kk].where(Mk[key][ik] != 0., other=0.)
    return Mk


def calc_multimoments(Mk, inhm=['ice', 'snow', 'graupel', 'hail'],
                      outhm='totice'):
    Mk[outhm] = {}
    for hm in inhm:
        assert (hm in Mk.keys()), \
            'Class %s to accumulate moments not in input moments dict' % hm
    for kk in Mk[inhm[0]]:
        Mk[outhm][kk] = xr.zeros_like(Mk[inhm[0]][kk])
        for hm in inhm:
            Mk[outhm][kk] += Mk[hm][kk]
    return Mk


def calc_Dmean(Mk, meantype='vol'):
    k_needed = {'vol': [4, 3], 'mass': [3, 0]}
    assert(meantype in k_needed.keys()), 'Meantype "%s" unknown.' %meantype

    Dmean = {}
    for hm in Mk.keys():
        for k in k_needed[meantype]:
            assert(k in Mk[hm].keys()), \
              'Moment %i needed for meantype=%s, but not available for hymet %s' \
              %(k,meantype,hm)

        Dmean[hm] = xr.where(Mk[hm][k_needed[meantype][0]] > 0,
                             (Mk[hm][k_needed[meantype][0]] /
                              Mk[hm][k_needed[meantype][1]]).where(Mk[hm][3]>0.) ** #!!! This where condition is not on Julian S code
                             (1. / (k_needed[meantype][0] -
                                    k_needed[meantype][1])),
                             np.nan) #!!! In Julian S implementation the alternative value here is 0

    return Dmean

def calc_microphys(icon_fields, mom=2):
    """
    Calculate volumetric versions of qx and qnx and mean diameters.

    Parameters
    ----------
    icon_fields : xarray.Dataset
        Dataset with icon fields. Must include hydrometeors qx and qnx (if available),
        qv (water vapor content), temp (temperature), pres (pressure).
    mom : int
        Use 1- or 2- moment scheme.

    Returns
    -------
    icon_nc : xarray.Dataset
        A dataset with the same data as icon_fields and the calculated new fields.
    """
    icon_nc = icon_fields.copy()

    hymets = icon_hydromets(mom=mom)

    if mom>1:
      q_dens, qn_dens = adjust_icon_fields(icon_nc, hymets, mom=mom)
      multi_params = mgdparams(q_dens, qn_dens, hymets)
    else:
      q_dens, qn_dens = adjust_icon_fields(icon_nc, hymets, mom=mom)
      if "hail" in q_dens.keys(): del(q_dens["hail"]) # remove hail in case it is present
      t = icon_nc['temp']
      multi_params, qn_dens = mgdparams_1mom(q_dens, hymets, t=t, qn_out=True)

    moments = calc_moments(multi_params, hymets=hymets, adjust=1) #!!! Julian S uses adjust=0

    if mom>1:
        # Add totice, totliq and tot
        multimoments = calc_multimoments(moments)
        multimoments = calc_multimoments(multimoments, inhm=['cloud', 'rain'], outhm='totliq')
        multimoments = calc_multimoments(multimoments, inhm=['ice', 'snow', 'graupel', 'hail',
                                                             'cloud', 'rain'], outhm='tot')
    else:
        warnings.warn("WARNING calc_microphys: Results of 1-mom scheme are probably wrong (unrealistic D0 values)")
        multimoments = calc_multimoments(moments, inhm=['ice','snow','graupel'])
        multimoments = calc_multimoments(multimoments, inhm=['cloud', 'rain'], outhm='totliq')
        multimoments = calc_multimoments(multimoments, inhm=['ice', 'snow', 'graupel',
                                                             'cloud', 'rain'], outhm='tot')
    try:
        mean_volume_diameter = calc_Dmean(multimoments)
    except:
        warnings.warn("Calculation of Dm not possible")

    for hm in ['cloud', 'rain', 'ice', 'snow', 'graupel', 'hail']:
        try:
            icon_nc['vol_q' + hm[0]] = (q_dens[hm] * 1000).assign_attrs(
                dict( standard_name='volume ' +
                         " ".join(icon_nc['q' + hm[0]].long_name.split(" ")),
                    units='g m-3'))
        except:
            warnings.warn("Creation of vol_q"+hm[0]+" not possible")
        try:
            icon_nc['vol_qn' + hm[0]] = np.log10(qn_dens[hm]/1000).assign_attrs(
                dict( standard_name=
                         " ".join(icon_nc['qn' + hm[0]].long_name.split("_")) +
                              ' per volume',
                    units='log10(1/L)'))
        except:
            warnings.warn("Creation of vol_qn"+hm[0]+" not possible")
        try:
            icon_nc['Dm_' + hm[0]] = (mean_volume_diameter[hm]*1000).assign_attrs(
                    dict(standard_name='mean volume diameter of ' +
                                     " ".join(icon_nc['q' + hm[0]].long_name.split(" ")[1:-1]),
                         units='mm'))
        except:
            warnings.warn("Creation of Dm_"+hm[0]+" not possible")

    # Generate vol_qtotice, vol_qtotliq and vol_qtot

    vol_qtotice = icon_nc["vol_qi"].copy()
    comment = "vol_qi"
    for hm in ['snow', 'graupel', 'hail']:
        if 'vol_q' + hm[0] in icon_nc.keys():
            vol_qtotice += icon_nc['vol_q' + hm[0]].copy()
            comment += " + vol_q" + hm[0]

    icon_nc['vol_qtotice'] = vol_qtotice.assign_attrs( dict (
        standard_name='volume specific total ice water content',
        comments=comment,
        units='g m-3'))

    icon_nc['vol_qtotliq'] = (icon_nc["vol_qc"] + icon_nc["vol_qr"] ).assign_attrs( dict (
        standard_name='volume specific total liquid water content',
        comments="vol_qc + vol_qr",
        units='g m-3'))

    icon_nc['vol_qtot'] = (icon_nc["vol_qtotice"] + icon_nc["vol_qtotliq"] ).assign_attrs( dict (
        standard_name='volume specific total water content',
        comments="vol_qtotice + vol_qtotliq",
        units='g m-3'))

    # Generate vol_qntotice, vol_qntotliq and vol_qntot

    try:
        vol_qntotice = qn_dens["ice"].copy()
        comment = "vol_qni"
        for hm in ['snow', 'graupel', 'hail']:
            if 'vol_qn' + hm[0] in icon_nc.keys():
                vol_qntotice += qn_dens[hm].copy()
                comment += " + vol_qn" + hm[0]
        icon_nc['vol_qntotice'] = np.log10(vol_qntotice/1000).assign_attrs( dict (
            standard_name='number concentration total ice water content per volume',
            comments=comment,
            units='log10(1/L)'))
    except:
        warnings.warn("Creation of vol_qntotice not possible")

    try:
        icon_nc['vol_qntotliq'] = np.log10((qn_dens["cloud"] + qn_dens["rain"] )/1000).assign_attrs( dict (
            standard_name='number concentration total liquid water content per volume',
            comments="vol_qnc + vol_qnr",
            units='log10(1/L)'))
    except:
        warnings.warn("Creation of vol_qntotliq not possible")

    try:
        icon_nc['vol_qntot'] = np.log10((vol_qntotice + qn_dens["cloud"] + qn_dens["rain"] )/1000).assign_attrs( dict (
            standard_name='number concentration total water content per volume',
            comments="vol_qntotice + vol_qntotliq",
            units='log10(1/L)'))
    except:
        warnings.warn("Creation of vol_qntot not possible")

    # Generate Dm_totice, Dm_totliq and Dm_tot

    try:
        icon_nc['Dm_totice'] = (mean_volume_diameter['totice'] *1000).assign_attrs(dict(
            units='mm'))
    except:
        warnings.warn("Creation of Dm_totice not possible")

    try:
        icon_nc['Dm_totliq'] = (mean_volume_diameter['totliq'] *1000).assign_attrs(dict(
            standard_name='mean volume diameter of total liquid',
            units='mm'))
    except:
        warnings.warn("Creation of Dm_totliq not possible")

    try:
        icon_nc['Dm_tot'] = (mean_volume_diameter['tot'] *1000).assign_attrs(dict(
            standard_name='mean volume diameter of total',
            units='mm'))
    except:
        warnings.warn("Creation of Dm_tot not possible")

    return icon_nc

#testing fields
'''
ff = "/automount/realpep/upload/jgiles/ICON_EMVORADO_radardata/eur-0275_iconv2.6.4-eclm-parflowv3.12_wfe-case/2020/2020-01/2020-01-02/pro/vol/cdfin_allsim_id-010392_*_volscan"
data = utils.load_emvorado_to_radar_volume(ff, rename=True)
radar_volume=data.copy()

ff_icon = "/automount/realpep/upload/jgiles/ICON_EMVORADO_test/eur-0275_iconv2.6.4-eclm-parflowv3.12_wfe-case/run/iconemvorado_2020010222/out_EU-R13B5_inst_DOM01_ML_20200102T220000Z_1h.nc"
ff_icon_z = '/automount/realpep/upload/jgiles/ICON_EMVORADO_test/eur-0275_iconv2.6.4-eclm-parflowv3.12_wfe-case/run/iconemvorado_2020010222/out_EU-R13B5_constant_20200102T220000Z.nc'

ff_icon = "/automount/data02/agradar/jgiles/out_EU-R13B5_inst_DOM01_ML_20200102T220000Z_1h.nc"
ff_icon_z = '/automount/data02/agradar/jgiles/out_EU-R13B5_constant_20200102T220000Z.nc'

icon_field = utils.load_icon(ff_icon, ff_icon_z)

'''

def calc_microphys_nocloud(icon_fields, mom=2):
    """
    Same as calc_microphys but without considering qc and qnc.
    Calculate volumetric versions of qx and qnx and mean diameters.

    Parameters
    ----------
    icon_fields : xarray.Dataset
        Dataset with icon fields. Must include hydrometeors qx and qnx (if available),
        qv (water vapor content), temp (temperature), pres (pressure).
    mom : int
        Use 1- or 2- moment scheme.

    Returns
    -------
    icon_nc : xarray.Dataset
        A dataset with the same data as icon_fields and the calculated new fields.
    """
    icon_nc = icon_fields.copy()

    hymets = icon_hydromets(mom=mom)

    if mom>1:
      q_dens, qn_dens = adjust_icon_fields(icon_nc, hymets, mom=mom)
      multi_params = mgdparams(q_dens, qn_dens, hymets)
    else:
      q_dens, qn_dens = adjust_icon_fields(icon_nc, hymets, mom=mom)
      if "hail" in q_dens.keys(): del(q_dens["hail"]) # remove hail in case it is present
      t = icon_nc['temp']
      multi_params, qn_dens = mgdparams_1mom(q_dens, hymets, t=t, qn_out=True)

    moments = calc_moments(multi_params, hymets=hymets, adjust=1) #!!! Julian S uses adjust=0

    if mom>1:
        # Add totice, totliq and tot
        multimoments = calc_multimoments(moments)
        multimoments = calc_multimoments(multimoments, inhm=['rain'], outhm='totliq')
        multimoments = calc_multimoments(multimoments, inhm=['ice', 'snow', 'graupel', 'hail',
                                                             'rain'], outhm='tot')
    else:
        warnings.warn("WARNING calc_microphys: Results of 1-mom scheme are probably wrong (unrealistic Dm values)")
        multimoments = calc_multimoments(moments, inhm=['ice','snow','graupel'])
        multimoments = calc_multimoments(multimoments, inhm=['rain'], outhm='totliq')
        multimoments = calc_multimoments(multimoments, inhm=['ice', 'snow', 'graupel',
                                                             'rain'], outhm='tot')
    try:
        mean_volume_diameter = calc_Dmean(multimoments)
    except:
        warnings.warn("Calculation of Dm not possible")

    for hm in ['rain', 'ice', 'snow', 'graupel', 'hail']:
        try:
            icon_nc['vol_q' + hm[0]] = (q_dens[hm] * 1000).assign_attrs(
                dict( standard_name='volume ' +
                         " ".join(icon_nc['q' + hm[0]].long_name.split(" ")),
                    units='g m-3'))
        except:
            warnings.warn("Creation of vol_q"+hm[0]+" not possible")
        try:
            icon_nc['vol_qn' + hm[0]] = np.log10(qn_dens[hm]/1000).assign_attrs(
                dict( standard_name=
                         " ".join(icon_nc['qn' + hm[0]].long_name.split("_")) +
                              ' per volume',
                    units='log10(1/L)'))
        except:
            warnings.warn("Creation of vol_qn"+hm[0]+" not possible")
        try:
            icon_nc['Dm_' + hm[0]] = (mean_volume_diameter[hm]*1000).assign_attrs(
                    dict(standard_name='mean volume diameter of ' +
                                     " ".join(icon_nc['q' + hm[0]].long_name.split(" ")[1:-1]),
                         units='mm'))
        except:
            warnings.warn("Creation of Dm_"+hm[0]+" not possible")

    # Generate vol_qtotice, vol_qtotliq and vol_qtot

    vol_qtotice = icon_nc["vol_qi"].copy()
    comment = "vol_qi"
    for hm in ['snow', 'graupel', 'hail']:
        if 'vol_q' + hm[0] in icon_nc.keys():
            vol_qtotice += icon_nc['vol_q' + hm[0]].copy()
            comment += " + vol_q" + hm[0]

    icon_nc['vol_qtotice'] = vol_qtotice.assign_attrs( dict (
        standard_name='volume specific total ice water content',
        comments=comment,
        units='g m-3'))

    icon_nc['vol_qtotliq'] = (icon_nc["vol_qr"] ).assign_attrs( dict (
        standard_name='volume specific total liquid water content',
        comments="vol_qr",
        units='g m-3'))

    icon_nc['vol_qtot'] = (icon_nc["vol_qtotice"] + icon_nc["vol_qtotliq"] ).assign_attrs( dict (
        standard_name='volume specific total water content',
        comments="vol_qtotice + vol_qtotliq",
        units='g m-3'))

    # Generate vol_qntotice, vol_qntotliq and vol_qntot

    try:
        vol_qntotice = qn_dens["ice"].copy()
        comment = "vol_qni"
        for hm in ['snow', 'graupel', 'hail']:
            if 'vol_qn' + hm[0] in icon_nc.keys():
                vol_qntotice += qn_dens[hm].copy()
                comment += " + vol_qn" + hm[0]
        icon_nc['vol_qntotice'] = np.log10(vol_qntotice/1000).assign_attrs( dict (
            standard_name='number concentration total ice water content per volume',
            comments=comment,
            units='log10(1/L)'))
    except:
        warnings.warn("Creation of vol_qntotice not possible")

    try:
        icon_nc['vol_qntotliq'] = np.log10(( qn_dens["rain"] )/1000).assign_attrs( dict (
            standard_name='number concentration total liquid water content per volume',
            comments="vol_qnr",
            units='log10(1/L)'))
    except:
        warnings.warn("Creation of vol_qntotliq not possible")

    try:
        icon_nc['vol_qntot'] = np.log10((vol_qntotice + qn_dens["rain"] )/1000).assign_attrs( dict (
            standard_name='number concentration total water content per volume',
            comments="vol_qntotice + vol_qntotliq",
            units='log10(1/L)'))
    except:
        warnings.warn("Creation of vol_qntot not possible")

    # Generate Dm_totice, Dm_totliq and Dm_tot

    try:
        icon_nc['Dm_totice'] = (mean_volume_diameter['totice'] *1000).assign_attrs(dict(
            standard_name='mean volume diameter of total ice',
            units='mm'))
    except:
        warnings.warn("Creation of Dm_totice not possible")

    try:
        icon_nc['Dm_totliq'] = (mean_volume_diameter['totliq'] *1000).assign_attrs(dict(
            standard_name='mean volume diameter of total liquid',
            units='mm'))
    except:
        warnings.warn("Creation of Dm_totliq not possible")

    try:
        icon_nc['Dm_tot'] = (mean_volume_diameter['tot'] *1000).assign_attrs(dict(
            standard_name='mean volume diameter of total',
            units='mm'))
    except:
        warnings.warn("Creation of Dm_tot not possible")

    return icon_nc

#### Vapor pressure and Relative humidity calculations
# According to ERA5 IFS Documentation CY49R1 - Part IV: Physical Processes (version 11/2024)
# https://www.ecmwf.int/en/elibrary/81626-ifs-documentation-cy49r1-part-iv-physical-processes

def saturation_vapor_pressure_water(T):
    return 611.21 * xr.ufuncs.exp(17.502 * (T - 273.16) / (T - 32.19))

def saturation_vapor_pressure_ice(T):
    return 611.21 * xr.ufuncs.exp(22.587 * (T - 273.16) / (T + 0.7))

def mixed_phase_parameter(T, T0 = 273.16, Tice = 250.16):
    return ( ((T - Tice)/(T0 - Tice))**2 ).where(T > Tice, other=0.).where(T < T0, other=1.)

def saturation_vapor_pressure_mixed(e_sw, e_si, alpha):
    return alpha*e_sw + (1-alpha)*e_si

def vapor_pressure(p, q):
    # pressure in Pa
    epsilon = 0.621981
    epsilon_ = 1/epsilon
    return p*q*epsilon_ / (1 + q*(epsilon_ - 1))

def relative_humidity(e, e_s):
    return e/e_s

def relative_humidity_water_ice(RH, T):
    '''
    Calculate the relative humidity with regards to water and ice separately
    from the general relative humidity and temperature.

    RH must be in fractional units (between 0 and 1)
    T must be in Kelvin

    Returns two objects, RH_w and RH_i separately.
    '''

    e_sw = saturation_vapor_pressure_water(T)
    e_si = saturation_vapor_pressure_ice(T)
    alpha = mixed_phase_parameter(T)
    e_sm = saturation_vapor_pressure_mixed(e_sw, e_si, alpha)
    e = RH * e_sm
    return e/e_sw, e/e_si