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Illustrations of model levels, model half levels and model layers

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Figure 1. An illustration of IFS model levels, showing
how they follow the terrain near the surface of the
Earth. Level=1 is near the top of the atmosphere
and Level=137 is near the surface of the Earth. The
left hand axes are altitude (km) and pressure (hPa),
while the right hand axis is level number.

Figure 2. An illustration of IFS model levels, model half-levels and model layers. The pressure
on model levels is in the middle of the layers defined by the model half
levels immediately above and below. The uppermost layer is adjacent to the
top of the atmosphere (where p=0), while the lowest layer is adjacent to the
surface of the Earth (where p=sp).

Geopotential on model levels

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We use a Python script to download the ERA5 data from the MARS catalogue using the CDS API. The procedure is:

  1. Copy the script below to a text editor on your computer
  2. Edit the date, type, step, time, grid and area in the script to meet your requirements
  3. Save the script (for example with the filename as 'get_data_geopotential_on_ml.py')
  4. Run the script
Code Block
languagepy
titlePython script to download ERA5 data NOT listed in CDS through CDS API
linenumberstrue
collapsetrue
#!/usr/bin/env python
import cdsapi
c = cdsapi.Client()

# data download specifications:
cls     = "ea"         # do not change
expver  = "1"          # do not change
levtype = "ml"         # do not change
stream  = "oper"       # do not change
date    = "2018-01-01" # date: Specify a single date as "2018-01-01" or a period as "2018-08-01/to/2018-01-31". For periods > 1 month see https://confluence.ecmwf.int/x/l7GqB
tp      = "an"         # type: Use "an" (analysis) unless you have a particular reason to use "fc" (forecast).
time    = "00:00:00"   # time: ERA5 data is hourly. Specify a single time as "00:00:00", or a range as "00:00:00/01:00:00/02:00:00" or "00:00:00/to/23:00:00/by/1".

c.retrieve('reanalysis-era5-complete', {
    'class'   : cls,
    'date'    : date,
    'expver'  : expver,
    'levelist': '1/2/3/4/5/6/7/8/9/10/11/12/13/14/15/16/17/18/19/20/21/22/23/24/25/26/27/28/29/30/31/32/33/34/35/36/37/38/39/40/41/42/43/44/45/46/47/48/49/50/51/52/53/54/55/56/57/58/59/60/61/62/63/64/65/66/67/68/69/70/71/72/73/74/75/76/77/78/79/80/81/82/83/84/85/86/87/88/89/90/91/92/93/94/95/96/97/98/99/100/101/102/103/104/105/106/107/108/109/110/111/112/113/114/115/116/117/118/119/120/121/122/123/124/125/126/127/128/129/130/131/132/133/134/135/136/137',         # For each of the 137 model levels
    'levtype' : 'ml',
    'param'   : '130/133', # Temperature (t) and specific humidity (q)
    'stream'  : stream,
    'time'    : time,
    'type'    : tp,
	'grid'    : [1.0, 1.0], # Latitude/longitude grid: east-west (longitude) and north-south resolution (latitude). Default: 0.25 x 0.25
	'area'	  : area, #example: [60, -10, 50, 2], # North, West, South, East. Default: global
}, 'tq_ml.grib')


c.retrieve('reanalysis-era5-complete', {
    'class'   : cls,
    'date'    : date,
    'expver'  : expver,
    'levelist': '1',       # Geopotential (z) and Logarithm of surface pressure (lnsp) are 2D fields, archived as model level 1
    'levtype' : levtype,
    'param'   : '129/152', # Geopotential (z) and Logarithm of surface pressure (lnsp) 
    'stream'  : stream,
    'time'    : time,
    'type'    : tp,
	'grid'    : [1.0, 1.0], # Latitude/longitude grid: east-west (longitude) and north-south resolution (latitude). Default: 0.25 x 0.25
	'area'	  : area, #example: [60, -10, 50, 2], # North, West, South, East. Default: global
}, 'zlnsp_ml.grib')

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For users experienced in Metview, there is a built-in function called mvl_geopotential_on_ml.

Interpolation of variables from model levels to custom pressure levels

The procedure described below is to convert ERA5 model levels data to custom pressure levels data.

Input:

  • variable(s) on model levels and related logarithm surface pressure in grib format
  • list of custom pressure levels required for interpolation to.

Output: NetCDF file containing variable(s) at each custom pressure level

Prerequisites for interpolating variables on model levels to custom pressure levels

You will need:

Step 1: Download input data

First the required ERA5 variable(s) on model levels data are downloaded. The suggested procedure is:

  1. Copy the script below to a text editor on your computer
  2. Edit the date, type, step, time and grid in the script to meet your requirements. Note the 'area' keyword can also be used. The output filename can be modified accordingly.
  3. Save the script (for example with the filename as 'get_data.py')
  4. Run the script i.e. python3 get_data.py
Code Block
languagepy
titleget_data
collapsetrue
# **************************** LICENSE START ***********************************
#
# Copyright 2022 ECMWF. This software is distributed under the terms
# of the Apache License version 2.0. In applying this license, ECMWF does not
# waive the privileges and immunities granted to it by virtue of its status as
# an Intergovernmental Organization or submit itself to any jurisdiction.
#
# ***************************** LICENSE END ************************************
import cdsapi

c = cdsapi.Client()

c.retrieve('reanalysis-era5-complete', {

    'class': 'ea',

    'date': '2021-01-01',

    'expver': '1',

    'levelist':'1/to/137',

    'levtype': 'ml',

    'param': '130/152',

    'step': '0',

    'stream': 'oper',

    'time': '00/to/06/by/1',

    'type': 'an',

    'grid': '1.0/1.0'

}, 'output_00_06_130_152_1x1.grib')

Running the script produces a file in the current working directory called 'output_00_06_130_152_1x1.grib' (a GRIB file containing the ERA5 variables needed.). 

Step 2: Interpolate variables on model levels to custom pressure levels

The suggested procedure to run the Python script to compute the conversion of the variable from model levels to the custom pressure level is:

  1. Copy the script below to a text editor
  2. Save the script as 'conversion_from_ml_to_pl.py'
  3. Run the script 'conversion_from_ml_to_pl.py' with the correct arguments, i.e. :  python3 conversion_from_ml_to_pl.py -p 70000 -o output.nc -i output_00_06_130_152_1x1.grib
Code Block
languagepy
titleconversion_from_ml_to_pl.py
collapsetrue
# **************************** LICENSE START ***********************************
#
# Copyright 2022 ECMWF. This software is distributed under the terms
# of the Apache License version 2.0. In applying this license, ECMWF does not
# waive the privileges and immunities granted to it by virtue of its status as
# an Intergovernmental Organization or submit itself to any jurisdiction.
#
# ***************************** LICENSE END ************************************


import cfgrib
import xarray as xr
import numpy as np
from eccodes import *
import matplotlib.pyplot as plt
import argparse
import sys
import os

def parse_args():
    ''' Parse program arguments using ArgumentParser'''
    parser = argparse.ArgumentParser(description ="Python tool to calculate the model level variable at a given pressure level and write data to a netCDF file")         
    parser.add_argument('-p', '--pressure', required=True, nargs='+',type=float,
                        help='Pressure levels (Pa) to calculate the variable')
    parser.add_argument('-o', '--output', required=False, help='name of the output file (default "output.nc"')
    parser.add_argument('-i', '--input', required=True, metavar='input.grib', type=str,
                        help=('grib file with required variable(s) on model level and surface pressure fields',
                              'the model levels'))
    args = parser.parse_args()
    if not args.output:
        args.output = 'output.nc' 
    return args

def get_input_variable_list(fin):
    f = open(fin)
    var_list = []
    while 1:
        gid = codes_grib_new_from_file(f)
        if gid is None:
            break
        keys = ('dataDate', 'dataTime', 'shortName')
        for key in keys:
            if key == 'shortName':
              var_list.append(codes_get(gid, key))
        codes_release(gid)
    var_list_unique = list(set(var_list))
    f.close()
    if 'lnsp' not in var_list_unique:
      print("Error - lnsp variable missing from input file -exiting")
      sys.exit()
    if len(var_list_unique) < 2:
      print("Error - Data variable missing from input file -exiting")
      sys.exit()
    return var_list_unique

def check_requested_levels(plevs):
    check_lev = True
    if len(plevs) > 1:
        error_msg = "Error - only specify 1 input pressure level to interpolate to"
    else:
        for lev in plevs:
           if lev < 0 or lev > 110000 :
              check_lev = False
              error_msg = "Error - negative values and large positive values for pressure are not allowed -exiting"
    if check_lev == False:
        print(error_msg)  
        sys.exit()    
    return check_lev

def check_in_range(data_array,requested_levels):
    amin = data_array.minimum()
    amax = data_array.maximum()
    print("min max ",amin,amax)          


def vertical_interpolate(vcoord_data, interp_var, interp_levels):
    """A function to interpolate sounding data from each station to
    every millibar. Assumes a log-linear relationship.

    Input
    -----
    vcoord_data : A 1D array of vertical level values (e.g., pressure from a radiosonde)
    interp_var : A 1D array of the variable to be interpolated to all pressure levels
    vcoord_interp_levels : A 1D array containing veritcal levels to interpolate to

    Return
    ------
    interp_data : A 1D array that contains the interpolated variable on the interp_levels
    """
    l_count = 0
    for l in interp_levels:
      if l < np.min(vcoord_data) or l > np.max(vcoord_data):
          interp_data[l_count] = np.NAN           
    # Make vertical coordinate data and grid level log variables
    lnp = np.log(vcoord_data)
    lnp_intervals = [np.log(x) for x in interp_levels]
    # Use numpy to interpolate from observed levels to grid levels
    interp_data = np.interp(lnp_intervals, lnp, interp_var)
    return interp_data[0]

def calculate_pressure_on_model_levels(ds_var,ds_lnsp):
    # Get the number of model levels in the input variable 
    nlevs=ds_var.sizes['hybrid']
    # Get the a and b coefficients from the pv array to calculate the model level pressure 
    pv_coeff = np.array(ds_var.GRIB_pv)
    pv_coeff=pv_coeff.reshape(2,nlevs+1)
    a_coeff=pv_coeff[0,:]
    b_coeff=pv_coeff[1,:]
    # get the surface pressure in hPa
    sp = np.exp(ds_lnsp)
    p_half=[]
    for i in range(len(a_coeff)):  
        p_half.append(a_coeff[i] + b_coeff[i] * sp)
    p_ml=[]
    for hybrid in range(len(p_half) - 1):
        p_ml.append((p_half[hybrid + 1] + p_half[hybrid]) / 2.0)   
    ds_p_ml = xr.concat(p_ml, 'hybrid')
    return ds_p_ml

def plot_profile(var_ml,press_ml, var_int_press,var_int_plevs,tstep,lat,lon):

    var_v= var_ml.sel(time = var_ml.time[tstep],longitude=lon, latitude=lat, method='nearest')
    var_v_values = var_v.values
    var_p= press_ml.sel(time = var_ml.time[tstep],longitude=lon, latitude=lat, method='nearest')
    var_p_values = var_p.values
    var_ip= var_int_press.sel(time = var_ml.time[tstep],longitude=lon, latitude=lat, method='nearest')
    var_ip_values = var_ip.values 
    var_ip_p = var_ip.pressure
    var_ip_p_values = var_ip_p.values
    plt.axis([min(var_v_values), max(var_v_values), max(var_p_values), min(var_p_values)])
    plt.plot(var_v_values,var_p_values, 'o', color = 'black')
    plt.plot(var_ip_values,var_ip_p_values,'o', color = 'red')
    plt.show()
    return

def calculate_interpolated_pressure_field(data_var_on_ml, data_p_on_ml,plevs):
    nlevs = len(data_var_on_ml.hybrid)
    p_array = np.stack(data_p_on_ml, axis=2).flatten()
    # Flatten the data array to enable faster processing
    var_array = np.stack(data_var_on_ml, axis=2).flatten()
    no_grid_points =  int(len(var_array)/nlevs)
    interpolated_var = np.empty((len(plevs), no_grid_points))
    ds_shape = data_var_on_ml.shape
    nlats_values = data_var_on_ml.coords['latitude']
    nlons_values = data_var_on_ml.coords['longitude']
    nlats = len(nlats_values)
    nlons = len(nlons_values)
 
#     Iterate over the data, selecting one vertical profile at a time
    count = 0
    profile_count = 0
    interpolated_values=[]
    for point in range(no_grid_points):
        offset =  count*nlevs
        var_profile = var_array[offset:offset+nlevs]
        p_profile = p_array[offset:offset+nlevs]
        interpolated_values.append(vertical_interpolate(p_profile, var_profile, plevs))
        profile_count += len(p_profile)
        count = count + 1
    interpolated_field=np.asarray(interpolated_values).reshape(len(plevs),nlats,nlons)    
    return interpolated_field  

def check_data_cube(dc):
    checks = True
    for var_name in dc.variables:
        if var_name in ['time','step','hybrid','latitude','longitude','valid_time']:
            continue               
        if var_name == 'lnsp':
            lnsp_dims = ['time','latitude','longitude']
            if all(value in lnsp_dims for value in dc.variables[var_name].dims):
                continue
            else:
                print("Not all required lnsp dimensions found -exiting ", dc.variables[var_name].dims)
                checks = False
        else:
            var_dims = ['time','hybrid','latitude','longitude']
            if all(value in var_dims for value in dc.variables[var_name].dims):
                continue
            else:
                print("Not all required variable dimensions found -exiting ",dc.variables[var_name].dims)
                checks = False
            continue
    return checks

def main():
    '''Main function'''
    print("-p <pressure level (Pa) > -o <output_file> -i <input grib file>")
    print("e.g. to process a grib file containing 6 hours of lnsp and temperature data to the 500 hPa level:")
    print("python3 script.py -o output_press.nc -p 50000  -i output_00_06_130_152_1x1.grib`n")
    args = parse_args()
 
    print('Arguments: %s' % ", ".join(
        ['%s: %s' % (k, v) for k, v in vars(args).items()]))

    plevels = args.pressure
    plevels.sort(reverse = True) 

    check_requested_levels(plevels)

    input_fname = args.input 
    output_fname = args.output
    if not os.path.isfile(input_fname):
        print("Input file does not exist - exiting")
        sys.exit()
    variable_list = get_input_variable_list(input_fname)
    # Create a data object to hold the input and derived data
    data_cube = xr.merge(cfgrib.open_datasets(input_fname, backend_kwargs={'read_keys': ['pv']}), combine_attrs='override')
    if not check_data_cube(data_cube):
        sys.exit()
   # Get the ln surface pressure
    lnsp = data_cube['lnsp']
    for var in variable_list:
      if var == 'lnsp':
          continue
      else:
          data_cube['pml']=data_cube[var].copy()
          break
    for var in variable_list:
        if var == 'lnsp' :
            continue
        data_pressure_on_model_levels_list =[]
        for time_step in range(len(data_cube[var].time)):
            data_slice_var=data_cube[var][time_step,:,:,:]
            data_slice_lnsp=data_cube['lnsp'][time_step,:,:]
#   Get the pressure field on model levels for each timestep            
            data_cube['pml'][time_step,:,:,:] = calculate_pressure_on_model_levels(data_slice_var,data_slice_lnsp)
    data_cube['pml'].attrs = {'units' : 'Pa','long_name':'pressure','standard_name':'air_pressure','positive':'down'}
    all_interpolated_var_fields_list = []
    for var in variable_list:
        if var == 'lnsp' or var == 'pml':
            continue
        interpolated_var_field = data_cube[var].copy()
        interpolated_var_field = interpolated_var_field[:,0:len(plevels),:,:]
        interpolated_var_field = interpolated_var_field.rename({'hybrid':'pressure'})
        interpolated_var_field['pressure'] = plevels
        for time_step in range(len(data_cube[var].time)):
            var_on_ml = data_cube[var][time_step,:,:,:]
            p_on_ml = data_cube['pml'][time_step,:,:,:]
            interpolated_var_field[time_step,:,:,:] = calculate_interpolated_pressure_field(var_on_ml,p_on_ml,plevels)
        all_interpolated_var_fields_list.append(interpolated_var_field)
    all_interpolated_var_fields = xr.merge(all_interpolated_var_fields_list)   
    all_interpolated_var_fields['pressure'].attrs = {'units' : 'Pa','long_name':'pressure','standard_name':'air_pressure','positive':'down'}
    all_interpolated_var_fields.to_netcdf(output_fname)
#   Write interpolated data variable to output filename    
    PLOT_DATA = False     
    if PLOT_DATA:
        latitude = 45.0
        longitude = 0
        tstep =0
        plot_profile(data_cube[var],data_cube['pml'],interpolated_var_field,plevels,tstep,latitude,longitude)
    print("Finished interpolation of variables to pressure level")

if __name__ == '__main__':
    main()

This produces a netCDF file called 'output.nc' in the current directory containing the interpolated data.

Geopotential height

In ERA5, and often in meteorology, heights (the height of the land and sea surface, or specific heights in the atmosphere) are not represented as geometric height, or altitude (in metres above the spheroid), but as geopotential height (in metres above the geoid, which is represented by the mean sea level in ERA5). Note, that ECMWF usually archive the geopotential (in m2/s2), not the geopotential height.

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