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Introduction

In ERA5, geopotential (z) is provided at the surface, but not on individual model levels (ml). However, geopotential on model levels can be computed using the procedure described below.

Inputs:

• geopotential (z) at the surface
• logarithm of surface pressure (lnsp)
• temperature and specific humidity on all the model levels

Output: Geopotential for each level, in m²/s². To get the height in metres, divide the geopotential by the gravity constant 9.80665 m/s².

In the procedure below the output data is written in GRIB format.

Note, this procedure is an approximation to the calculation in the IFS, which also takes account of the effects of cloud ice and water and rain and snow.

Prerequisites

You will need:

• A computer running Linux
• Python 2.7 or later

• Your computer must be set up for downloading ERA5 model level data (from the 'reanalysis-era5-complete' dataset, stored in ECMWF's MARS catalogue) through the CDS API. For details, please follow the instructions here (step C).

• The ecCodes library to read and write data. Get ecCodes here.

Step 1: Download input data

First we retrieve the required ERA5 data. We need:

• Temperature (t) and specific humidity (q) on each model level.
• The logarithm of surface pressure (lnsp) and geopotential (z)

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

1. Copy the script below to a text editor
2. Amend 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

#!/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://software.ecmwf.int/wiki/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')

The script produces two files in the current working directory:

• 'tq_ml.grib' (a GRIB file containing temperature and specific humidity)
• 'zlnsp_ml.grib' (a GRIB file containing geopotential and log of surface pressure).

Step 2: Compute geopotential on model levels

We then use a Python script to compute geopotential (z) for all model levels:

1. Copy the script below to a text editor
2. Save the script as 'compute_geopotential_on_ml.py'
3. Run the script 'compute_geopotential_on_ml.py' with the correct arguments, i.e. :  python compute_geopotential_on_ml.py tq_ml.grib zlnsp_ml.grib -o z_on_ml.grib

This script is from ECMWF's generic article Compute geopotential on model levels .

Alternatively, there is a customer-supplied script that computes geopotential on model levels from NetCDF files (i.e. works on Microsoft Windows), and for a specific location. This script was written for the ERA-Interim dataset, but can be adapted to ERA5. Please see the article ERA-Interim: compute geopotential on model levels for details.

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