WTG-TM: The Weak Temperature Gradient forced Tropical Model

About

(c) 2026 RMIB - Climdyn - Dynamical Meteorology and Climatology

See LICENSE for license information.

This software is provided as supplementary material with:

• Vannitsem, S., and Demaeyer, J.: Emergence of chaos in the tropical atmosphere: Study of the Weak Temperature Gradient system. Submitted to Nonlinear Processes in Geophysics.

Please cite this article if you use (a part of) this software for a publication.

The authors would appreciate it if you could also send a reprint of your paper to jonathan.demaeyer@meteo.be and svn@meteo.be.

Consult the WTG-TM code repository for updates, and our website for additional resources.

Installation

Installing the scripts can be done using git:

git clone https://github.com/Climdyn/WTG-TM.git && cd WTG-TM

The code requires at least Python 3.10 and the LayerCake framework. In addition, the qgs model integrators and Lyapunov estimators are also used. To install LayerCake and qgs, the simplest way is to use pip. In a terminal, run:

pip install layercake-model
pip install qgs

and you are set. In addition, the generated Fortran codes need to be compiled, for example with GNU Fortran.

Finally, the generation of the movies requires the separate installation of FFmpeg.

Codes description

The model is defined first in the model_definition.py module, using the LayerCake syntax. This module is then imported in various scripts:

generate_fortran_code.py

Upon running

python generate_fortran_code.py

this code will generate a file WTG-TM_Heun.f90 with by default the equations of the model truncated at wavenumber 2. These equations are then integrated with the Heun algorithm to give the time evolution of the model. The Fortran code can then be compiled and run with:

gfortran WTG-TM_Heun.f90 && ./a.out

This result in a file evol_field.dat being produced, with the first column being the time, and the others being the spectral components $\psi_i$ of the fields. The default model resolution setup can be modified by editing the Python script. The parameters of the model can be changed by editing the generated Fortran code. Finally, the Fortran compiler used here is gfortran, but other compilers should work as well.

generate_ode_latex_equation.py

This code will generate and print the equations of the model in LaTeX. It was used to get the equations appearing in the manuscript above. By default, it will print the equations of the model truncated at wavenumber 2, but this can be changed by editing the script.

compute_trajectory.py

This code computes a trajectory of the model and saves it like the Fortran code does, but in addition it rescales the time in days. By default, it also generates a movie of the spatial fields of the model, saved in the file movie.mp4, but this can be deactivated. Again, by default, it will compute the model truncated at wavenumber 2, but this can be changed by editing the script. The forcing $\chi$ can also be changed using this script, while the more general model parameters can be changed by editing the model_definition.py module.

compute_lyapunov_spectrum.py

This script computes and plots the Lyapunov spectrum, using the qgs integrators. By default, it will compute this for the model truncated at wavenumber 2, but this can be changed by editing the script. The forcing $\chi$ of the model can also be changed this way. More general model parameters can be changed by editing the model_definition.py module.