Data-Driven Equation Discovery of a Cloud Cover Parameterization

A hierarchical modeling framework to discover new machine learning-based equations for cloud cover, including symbolic regression

Grundner, A., Beucler, T., Gentine, P., & Eyring, V. (2023). Data-Driven Equation Discovery of a Cloud Cover Parameterization. Preprint

Author: Arthur Grundner, arthur.grundner@dlr.de

The current release on zenodo can be found here:

List of Figures

• Fig 1, Code: Comparison of the coarse-grained DYAMOND and ERA5 data
• Fig 2, Code: All cloud cover schemes in a performance x complexity plot
• Fig 3, Code: Predicted cloud cover distributions
• Fig 4, Code: Transfer to higher resolutions
• Fig 5.1, Code: Transfer learning to ERA5 data (selected schemes)
• Fig 5.2, Code: Transfer learning to ERA5 data (polynomials & NNs)
• Fig 6.1, Code: Plots of the terms I_1, I_2, I_3
• Fig 6.2, Code: Conditional average w.r.t. RH and T
• Fig 6.3, Code: Conditional average w.r.t. dzRH
• Fig 7.1, Code: Contour plot of dzRH
• Fig 7.2, Code: Cloud cover w.r.t. RH with and without modification to satisfy the RH-physical constraint
• Fig 8, Code: Ablation study of our analytic scheme on DYAMOND and ERA5 data
• Fig A1.1, Fig A1.2, Fig A1.3, Fig A1.4, Fig A1.5, Fig A1.6, Code: Maps of I1, I2, I3 on a specific vertical layer on ~1490m averaged over 10 days of DYAMOND data. Maps of the a5-term on three different altitudes
• Fig B1.1, Fig B1.2, Code: The distributions of cloud water and cloud ice on storm-resolving scales

Data

To reproduce the results it is first necessary to have access to accounts on DKRZ/Levante. Then one can coarse-grain and preprocess the DYAMOND and ERA5/ERA5.1 data sets:

• Guide for how to coarse-grain the DYAMOND data: strategy.md
• To then pre-process the DYAMOND data: preprocessing.ipynb
• Scripts to coarse-grain ERA5 data (1979-2021, first day of every quarter): horizontally, vertically

It suffices to coarse-grain the variables: clc/cc, cli/ciwc, clw/clwc, hus/q, pa, ta/t, ua/u, va/v, zg/z

Dependencies

The results were produced with the version numbers indicated below:

• PySR 0.10.1 [https://github.com/MilesCranmer/PySR]
• GP-GOMEA [https://github.com/marcovirgolin/GP-GOMEA]
• mlxtend 0.20.0 [https://github.com/rasbt/mlxtend]
• scikit-learn 1.0.2 [https://scikit-learn.org/]
• SymPy 1.10.1 [https://github.com/sympy]
• SciPy 1.8.1 [https://github.com/scipy/]
• TensorFlow 2.7.0 [https://tensorflow.org/]

To create a working environment you can run the following line:

conda install -c conda-forge tensorflow==2.7.0 scipy==1.8.1 sympy==1.10.1 scikit-learn==1.0.2 mlxtend==0.20.0 pysr==0.10.1

To install the GP-GOMEA dependency please refer to their website.

License

This code is released under Apache 2.0. See LICENSE for more information.