Data-Driven Equation Discovery of a Cloud Cover Parameterization

TL;DR

This paper introduces a hierarchical framework combining symbolic regression, feature selection, and physical constraints to discover interpretable, accurate, and transferable equations for cloud cover parameterization in climate models.

Contribution

It presents a novel method that produces simple, interpretable equations for cloud cover, outperforming traditional schemes and neural networks in transferability and physical consistency.

Findings

Achieves $R^2=0.94$ comparable to neural networks

Reproduces cloud cover distributions more accurately than Xu-Randall scheme

Demonstrates superior transferability to ERA5 reanalysis data

Abstract

A promising method for improving the representation of clouds in climate models, and hence climate projections, is to develop machine learning-based parameterizations using output from global storm-resolving models. While neural networks can achieve state-of-the-art performance within their training distribution, they can make unreliable predictions outside of it. Additionally, they often require post-hoc tools for interpretation. To avoid these limitations, we combine symbolic regression, sequential feature selection, and physical constraints in a hierarchical modeling framework. This framework allows us to discover new equations diagnosing cloud cover from coarse-grained variables of global storm-resolving model simulations. These analytical equations are interpretable by construction and easily transferable to other grids or climate models. Our best equation balances performance and complexity, achieving a performance comparable to that of neural networks ($R^2=0.94$) while remaining simple (with only 11 trainable parameters). It reproduces cloud cover distributions more accurately than the Xu-Randall scheme across all cloud regimes (Hellinger distances $<0.09$), and matches neural networks in condensate-rich regimes. When applied and fine-tuned to the ERA5 reanalysis, the equation exhibits superior transferability to new data compared to all other optimal cloud cover schemes. Our findings demonstrate the effectiveness of symbolic regression in discovering interpretable, physically-consistent, and nonlinear equations to parameterize cloud cover.