Imposing the Fundamental Dynamical Constraint of Hydrostatic Balance to Improve Global ML Weather Prediction

TL;DR

Incorporating the hydrostatic balance constraint into data-driven weather prediction models enhances forecast accuracy and physical realism, especially at longer lead times, without significant computational overhead.

Contribution

This work introduces a method to impose hydrostatic balance constraints in deep learning weather models, improving forecast skill and physical consistency.

Findings

Improved RMSE for forecast fields beyond 7-10 days.

Enhanced physical realism in hurricane forecast simulations.

No significant increase in computational resources required.

Abstract

Forecasting weather accurately and efficiently is a critical capability in our ability to adapt to climate change. Data driven approaches to this problem have enjoyed much success recently providing forecasts with accuracy comparable to physics based numerical prediction models but at significantly reduced computational expense. However, these models typically do not incorporate any physics priors. In this work, we demonstrate improved skill of data driven weather prediction approaches by incorporating physical constraints, specifically in the context of the DLWP model (Karlbauer et. al. 2024). Near hydrostatic balance, between the vertical pressure gradient and gravity, is one of the most fundamental and well satisfied constraints on atmospheric motions. We impose this balance through both hard and soft constraints, and demonstrate that the soft constraint improves the RMSE of many forecast fields, particularly at lead times beyond 7-10 days. The positive influence of hydrostatic balance is also clearly evident in improving the physicality and strength of a 10-day forecast for hurricane Irma. These results show that adding appropriate physical constraints can improve the skill and fidelity of data driven weather models in a way that does not impose any significant additional memory capacity or scalability challenges.