Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers

TL;DR

This paper introduces a physically consistent data-driven weather forecasting framework that integrates equivariance-preserving neural networks, data assimilation, and multi-time-step algorithms, significantly improving forecast accuracy and stability.

Contribution

It proposes a novel integration of deep spatial transformers with data assimilation and multi-time-step methods to enhance physical consistency and accuracy in data-driven weather prediction.

Findings

Equivariance-preserving networks outperform standard U-NETs by 45%.

Data assimilation with large ensembles improves forecast stability and accuracy.

Multi-time-step approach reduces forecast error by 2-3 times.

Abstract

There is growing interest in data-driven weather prediction (DDWP), for example using convolutional neural networks such as U-NETs that are trained on data from models or reanalysis. Here, we propose 3 components to integrate with commonly used DDWP models in order to improve their physical consistency and forecast accuracy. These components are 1) a deep spatial transformer added to the latent space of the U-NETs to preserve a property called equivariance, which is related to correctly capturing rotations and scalings of features in spatio-temporal data, 2) a data-assimilation (DA) algorithm to ingest noisy observations and improve the initial conditions for next forecasts, and 3) a multi-time-step algorithm, which combines forecasts from DDWP models with different time steps through DA, improving the accuracy of forecasts at short intervals. To show the benefit/feasibility of each component, we use geopotential height at 500~hPa (Z500) from ERA5 reanalysis and examine the short-term forecast accuracy of specific setups of the DDWP framework. Results show that the equivariance-preserving networks (U-STNs) clearly outperform the U-NETs, for example improving the forecast skill by $45\%$. Using a sigma-point ensemble Kalman (SPEnKF) algorithm for DA and U-STN as the forward model, we show that stable, accurate DA cycles are achieved even with high observation noise. The DDWP+DA framework substantially benefits from large ($O(1000)$) ensembles that are inexpensively generated with the data-driven forward model in each DA cycle. The multi-time-step DDWP+DA framework also shows promises, e.g., it reduces the average error by factors of 2-3.