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There is growing interest in data-driven weather prediction (DDWP), forexample using convolutional neural networks such as U-NETs that are trained ondata from models or reanalysis. Here, we propose 3 components to integrate withcommonly used DDWP models in order to improve their physical consistency andforecast accuracy. These components are 1) a deep spatial transformer added tothe latent space of the U-NETs to preserve a property called equivariance,which is related to correctly capturing rotations and scalings of features inspatio-temporal data, 2) a data-assimilation (DA) algorithm to ingest noisyobservations and improve the initial conditions for next forecasts, and 3) amulti-time-step algorithm, which combines forecasts from DDWP models withdifferent time steps through DA, improving the accuracy of forecasts at shortintervals. To show the benefit/feasibility of each component, we usegeopotential height at 500~hPa (Z500) from ERA5 reanalysis and examine theshort-term forecast accuracy of specific setups of the DDWP framework. Resultsshow that the equivariance-preserving networks (U-STNs) clearly outperform theU-NETs, for example improving the forecast skill by $45\%$. Using a sigma-pointensemble Kalman (SPEnKF) algorithm for DA and U-STN as the forward model, weshow that stable, accurate DA cycles are achieved even with high observationnoise. The DDWP+DA framework substantially benefits from large ($O(1000)$)ensembles that are inexpensively generated with the data-driven forward modelin 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.

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