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

• URL: http://arxiv.org/abs/2103.09360v1
• Date: Tue, 16 Mar 2021 23:15:00 GMT
• Title: Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers
• Authors: Ashesh Chattopadhyay, Mustafa Mustafa, Pedram Hassanzadeh, Eviatar Bach, Karthik Kashinath
• Abstract summary: We propose 3 components to integrate with commonly used data-driven weather prediction models. These components are 1) a deep spatial transformer added to latent space of U-NETs to preserve equivariance, 2) a data-assimilation algorithm to ingest noisy observations and improve the initial conditions for next forecasts, and 3) a multi-time-step algorithm, improving the accuracy of forecasts at short intervals.
• Score: 2.7998963147546148
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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