An adaptive variance adjusting strategy for the climatological background error covariance matrix based on deep reinforcement learning

Precision in the initial state is pivotal for the prediction accuracy of numerical weather prediction models. A mature method for providing the initial state, variational data assimilation (VarDA) relies notably on a climatological background error covariance matrix, especially its diagonal, which encapsulates variance information. Nevertheless, variance estimation often contains errors, and current adjustment methods are manual or semi-adaptive. In this paper, an innovative adaptive strategy for adjusting variance, based on deep reinforcement learning is proposed. Harnessing the robust data-sensing capabilities of deep learning alongside the adept decision-making skills of reinforcement learning, our strategy aims to optimize assimilation performance by end-to-end learning from sensing VarDA state input to generating a variance-adjusted vector as output. Numerical experiments on the Lorenz96 model demonstrate that the initial state generated by the VarDA system adjusted by our method exhibits almost consistently the lowest climatological root mean square error compared to state-of-the-art methods, regardless of the quality of observations. With the initial state more aligned with the dynamic properties of the forecast model, the prediction capabilities of the experimental forecast model are enhanced to two Lyapunov times and the mean days of available forecast to the model are maximal in a one-month cycle statistic.