On‐line machine‐learning forecast uncertainty estimation for sequential data assimilation

Abstract

Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on multiple model integrations. However, this approach is demanding in terms of computations and development. In this work, a machine-learning method is presented based on convolutional neural networks that estimates the state-dependent forecast uncertainty represented by the forecast error covariance matrix using a single dynamical model integration. This is achieved by the use of a loss function that takes into account the fact that the forecast errors are heteroscedastic. The performance of this approach is examined within a hybrid data assimilation method that combines a Kalman-like analysis update and the machine-learning-based estimation of a state-dependent forecast error covariance matrix. Observing system simulation experiments are conducted using the Lorenz´96 model as a proof-of-concept. The promising results show that the machine-learning method is able to predict precise values of the forecast covariance matrix in relatively high-dimensional states. Moreover, the hybrid data assimilation method shows similar performance to the ensemble Kalman filter, outperforming it when the ensembles are relatively small.