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 heterodastic. 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.

本研究提出一种基于卷积神经网络的机器学习方法，利用单个动力学模型集成来对表示预测误差协方差矩阵的状态相关预测不确定性进行估计，并在杂交数据同化方法中进行性能测试，证明该方法能够相对精确地预测高维状态中的预测协方差矩阵值。