A hybrid deep learning and data assimilation method for model error estimation

Forecast errors of numerical weather prediction consist of model errors and the growth of initial condition errors, while the initial condition is often optimized based on short-term forecasts. Thus it is difficult to untangle the initial condition error and model error, but it is essential to infer model errors not just for prediction but also for data assimilation (DA). A hybrid deep learning (DL) and DA method is proposed here, aiming to correct model errors. It uses a convolutional neural network (CNN) to extract characteristics of initial conditions and forecast errors, and then provides estimations for model errors. The CNN-based model error estimation method can consider the model error resulted from inaccurate model parameters, or simultaneously consider the model error and initial condition error. Based on the Lorenz05 model, offline and online experiments demonstrate that the CNN-based model error estimation method can effectively correct model errors resulted from inaccurate model parameters, including the forcing F, coupling coefficient c, and relative scale b. For both online and offline model error estimations, simultaneously considering model errors and initial condition errors are beneficial to infer the model errors, compared to considering model errors only. Moreover, using the observations to verify the forecasts has advantages over using the analyses, to estimate the model errors. Using observations can also achieve a faster convergence of model error estimation with online DA than using analyses.