Using machine learning to correct model error in data assimilation and forecast applications

The recent and remarkable emergence of machine learning (ML) methods, and in particular deep learning (DL), can be explained by several factors, among which (i) the increasing computational capabilities, (ii) the access to large datasets for training, and (iii) the development of efficient and user-friendly libraries (LeCun et al., 2015; Goodfellow et al., 2016; Chollet, 2018). Impressive results have been obtained in a wide range of problems using DL to the extent that DL has become state-of-the-art for many different applications: computer vision, natural language processing, signal processing, etc... In numerical weather prediction, even if the physical laws governing the system dynamics are reasonably well known, the numerical models are affected by errors. This model error could come, for example, from misrepresented physical processes or from unresolved small-scale processes. It is legitimate to wonder whether ML methods can make use of the large amount of Earth observations, available in particular through remote sensing, to try and provide better numerical models. This question is the topic of numerous studies in the geosciences, whose objective is to construct a dynamical model using only observations of a physical system. The output dynamical model is often called the surrogate model to emphasise its difference with the (true) dynamical model. Several ML methods have already been tested to construct a surrogate model for low-order chaotic systems.