A Posteriori Learning for Quasi‐Geostrophic Turbulence Parametrization. (1st November 2022) - Frezat, Hugo; Le Sommer, Julien; Fablet, Ronan; Balarac, Guillaume; Lguensat, Redouane
Abstract: The use of machine learning to build subgrid parametrizations for climate models is receiving growing attention. State‐of‐the‐art strategies address the problem as a supervised learning task and optimize algorithms that predict subgrid fluxes based on information from coarse resolution models. In practice, training data are generated from higher resolution numerical simulations transformed in order to mimic coarse resolution simulations. By essence, these strategies optimize subgrid parametrizations to meet so‐called a priori criteria. But the actual purpose of a subgrid parametrization is to obtain good performance in terms of a posteriori metrics which imply computing entire model trajectories. In this paper, we focus on the representation of energy backscatter in two‐dimensional quasi‐geostrophic turbulence and compare parametrizations obtained with different learning strategies at fixed computational complexity. We show that strategies based on a priori criteria yield parametrizations that tend to be unstable in direct simulations and describe how subgrid parametrizations can alternatively be trained end‐to‐end in order to meet a posteriori criteria. We illustrate that end‐to‐end learning strategies yield parametrizations that outperform known empirical and data‐driven schemes in terms of performance, stability, and ability to apply to different flow configurations. These results support the relevance of differentiable programming paradigms for climate models in the future. Plain Language Summary: Climate projection and weather forecast heavily rely on computer simulations. But, if the physical laws governing the evolution of the climate system are well known, their simulation is still rather challenging. Fluid flows being essentially turbulent, small details at fine scales can have a tremendous impact on larger scales. Still, because of the limitations in computing power, all these interactions across scales cannot be explicitly resolved in computer simulations. Some of these interactions can only be represented approximately, and the design of these approximations is an active research area. Here, we describe a new method which leverages recent advances in machine learning. We propose to train an approximate representation of unresolved scales of motions that optimizes the quality of the climate model over some temporal horizon. This results in more accurate and stable predictions. Our method shows very promising results in toy example flow simulations, but its deployment at scale may seriously challenge the overall design of legacy climate models. Key Points: Subgrid parametrizations can be learned end‐to‐end with a posteriori criteria involving model integration over several time‐steps A posteriori learning for quasi‐geostrophic turbulent flows can solve numerical stability issues related to energy backscatter Learned parametrizations outperform existing baselines for various evaluation metrics and apply to different flow configurations