Data-driven super-parameterization using deep learning: Experimentations with a multi-scale Lorenz 96 model

Some of the physical processes that play key roles in the weather/climate system occur at such small spatial and fast time scales that trying to explicitly solve for them can lead to computationally intractable numerical models. These processes sub-grid scale processes (denoted by variable Y hereafter) are often parameterized using semi-empirical/physics-based schemes as a function of the large-scale/slow variables (X) that are explicitly solved. Recently, multi-scale numerical models that explicitly solve for X and Y, but at different numerical resolutions, have been developed. This approach, dubbed super-parameterization (SP), has been shown to improve simulation of climate variabilities and extremes, but can still be computationally prohibitive for many applications. More recently, several studies have shown promises of using feed-forward deep neural networks, trained on data from high resolution or super-parameterized climate models, for data-driven parameterization (DD-P) of Y as a function of X for problems involving moist convection and sub-mesoscale oceanic eddies. Here, we first examine and compare the performance of several prominent recurrent neural network (RNN) architectures, i.e., reservoir computing (RC), long short-term memory (LSTM), and gated recurrent unit (GRU), for data-driven modeling of multi-scale chaotic systems using a Lorenz 96 model as the testbed. Then we investigate whether RNNs can be used for data-driven super-parameterization (DD-SP): To solve the equations for X numerically at low resolution, and emulate the evolution of Y at higher numerical resolutions using RNNs. Using a multi-scale Lorenz 96 chaotic system as the testbed and the best RNN identified earlier (RC), we examine both predicted short-term trajectory (weather forecasting) and reproducing long-term statistics (climate simulation). We show that DD-SP outperforms DD-P, and can achieve the accuracy of SP at a much lower computational cost. Potential advantages and limitations of DD-SP for practical climate/weather modeling problems are discussed.