Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz `96 Model

Stochastic parameterizations account for uncertainty in the representation of unresolved subgrid processes by sampling from the distribution of possible subgrid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant structural assumptions that can limit their scalability. Machine learning models, including neural networks, are able to represent a wide range of distributions and build optimized mappings between a large number of inputs and subgrid forcings. Recent research on machine learning parameterizations has focused only on deterministic parameterizations. In this study, we develop a stochastic parameterization using the generative adversarial network (GAN) machine learning framework. The GAN stochastic parameterization is trained and evaluated on output from the Lorenz 96 model, which is a common baseline model for evaluating both parameterization and data assimilation techniques. We evaluate different ways of characterizing the input noise for the model and perform model runs with the GAN parameterization at weather and climate time scales. Some of the GAN configurations perform better than a baseline bespoke parameterization at both time scales, and the networks closely reproduce the spatiotemporal correlations and regimes of the Lorenz 96 system. We also find that, in general, those models which produce skillful forecasts are also associated with the best climate simulations. Plain Language Summary Simulations of the atmosphere must approximate the effects of small-scale processes with simplified functions called parameterizations. Standard parameterizations only predict one output for a given input, but stochastic parameterizations can sample from all the possible outcomes that can occur under certain conditions. We have developed and evaluated a machine learning stochastic parameterization, which builds a mapping between large-scale current conditions and the range of small-scale outcomes from data about both. We test the machine learning stochastic parameterization in a simplified mathematical simulation that produces multiscale chaotic waves like the atmosphere. We find that some configurations of the machine learning stochastic parameterization perform slightly better than a simpler baseline stochastic parameterization over both weather- and climate-like time spans.