Learning Weather Models from Data with WSINDy

Since its modern inception in the pioneering computational work of Charney, Fjörtoft, and Von Neumann (see Charney et al. (1950)), numerical weather prediction (NWP) has proven to present formidable mathematical challenges. In particular, many dynamic models of weather phenomena exhibit multiscale and turbulent features which have been known since the seminal work of Lorenz (1963) to lead to a sensitive dependence on initial conditions. As a consequence, the uncertainties present in a set of initial observations grow exponentially in time under these models, bounding the predictive power of most numerical weather forecasts to medium-range time scales ( 14 days). This chaotic behavior is exacerbated by the computational reality that simulations of the relevant physics can only capture a finite range of scales, so that the physical influence of unresolved scales is either ignored or approximated by subgrid closure models. In recent years, there has been an explosion of interest surrounding data-driven approaches to weather modeling (see, e.g., Rasp et al. (2024) and Karlbauer et al. (2024) for a discussion and recent benchmarks). In contrast to traditional NWP, which relies on numerical simulations of physics-based weather models, these novel data-driven approaches learn effective weather models directly from empirical data.