A PDE-Informed Latent Diffusion Model for 2-m Temperature Downscaling

Earth system models (ESMs) are critical for weather forecasting, tracking weather extremes, and supporting impact studies. In particular, numerical weather prediction (NWP) methods track surface and atmospheric data by dissecting the Earth's surface into grids, tracking variables of interest (e.g., temperature, wind speed, direction) as scalar/vector fields, and numerically solving partial differential equations (PDEs) to either physically interpolate into unknown regions or temporally evolve the model--a process known as reanalysis [20, 15]. Historical reanalysis datasets such as ERA5, MERRA-2, and NCEP primarily consist of coarse-scale grid resolutions of 31 31 km to 500 500 km collected by weather stations, aircrafts, and meterological satellites [5, 6, 10]. However, climate simulations at finer resolutions down to 2 2 km are critical for understanding short-term forecasting (nowcasting and medium-range forecasting) and predicting localized weather extremes described by highly resolved fields. As manual collection of such high-resolution data on a global scale is too resource-intensive, global climate models (GCMs) perform downscaling to increase the resolution of surface data by employing two general types of techniques: dynamical and statistical downscaling [3, 11].