A Bayesian Dynamic Spatiotemporal Model with Advection-Diffusion Motivation for Short-Term Probabilistic Forecasting of Shortwave Radiation Fields

Abstract

This study applies a Bayesian dynamic spatio-temporal modeling (DSTM) framework, motivated by advection–diffusion processes, to generate short-term probabilistic forecasts of shortwave radiation (SWR) fields over Mindanao, Philippines. Using the Himawari-9 Level 2 Short Wave Radiation product at 5km spatial and 10-minute temporal resolution, we model the latent irradiance field as evolving under a stochastic partial differential equation (SPDE) with diffusion and time-varying advection components. The continuous formulation is discretized via a finite-difference scheme, resulting in sparse, linear-Gaussian dynamics suitable for state-space modeling. Inference is carried out using a Gibbs sampling algorithm that integrates a fixed-lag ensemble Kalman smoother (EnKS) to efficiently approximate posterior distributions of the high-dimensional latent states. The model is applied to collected satellite observations, and posterior summaries provide insight into the temporal evolution of advection parameters, spatial uncertainty, and irradiance exceedance probabilities. Posterior predictive simulations yield short-term forecasts that remain coherent up to 30 minutes ahead, after which forecast uncertainty increases substantially. Results demonstrate the potential of the DSTM framework for assimilating satellite data and delivering calibrated probabilistic nowcasts of irradiance in tropical environments, supporting decision-making in solar energy operations and other weather-sensitive sectors.