Exploring spatiotemporal vector autoregressive models for radar nowcasting

Radar nowcasting methodologies have evolved from traditional optical flow and extrapolation techniques to advanced deep learning algorithms. However, accurately modeling growth and decay processes remains a significant challenge. This study explores spatio-temporal statistical models inspired by physics-based stochastic partial differential equations (SPDEs). Specifically, the solution to the advection-diffusion PDE is framed as a vector autoregressive process with coloured noise, characterized by non-uniform spectral properties.

We investigate the stochastic component using Gaussian Processes (GPs) and Gauss Markov Random Fields (GMRFs), evaluating covariance structures such as exponential, squared exponential, and dynamically weighted covariance and precision matrices. Nowcasts employing state-dependent GPs and GMRFs are assessed over lead times ranging from 15 minutes to 2 hours. The approach is tested on simulated data and UK precipitation events from the Met Office Nimrod system, focusing on a 200 km × 200 km region. Training data spans January 2014 to December 2020, with observational dimensions on the order of 10^4. To enable computationally efficient Bayesian inference, we utilize sparse matrix methods and Laplace approximations.