A Bayesian spatio-temporal model for short-term forecasting of precipitation fields

Abstract

With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating short-term, probabilistic forecasts of localised precipitation on a spatial grid. Our generative hierarchical dynamic model is formulated in discrete space and time with a lattice-Markov spatio-temporal auto-regressive structure, inspired by continuous models of advection and diffusion. Observations from both weather radar and ground based rain gauges provide information from which we can learn the precipitation field through a latent process in addition to unknown model parameters. Working in the Bayesian paradigm provides a coherent framework for capturing uncertainty, both in the underlying model parameters and in our forecasts. Further, appealing to simulation based sampling using MCMC yields a straightforward solution to handling zeros, treated as censored observations, via data augmentation. Both the underlying state and the observations are of moderately large dimension ($𝒪\left(10^4\right)$ and $𝒪\left(10^3\right)$ respectively) and this renders standard inference approaches computationally infeasible. Our solution is to embed the ensemble Kalman smoother within a Gibbs sampling scheme to facilitate approximate Bayesian inference in reasonable time. Both the methodology and the effectiveness of our posterior sampling scheme are demonstrated via simulation studies and by a case study of real data from the Urban Observatory project based in Newcastle upon Tyne, UK.