Scalable non-separable spatio-temporal Gaussian process models for large-scale short-term weather prediction

TL;DR

This paper develops scalable Gaussian process models for large-scale short-term weather prediction, enabling accurate and computationally feasible forecasts across the entire United States.

Contribution

It introduces novel scalable approximation methods and GPU acceleration techniques for spatio-temporal Gaussian processes applied to continental-scale weather forecasting.

Findings

Models achieve accurate forecasts at continental scale.

GPU acceleration significantly reduces computation time.

Methods outperform traditional approaches in large datasets.

Abstract

Monitoring daily weather fields is critical for climate science, agriculture, and environmental planning, yet fully probabilistic spatio-temporal models become computationally prohibitive at continental scale. We present a case study on short-term forecasting of daily maximum temperature and precipitation across the conterminous United States using novel scalable spatio-temporal Gaussian process methodology. Building on three approximation families - inducing-point methods (FITC), Vecchia approximations, and a hybrid Vecchia-inducing-point full-scale approach (VIF) - we introduce three extensions that address key bottlenecks in large space-time settings: (i) a scalable correlation-based neighbor selection strategy for Vecchia approximations with point-referenced data, enabling accurate conditioning under complex dependence structures, (ii) a space-time kMeans++ inducing-point selection algorithm, and (iii) GPU-accelerated implementations of computationally expensive operations, including matrix operations and neighbor searches. Using both synthetic experiments and a large NOAA station dataset containing more than one million space-time observations, we analyze the models with respect to predictive performance, parameter estimation, and computational efficiency. Our results demonstrate that scalable Gaussian process models can yield accurate continental-scale forecasts while remaining computationally feasible, offering practical tools for weather applications.