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

TL;DR

This work tackles the challenge of scalable, fully probabilistic spatio-temporal Gaussian process modeling for continental-scale short-term weather forecasting. It compares three scalable GP families—FITC, Vecchia, and the Vecchia-inducing-point full-scale (VIF)—and introduces correlation-based Vecchia neighbor selection and space-time separated sts-kMeans++ inducing-point placement, plus GPU acceleration. On a NOAA dataset of about $1.7$ million space-time observations across $\approx 3{,}000$ stations and 608 days, the VIF approach generally achieves the best predictive performance and uncertainty quantification for both Gaussian (temperature) and non-Gaussian (precipitation) settings, with Vecchia-Corr offering strong results and FITC providing a faster but less accurate alternative. The results reveal realistic non-separable space-time dependence, with temperature showing longer spatial coherence and memory than precipitation, and demonstrate that these scalable GP methods can deliver high-quality forecasts with practical training and prediction times, enabling uncertainty-aware decision support at continental scales.

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 approximately 1.7 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.

Figures (26)

• Figure 1: Average RMSE and CRPS (log scale) $\pm$ one standard error vs. lead time for the Vecchia, FITC, and VIF approximations.
• Figure 2: Runtimes in seconds (log-scale) and GPU speedups per optimization step across sample sizes for the Vecchia, FITC, and VIF approximations.
• Figure 3: Temperature modeling results: average RMSE and CRPS (log scale) $\pm$ one standard error vs. lead time (days) for one- to five-day spatio-temporal forecasts using the Vecchia, FITC, and VIF approximations. Persistence and fixed-effects-only baselines are included.
• Figure 4: Precipitation modeling results: Average MAE and CRPS for precipitation amounts and brier score (BS) and log score (LS) for precipitation occurrence (log scale) $\pm$ one standard error vs. lead time (days) for one- to three-day spatio-temporal forecasts using the Vecchia, FITC, and VIF approximations. Persistence and fixed-effects-only baselines are included.
• Figure 5: Daily maximum temperature (°C with resolution: 0.1) across the conterminous United States, shown for four selected dates in 2025.