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.

翻译：监测每日天气场对于气候科学、农业和环境规划至关重要，然而完全概率性的时空模型在大陆尺度上计算成本过高。本文通过新型可扩展时空高斯过程方法，针对美国本土的日最高气温和降水短期预报进行了案例研究。基于三种近似方法族——诱导点方法（FITC）、Vecchia近似法以及混合Vecchia-诱导点全尺度方法（VIF）——我们提出了三项扩展技术以解决大规模时空场景中的关键瓶颈：（i）针对点参考数据Vecchia近似的可扩展基于相关性的邻域选择策略，能够在复杂依赖结构下实现精确条件化；（ii）时空kMeans++诱导点选择算法；（iii）对计算密集型操作（包括矩阵运算和邻域搜索）的GPU加速实现。通过合成实验和包含超百万时空观测数据的NOAA大型站点数据集，我们从预测性能、参数估计和计算效率三个维度对模型进行了分析。结果表明，可扩展高斯过程模型能够在保持计算可行性的同时，提供准确的大陆尺度天气预报，为气象应用提供了实用工具。