Accurately representing surface weather at the sub-kilometer scale is crucial for optimal decision-making in a wide range of applications. This motivates the use of statistical techniques to provide accurate and calibrated probabilistic predictions at a lower cost compared to numerical simulations. Wind represents a particularly challenging variable to model due to its high spatial and temporal variability. This paper presents a novel approach that integrates Gaussian processes and neural networks to model surface wind gusts at sub-kilometer resolution, leveraging multiple data sources, including numerical weather prediction models, topographical descriptors, and in-situ measurements. Results demonstrate the added value of modeling the multivariate covariance structure of the variable of interest, as opposed to only applying a univariate probabilistic regression approach. Modeling the covariance enables the optimal integration of observed measurements from ground stations, which is shown to reduce the continuous ranked probability score compared to the baseline. Moreover, it allows the generation of realistic fields that are also marginally calibrated, aided by scalable techniques such as random Fourier features and pathwise conditioning. We discuss the effect of different modeling choices, as well as different degrees of approximation, and present our results for a case study.

翻译：精确表征亚公里尺度的地表天气对于广泛应用中的最优决策至关重要。这促使我们采用统计技术，以相比数值模拟更低的成本提供准确且经过校准的概率预测。由于风具有高度的时空变异性，它代表了一个特别具有挑战性的建模变量。本文提出了一种新颖方法，该方法整合了高斯过程与神经网络，利用包括数值天气预报模型、地形描述因子和现场测量在内的多种数据源，对亚公里分辨率的地表阵风进行建模。结果表明，与仅应用单变量概率回归方法相比，对目标变量的多元协方差结构进行建模具有额外价值。对协方差进行建模能够实现地面站点观测测量的最优融合，这被证明可以降低连续分级概率评分（相比基线）。此外，借助于随机傅里叶特征和路径条件化等可扩展技术，该方法能够生成真实且边缘校准的场。我们讨论了不同建模选择以及不同近似程度的影响，并展示了一个案例研究的结果。