Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high spatial resolution requires the interpolation of global datasets at the location where ground stations are available with statistical models able to capture complex non-Gaussian global space-time dependence structures. In this work, we propose a new approach based on capturing the spatial dependence of a latent Gaussian process via a locally deformed Stochastic Partial Differential Equation (SPDE) with a buffer allowing for a different spatial structure across land and sea. The finite volume approximation of the SPDE, coupled with Integrated Nested Laplace Approximation ensures feasible Bayesian inference for tens of millions of observations. The simulation studies showcase the improved predictability of the proposed approach against stationary and no-buffer alternatives. The proposed approach is then used to yield high resolution simulations of daily precipitation across the United States.

翻译：获取高分辨率的降水量数据可为利益相关者提供关键见解，以评估城市尺度上水资源的可持续获取。在高空间分辨率下映射降水量这类非平稳稀疏过程，需要利用能够捕捉复杂非高斯全局时空依赖结构的统计模型，对全球数据集在现有地面站点位置进行插值。本文提出了一种新方法，该方法通过带有缓冲区的局部变形随机偏微分方程（SPDE）捕捉潜高斯过程的空间依赖性，使得陆地和海洋可具有不同的空间结构。SPDE的有限体积近似与集成嵌套拉普拉斯近似相结合，确保了数千万观测数据下的可行贝叶斯推断。模拟研究表明，与平稳和无缓冲区替代方案相比，所提方法具有更优的可预测性。随后，该方法被用于生成美国全境的高分辨率日降水量模拟。