Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, hence increasing the need for covariance functions that can capture spatial dependence on spherical domains. We propose a general method of constructing nonstationary, locally anisotropic covariance functions on the sphere based on covariance functions in \(\mathbb {R}^3\). We also provide theorems that specify the conditions under which the resulting correlation function is isotropic or axially symmetric. For large datasets on the sphere commonly seen in modern applications, the Vecchia approximation is used to achieve higher scalability on statistical inference. The importance of flexible covariance structures is demonstrated numerically using simulated data and a precipitation dataset. Supplementary materials accompanying this paper appear online.

卫星遥感技术的快速发展使得能够在全球范围内收集地理空间数据，因此增加了对能够捕获球域空间依赖性的协方差函数的需求。我们提出了一种基于\(\mathbb {R}^3\)中的协方差函数在球体上构造非平稳、局部各向异性协方差函数的通用方法。我们还提供了定理，指定了所得相关函数是各向同性或轴对称的条件。对于现代应用中常见的大型数据集，Vecchia 近似用于在统计推断上实现更高的可扩展性。使用模拟数据和降水数据集以数值方式证明了灵活协方差结构的重要性。本文附带的补充材料出现在网上。