Locally anisotropic covariance functions on the sphere

TL;DR

This paper introduces a flexible method for constructing nonstationary, locally anisotropic covariance functions on the sphere, enhancing modeling of global geospatial data with improved scalability for large datasets.

Contribution

It presents a novel approach to build nonstationary covariance functions on the sphere using R^3, with theoretical conditions for isotropy and axial symmetry, and applies Vecchia approximation for scalability.

Findings

The proposed covariance functions effectively model spatial dependence on the sphere.

Numerical experiments demonstrate improved fit to simulated and real precipitation data.

The method enhances scalability for large geospatial datasets.

Abstract

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 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.