Multi-Resolution Spatial Methods on the Sphere: Efficient Prediction for Global Data

Abstract

Accurate spatial prediction on the sphere is fundamental for global environmental applications such as climate monitoring and oceanographic analysis. Existing approaches, however, often struggle to balance computational efficiency, predictive accuracy, and the ability to accommodate heterogeneous spatial structures. We propose a multi-resolution spatial modeling framework that integrates thin-plate spline (TPS) basis functions with Gaussian process modeling. The framework begins with a fixed-effects representation based on a hierarchy of nearly orthogonal TPS basis functions ordered by smoothness, thereby providing a multi-resolution decomposition of spatial variation. This allows large-scale patterns to be captured efficiently while preserving interpretability. To represent localized dependencies, we extend the model with a random effect governed by a tapered Matérn covariance, which models fine-scale structure while ensuring scalability through sparse matrix operations. Model complexity is adaptively controlled using the conditional Akaike information criterion (cAIC), which simultaneously selects the number of basis functions and determines the contribution of the Gaussian process component. Numerical experiments and a global sea surface temperature application show how our method balances predictive accuracy with computational feasibility, establishing its role as a powerful solution for large-scale spatial modeling on the sphere.