A Multi-Resolution Model for Non-Gaussian Random Fields on a Sphere with Application to Ionospheric Electrostatic Potentials

TL;DR

This paper introduces a multi-resolution non-Gaussian spatial model on a sphere using spherical needlets, enabling efficient estimation and prediction, demonstrated through ionospheric potential data analysis.

Contribution

It presents a novel non-Gaussian, isotropic spherical model based on needlets with adaptive MCMC estimation, extending spatial modeling capabilities.

Findings

Model accurately captures non-Gaussian features.

Outperforms Gaussian models in prediction tasks.

Successfully applied to ionospheric data.

Abstract

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial models for non-Gaussian random fields on a sphere based on a multi-resolution analysis. Using a special wavelet frame, named spherical needlets, as building blocks, the proposed model is constructed in the form of a sparse random effects model. The spatial localization of needlets, together with carefully chosen random coefficients, ensure the model to be non-Gaussian and isotropic. The model can also be expanded to include a spatially varying variance profile. The special formulation of the model enables us to develop efficient estimation and prediction procedures, in which an adaptive MCMC algorithm is used. We investigate the accuracy of parameter estimation of the proposed model, and compare its predictive performance with that of two Gaussian models by extensive numerical experiments. Practical utility of the proposed model is demonstrated through an application of the methodology to a data set of high-latitude ionospheric electrostatic potentials, generated from the LFM-MIX model of the magnetosphere-ionosphere system.