Book Description

Scalar and vectorial random fields defined on a spherical domain are principal objects of study in many branches of science. Many vector fields are often subject to physical constraints, such as being tangential to a sphere and being curl-free or divergence-free, while many scalar fields exhibit a significant degree of non-Gaussianity. However, existing literature on modeling these two types of random fields is still rare. In this dissertation, we propose new spatial models for random tangential vector fields and scalar non-Gaussian random fields on a sphere. We study properties of the models, and develop efficient estimation and prediction procedures based on maximum likelihood estimation (MLE) and Markov Chain Monte Carlo (MCMC). The accuracy of parameter estimation of the models is investigated, and their predictive performance is compared with existing state-of-the-art models by extensive numerical experiments. We demonstrate practical utility of the models through applications to data sets of ocean surface wind fields and high-latitude ionospheric electrostatic potentials.