  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.
