JAEHONG JEONG 
Ph.D. Candidate, Department of Statistics
Texas A&M University
“Spatial-Temporal Models for Processes on the Sphere and their Application in Climate Problem”
ABSTRACT
There have been noticeable advancements in developing parametric covariance models for spatial and spatial-temporal data with various applications to environmental problems. In this dissertation, we study random fields and covariance functions on the surface of a sphere. At first, we propose parametric covariance functions using the great circle distance for spatial processes, geared towards smooth processes on the surface of a sphere. The resulting model is isotropic and valid on the surface of a sphere, with a natural extension for nonstationarity case. Next we study a several classes of covariance functions on the surface of a sphere, defined with either the great circle distance or the Euclidean distance, and investigate their impact upon prediction. We demonstrate the covariance functions originally defined in the Euclidean distance may be limited to global data. Finally, we consider the extension of the bivariate Matérn models (Gneiting et al. 2010) for space-time processes on the surface of a sphere. We present a method to compute the approximate likelihood efficiently for the case of regularly spaced data of large dimension.
