An Approach for Valid Matern-Like Covariance Functions on the Sphere

• Activity Number: 505
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: International Indian Statistical Association
• Author(s): Jaehong Jeong and Mikyoung Jun*+
• Companies: Texas A&M University and Texas A&M University
• Keywords: process on the sphere ; Matern covariance function ; great circle distance ; kriging ; maximum likelihood estimation ; climate data

Abstract

There has been noticeable advancement in developing parametric covariance models for spatial and spatio-temporal data with various applications to environmental problems. However, literature on covariance models for processes on the surface of a sphere with great circle distance, which is natural for global data, is still sparse, due to its mathematical difficulties. It is shown that the popular Matern covariance function, with smoothness parameter greater than 0.5, is not valid for processes on the surface of a sphere (Gneiting, 2011). We introduce an approach to produce Matern-like covariance functions for smooth processes on a sphere. Resulting model is isotropic and positive definite on a sphere with great circle distance. We present an extensive numerical comparison of our model with Matern covariance model using great circle distance as well as chordal distance. We also apply our new model class to CMIP5 climate model outputs.