Covariance Functions for Mean Square Differentiable Processes on Spheres

• Activity Number: 535
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Joseph Guinness*+ and Montserrat Fuentes
• Companies: NC State University and North Carolina State University
• Keywords: covariance function ; spectral analysis ; Fourier transform ; sphere ; isotropic ; spatial statistics

Abstract

Many applications in spatial statistics involve data that are observed over large regions on the surface of the Earth. For data on Euclidean spaces, there is a large statistical literature devoted to covariance functions with the ability to capture the varying degree of smoothness across different datasets. We extend some of this work to covariance functions that can be applied when the domain is a sphere, where the natural measure of distance is the great circle distance. In doing so, we define the notion of an m times mean square differentiable process and give necessary and sufficient conditions for a covariance function to correspond to an m times mean square differentiable process. We develop a new analog to the Matérn covariance function that is valid on the sphere with great circle distance metric, as opposed to the Matérn, which is only generally valid when chordal distance is used. The performance of these two covariance functions are compared to each other and to several other covariance functions in applications involving Level 2 total column ozone data and climate model output data.