Spatial Methods for Nonstationary Fields Using Compact Basis Functions

• Activity Number: 101
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Douglas Nychka*+ and Soutir Bandyopadhyay
• Companies: National Center for Atmospheric Research and Lehigh University
• Keywords: Spatial statistics ; Geostatistics

Abstract

Kriging is a non-parametric regression method used in geostatistics for estimating curves and surfaces and forms the core of most statistical methods for spatial data. In climate science these methods are very useful for estimating how climate varies over a geographic region when the observational data is sparse or the computer model runs are limited. A statistical challenge is to implement spatial methods for large sample sizes and also account for the heterogenity in the physical fields, both common features of many geophysical problems. Equally important is to provide companion measures of uncertainty so that the estimated surfaces can be compared in an objective way and are suitable for decision making. Here we present a statistical method that expands the spatial field in a large number of basis functions of varying resolution but all with compact support. Parsimonous models for the precision matrix of the basis coefficients are able to approximate standard covariance models but also scale to large numbers of spatial locations. A practical example is also presented for a subset of the North American Regional Climate Change and Assessment Program numerical output.