Detrending and Transformation Techniques for Nonstationarity in Geostatistical Data

• Activity Number: 308
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics & the Environment*
• Author(s): Konstantin Krivoruchko*+ and Alexander Gribov
• Affiliation(s): Environmental Systems Research Institute and Environmental Systems Research Institute
• Keywords: geostatistics ; non-stationarity ; detrending ; transformation ; interplation

Abstract

Standard geostatistical models assume data are stationary. Part of this assumption is that the mean and variance are finite and constant. In practice, this assumption is often violated. There are two ways to use geostatistics in the case of non-stationarity: 1.) to estimate a heterogeneous covariance; or, 2.) to make data close to stationarity using detrending and transformation techniques. First, we discuss tools for identifying the extent of non-stationarity. Second, we use local polynomial interpolation to absorb variability into a nonconstant mean. Third, we transform data to make remaining variance constant using functionals. In the last case we estimate data variance using local polynomial interpolation technique and then we use a nonlinear transformation based on local estimation of the mean and variance. Then standard kriging techniques can be safely used on transformed data, and the back-transformation is usually straightforward. We apply this approach to an example of agriculture data of soil properties and yield, under circumstances when the usual assumptions of stationarity do not apply.