A multigrid method for the estimation of geometric anisotropy in environmental data from sensor networks

This paper addresses the estimation of geometric anisotropy parameters from scattered spatial data that are obtained from environmental surveillance networks. Estimates of geometric anisotropy improve the accuracy of spatial interpolation procedures that aim to generate smooth maps for visualization of the data and for decision making purposes. The anisotropy parameters involve the orientation angle of the principal anisotropy axes and the anisotropy ratio (i.e., the ratio of the principal correlation lengths). The approach that we employ is based on the covariance Hessian identity (CHI) method, which links the mean gradient tensor with the Hessian matrix of the covariance function. We extend CHI to clustered CHI for application in data sets that include patches of extreme values and clusters of varying sampling density. We investigate the impact of CHI anisotropy estimation on the performance of spatial interpolation by ordinary kriging using a data set that involves both real background radioactivity measurements and a simulated release of a radioactive plume.