Nonstationary Spatial Covariance Functions * Michael L. Stein ABSTRACT: A method is described for producing explicit nonstationary spatial covariance func- tions that, for example, allows both the local geometric anisotropy and the degree of differentiability to vary spatially. Keywords: Spatial anisotropy, Spectral density, Mat´ern model, Long-range dependence * Michael L. Stein is Professor, Department of Statistics, University of Chicago, Chicago, IL 60637 (email: stein@galton.uchicago.edu). Although the research described in this article has been funded wholly or in part by the United States Environmental Protection Agency through STAR cooperative agreement R-82940201-0 to the University of Chicago, it has not been subjected to the Agency’s required peer and policy review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.