Modeling Spatial Means of Surfaces With Stratified Nonhomogeneity

In geosciences, one often needs to estimate the spatial means of surfaces representing physical attributes. Under certain conditions, this kind of estimation is often performed by a simple summation of a random sample or by some kind of a Kriging (spatial regression) technique. For example, the naive sample mean assumes that the sample is randomly distributed across space, which is a restrictive assumption with limited applicability in real-world situations (e.g., in the case of nonhomogeneous surfaces, the naive sample mean is a biased estimate of the actual surface mean). Kriging techniques can generate unbiased estimates for certain kinds of homogeneous surfaces but may be not appropriate in cases of stratified nonhomogeneity when the covariances exhibit considerable differences between different strata of the surface. In this paper, we extend the Kriging concept to study surfaces with stratified nonhomogeneity. The corresponding analytical formulas are derived, and empirical studies are performed that involve real-world and simulated data sets. Numerical comparative analysis showed that the proposed method performed well compared to other methods commonly used for the purpose of estimating surface means across space.