Constructing empirical resolution diagnostics for kriging and minimum curvature gridding

Abstract

Resolution analysis is a crucial appraisal procedure in solving general estimation problems, especially for correctly interpreting the results of spatial analysis schemes. Resolution analyses based on the resolving kernels are typically applied to small inverse problems only when the inverse operators are explicitly accessible. Stochastic simulation schemes have been proposed to extract empirical resolution information for solving large inverse problem. In this study, we generalize the formulation of the empirical resolution length and derive the characteristic length of the point spread function for general estimation methods such as minimum curvature gridding and kriging interpolation schemes that are not equipped with explicitly accessible resolving kernels. The implementation of these resolution diagnostics has not been possible in the past and is demonstrated in this study to facilitate clarifying the advantages and limitations of these widely used methods. In addition, we compare these schemes, based on the resolution appraisal, with a multiscale gridding algorithm in the spatial analysis of the Pacific seafloor heat flow observations. By depicting the pattern of the resolution length variations of both the empirical averaging function and the point spread function for each of the estimated models, we demonstrate that schemes equipped with multiscale capability are more favorable for accommodating sparse, nonuniform data distribution than stationary schemes, such as the kriging method. Furthermore, the empirical resolution pattern constructed in this study facilitates the selection of an appropriate reference function and radii of influence for fitting the variogram, which is difficult but critical when using the kriging method. Key Points Stochastic simulation is invoked to estimate resolution diagnostics Useful for schemes lack of explicit mapping kernels and the resolution matrices Facilitate appraising geospatial schemes like kriging and spline interpolation ©2014. American Geophysical Union. All Rights Reserved.