Modeling locally varying anisotropy of CO₂ emissions in the United States

Abstract

In a spatial property modeling context, the variables of interest to be modeled often display complex nonlinear features. Techniques to incorporate these nonlinear features, such as multiple point statistics or cummulants, are often complex with input parameters that are difficult to infer. The methodology proposed in this paper uses a classical vector-based definition of locally varying anisotropy to characterize nonlinear features and incorporate locally varying anisotropy into numerical property models. The required input is an exhaustive field of anisotropy orientation and magnitude. The methodology consists of (1) using the shortest path distance between locations to define the covariance between points in space (2) multidimensional scaling of the domain to ensure positive definite kriging equations and (3) estimation or simulation with kriging or sequential Gaussian simulation. The only additional parameter required when kriging or simulating with locally varying anisotropy is the number of dimensions to retain in multidimensional scaling. The methodology is demonstrated on a CO₂ emissions data set for the United States in 2002 and shows an improvement in cross validation results as well as a visual reproduction of nonlinear features.