Extending Kriging with Azimuthal Weighting and Material-Dependent Variance

Abstract

Greg Passmore

This paper introduces a method called KRAM (Kriging with Regularization for Azimuth and Material), developed to address specific requirements in geospatial applications involving sparse, anisotropic, or heterogeneous elevation data. KRAM extends ordinary kriging by adding two targeted modifications: azimuthal regularization to reduce overreliance on collinear samples, and material-dependent variance modeling to capture localized surface roughness without requiring multiple covariance models. These enhancements improve interpolation accuracy in structured terrain, urban environments, and damage assessment scenarios, where geospatial data typically exhibit significant variability in both sampling geometry and surface materials. The method maintains the statistical foundation of ordinary kriging while improving structural accuracy, robustness to sampling geometry, and the interpretability of spatial uncertainty. KRAM is suited for use in terrain densification, surface reconstruction, and predictive modeling tasks where accuracy and auditability are operational requirements.

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