Geostatistical model validation using orthonormal residuals

Geostatistical models are widely used to describe the structure of the spatial function in many areas of hydrosciences and environmental engineering. A model developed for geostatistical estimation must be tested against field data to check its validity. Orthonormal residuals as a diagnostic tool have advantages over conventional standardized residuals in that they are easy to calculate and the determination of the sampling distributions of statistics based on them is computationally efficient. In this paper, the applicability of two test methods based on orthonormal residuals is studied. For a set of groundwater head measurements, two different models of the structure of the head field are tested. Results indicate that two tests agree with each other and thus can be used for diagnosing model adequancy.