Performance Evaluation of Multivariate Interpolation Methods for Scattered Data in Geoscience Applications

Interpolation methods are widely used in geoscience applications to reconstruct multivariate data from irregular samples. This paper describes a quantitative methodology for assessing the performance of various state-of-the-art interpolation methods. The methodology consists of simulation-validation and cross-validation using simulated and real data respectively, and has recently been applied to study the reconstruction of total electron content maps of the ionosphere. These two approaches are described and a study of the various artefacts associated with different interpolation methods also presented, including their origins and typical locations. Finally, the use of the statistical moments of error histograms as a method of evaluating techniques for biases and skew is described, as well as providing confidence bounds on error values. The methodology and artefact analysis should be of use to anyone who uses multivariate interpolation methods.