New indices to quantify patterns of relative errors produced by spatial interpolation models – A comparative study by modelling soil properties

Abstract

Spatial interpolation has been applied for mapping various variables in a wide range of environmental disciplines. This study aims to develop novel tools for examining the relative performance of different interpolation methods. We shall quantify and compare the quality of interpolation models by applying, among others, some inequality indices of error distributions. Such indices can generally be classified as non-dimensional and global. The performance measures explored here provide a valuable supplement to the conventional accuracy assessment, and have so far received only scant attention in the relevant literature. Given a wide range of potential applications for the methods discussed here, the main focus of the paper will be on empirical research concerning variability of soil properties. The eight interpolation methods, i.e., Inverse Distance Weighting (IDW), Modified Shepard’s Method (MS), Radial Basis Function (RBF), Natural Neighbour (NaN), Nearest Neighbour (NeN), Triangulation with Linear Interpolation (TIN), Local Polynomial (LP) and Ordinary Kriging (OK) were applied to estimate spatial distribution of soil pH, nitrogen, potassium and phosphorus content. Biplot methods were applied to visually examine the numerical results on the assessment of prediction quality. The ordinary kriging showed superior performance compared to the competing methods in majority of the cases. Significantly, predictions by kriging approaches revealed substantial improvement by considering data transformations. As concerns the other tested methods, the IDW and the LP algorithms tend to share similar characteristics. In turn, the NeN, RBF and MS algorithms scored relatively small inequality indices, when compared to the other methods. The use of new proposed measures will enable practitioners to gain more insightful and comprehensive evaluations of spatial interpolation techniques.