Visual and Statistical Comparisons of Surface Modeling Techniques for Point-based Environmental Data

Abstract

Existing studies on spatial interpolation tend to overplay statistical perspective, paying little attention the locality and the visual performance of generated surface models. In an attempt to bridge these gaps in literatures, the authors compared the performance of five surface modelling methods, using a set of integrative criteria including absolute and relative statistical accuracy, visual pleasantness and faithfulness of generated surface models, sensitivity to changing sample size and search conditions, and computational intensity. The modeling methods used were: inverse distance, kriging, linear triangulation, minimum curvature, and radial basis functions. Because terrain relief is one of few environmental attributes whose continuous surfaces can be directly observed through appropriate procedures, we used as input data two sets of elevation points sampled irregularly from a USGS 1:24,000 topographical map covering a hilly area. We found that surface modeling methods, even if statistically accurate, may not always ensure a graphically faithful representation of the reality. The surprising result of this study was that the surface models generated from a larger sample were less statistically accurate than those generated from a smaller sample.