Application in Accuracy Assessment for DEM Interpolation Methods Based on a Variance-scale Law

A new accuracy assessment framework for interpolations, based on a variance-scale law, is proposed in this paper. Based findings in different research areas, it has been shown that the variance of a certain variable decreases with agrowing scale. According to this theoretical law, three presupposed assessment criteria have been proposed. Application cases in DEM interpolation were selected and four common methods, i.e., HASM, Spline, Kriging, and IDW were chosen for comparison in this new framework. The second assessment criterion, regarding changing trends, was found to be questionable in a numerical test. The results of two real-world DEM interpolation cases indicate that the theoretical changing trend in the variance-scale relation cannot be obtained in real terrain cases because of an complicated integrated effects, characteristic of the real-world terrain, and the smoothing effect of interpolators and interpolation scales. However, as the original sampling variance was introduced into the framework, the general changing trend of variances and the overall level of variances at most scales could still be used as accuracy assessment measures even under different sampling densities. After modifying the second and the third criterion, the final three criteria in this assessment framework were established. Both the numerical surface case and real-world DEM examples indicate that this assessment framework is simple in theory, convenient for usie, and is an objective and effective assessment method, widening the field of accuracy assessment in DEM interpolation. Moreover, based on the results of different sampling densities, this framework can also provide valuable application suggestions for choosing suitable interpolation methods in real-world cases.