The validity of cross-validation usage in generating digital relief model of an anthropogenically transformed area

Abstract

Digital relief models deliver a valuable information about the morphology of a particular area. They are useful in structural geomorphology analysis. However, their correct generation requires knowledge of geostatistic methods, including cross-validation. This article presents the importance of cross-validation, using the example of the Grodziec area (Silesian Upland, southern Poland). The choice of the test area was determined by its geomorphology – high altitude differences (140 meters maximum) and the co-occurence of landforms of different rank, genesis and size. This area includes some towering hills – monadnocks, which are Middle-Triassic cuesta remainders. These forms clearly dominate in the surrounding area incised by river valleys. Besides the large forms sculptured by erosion and denudation processes, there are also anthropogenic landforms – stone pits – of much smaller size. We asked the question whether and to what extent they will be “visible” on digital relief models depending on the variogram model setup. Two digital relief models were generated (one with a deliberately incorrect and one with the correct variogram setup) and verified using the cross-validation method. The results of this experiment show that correct digital model carries only slight overestimation of mean squared standardized error while the incorrect model shows substantial underestimation of sampling points values. The correct model is more vivid – it clearly shows most of the relief details while the DTM (digital terrain model) generated by the incorrect setup is misrepresented and blurred. This indicates that conclusions based on incorrect relief models may be subject to high errors.