Error Analysis Of Terrain Curvatures Based On Grid DEM

Digital Terrain Analysis (DTA) is a topographical information analysis technology that calculates and extracts terrain surface parameters and morphological features on Digital Elevation Model (DEM). Many factors, such as, DEM data structure, DEM grid resolution, DEM grid direction, data accuracy, algorithm, analysis methods, etc. can affect the accuracy of the extracting and calculating of terrain surface parameters and morphological features on DEM. The accuracy of DTA affects the applications of GIS models. So, it's a necessary and urgent task to go deep to study the problems of DTA accuracy if the results of DTA are to be applied in the real world cases.Terrain curvatures is one of the primary terrain surface parameters, and they are primary variables in the earth's surface process modeling, soil erode modeling, classifying of soil utilizing. Though there are many people study terrain curvatures, there's a great shortage in this field comparing with slop and aspect. In this article, we summarize the former studies in terrain curvature and find the shortage of this field. Here we use the method of data-independent assessment of errors (put forward by xuejun liu, 2002) to study the accuracy of terrain curvatures calculation on DEM. We select nine terrain curvatures studied in this article. And the study include three main contents.1) Accuracy of Algorithms for calculation of terrain curvature based on grid DEM. In this section, we appraise three in common use algorithms for calculation of terrain curvature (shary model, evans model, zevenbergen model) in artificial surface and test the conclusion in real surface.. The experiments are carried out in different error condition.2) The relation of terrain curvatures calculation and DEM structures. In this section, we study how the DEM structures (DEM grid resolution, DEM grid direction, data accuracy) affect the curvatures calculation.3) The study of spatial distributing of curvatures error. In this section, we study how the error of curvatures calculation distributes in space.In this study, we have conclusion as follows:1) The higher-order local surface (partial quartic surface- Zevenbergen model) can describe the terrain surface accurately. But it is sensitive to data errors. So it is not fit for calculating terrain parameters, lower-order local surface (quadraticsurface-Shary model or Evans model) which is not so sensitive to error can derive more accurate results.2) Zevenbergen model is best if the DEM data is very accurate, otherwise, Evans model is better. There are data errors in DEM presently, so we recommend Evans model to calculate terrain curvatures in actual applications.3) Contour Curvature and flowpath Curvature are sensitive to DEM data errors, they are affected by not only local surface but also slop. Calculating slop accurately is the precondition of enhance the accuracy of this two curvatures calculation. We recommend Evans model to calculate fx and fy in curvature definition.4) Only in the condition that the DEM data is very accurate, accurate resolution DEM can calculate curvatures more accurately. But there are unavoidable and considerable data errors in real DEM, so, the accuracy of curvature enhance by the decrease of DEM resolution.5) DEM direction have a little affect to contour curvature and flowpath curvature. But it count for little. Due to the effect of data error in real DEM, the effect of DEM direction to other seven curvatures is very little.6) There are a reverse relation between true curvature and true error. If the true curvature has a big value in some place, the true error is small in the same place. The inverse is correct too.