Derivation of topographic variables from a digital elevation model given by a spheroidal trapezoidal grid

Abstract

Digital elevation models (DEMs) given by spheroidal trapezoidal grids are more appropriate for large regional, sub-continental, continental and global geological and soil studies than square-spaced DEMs. Here we develop a method for derivation of topographic variables, specifically horizontal (k) and vertical h (k) landsurface curvatures, from spheroidal trapezoidal-spaced DEMs. First, we v derive equations for calculation of partial derivatives of elevation with DEMs of this sort. Second, we produce formulae for estimation of the method accuracy in terms of root mean square errors of partial derivatives of elevation, as well as k h and k (m and m respectively). We design the method for the case that the v kh k v Earth's shape can be ignored, that is, for DEM grid sizes of no more than 225 km. We test the method by the example of fault recognition using a DEM of a part of Central Eurasia. A comparative analysis of test results and factual geological data demonstrates that the method actually works in regions marked by complicated topographic and tectonic conditions. Upon increasing DEM grid size, one can produce generalised maps of k and k. Spatial distributions of m and m h v kh k v depend directly on the distribution of elevation RMSE. Areas with high values of m are marked by low values of m, and vice versa, areas with high values kh k v of m are marked by low values of m. Data on m and m should be utilised k v kh kh k v to control and improve applications of k and k to geological studies. The method h v developed opens up new avenues for carrying out some 'conventional' raster operations directly on geographical co-ordinates.