Numerical evaluation of mean values of topographical effects

Abstract

Numerical evaluation of mean values of topographical effects The main problem treated in this paper is the determination of accurate mean values of the topographical effects from point values known on a regular geographical grid. Three kinds of topographical effects are studied: terrain correction, condensed terrain correction and direct topographical effect. The relation between the terrain roughness and optimal density of the points to be used in the computations is investigated in five morphologically different areas of Canada. The error of the geoid caused by the inaccuracy of the mean values computed from a variable number of points in a cell is estimated. These errors are then compared against the one centimetre target to give us the sufficient minimum number of points needed for the averaging. The mean terrain effects are computed from the point values as a simple average over a particular cell. Point values are assumed to be errorless so that the accuracy of the mean values is a function of the density of the point values only. The mentioned one centimetre criterion is applied in the sense of the Chebyshev norm. It has been observed that the relation between the number of points needed for the averaging and the terrain roughness as quantified by the terrain RMS is almost linear. After estimating the two parameters of this linear relation, seven minimally required grid densities are suggested for different intervals of terrain roughness. The results are applied to produce maps of a minimal density of points needed for sufficiently accurate determination of mean topographical effects for Canada.