Accuracy of local topographic variables derived from digital elevation models

Abstract

We study the accuracy of data on some local topographic attributes derived from digital elevation models (DEMs). First, we carry out a test for the precision of four methods for calculation of partial derivatives of elevations. We ® nd that the Evans method is the most precision algorithm of this kind. Second, we produce formulae for root mean square errors of four local topographic variables (gradient, aspect, horizontal and vertical landsurface curvatures), provided that these variables are evaluated with the Evans method. Third, we demonstrate that mapping is the most convenient and pictorial way for the practical implementation of the formulae derived. A DEM of a part of the Kursk Region (Russia) is used as an example. We ® nd that high errors of data on local topographic variables are typical for¯at areas. Results of the study can be used to improve landscape investigations with digital terrain models.

Evaluating Topographic Effects on Ground Deformation: Insights from Finite Element Modeling

“…provides the most precise estimate of topographic variables in the presence of elevation 880 errors (Florinsky 1998…”

“…This fitting provides an easy 872 calculation of the first and second derivate of the surface used to calculate the slope, theThe polynomial (Eq. A1) approximates the z coordinates of the 3×3 submatrix 875 rather than passing exactly through these values (Florinsky 1998). This leads to some 876 smoothing of the z function within the 3×3 submatrix, that is, a low-pass filtering that 877 can provide more correct calculation of derivative (Florinsky 1998).…”

“…A1) approximates the z coordinates of the 3×3 submatrix 875 rather than passing exactly through these values (Florinsky 1998). This leads to some 876 smoothing of the z function within the 3×3 submatrix, that is, a low-pass filtering that 877 can provide more correct calculation of derivative (Florinsky 1998). Among the several 878 methods proposed for trend surface analysis, the quadratic approximation approach 879…”

The influence of resolution and topographic uncertainty on melt modelling using hypsometric sub‐grid parameterization

“…SRTM or GLOBE DEMs, Jarvis et al, 2006;Hastings and Dunbar, 1998) to resolutions as low as 5, 10 or even 20km. The smoothing effect this resampling has on topography and consequently on any associated parameter has been widely noted and the subject of a number of experiments, ranging from calculation of derivatives (Florinsky, 1998;Zhang et al, 1999) to effects on spatial variability of parameters (Hu and Islam, 1997) and automatic analysis for environmental modelling (Albani et al, 2004). In hydrology, effects of scale and consequently methods to minimise these effects have been explored, for example by Armstrong and Martz (2003).…”

Effects of spatial resolution on slope and aspect derivation for regional-scale analysis

“…Gao (1997) studied the influence of spatial resolution at the micro-scale of three 1 km 2 areas representing a valley, a peak and a ridge; he reports that resolution has little influence on mean gradient, but affects significantly the standard deviation of slope, especially for a simple terrain. Florinsky (1998) mapped the root mean square errors (RMSE) of the local topographic variables slope, aspect, plan and profile curvatures, in order to analyse their accuracy. He concluded that high data errors on these variables are typical for flat areas.…”