Analytical basis for determining slope lines in grid digital elevation models

Abstract

[1] An analytical basis for the determination of slope lines in grid digital elevation models is provided by using the D8-LTD method (eight slope directions, least transverse deviation). The D8-LTD method's capability to predict consistently exact slope lines as the grid cell size goes to zero is shown analytically by applying mathematical analysis methods. The use of cumulative, least transverse deviations is found to be the key factor allowing for globally unbiased approximations of slope lines. The D8-LTD method's properties are also demonstrated numerically by using digital elevation models of a synthetic sloping surface obtained from the Himmelblau function. It is shown that slope lines obtained from the D8-LTD method can approximate the exact slope lines as close as desired by selecting a grid cell size that is small enough. In contrast, the standard D8 method is found to produce significantly biased results even when small grid cells are used. The D8-LTD method outperforms the D8 method over a wide range of grid cell sizes (up to 20 m in this application), beyond which grid cell size becomes too large to validly represent the underlying sloping surface. It is therefore concluded that the D8-LTD method should be used in preference to the standard D8 method in order to obtain slope lines that are only limited in reliability by the detail of topographic data, and not by the accuracy of the slope direction method applied.Citation: Orlandini, S., G. Moretti, and A. Gavioli (2014), Analytical basis for determining slope lines in grid digital elevation models, Water Resour. Res., 50, 526-539,

High-resolution global topographic index values for use in large-scale hydrological modelling

“…We acknowledge that recent advances in creating DEM-based drainage networks (e.g. D8-LTD or other options such as FD8 or MD8; Orlandini et al, 2014) provide avenues to alter and potentially improve the drainage-direction calculations and, in consequence, the topographic index values, but testing for the individual effects is beyond the scope of this project due to the multiscale complexity involved (see Appendix B for further explanations). We believe, however, that while these methods may have a significant effect on local drainage directions and channel routing, the cumulative calculation of "contributing upstream area" is less affected.…”

“…However, in GA2 we instead used a direction-of-steepest-descent model: the deterministic eight node (D8) routing model (Moore et al, 1993;Wolock and McCabe, 1995;Wilson and Gallant, 2000;Zhao et al, 2009;Orlandini et al, 2014). This was for consistency with the HydroSHEDS drainage direction approach used to derive UPLAND areas in this study, which were calculated using D8.…”

“…TRIP, Grid-2-Grid, Dadson and Bell, 2010). However, in areas where turbulence or diffusional effects lead to significant hydrologic dispersion, flow lines may not coincide uniformly with slope lines (Rice et al, 2008;Orlandini et al, 2014). Deriving channel networks from terrain data has been an area of active recent research (e.g.…”

“…Deriving channel networks from terrain data has been an area of active recent research (e.g. Orlandini et al, 2014) and there…”

“…is not yet universal agreement between the many different methods for calculating drainage/flow directions from DEM data (see discussions in Wilson and Gallant, 2000;Zhao et al, 2009;Orlandini et al, 2014).…”