A new topographic index to quantify downslope controls on local drainage

Abstract

Topography is an important control on hydrological processes. One approach to quantify this control is the topographic ln(a/tanβ) index. This index has become widely used in hydrology, but it utilizes a relatively small portion of the information contained in a digital elevation model (DEM). One potentially important feature not considered in the implementation of the ln(a/tanβ) index is the enhancement or impedance of local drainage by downslope topography. This effect could be important in some terrain for controlling hydraulic gradients. We propose a new way of estimating the hydraulic gradient by calculating how far downhill (Ld, [m]) a parcel of water must move in order to lose a certain amount of potential energy (d, [m]). Expressed as a gradient, tanαd = d/Ld, values tend to be lower on concave slope profiles and higher on convex slope profiles compared with the local gradient, tanβ. We argue that the parameter d controls the deviation of hydraulic gradient from surface slope. While we determine this subjectively, landscape relief, DEM resolution, and soil transmissivity should be considered at the selection of d. We found the downslope index values to be less affected by changes in DEM resolution than local slope. Three applications are presented where the new index is shown to be useful for hydrological, geomorphological, and biogeochemical applications.