How Long Is a Hillslope?

Hillslope length is a fundamental parameter of landscapes, intrinsically linked to drainage density, landslide hazard, biogeomorphic cycling and hillslope sediment transport rates. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density and by identifying the kinks in slope area plots, where the hillslope domain transitions into the fluvial domain, but the reliability of these measures has never been evaluated. Here, a direct method of measuring flow paths from hilltop to channel is presented and used as the basis to evaluate the previous two methods. This technique models flow as a point source across each pixel in the DEM, based on the D-infinity flow direction and as such better models overland flow than a steepest descent algorithm.

Using this direct measurement technique estimating hillslope length from slope area plots and drainage data is shown to systematically underestimate hillslope length values, with slope area derived data showing extensive variations across similar catchments. An analysis of the influence of DEM resolution on the three methods shows that as pixel size increases both slope area and drainage density data increases approximately linearly, whereas the direct technique shows very little variation with pixel size producing consistent results on 1 to 100 metre datasets. A method is also presented to allow the direct measurement technique to be used in landscapes where the channel network cannot be constrained, highlighting the effectiveness of the technique across a range of input data types, landscapes and data resolutions. We also show how our flow path method can be further used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes.