Hydrological effects of within-catchment heterogeneity of drainage density

Local drainage density (dd) has been traditionally defined as the inverse of twice the distance one has to walk before encountering a channel. This formalization easily allows to derive raster-based maps of dd extracted straight off from digital elevation model data. Maps of local dd, which are continuous in space, are able to reveal the appearance of strong heterogeneities in the geological and geomorphological properties of natural landscapes across different scales. In this work we employ the information provided by these spatial maps to study the potential effects of the within-catchment variability of dd on the hydrologic response. A simple power law relationship between runoff yield at the local scale and the value of dd has been adopted; the hypothesis is supported by a large number of past empirical observations and modeling. The novel framework proposed (ddRWF) embeds this spatially variable runoff weight in the well-known Rescaled Width Function (RWF) framework, based on the more general geomorphological theory of the hydrologic response. The model is applied to four sub-basins in the Cascade Range Region (Oregon, USA) where strong contrasts in dissection patterns due the underlain geology have been broadly addressed in previous literature. The ddRWF approach is compared with the classic RWF in terms of shape, moments and peak of the simulated hydrograph response. Results hint that the variability of runoff yield due to the heterogeneity of dd (i.e. of hillslope lengths) determines a more rapid concentration of runoff, which implies shorter lag times, larger skewness and higher peak floods, especially in the case hillslope velocity is much smaller than channel velocity. The potential of the proposed framework relies on accounting for spatially variable losses related to geomorphologic heterogeneity in lumped rainfall–runoff models, still keeping the simple and robust structure of the IUH approach.