Field study on drainage densities and rescaled width functions in a high‐altitude alpine catchment

This paper addresses the effect of accurately mapping spatially heterogeneous drainage densities in high-altitude alpine basins on Rescaled Width Functions (RWFs), used in some applications as a minimalist model of the hydrologic response. The channel network and 373 of its channel heads were mapped in the field in a high mountain catchment in the Swiss Alps. The mapped channel network is characterized by highly uneven drainage density, here described by the distribution of the length to the first channelized site computed along steepest descent from any unchannelled site. Various channel networks were extracted from a 1 m lidar-derived digital terrain model and compared with the field-mapped channel network using geomorphologic parameters, hillslope-to-channel distance and RWFs. Our results show that the channel network derived by statistical analysis of surface morphology is consistent with the field-mapped network. Larger discrepancies were observed when the channel network was obtained with classical threshold-based approaches relying on cumulative drainage area and local slope. The actual arrangement of the drainage densities has a significant impact on the RWFs. The discrepancy was largest between RWFs derived from classical extraction methods and RWFs derived with the field-mapped network, indicating an inappropriate extraction of the channelled portion of the high-altitude catchment that is a reflection of the variety of channel initiation processes. Our results suggest that spatial heterogeneity of the drainage density might play an important role in modelling streamflow generation