Correlation between channel and hillslope lengths and its effects on the hydrologic response

In the geomorphologic approach based on width functions, the instantaneous response function (IRF) is completely determined once the distributions of hillslope and channel lengths in addition to flow parameters are assigned. The relative contributions of hillslopes and channels to the variance of the travel times have been analyzed in the literature, and three different variance-producing mechanisms, namely geomorphologic, kinematic and hydrodynamic have been identified. In this study the width function approach is employed to investigate a dispersive mechanism of geomorphologic and kinematic nature, due to the existence of a relevant correlation between hillslope and channel lengths distributions. The effects of this correlation on the variance of the IRF were neglected in previous works, assuming that the two distributions are uncorrelated. Here several basins of different size in the central Apennines (Italy) have been studied, finding that both positive and negative values of correlation can occur, their absolute values being seldom negligible. The sign of the correlation is related to the distribution of slopes within the basin, thus appearing to be influenced by typical morphologic signatures such as the presence of canyons or alluvial valleys. In particular, basins with large flat areas located near the outlet generally show negative values of correlation and are consequently more prone to produce peaked flow hydrographs. Finally an analytical expression is proposed to investigate the size of the catchments whose hydrologic response can be considerably affected by the hillslope–channel correlation.