Incorporating hillslope effects into the geomorphologic instantaneous unit hydrograph

Abstract

Use of gamma distributions of stream holding times, rather than the traditional exponential distributions, results in geomorphologic instantaneous unit hydrographs (GIUHs) that better fit data‐based IUHs. In this paper, hillslope effects are incorporated into the gamma GIUH (GGIUH) model by assuming that the hillslope travel distance in an area of a given order is approximated by the inverse of twice the local drainage density and introducing a hillslope velocity term. A method of moments fitting procedure is developed to estimate the channel and hillslope velocity terms in the GGIUH model from the moments of rainfall input and basin discharge output. It was found that hillslope velocities are 2 orders of magnitude smaller than channel velocities. The values found for the latter are reasonable given the range of values given in the literature for channel velocities. Similarly, the hillslope velocity term found by the method of moments procedure matches macropore velocities reported in the literature.