Curvature distribution within hillslopes and catchments and its effect on the hydrological response

Abstract. Topographic convergence and divergence are first order controls on the hillslope and catchment hydrological response, as evidenced by similarity parameter analyses. Hydrological models often do not take convergence as measured by contour curvature directly into account; instead they use comparable measures like the topographic index, or the hillslope width function. This paper focuses on the question how hillslope width functions and contour curvature are related within the Plynlimon catchments, Wales. It is shown that the total width function of all hillslopes combined suggest that the catchments are divergent in overall shape, which is in contrast to the perception that catchments should be overall convergent. This so-called convergence paradox is explained by the effect of skewed curvature distributions and extreme curvatures near the channel network. The hillslope-storage Bossiness (hsB) model is used to asses the effect of within-hillslope convergence variability on the hydrological response. It is concluded that this effect is small, even when the soil saturation threshold is exceeded. Also described in this paper is a novel algorithm to compute flow path lengths on hillslopes towards the drainage network, using the multidirectional flow redistribution method.