Control of Local Hillsope Velocity and Runoff Productivity on the Shape and Peak of Catchment Response

Abstract:

We propose a geomorphologically-based statistical framework where the distribution of travel times in a basin following an instantaneous rainfall is derived from the pdf of hillslope and channel lengths. Based on previous works, marginal distributions for hillslope and channel length pdfs are assumed to be Gamma and Beta with variation coefficients 0,4 and 0,9 respectively, while the bivariate probability model is obtained assuming a Gaussian copula function. We consider different scenarios involving both deterministic and random hillslope velocity (while a reference, constant channel velocity is kept); this allows to explore the role of the kinematic component of basin response across different scales. Further, we employ drainage density as a proxy measure to explore the effects of the variability of runoff yield. This conceptual framework is used as a virtual laboratory to understand what controls the scatter of arrival times of water drops and the peak flow of the hydrologic response. Numerical simulations are performed varying the following contolling factors (i) the ratio between streamflow velocity and average hillslope velocity (ii) the geomorphological characteristics and the scale of the basin and (iii) the correlation coefficient r’ between hillslope and channel lengths.

The approach is suitable to investigate how the relative roles of dispersion mechanisms change due to upscaling effects, up to very large scales (where channels completely dominates), and how this affects the hypothesis of simple scaling of peak floods.

We find that the hillslope kinematic dispersion alters the scatter of arrival times in a wide range of basin scales: it abridges the pdf of travel times for basin with negative r’ (which involves higher peak flows), while increases the dispersion of travel times when r’ is positive. Nonetheless, when random hillslope velocity with increasing variation coefficients are considered, the contribution of kinematic dispersion becomes invariantly positive, i.e. results in higher travel times variance and smaller peak flows. Non-uniform runoff production, represented through local drainage density as a proxy measure, introduces an additional component of dispersion which doesn't fade away under asymptotic conditions.