This study investigates the relations between the shape of hydrologic responses and the dynamic transport properties of channel networks within the framework of random walks on fractal networks, focusing on the shape parameter of Nash model. To this end, we evaluate the static fractal structures and the dynamic transport properties of various channel networks and, then, validate Liu's conjecture (1992) for the shape of hydrologic responses. In the context of random walks on fractal networks, the fractal dimensions of channel networks can directly connect the static structure to the dynamic transport properties of channel networks through Horton's law of drainage composition. It is observed that the peak coordinates of hydrologic responses would have a more intimate relation to the connectivity of channel networks than the conductivity of those. The characteristic times of hydrologic responses also tend to be related to the connectivity of channel networks. Thereby, the shape of hydrologic responses would be expected directly affected by the fractal dimension of channel networks in terms of their static structure, while interpreted a combined result of the conductivity and the connectivity of channel networks in terms of their dynamic transport properties. So, the runoff hydrographs of a river basin could be considered shaped by the fractal dimensions of its channel networks following the linear hydrologic system theory.
Keywords: Channel network; Fractal dimension; Horton's ratios; Nash model; Random walk.
© 2022 The Author(s).