How Do Channel Network Expansions and Retractions Affect the Shape of Hillslope Flowpath Length Distributions?

Abstract

The length of hillslope flowpaths plays a crucial role in various hydrological, geomorphological and ecological processes. However, hillslope lengths change as the flowing network expands or contracts in response to precipitation. Currently, there is limited understanding of how channel network dynamics influence the distribution of hillslope flowpaths, with existing studies primarily focusing on the numerical analysis of specific case studies. In this work, we propose an analytical framework to characterize the general principles underlying variations in the hillslope length distribution as a function of the total length of the drainage network, $$L$$. Our model provides a closed‐form solution for the probability density function of the distance‐to‐channel conditioned on the total flowing network length, $$\omega (\ell ,L)$$. As a benchmark, the model has been applied to 15 headwater catchments with a non‐perennial river network, achieving reasonably good performances. The model captures the change in shape of the hillslope length distribution as the network expands, in particular the increased probability associated with shorter flowpaths. Empirical data and model results suggest the existence of some universal features in the way the hillslope length pdf responds to variations in the flowing network: longer paths are systematically more affected than shorter ones, and the overall fraction of impacted pathways decreases as the channel network lengthens. Besides the theoretical insights, our method offers a simple analytical means to determine the shape of the hillslope length distribution for varying drainage densities, even when the numerical evaluation of $$\omega (\ell ,L)$$ is challenging.