Abstract
Abstract. Surface flow on rilled hillslopes tends to produce sediment yields that scale nonlinearly with total hillslope length. The widespread observation lacks a single unifying theory for such a nonlinear relationship. We explore the contribution of rill network geometry to the observed yield–length scaling relationship. Relying on an idealized network geometry, we formally develop probability functions for geometric variables of contributing area and rill length. In doing so, we contribute towards a complete probabilistic foundation for the Hack distribution. Using deterministic and empirical functions, we then extend the probability theory to the hydraulic variables that are related to sediment detachment and transport. A Monte Carlo simulation samples hydraulic variables from hillslopes of different lengths to provide estimates of sediment yield. The results of this analysis demonstrate a nonlinear yield–length relationship as a result of the rill network geometry. Theory is supported by numerical modeling, wherein surface flow is routed over an idealized numerical surface and a natural surface from northern Arizona. Numerical flow routing demonstrates probability functions that resemble the theoretical ones. This work provides a unique application of the Scheidegger network to hillslope settings which, because of their finite lengths, result in unique probability functions. We have addressed sediment yields on rilled slopes and have contributed towards understanding Hack's law from a probabilistic reasoning.
Highlights
Rilled hillslopes are common in semiarid, agricultural, and recently disturbed landscapes (Fig. 1)
We consider the role of the rill network geometry in contributing to this nonlinear relationship
We develop a theory for rill network geometry that is based on the Scheidegger model (Scheidegger, 1967)
Summary
Rilled hillslopes are common in semiarid, agricultural, and recently disturbed landscapes (Fig. 1). There is a long legacy of work that explores the mechanics and consequences of rill processes through field observation, experimentation (Govers, 1992; Liu et al, 2000), and numerical simulation (Hairsine and Rose, 1992; McGuire et al, 2013). This body of work highlights a number of key observations and relationships. We consider the role of the rill network geometry in contributing to this nonlinear relationship
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
