Hillslope Hack and hydraulic distributions: Theory and Mutual Information
Abstract
Hydraulic variables of overland flow are largely influenced by the arrangement of topographic roughness which tends to divert and focus surface flow. This process adds variance to the distribution of hydraulic variables which is key for sediment entrainment, transport, and the location of channel initiaion. This study details the probability distributions of topological variables (topography, flow length, contributing area) and hydraulic variables (flow depth, velocity) and the relationships between them. This work involves two main components. The first involves theory that develops probability distributions of contributing area and flow length, which are a hillslope version of the Hack distributions. These distributions depend on the average slope, magnitude of roughness, and the color of the topographic noise. Second, numerical flow routing provides estimates of hydraulic variables. We demonstrate a relationship between the two sets of variables by calculating their mutual information. We show that for shallow flows, distributions of contributing area and hydraulic variables have large mutual information that declines with increasing depth. Additionally, we show that distributions of topography and hydraulic variables have low mutual information for shallow flows which increases with deeper flows. The consequences of this study highlight how one might predict distributions of hydraulic and sediment transport variables, which are rarely observed, from topological ones which may be directly measured.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2020
- Bibcode:
- 2020AGUFMEP014..04D
- Keywords:
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- 1815 Erosion;
- HYDROLOGY;
- 1824 Geomorphology: general;
- HYDROLOGY;
- 1825 Geomorphology: fluvial;
- HYDROLOGY;
- 1826 Geomorphology: hillslope;
- HYDROLOGY