The use of extremal hypotheses as a means of predicting alluvial channel dimensions for river restoration
Abstract
In designing fluvial infrastructure and restoration projects the question often arises, what are the cross sectional characteristics of width, depth, roughness, and slope necessary to ensure no net aggradation or degradation occurs within a given reach of river? Current fluvial design utilizes empirical and numerical methods to calculate the required slope and geometry of alluvial channels; however, no solution has been proposed that fully incorporates the necessary 3-dimensional mechanics of open channels due to the complicated processes and feedbacks that occur during mobile bed conditions. This is further compounded by numerous local geologic constraints and perturbations that must be considered, which interrupt the evolution towards a balance of deposition and erosion, or the condition of dynamic-equilibrium. However, given the moderate success of power law relations, such as regime theory and hydraulic geometry, it is evident self-organizing processes are present in watersheds that scale channel size and sinuosity to some average condition in order to maintain a balance of fluid and sediment flux from the upstream catchment. Extremal hypotheses have been developed as an alternative to solving the reach scale 3-dimensional conservation laws for fluid and sediment, to provide a first order means of predicting channel dimensions in an objective and reproducible manner. This study evaluates the performance of extremal hypotheses in identifying the trend towards dynamic-equilibrium over unique spatial gradients in 2 gravel-bed river systems. Using a location-for-time-substitution approach, extremal hypotheses were examined over a longitudinal gradient of channel evolution towards reaches found to be near equilibrium in an unconfined, transport-limited river in the undisturbed rain forest of Chilean Patagonia and a supply-limited, semi-confined canyon system in Central Idaho, USA. Field data from these two sites imply alluvial systems attempt to minimize their energy expenditure as they approach dynamic-equilibrium. Those extremal hypotheses proposing to maximize certain criteria, such as maximum hydraulic radius, maximum sediment transport capacity, or maximum flow efficiency were not supported by the trend in field data. An analytical substitution method was employed for those extremal hypotheses that successfully identified the trend towards dynamic-equilibrium, in order to discern how channel variables differentiate the various hypotheses from one another. Similar response was seen in the extremal hypotheses when roughness was maximized and channel slope was minimized; however, differences emerged between the hypotheses when width and depth were allowed to vary. An analytical scaling coefficient was developed over the longitudinal gradient to examine how width and depth changed as the channel approached dynamic-equilibrium and was used to identify the most appropriate hypothesis for alluvial design projects. Results primarily support the minimum specific stream power hypothesis with secondary support for minimum Froude number and minimum unit stream power. Further investigation is required to evaluate how sensitive the resultant channel dimensions are when various sediment transport relations are used in combination with extremal hypotheses.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFMEP54A..01T
- Keywords:
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- 1825 HYDROLOGY Geomorphology: fluvial