UBC Theses and Dissertations
Runoff concentration in steep channel networks Kellerhals, Rolf
The objective of this study is the development of a runoff routing procedure, applicable to steep channel networks in the tumbling flow regime, and suitable for incorporation into more comprehensive mathematical representations of the runoff process. "Steep" is meant in the sense that degradation into existing, coarse deposits (e.g. Pleistocene materials, slide debris, scree) is assumed to be the major channel-forming process. Similarity considerations show that under these circumstances two relatively easily available parameters, such as channel slope and drainage area, or channel slope and width are adequate to define the geometry and hydraulic performance of the channels. The hydrologically significant aspects of channel flow are storage per unit length (area) and discharge, with the relation between the two defining the channel performance under steady conditions. This function, A = f(Q), can be obtained in the field by observing the dispersion of slug-injected tracers through fixed test reaches over a range of discharges. Measurements of this type were made on thirteen test reaches, covering a wide range of channel size and slope. The data from all test reaches can be closely approximated by exponential relations of the form [formula omitted]. As indicated by the similarity considerations, the constants aA and bA of this steady flow equation are predictable from basin parameters. The details of the statistical link between various basin parameters and the above constants are discussed in Day (1969) on the basis of the steady flow data of this study supplemented by extensive.additional measurements. Runoff concentration is an unsteady flow process, which can only be defined with a single flow equation if the flow system is truly kinematic. In order to investigate whether this holds for steep channels, all test reaches were located below lakes with outlets suitable for minor discharge modifications. Small, step-like surges (positive and negative) were created at the lake outlets and their propagation through the test reaches was observed with accurate water level gauges. These surge tests indicate consistently that the channels act as kinematic flow systems but with certain dispersive effects added and with a markedly higher-than-kinematic wave celerity at very low stage, which is probably the result of dynamic waves in pools. Due to the frequent occurrence of super-critical flow, dispersion can only be the result of storage in pools. The differential equation for a kinematic channel with storage in a large number of identical storage elements is derived and solved in linearized form for step-like input corresponding to the surge tests. The dispersion coefficient, which has dimensions L, is the only free parameter of the solution. Comparison with the field data shows that mean water surface width provides a good estimate of this parameter. As a computationally simpler alternative, a routing model which replaces the actual channels by a sequence of truly kinematic channels and deep pools with weir outlets, both obeying the same steady-flow equation, is also considered. Rules for determining the two free parameters of this solution are developed on the basis of the field data. Both routing methods provide approximately equal fit to the surge test data and they both appear to be suitable components for an operational channel runoff model. Being based mainly on the above steady flow equation, both methods are non-linear. This is supported by the field data, which show no tendency towards linearity, except possibly at very low stage.
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