Mathematical modeling of response from small watershed
Date
1974
Authors
Li, Ruh-Ming, author
Simons, Daryl B., advisor
Karaki, Susumu, committee member
Labadie, John W., committee member
Meiman, James R. (James Richard), committee member
Shen, H. W., committee member
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Abstract
The physical quantities which describe the major watershed response to the precipitation are the water yield, the sediment yield, and the resultant stream morphology. This study provides the theoretical background and numerical methods for modeling physical processes governing the watershed response. A method of nonlinear kinematic wave approximation for flow routing has been developed to route water and sediment over land and in channels. The numerical scheme developed in this study is unconditionally stable and may be used with a wide range of time increment to space increment ratio without loss of significant accuracy. From theoretical considerations, it has been found that the flow discharge is the better selection for the unknown in numerical computations than the depth or area. The applicability of the numerical method has been tested in various cases - overland flow, natural channel, and small drainage system and has been found satisfactory for modeling of watershed response. As the applications of this flow routing procedure, a rainfall-runoff model for simulating hydrographs from small watersheds and a rainfall erosion model for calculating time-dependent erosion rates from overland flow areas have been developed. The rainfall-runoff model simulates hydrographs on the single storm basis. The model includes the water balance simulation for land surface hydrologic cycle and the water routing features for both overland flow and channel systems. Unlike the conventional approach to parametric modeling of watershed response, this model contains much more information on the physics of flow and requires much less assistance from optimization schemes than any existing water models known to the writer. For the tested basin the simulated hydrographs agree reasonably well with the measured hydrographs. The sensitivity analysis indicates that soil data are very sensitive to the computed hydrograph. Flow resistance parameters and vegetation data are less sensitive to the simulated results. In addition, this physically oriented model has the capability to predict watershed treatment effects on water yields. The rainfall-erosion model simulates both water flow and sediment flow routing in overland flow areas and produces time-dependent erosion rates comparable with the available experimental data from a soil plot. The model can generate time-dependent land forms, and the generated land form tends to be concave in shape which frequently appears in nature. It was also found that the soil erosion rate was very sensitive to the bed slope and shape. The general practice of assuming a uniform shape may result in serious errors. The mathematical models in this study may provide the short-term and the long-term responses. Theoretical interpretation of the long-term response was also made. The equations describing the basic physical processes in small watershed channels sculptured in noncohesive alluvial materials have been employed to derive the hydraulic geometry equations. Both downstream and at-a-station relations were developed. This work provides information on stream morphology response to the modified amount of precipitation or to watershed treatment effects.
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Subject
Watersheds -- Mathematical models