Channel Routing Using Discrete Hayami Convolution Method with Applications to the Water Erosion Prediction Project (WEPP) Model

Li Wang

The primary goal of this research was to evaluate different channel routing methods that are suitable for watershed modeling and to develop channel routing routines that can be incorporated into typical watershed models. The specific objectives were (1) to investigate common channel-routing methods and apply them to a selected watershed model, i.e., the Water Erosion Prediction Project (WEPP) model; (2) to investigate the discrete Hayami convolution solution for linear diffusion-wave channel routing with uniformly-distributed lateral inflow; (3) to analyze the accuracy of the Muskingum-Cunge method for constant-parameter diffusion-wave channel routing with spatially and temporally variable lateral inflow; and, (4) to evaluate current channel-routing methods in the WEPP model. For the discrete Hayami convolution channel routing, there were two ways of calculating the discrete kernel function values: using the exact point values or the center-averaged values. When the exact point values were used, the mass balance error of channel routing was dependent on the number (<italic>N</italic>) of time steps on the rising limb of the kernel function. For the case applications, the mass balance error was negligible when <italic>N</italic>>1.8. When the average kernel function values were used, however, the mass balance was always preserved since the integration of the discrete kernel function was always unity. The constant-parameter Muskingum-Cunge (CPMC) method is generally second-order accurate. With specific discretizations such that the temporal and spatial intervals maintain a certain relationship, the CPMC can be third-order accurate. For channel routing in watershed modeling, lateral inflow is more important than upstream inflow and its accuracy can substantially affect the overall accuracy of channel routing. I derived the average lateral inflow terms in the second- and third-order accuracy CPMC. The derived equations indicate that for spatially and temporally variable lateral inflow, the average lateral inflow terms are affected not only by their spatial and temporal variations, but also by the numerical discretizations as well as wave celerity and diffusion coefficient of the channel flow. Three channel routing methods, including the linear kinematic-wave, CPMC, and modified three-point variable-parameter Muskingum-Cunge, have been incorporated into WEPP. A sensitivity analysis for a hypothetical watershed showed that the simulated peak discharge was sensitive to time-step size, channel length, and channel bed slope, and not sensitive to channel width and channel bank inverse slope. A brief guide for selecting the appropriate channel routing method in WEPP applications under different watershed and channel conditions was provided.

Channel Routing Using Discrete Hayami Convolution Method with Applications to the Water Erosion Prediction Project (WEPP) Model

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