REDUCTION OF THE DIFFUSION HYDRONAMIC MODEL TO KINEMATIC ROUTING

Introduction

The twodimensional DHM formulation of equation 32 can be simplified into a kinematic wave approximation of the twodimensional equations of motion by using the slope of the topographic surface rather than the slope of the water surface is the friction slope in equation 28. That is, flowrates are driven by Manning's equation, while backwater effects, reverse flows, and ponding effects are entirely ignored. As a result, the kinematic wave routing approach cannot be used for flooding situations such as considered in the previous chapter. Flows which escape from the channels cannot be modeled to pond over the surrounding land surface nor move over adverse slopes, nor are backwater effects being modeled in the open channels due to constrictions which, typically, are the source of flood system deficiencies.
In a recent report by Doyle et al. (1983), an examination of approximations of the onedimensional flow equation is presented. The authors write:
"It has been shown repeatedly in flowrouting applications that the kinematic wave approximation always predicts a steeper wave with less dispersion and attenuation than may actually occur. This can be traced to the approximations made in the development of the kinematic wave equations wherein the momentum equation is reduced to a uniform flow equation of motion that simply states the friction slope is equal to the bed slope. If the pressure term is retained in the momentum equation (diffusion wave method), then this will help to stop the accumulation of error that occurs when the kinematic wave approximation procedure is applied."
Application 8: Kinematic Routing (OneDimensional)
To demonstrate the kinematic routing feature of the DHM, the onedimensional channel problem used for the verification of the DHM is now used to compare results between the DHM model and the kinematic routing.

