J.E. Miller 1984 <p>The kinematic-wave model is one of a number of approximations of the dynamic-wave model. The dynamic-wave model describes onedimensional shallow-water waves (unsteady, gradually varied, openchannel flow). This report provides a basic reference on the theory and applications of the kinematic-wave model and describes the limitations of the model in relation to the other approximations of the dynamic-wave model. In the kinematic-wave approximation, a number of the terms in the equation of motion are assumed to be insignificant. The equation of motion is replaced by an equation describing uniform flow. Thus, the kinematic-wave model is described by the continuity equation and a uniform-flow equation such as the wellknown Chezy or Manning formulas. Kinematic-wave models are applicable to overland flow where lateral inflow is continuously added and is a large part of the total flow. For channel-routing applications, the kinematic-wave model always predicts a steeper wave with less dispersion and attenuation than actually occurs. The effect of the accumulation of errors in the kinematic-wave model shows that the approximations made in the development of the kinematic-wave equations are not generally justified for most channel-routing applications. Modified flow-routing models can be used which help to stop the accumulation of errors that occur when the kinematic-wave model is applied.</p> application/pdf 10.3133/pp1302 en U.S. Geological Survey Basic concepts of kinematic-wave models reports