Kinematic Wave Controversy

Abstract

Kinematic and diffusion waves are reviewed prompted by the continuing controversy regarding their nature and applicability. Kinematic waves are shown to be nondiffusive, but to undergo change in shape due to nonlinearity. This latter feature gives kinematic waves the capability of steepening, eventually leading to the formation of the kinematic shock. Kinematic wave solutions using finite differences are shown to possess intrinsic amounts of numerical diffusion and dispersion. These numerical effects are artificial and tend to disappear as the grid size is refined, making the solution dependent on the choice of grid size. Kinematic wave theory can be improved by extending it to the realm of diffusion waves. In this way, the diffusion inherent in many practical runoff computations can be accounted for directly in the modeling, rather than as an afterthought. The use of a kinematic wave method is indicated for small catchments, in cases where it is possible to resolve the physical detail without compromising the deterministic nature of the model. Conversely, the unit hydrograph is advocated for midsize catchments, where the kinematic wave method may prove difficult to implement. The dynamic extension to kinematic and diffusion models shows promise, particularly for modeling channel and flow conditions in which the Vedernikov number is substantially different from zero.