Computational Aspects in Kinematic Modelling

Mathematical and computational properties of kinematic wave models in hydrology are reviewed and discussed. Special attention is paid to questions relating to the formation and propagation of shocks as well as the presence of numerical diffusion in certain finite difference schemes. As shocks and shock structures (the latter obtained from higher-order “parent” models) travel with the same celerity, locally increased error in the vicinity of a solution discontinuity does not invalidate the kinematic model. Care must be taken, however, in the evaluation of numerical results, as parasitic oscillations may develop. Numerical diffusion inherent in several numerical schemes should either be suppressed or matched to a previously determined amount of physical diffusion. The practical usefulness of kinematic models in hydrology is discussed, and so are certain recent modelling attempts aiming beyond the micro-catchment scale. Finally, fields of future research are indicated.