MODELING SURFACE RUNOFF WITH KINEMATIC, DIFFUSION, AND DYNAMIC WAVES V.M.PONCE Department o/Civil Engineering San Diego State University San Diego, California 92182 USA ABSTRACT. Surface runoff can be modeled detenninistically with kinematic, diffusion, or dynamic waves. Kinematic waves convect runoff, but do not diffuse it. Diffusion waves convect runoff under a small but perceptible amount of diffusion. Dynamic waves convect runoff and strongly diffuse it. Kinematic and dy- namic waves are well established in hydrologic engineering research and practice. Diffusion waves, how- ever, have only recently been accepted in practice, as shown by their inclusion in Version 4.0 of HEC-l: Hood Hydrograph Package (Hydrologic Engineering Center, 1990). Given the current emphasis on compu- tational modeling of surface runoff, a review of these three models is warranted at this time. This paper focuses on the following: (1) definition and properties of kinematic, diffusion, and dynamic waves, (2) role of numerical diffusion in kinematic wave modeling, (3) nature of kinematic shock, and (4) role of Vedemi- kov number in surface runoff modeling. 1. Introduction The modeling of surface runoff using physically based methods with the aid of a computer is well established in research and practice. Any such modeling uses either kinematic, diffusion, or dynamic waves, with papers continuing to appear in the literature describing applications of the three models. However, there is still some confusion as to their appli- cability, as demonstrated by a recent paper by Tayfur et al. (1993), where a comparison is made of results obtained by the three models using a very steep slope (So= 0.086), while disregarding the effect of time-of-rise t r . The comparison showed essentially no difference between results obtained with any of the three models. Kinematic and dynamic waves have been established since the 1960's, first in research, and then in practice. Diffusion waves, however, have remained within the realm of re- search until only recently, when they were incorporated into Version 4.0 of HEC-l: Flood Hydrograph Package (Hydrologic Engineering Center, 1990). Given the current emphasis on computational models of surface runoff, for both water quantity and water quality ap- plications, a review of the three models is warranted at this time. Accordingly, this paper focuses on the following: (1) definition and properties of kinematic, diffusion, and dy- namic waves, (2) role of numerical diffusion in kinematic wave modeling, (3) nature of kinematic shock, and (4) role of Vedemikov number in surface runoff modeling. 121 V. P. Singh and B. Kumar (eds.), Surface-Water Hydrology, 121-132. © 1996 Kluwer Academic Publishers.