In the traditional formulation of kinematic wave theory the kinematic wave friction relationship parameter is treated as constant. The present study relaxes this assumption of parameter constancy, allows continuous spatial variability in the parameter and attempts to develop a more general formulation of the kinematic wave theory. This concept of parameter variability leads to a completely distributed model, and might hopefully eliminate the necessity of utilizing a complex network model to represent the watershed system. Furthermore, this more general formulation appears to reduce the complexity of modeling watershed surface runoff and save greatly the computational time and effort.

A converging geometry is chosen to represent the natural watershed geometry, and is utilized to develop the converging overland flow model. A laboratory investigation is performed to study the behavior of kinematic wave parameters. It is demonstrated that for many hydrologic problems the kinematic wave parameter n can be fixed at 1.5 and thus the two-parameter model can be reduced to a one-parameter model.

The converging overland flow model is studied on a number of natural, agricultural watersheds. It is found that the topographic map of a watershed is sufficient to transform its natural geometry into an equivalent converging geometry. The concept of both parameter constancy and variability is studied in detail on several agricultural watersheds. The model, in both lumped and distributed forms, is applied to predict surface runoff from several of these watersheds.

The converging overland flow on infiltrating watersheds is formulated as a free boundary problem. Mathematical solutions are developed to study the effect of infiltration on nonlinear overland flow dynamics. To develop explicit solutions rainfall and infiltration are represented by simple space-and-time invariant functions.

Project No. 3109-206