Studies on Rainfall-Runoff Modeling, 2. A Distributed Kinematic Wave Model of Watershed Surface Runoff

The traditional formulation of kinematic wave theory assumes the kinematic wave friction relationship parameter to be constant. The present study waives this assumption of parameter constancy, allows continuous spatial variability in the parameter and develops a more general formulation of the kinematic wave theory. This concept of parameter variability leads to a completely distributed model, and might eliminate the necessity of utilizing a complex network model to represent the watershed system. Furthermore, this more general formulation will reduce the complexity of modeling watershed surface runoff, and will greatly save computational time and effort.

A systematic treatment to the problem of surface runoff is developed. It is shown when and where explicit analytical solutions are feasible. To develop mathematical solutions two cases are distinguished: one leading to the equilibrium hydrograph and the other leading to the partial equilibrium hydrograph.

The overland flow on an infiltrating plane 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 mathematical solutions infiltration and rainfall are represented by simple space-and-time invariant functions.

The proposed distributed kinematic wave model is utilized to predict surface runoff from three natural agricultural watersheds. For determination of the kinematic wave friction relationship parameter a simple relationship between the parameter and topographic slope is hypothesized. The simple relation contains two constants which are optimized for each watershed by the Rosenbrock-Palmer optimization algorithm. The model results are in good agreement with runoff observations from these watersheds. It is shown that if model structure 18 sound it will suffice to optimize parameters on hydrograph peak only, even for prediction of the entire hydrograph.

Current kinematic wave models of watershed runoff incorporate either numerical or analytical solutions, depending upon the type of input (rainfall pattern) and representation of watershed geometry. Numerical solutions are time-consuming; analytical solutions are not always feasible. This study formulates these models in terms of an approach called hybrid approach which is part numerical and part analytical. By applying it to a set of nine rainfall-runoff events on a natural watershed it is demonstrated that this approach is computationally far more efficient than a totally numerical one, and is applicable where analytical solutions are not feasible.

Project No. 3109-206