Simplifications of watershed geometry affecting simulation of surface runoff

In formulating the equations describing the flow of water on the surface of a watershed, geometric simplifications must be made. A geometric simplification is the substitution of a simple geometry for a more complex one. The problem is to examine techniques for and consequences of such simplifications, and thereby develop objective procedures for geometric simplification of complex watersheds. Watershed geometry is represented by a series of planes and channels in cascade. When overland flow and open-channel flow in the cascade are described by the kinematic wave equations, the resulting mathematical model is called the kinematic cascade model. Planes are fitted to coordinate data from topographic maps by a least-squares procedure. Residuals of this fit form a geometric goodness-of-fit statistic as the improvement over using the mean elevation. Channel elements are determined, using Gray's method, as the slope of the hypotenuse of a right triangle with the same area as that under the observed stream profile. The ratio of the altitude of this right triangle to the total relief of a stream is the index of concavity, a channel goodness-of-fit statistic. An overall goodness-of-fit statistic is the drainage density ratio, the ratio of drainage density in the cascade of planes and channels to drainage density of the watershed. The mean value of a hydrograph goodness-of-fit statistic, as the improvement over using the mean discharge, increases as the geometric goodness-of-fit statistic increases but also decreases as the drainage density increases. A combined goodness-of-fit statistic, the product of the drainage density ratio and the geometric goodness-of-fit statistic, is related to the degree of distortion in optimal-hydraulic roughness parameters. Distortions in watershed geometry result in optimal roughness parameters smaller than the corresponding empirically derived values for simple watersheds where less distortion is involved. Given rainfall, runoff and topographic data for a small watershed, it is possible to define the simplest kinematic cascade geometry which when used in simulation will, on the average, preserve selected hydrograph characteristics to given degree of accuracy.