A Proposed Mechanics for the Investigation of Surface Runoff From Small Watersheds: 1, Development

Abstract

The difficulties of predicting runoff rates and volumes owing to the inadequacy of existing functional forms of the prediction equation and a lack of analytic definitions for the pertinent parameters related to the runoff process are discussed. An analogy is established between the path of water on the watershed surface and the phenomenon of Brownian motion. Probabilistic approaches are used to model a watershed surface and to obtain a stochastic surface impressed force, which acts upon a fluid particle and is found to be a statistically homogeneous function of position. Analogously to Brownian motion theory, a Langevin‐type equation containing the stochastic surface impressed force is postulated as a model for fluid particle motion on an impermeable watershed surface. The influence of surface roughness on the amount of energy available to induce and perpetuate fluid motion on a surface is considered by examining the rate of available energy degradation for a particle collection undergoing random motion induced by surface‐impressed forces.