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A Proposed Mechanics for the Investigation of Surface Runoff From Small Watersheds: 1, Development
Author(s) -
Merva George E.,
Brazee Ross D.,
Schwab Glenn O.,
Curry R. Bruce
Publication year - 1969
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr005i001p00076
Subject(s) - brownian motion , mechanics , surface roughness , langevin equation , surface runoff , surface (topology) , watershed , particle (ecology) , stochastic process , statistical physics , classical mechanics , environmental science , mathematics , physics , geology , statistics , thermodynamics , computer science , geometry , ecology , biology , oceanography , machine learning
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.