Application of shallow water equations to analyze runoff processes in hilly farmlands

Abstract

Analysis of runoff processes in farmlands during storm events in particular is an important engineering topic. The shallow water equations describing the physical conservation laws are attractive tools for understanding motion of surface water. A numerical model is developed to reproduce surface water flows during storm events, using the finite element method and the finite volume method applied to the one-dimensional shallow water equations. The numerical model has the advantage of dealing with transcritical flows, wet, and dry processes, irregular channel bed slopes, and channel junctions involving multiply connected networks. Standard numerical tests demonstrated some of these features. Runoff processes from farmlands in a Japanese hilly area is analyzed with the numerical model coupled with another runoff model of black-box type. Parameters of the models are calibrated and validated using observed series of rainfall and runoff discharge data. Simulated results included submergence of hydraulic jumps and flood storage in farming plots, which are very informative in terms of assessing diverse functions of the farmlands.