Kinematic Wave Analysis of Sheet Flow Using Topography Fitted Coordinates

Abstract

A methodology for simulating 2D sheet flow is examined. Although used in the past, a mathematical derivation of the methodology was not presented, and methodology performance without uncertainties introduced by infiltration estimates was not examined. The methodology solves a 1D kinematic wave equation for variable width, curvilinear flow paths. This equation is derived from the 2D kinematic wave equation expressed in orthogonal-curvilinear coordinates by aligning the coordinate system with runoff surface topography. The 1D equation is solved by a four-point, implicit finite-difference scheme. A sheet flow model using multiple flow paths is described and tested on an impervious surface. Although simulated discharges agree well with observed values, additional testing is needed to further validate model accuracy. Practical considerations for model use are discussed.