RN-11 : Overland flow

Abstract

Overland flow is defined as a thin sheet flow occurring before surface irregularities cause a gathering of runoff into discrete stream channels. The primary distinguishing characteristic of overland flow is its shallow depth relative to roughness elements. The overland flow is an unsteady free surface flow and the most dynamic part of the response of a watershed due to excess precipitation. Since the floods are mainly due to direct surface runoff resulting from excess precipitation, therefore the accurate estimation of the direct surface runoff will provide the better estimates of the flood peaks and frequencies to the engineers and scientists involved for the design of flood control structures. Linear mathematical models describing stream or river out flow due to storm runoff do not explain several important observed features, such as the change in shape of the discharge hydrograph, the non-linear variation of peak discharge rate with variation of rainfall intensity. Numerical model based upon the shallow water equations or the kinematic wave equations can be used to calculate runoff hydrographs resulting from rainfall on small watershed as it overcomes the deficiencies associated with the linear models. The kinematic wave approximation model has also advantages over the linear model for predicting runoff for ungauged watersheds because the model structures and resistance parameters can be estimated without prior rainfall and runoff records.

The first step in applying these models is to decide upon the model geometry The simplest way is to represent the catchments by simple geometric elements such as a combination of two planes and channel or linearly converging or diverging sections. The next step is the solution for the overland flow. Horton and Izzard had solved the mass balance equation for the estimation of overland flow. Later on Behlke, Henderson, Wooding, Morgali,Linsley,Abbott,Brakensick and Woolhiser had applied method of characteristics for solving continuity and momentum equations numerically. Different shapes of input are considered as a separate case, out of those three cases are of our interest: (i) the rising hydrograph for a constant input and initially dry conditions, (ii) the recession from steady outflow conditions after the cessation of input and (iii) the transition from one steady state to another when there are two different constant supply rates in successive intervals of time.

Generally two main problems arise with kinematic flow modelling (i) the physical relevance of the kinematic shocks that result from the mathematics (ii) the adequacy of the numerical scheme with respect to its stability and convergence to the equations that the scheme is intended to represent it. Indeed numerical schemes based upon a direct discretization of the partial differential equations are incapable of predicting and tracking the shocks that are known to occur in the exact solution. Instead, instability or convergence to a different set of equations result. A general review has been made for different numerical schemes utilized by various investigators for modelling the overland flow, The advantages and limitations of these numerical schemes are also described.