ACCURACY CRITERIA FOR LINEARIZED DIFFUSION WAVE FLOOD ROUTING

The spatial step size for the second-order accurate Muskingum-Cunge (M -C) method is determined by the spatial weighting factor. Both the spa tial weighting factor and the time step must be selected judiciously t o obtain accurate solutions. In this study, accuracy criteria for the linearised diffusion routing problem are discussed. Starting from the truncation error analysis of the general finite-difference scheme used to solve the kinematic wave equation (of which the M-C method is a sp ecial case), conditions necessary to obtain second-, third- and fourth -order accurate solutions to the linearised diffusion routing equation are derived. For given diffusion coefficient and celerity, the spatia l step of the fourth-order scheme is fixed, whereas third- and second- order solutions are available for independently selected spatial steps . In order to achieve optimal solutions to the second-order accurate s cheme, the truncation error criteria are combined with a condition der ived from the concept of column holdup. This combination is shown to p roduce results as good as those from the third-and fourth-order accura te schemes. The simplest explicit method is shown to give satisfactory results for flood data from the River Wye (UK).