43 Journal of Hydrology, 69 (1984) 43-58 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands [ 4] A NEW NON-LINEAR CONCEPTUAL MODEL OF FLOOD WAVES j  JAROSLAW J. NAPIORKOWSKI AND PHILIP O'KANE Institute of Geophysics, Polish Academy of Sciences, Warsaw (Poland) Department of Civil Engineering, University College Dublin, Dublin (Ireland) (Received February 22, 1983; revised and accepted April 8, 1983) ABSTRACT Napiorkowski, J.J. and O'Kane, P., 1984. A new non-linear conceptual model of flood waves. J. Hydro!., 69: 43-58. This paper reports the successful simulation of St. VEmant's nonlinear distributed model of flood waves in open channels using a much simpler nonlinear lumped concep- tual model. The simpler model is composed of a cascade of equal nonlinear storage elements preceded by an element of pure delay. The simpler model depends on four parameters only. The first two terms of the Taylor expansion of the state trajectory are shown to be equivalent to the first two terms of a Volterra convolution series. The accuracy of this quadratic approximation is shown by an example. 1. INTRODUCTION The problem of synthesis or simulation in systems hydrology is the quest for a model which will convert a known input to a known output within certain limits of accuracy. It involves the selection of a model and the testing of the operation of this model by analysis (Dooge, 1973, pp. 10-12). The "known input" in this study is an assumed flood wave at a measuring station on a river. The "known output" is the corresponding flood wave at a station further downstream as given by a numerical solution of the non- linear St. Venant model. A relatively simple non-linear conceptual model is chosen. The parameters of the model are selected so as to convert the "known input" into an output which is as close as possible to the "known output". A second input is chosen and the model is tested by comparing the outputs from the concep- tual model and the St. Venant model. Such a test can be repeated as often as desired, in order to establish the accuracy with which the conceptual model simulates the more complex St. Venant model. If the conceptual model can be made to match the output from the St. Venant equations for a variety of inputs, then a considerable simplification would be achieved. The advantages to be gained are: 0022-1694/84/$03.00 © 1984 Elsevier Science Pu blishers B. V.