The generalized Nash model for river flow routing

•An analytical expression of a generalized Nash model was deduced.•A real-time forecasting method based on the generalized Nash model was proposed.•The proposed approach improves the predictive ability of the IUH method. The widely used instantaneous unit hydrograph (IUH) based on the Nash cascade reservoir model was obtained under a zero initial condition, or equivalently an empty reservoir assumption. In this study, a more general case with a non-zero initial condition is considered in the derivation of the classical Nash model. A generalized Nash model (GNM) has been deduced using the Laplace transform and the principle of mathematical induction. For river flow routing, the GNM physically interprets the formation of downstream outflow, i.e. the summation of the recession flow of the initial channel storage and the response to upstream inflow. The GNM, written in a state-space representation, is able to update the state of the river system in time, and hence can be applied in real-time forecasting. Two separate case studies have been used for illustration. It is indicated that the proposed updating procedure results in improved river flow forecasts when compared with the traditional IUH method.