Discretization of the Generalized Nash Model for Flood Routing

The discretization of the generalized Nash model (GNM) has been made in such a way that it can be applied easily to the sample-data system for flood routing. First, the variable $S_n$-curve was introduced to simplify the GNM. Under a commonly used assumption that the streamflow changes linearly between any two measurements, the simplified GNM was further discretized to a linear expression of the inflows and outflows. Then, the discrete generalized Nash model (DGNM), as well as its multistep-ahead form, that is, $m$-DGNM, was obtained, by which the outflow was produced by the old water stored in the river reach and new water from the upstream inflows. The weight coefficients of the old and new water were expressed in explicit functions of the $S_n$-curve, which makes the DGNM and $m$-DGNM easy to compute and more intuitive than the GNM. To test the predictive ability of the DGNM, a comparison with the widely used Muskingum method and dynamic wave model was made. Results showed that with some historical information included, the DGNM is more adaptive and accurate than the Muskingum method. Compared to the complicated dynamic wave model, the DGNM is relatively simple to implement and reasonably accurate. Then, the DGNM and $m$-DGNM were further applied to the Qingjiang River for flood routing. Reasonable results obtained suggest that they are highly suitable for practical flood routing applications.