Abstract
This paper describes some theoretical considerations on reproducing unsteady flood waves in supercritical flow state using one depth hydrograph given at one site in the downstream section of a river course. Based on the method of characteristics for shallow water equations, the analytical solutions of linearized equations were previously derived for the region just downstream of the upstream boundary. In this study, the analytical solutions are derived for the region far from the upstream boundary and are verified through the comparison to the results of numerical analysis. It is pointed out through the theoretical consideration of the derived analytical solutions that depth and velocity hydrographs at the upstream boundary can be reproduced in principle using a depth hydrograph at one site in the downstream region. Further investigations are still required to develop a practical computational method to reproduce flood flows in an actual river using only a water stage hydrograph observed at one site.
