Abstract
This paper describes some theoretical considerations on reproducing flash floods in super-critical flow state using the depth hydrograph given at one site in the downstream section of a river. Based on the method of characteristics, the analytical solution of linearized shallow water equations is firstly derived under the depth and velocity hydrographs at the upstream boundary, which are given as the power series of time. It should be pointed out through the theoretical examination of the derived analytical solution that the depth and velocity hydrographs at the upstream boundary can be calculated in principle using the depth hydrograph at one site in the downstream region. Further investigations are required to develop the practical computational method to reproduce flood flows in an actual river using only the water stage hydrograph observed at one site.
