This paper is concerned with the reproduction of flash floods with high Froude number. In order to reproduce unsteady super-critical flows, it is common to give two hydrographs of depth and discharge based on the method of characteristics. Since we pointed out recently the possibility and the computational method to reproduce flood flows for sub-critical flows using one depth hydrograph, the theory and method are extended to unsteady super-critical flows in this paper. Non-linear analytical solutions with boundary hydrographs at the upstream end are firstly derived. Then, it is proved that the boundary hydrographs at the upstream end can be reproduced inversely, using the solution of one depth hydrograph at one site.