Synthetic Unit Hydrograph Based on Fractal Characteristics of Watersheds

Time of concentration is one of the main topics of physiographic and hydrology studies in watersheds, and it has relatively large impact in calculation of other hydrology parameters, especially flood peak discharge. Moreover, it is used to derive the unit hydrograph of watershed. Fractal geometry can be used as a qualitative tool in order to examine the geomorphology of rivers and also modeling of complex natural phenomena. The most important feature which is analyzed about the phenomena is the fractal dimension that has a great importance to understand and predict the behavior of river changes. This article is aimed to find relationships for time of concentration based on fractal dimension using the production of fractal triangular unit hydrograph of Walnut Gulch watershed. Accordingly, all sub-watersheds and waterways of Walnut Gulch watershed were separated using the GIS software, image of sub-watersheds were digital image processed and the fractal dimension of waterways were calculated using box counting method. Then, by fitting the curve of watershed fractal dimension with the concentration time, which had been calculated by the Kirpich method, a new time of concentration relation was obtained based on the fractal dimension. Finally, fractal triangular unit hydrograph was developed using the new time of concentration. Results showed that the developed triangular unit hydrographs had a relatively appropriate match with NRCS triangular unit hydrograph.