The relationship between watershed compactness coefficient and the fractal characteristics

The effect of watershed form on the surface runoff and hydrograph is an obvious issue. Hence a large number of researchers have considered the issue. Fractal geometry, as one of new methods, can be applied in geomorphology of rivers and also help to find some relationship between watershed form and hydrograph. The most fundamental fractal characteristic which is analyzed about the phenomenon is the fractal dimension that have a great importance for understand and prediction of river changes. In this study, we consider the consistency (match) level of artificial unit hydrograph of fractal and NRCS triangular unit hydrograph and its relationship with the compactness coefficient of watershed. To this end, Walnut Gulch watershed of America was chosen and the compactness coefficient was also calculated for its 11 sub-watershed (sub- basin), and then, NRCS triangular unit hydrograph, fractal triangular unit hydrograph were depicted and compared with each other. Results showed that whether compactness coefficient is closer to 1.5, namely watershed is more circular, hydrographs are more compatible. In fact, the innovative method of fractal hydrograph is more appropriate, like watersheds 5,7,9 and 11, and whether compactness coefficient is far from 1.5, the consistency is reduced, like sub-basins 1 and 11.