Determination of flow drainage patterns using fractal tree method (Case study: Zarrineh Rud sub-basin in Kurdistan province)

The behavior of many complex natural phenomena, such as rivers, can be analyzed by fractal tree geometry. Zarrineh Rud sub-basin in Kurdistan province is one of the most watery basins of Urmia basin, which hydrological condition has a great impact on runoff management and downstream flows. Therefore, it is necessary to study the characteristics of this basin using fractal geometry. In the present study, the fractal behavior of Zarrineh rud basin in Kurdistan province has been investigated using GIS layers of stream, DEM map, and application of Strahler, Hack, Horton and fractal tree geometry by Richardson method. According to Hack's law, the slope of the basin trend line is high and this indicates a relatively high erosion in the Zarrineh Rud basin. According to Horton's law, the form factor decreases between stream order 1 and 2 and is almost the same for stream order 3 and higher. In addition, the fractal structure indicates that there is a fractal behavior in the range of stream order 2 and higher. Finally, based on the Richardson method, the fractal dimension of the basin was calculated in the range of 1.695- 1.837, which includes a significant part of the basin space. In addition, the results indicated that the fractal dimension obtained for the stream order 4 by the Horton method was 1.67, which is consistent with the results obtained by the Richardson method. Finally, it can be mentioned that, considering the special topography, climate, and hydrologic conditions of Zarrineh rud sub-basin, it is possible to help the country's planners and decision-makers to better manage this basin by identifying the hydrological behavior of the river.