The accuracy of single and multiple flow direction algorithms for extracting fractal dimension of drainage networks in arid area

Digital elevation models and its derivatives are important factors for watershed modeling. It is obvious that DEM errors adversely affect the accuracy and thereby modeling of natural processes. This problem along with the impossibility of measuring all elements of nature, has led to a major evolution in the way of understanding and explaining phenomena. In this way, we can use the fractal geometry as a quantitative tool for modeling many complex natural phenomena. In fact, geophysical phenomena such as drainage networks are fractal phenomena with fractal behavior. The purpose of this paper is to evaluate sensitivity of the drainage networks based on DEMs (ASTER & SRTM), flow direction algorithms (Single Flow Direction (D8) and Multiple Flow Direction (MD8)) and topographic maps of 1:25000 in order to study the fractal dimension of drainage network on geological formations of Yazd-Ardakan basin. The results showed that the least difference in the length and the rank of the stream belonged to the drainage network obtained from the topographic maps of 1:25000. After the topographic maps, ASTER and the multi-flow direction algorithm are close to real ground map. Even though the multi-flow direction algorithm shows more detail on the drainage network. But it is not close to real ground map. The difference is particularly noticeable in the first rank of streams. Due to the very high sensitivity of the fractal dimension to the smallest change in drainage network conditions, the drainage network obtained from topographic maps were used to calculate the fractal dimension. The mean fractal dimension of 1.149, 1.16 and 1.207, respectively, represents Taft, Granite and Kahar formations. There is a significant correlation between fractal dimension and sensitivity to erosion of geological formations (level 0.99). In fact, the fractal dimension increases with increasing the sensitivity to erosion along with the drainage density in geological formations. The results showed that fractal dimension allows for a quick and accurate analysis of sensitivity to erosion of the formations of this area.