The Relation of Fractal Dimension with Discharge and Sediment Indices in Ilam Watershed

Since there are not enough tools to measure flood, erosion and sediment in many watersheds of the country, it is necessary to use indirect methods such as fractal geometry to estimate them. There is very little accurate information about erosion in our country (Mohammadi et al. 2008). Understanding the sedimentation status and sedimentation of basins provides an accurate understanding of erosion and its consequences (Piri et al. 2005). Some parameters of watersheds have a special geometric shape that can be examined with fractal geometry. Mathematically, the basins that have the same fractal dimensions are equivalent to each other and are very similar in terms of geomorphological and hydrological characteristics (Adl and Mehrvand, 2004). The aim of this study is to obtain a significant relationship between fractal drainage network and erosion and sedimentation rates, and to generalize the results to unmeasured areas. 2. Introducing the studied area The studied area consists of 12 basins of Ilam province, which are in the western foothills of Zagros Mountain. Figure 1- The position of studied basins in the country and in the Ilam province Table 1- Specifications of basins and their stream gauging stations

These networks were provided based on 50DEM coordinates that in many cases, there isn’t enough accuracy and some channels are not displayed. Therefore, after transferring data to Google Earth, it was fully matched with the natural drainages and with a 5-meter accuracy, hydrographic network map was drawn and completed to reflect the full details of the network.Thence one cannot scale maps via “Fractalys”, fields with the same space of 25 kilometers on similar formations in different areas were accidentally chosen via “Fish Net” –in Arc GIS, to fix this problem. For each study formation, three 25sq.km. Fields were chosen and by the accuracy of 5 meters. These maps that had the same drawing accuracy and space, were drawn in the same scales via GIS on an A4 page in .bmp” and then were brought to Fractalys and finally, their fractal dimensions were calculated and extracted by the geometric method of counting boxes.

Figure 2- Hydrographic network and fractal dimension of the nazarabad watersheds before hydrographic network modification Table 2- Fractal dimension of watersheds before and after hydrographic networks modification In the following figures, the calculated fractal dimensions are observed for several samples of 25 km units before and after the hydrographic network modification. After the modification before the modification Amiran Aghajari 1.134 1.481 1.149 1.435 Figure 3- Fractal dimension of a hydrographic network of Aghajari and Amiran formations before and after hydrographic network modification. Quaternery Gachsaran Figure 4- Hydrographic network modification in the 25km unit on Google Earth Figures (3) to (4) show that after hydrographic network modification, the density of the hydrographic network and consequently the fractal dimension are increased in units of 25 km. Also, hydrographic network density changes in more sensitive formations are more than resistant formations, so their fractal dimension changes are also higher.Figure 5- Investigating the correlation of fractal dimension with hydrological indexes of Ilam watersheds the R2 value that is representing the correlation value is 0.0905. Therefore there is no significant relationship between the specific flood discharge of watershed and its fractal number. Table (3) Correlation test of specific flooddischarge data (Qw) in terms of (m3/s/ Km2) and fractal number (Fr) of the basins after modification of 25km units In Table 3, the specified number (-.240) indicates the correlation value of the data. Due to the obtained value, there is no correlation between the specific flood discharge and the fractal number of the basin.Figure 6- Correlation line chart of specific flood discharge data and fractal number of basins after modification of 25km un its Figure 7- Investigating the correlation of fractal dimension with the sedimentation index of Ilam watersheds In Figure 8, Due to the R2 value (0.939), it can be also concluded that there is a significant and direct correlation between the specific sediment discharge value and fractal dimension of the watershed. The following tables show the results of the calculations performed in SPSS software. Table 4- Correlation test of specific sediment discharge data (Qs) and fractal number (Fr) of basins after modification of 25km units The results of SPSS in Table (4) show that there is a high correlation between the specific sediment discharge data and fractal number. Because the number of 0.996 equals the correlation value between the two variables of the specific sediment discharge and the fractal dimension of the basins. The dispersion of data in the figure represents a high correlation in the data. Because the data are not scattered.

The fractal dimension gives more accurate results by the box-counting method than the magnification and radial methods..The results of the research show that there is a significant and inverse relationship between the fractal dimension of the formations and their resistance to erosion.As the strength of the formation increases, its fractal dimension decreases and therefore the density of the hydrographic network is lower.There is no regular trend between the hydrographic network density and the fractal dimension of the basin with the specific flood discharge of basins.Also, there is no significant relationship between this index and the fractal dimension of the basin.There is a significant and direct relationship between the fractal number and the specific sediment discharge (at a level of 5%), which indicates the erosion and roughness rate in the basin The highest value of fractal dimension can be observed in areas that are very sensitive, including Doiraj basin to 1.49.The least value of fractal dimension can be observed in areas that are resistant to semi-resistant in terms of geological formations, such as Kolm and Chamagaz equal to 1.14 and 1.11, respectively.