Relationship between fractal dimensions of stream and morphometric characteristics of basin for the soil conservation

River behavior is affected by two categories of natural, and human factors. Natural factors such as floods, soil erosion, mass movement and human factors such as facility construction, land-use change, and sand removal from the bed, play a key role in the behavior and intensification of river changes. The serious and irreparable dangers that may be posed by river movements and changes indicate the need to study its morphology in the study phase before any action is taken. The network of streams continuously changes its location based on time, environmental factors and human interventions. It is very important to study the stream changes to provide the should be omitted management solutions for the should be omitted soil conservation. One of the new methods in this regard is to use the should be omitted fractal geometry. The purpose of this study was to calculate the fractal dimensions of the stream and to investigate its relationship with the morphometric characteristics of the basin

To do this, a should be added topographic map of the should be added basin in Firouzkouh, Tehran province was prepared. The map of the streams was prepared and the morphometric characteristics of the basin were determined by using the ARC GIS 10.3 software. Then, three fractal dimensions of the should be added drainage network (stream branch), drainage density, and basin area were calculated. Finally, the morphometric characteristics of the basin associated with the fractal dimensions were investigated by entering the data obtained from the calculations in the SPSS 18 and Curve Expert software 

The results showed that the minimum and maximum fractal dimensions of the bifurcation ratio were 0.25 and 2.99, of should be omitted the drainage density was 0.19 and 2.34, and of should be omitted the area was 0.76 and 2.60. The fractal dimension of the should be added, the should be added dimension of drainage density, and the should be added fractal dimension of the should be added total area of the basin were 1.84, 0.71, and 1.46, respectively. The fractal dimension of the should be added ratio and the sub-basin area were inversely related with the determination coefficient of 0.90, and the fractal dimension of drainage density and the area and the fractal dimension of an should be added area with the sub-basin area was directly related with the determination coefficients of 0.88, and 0.87, respectively. The more elongated the basin and the lower the form, roundness, and elongation factors, the smaller the bifurcation dimension. the fractal dimension of the area is directly related to the compactness factor, elongation factor, form factor, bifurcation ratio, equivalent rectangle width, and equivalent rectangular length, and is inversely related to other variables. Based on the results, the more elongated the basin and the smaller the form, and elongation factors, the lower the area dimension. The fractal dimension of drainage density is directly associated with the circularity factor, compactness factor, elongation factor, form factor, area ratio, bifurcation ratio, equivalent rectangle width and equivalent rectangular length, and is inversely associated with other variables. Therefore, as the basin becomes more circular, the fractal dimension of the drainage density is increased. Therefore, the fractal dimension of drainage density is increased then as the basin becomes more rounded

According to the coefficient of explanation of the obtained models for the relationship between fractal dimensions, and morphometric properties, the studied fractal dimensions can be easily calculated and analyzed using morphometric properties. Due to the importance of stream characteristics in the management of watersheds in terms of flood, erosion, and soil conservation, the fractal models can be used to make quick and accurate decisions for the should be omitted management. Finally, considering that the use of fractal geometry is a new method in studying the characteristics of waterway networks, it is suggested that basins be analyzed fractally in different regions with different morphometric conditions.