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

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 in order to provide management solutions for soil conservation. One of the new methods in this regard is to use fractal geometry. The purpose of this study was to investigate the relationship between fractal and morphometric characteristics of the basin and the possibility of fast, low-cost and accurate management of the stream network based on this relationship. For this purpose, using data basic maps, drainage networks map and digital elevation model (10 m) of the ground by ArcGIS 10.7 was prepared. Then applying the rules of the Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimensions, and some rivers' geomorphic features were investigated. Finally, by entering the data obtained from the calculations in SPSS 22 and Curve Expert software, the morphometric characteristics of the basin associated with the fractal dimensions were investigated. In the Curve Expert software, the exponential, logarithmic, linear and power models of the dependent variable (fractal dimension) and the independent variable (morphometric characteristics) were investigated and the model that had the higher determination coefficient and was significant in SPSS 22 software for the nonlinear univariate regression was selected and introduced as the appropriate model for the relationship between the two studied variables. Results showed that the fractal dimension of stream branch, the fractal dimension of drainage density and the fractal dimension of total basin area were 1.84, 0.71 and 1.46, respectively. The results also showed that the fractal dimension of watersheds has meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds. 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 about the stream management.