Comparison and analysis for the calculation methods of fractal dimension of river system

The calculation of fractal dimension of river system is the prime issue in studying the fractal characteristics of valley and defining the fractal type, which is significant to the development of valley concentration flow theory. Concerning the inconsistent results on the diverse calculation methods of valley fractal dimension, therefore, this paper analyzes from the angles of river network forming and valleys difference. According to the quantitative geomorphology theory, it puts forward the proposition that the attraction factor of a valley is the right angle consisting of branch angle, chain length and “critical distance”. Combined with the theories of the finiteness and self-affinity of the water system, the mathematical relations between dimensions of different spaces and kinds are clarified and the factors that influence the values of fractal dimension are analyzed. Different dimension values are calculated and compared through the DEM grid data of the three valleys so as to demonstrate the impact of those factors on the distinct dimension calculation methods.