Multifractal arithmethic for watershed topographic feature

In this paper,taking Dali River Chabagou watershed and Dabucha watershed on Loess Plateau as examples,a new multifractal mathematic model for the large region based on the height distribution probability(HDP)is provided and established for describing the topographic characteristics of watershed by using multifractal theory.The meaning of multifractal spectrum of the topographic characteristics is discussed.The results show that:(1)the multifractal spectrum can express the topographic characteristics of a watershed more sensitive and comprehensive than the simple fractal one.The width of the multifractal spectrum can characterize the degree of the undulation of a surface quantitatively.The difference of the fractal dimensions between the maximum and minimum probability subset can give a statistical result of the ratio between the numbers of lowest and highest sites,which reflects the ratio between the peaks and valleys indirectly.(2)The multifractal spectrum can scientifically represent inner fine structure of a watershed and emphasize the abnormity partial variations of a watershed.And(3)the rational range of the non-scale domain should be identified from the cell size to the 1.5 times the height extremum of the watershed.