Abstract
Application of fractal theory on the evolution of nonlinear study of the hydrological system, which found its internal rules from the complex hydrologic system, could make us more fully understand the hydrodynamic characteristics of the complex motion of this system. Taking Weihe River as study area, this paper analyzes daily runoff series’ multi-fractal character and relative fluctuation feature by using the De-trended Fluctuation Analysis (DFA) method. Result shows that the daily runoff series of main channel and branches of Weihe river all shows multi-fractal characteristics clearly, and the turns of multi-fractal intensity of daily runoff series in Weihe river are: Xianyang station (1.388) > Yingge station (0.697) > Linjiacun station (0.665) > Zhangjiashan station (0.662) > Zhuangtou station (0.635). Rainfall, evaporation, water income and human activity and other factors affect the fluctuation character and multi-fractal intensity of daily runoff series through these factors’ superimposition and pining down mutually. This study could provide a theoretical supply for obtaining the quantitative indicators on multi-fractal characteristics about eco-environment situation of watershed, and for runoff forecasting.
Highlights
Result shows that the daily runoff series of main channel and branches of Weihe river all shows multi-fractal characteristics clearly, and the turns of multi-fractal intensity of daily runoff series in Weihe river are: Xianyang station (1.388) > Yingge station (0.697) > Linjiacun station (0.665) > Zhangjiashan station (0.662) > Zhuangtou station (0.635)
Huaxian station’s runoff fluctuation is weaker than Linjiacun and Xianyang station, the reason is Huaxian station situate at downstream of main channel of Weihe River, many factors, such as rainfall, evaporation, water income from tributaries and human activity have an effect of interaction and adjustment each other, cause the result of smaller runoff process fluctuation and tends to steadily
To 2 - 5 step MF-De-trended Fluctuation Analysis (DFA), generalized Hurst coefficient h (q) of main channel’s three stations and the north and south branch stations’ daily runoff process is all not a constant in Weihe River, and all changes along with the change of q, h (q) displays as a digression function of q. These disclosed that the daily runoff process of Weihe River’s main channel and braches all have characteristic of multiple fractals
Summary
Runoff is one of key links of water cycle, its form and development affected by the comprehensive factors which include the climate, the terrain landform, soil and vegetation, so, describing it with multi-scales tool could be better, it may be used to well describe the fluctuation distributed condition of different partial. Wang Wensheng et al (2005) utilized the boxes calculation method to disclose the fractal dimension of daily runoff process, to carry out the related analysis and the discussion, and, emphatically discussed the relationship between runoff process’ fractal characteristic and the shape factors [5]. Ding Jing et al, Li Xianbin (1999) utilized the fractal theory on the seasonal flood, to do analysis on the linear fluctuation property, discovered that the flood season’s current capacity process shows fractal feature [6] [7]. Authors et al (2011) discussed the sole fractal characteristic of monthly runoff series of main channel and branches of Weihe River, tried to describe the hydrology system’s non-linear complexity characteristic, but this river’s multiple fractal characteristic research was not yet carried on [14].
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