Abstract
Based on the time series data from the Aral hydrological station for the period of 1958–2005, the paper reveals the long-term trend and fractal of the annual runoff process in the mainstream of the Tarim River by using the wavelet analysis method and the fractal theory. The main conclusions are as follows: 1) From a large time scale point of view, i.e. the time scale of 16 (24) years, the annual runoff basically shows a slightly decreasing trend as a whole from 1958 to 2005. If the time scale is reduced to 8 (23) or 4 (22) years, the annual runoff still displays the basic trend as the large time scale, but it has fluctuated more obviously during the period. 2) The correlation dimension for the annual runoff process is 3.4307, non-integral, which indicates that the process has both fractal and chaotic characteristics. The correlation dimension is above 3, which means that at least four independent variables are needed to describe the dynamics of the annual runoff process. 3) The Hurst exponent for the first period (1958–1973) is 0.5036, which equals 0.5 approximately and indicates that the annual runoff process is in chaos. The Hurst exponents for the second (1974–1989) and third (1990–2005) periods are both greater than 0.50, which indicate that the annual runoff process showed a long-enduring characteristic in the two periods. The Hurst exponent for the period from 1990 to 2005 indicates that the annual runoff will show a slightly increasing trend in the 16 years after 2005.
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References
Ai Nanshan, Li Houqiang, 1993. The nonlinear science methods for Quaternary studies. Quaternary Research, (2): 109–120. (in Chinese)
Chen Yaning, Li Weihong, Chen Yapeng et al., 2003. Water resources and ecological problems in Tarim River Basin, Xinjiang, China. In: Wilderer P A et al. (eds.). Water and Environmental Management. London: IWA Publishing, 3–12.
Chen Yaning, Takeuchi Kuniyoshi, Xu Changchun et al., 2006. Regional climate change and its effects on river runoff in the Tarim Basin, China. Hydrological Processes, 20: 2207–2216. DOI: 10.1002/hyp.6200
Chen Yaning, Xu Zongxue, 2005. Plausible impact of global climate change on water resources in the Tarim River Basin. Science in China (Series D), 48(1): 65–73. DOI: 10.1360/04yd0539
Chen Yaning, Zhang Xiaolei, Li Weihong et al., 2004. Analysis on the ecological benefits of the stream water conveyance to the dried-up river of the lower reaches of the Tarim River, China. Science in China (Series D), 47(11): 1053–1064. DOI: 10.1360/03yd0101
Comte F, Renault E, 1996. Long memory continuous time models. Journal of Econometrics, 73(1): 101–149.
Gan T Y, 2000. Reducing vulnerability of water resources of Canadian Prairies to potential droughts and possible climate warming. Water Resources Management, 14(2): 111–135. DOI: 10.1023/A:1008195827031
Grassberger P, Procacia I, 1983. Characterization of strange attractor. Physical Review Letters, 50(5): 346–349.
Hurst H E, 1951. Long-term storage capacity of reservoirs. Transactions of American Society of Civil Engineers, 116: 770–808.
Hurst H E, Black R P, Simaike Y M, 1965. Long-term Storage: An Experimental Study. London: Constable, 1–155.
Jiang Yan, Zhou Chenghu, Cheng Weiming, 2007. Streamflow trends and hydrological response to climatic change in Tarim headwater basin. Journal of Geographical Sciences, 17(1): 51–61. DOI: 10.1007/s11442-007-0051-8
Li Xin, Yang Degang, 2001. Benefit and ecological loss of water utilization in Tarim River. Arid Land Geography, 24(4): 327–331. (in Chinese)
Li Zhou, Bao Xiaobin, 2003. Studies on water resources utilization and management in Tarim watershed. South-to-North Water Transfers and Water Science & Technology, 1(4): 28–32. (in Chinese)
Mandelbrot B B, 1973. Formes nouvelles du hasard dans les sciences. Èconomie Appliqué, 26(2): 307–319. (in French)
Mandelbrot B B, Wallis J R, 1968. Noah, Joseph and operational hydrology. Water Resources Research, 4(5): 909–918.
Packard N H, Crutchfield J P, Farmer J F et al., 1980. Geometry from a time series. Physical Review Letters, 45: 712–716.
Smith L C, Turcotte D L, Isacks B L, 1998. Streamflow characterization and feature detection using a discrete wavelet transform. Hydrological Processes, 12: 233–249. DOI: 10.1002/(SICI)1099-1085(199802)12:2〈233::AID-HYP573〉3.0.CO; 2–3
Wang Yangui, Hu Chunhong, 2003. The treatment countermeasures for the mainstream of Tarim River. China Water Resources, 7: 53–55. (in Chinese)
Wilcox B P, Seyfried M S, Matison T H, 1991. Searching for chaotic dynamics in snowmelt runoff. Water Resources Research, 27(6): 1005–1010. DOI: 10.1029/91WR00225
Xu Jianhua, Lu Yan, Su Fanglin et al., 2004. R/S and wavelet analysis on the evolutionary process of regional economic disparity in China during the past 50 years. Chinese Geographical Science, 14(3): 193–201.
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Foundation item: Under the auspices of the Second-stage Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-XB2-03), Major Direction of Knowledge Innovation Progromt of Chinese Academy of Sciences (No. KZCX2-YW-127), Shanghai Academic Discipline Project (Human Geography) (No. B410)
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Xu, J., Chen, Y., Li, W. et al. Long-term trend and fractal of annual runoff process in mainstream of Tarim River. Chin. Geogr. Sci. 18, 77–84 (2008). https://doi.org/10.1007/s11769-008-0077-6
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DOI: https://doi.org/10.1007/s11769-008-0077-6