Long-term trend and fractal of annual runoff process in mainstream of Tarim River

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.