水文序列分形维数估计的小波方法

根据小波多分辨率分析和水文序列的统计自相似性，提出了水文序列分形维数的小波估计方法，给出了其计算步骤。运用实际月径流序列的统计分析，探讨了小波分维估计法的影响因素和稳定性，指出紧支撑的Db4、Db6正交小波效果最稳定。最后运用小波方法估计黄河三门峡站年径流和长江屏山站日资料的分维值。研究表明，小波分维估计法稳健，计算成果可靠。

Estimating the Fractal Dimension of Hydrological Time Series by Wavelet Analysis

Based on the multi-resolution analysis of wavelet analysis and the statistical self-similarity of hydrology time series, a new approach of the fractal dimension estimation with wavelet analysis has been presented. The basic calculation steps have also been given. In term of the real hydrology time series, the paper probes the robustness and impact factors of the wavelet estimation approach with statistical test. The results show that the tight support orthogonal wavelet functions, i.e., Db4 and Db6 are best. Finally, the fractal dimensions of the annual runoff series of San Menxia station in Yellow River and the daily discharge series of Ping Shan station in Yangtze River are obtained with suggested approach. The research results have shown that the suggested wavelet estimation method is satisfied.