%0 Journal Article
%T Chaotic Analysis and Simulation of Time Series of Daily Runoff in the Kaidu River Basin<br>开都河日径流时间序列混沌分析与模拟
%A HU Zengyun
%A YUAN Shanlin
%A JI lili Abduweli
%A LI Lanhai
%A LIU Ying
%A <br>胡增运
%A 袁山林
%A 吉力力·阿不都外力
%A 李兰海
%A 刘英
%J 资源科学
%D 2012
%I 
%X The runoff process is very complex. It is influenced by various environmental factors, such as precipitation, temperature, topographic conditions and the types of land utilization. In this paper, Chaos Theory, a mathematical sub-discipline that studies complex systems and the phase space reconstruction technology were used to investigate the chaotic characteristics of daily runoff process in Kaidu River Basin. By power spectrum analysis of the daily runoff time series, the chaos characteristics were discussed from qualitative perspective. The time delay of phase space reconstruction was calculated by the mutual information method and the optimal embedding dimension was determined by the Cao method. With Matlab software, the time delay and optimal embedding dimension were calculated as τ =6 and m=14 respectively. Thus, the one-dimensional daily runoff time series in the basin was successfully reconstructed into a multi-dimensional phase space. Furthermore, the chaos regarding the daily runoff time series in Kaidu River Basin was quantitatively analyzed by the maximum Lyapunov index. In the end, the simulation was implemented by the second order Volterra adaptive one- step model. The results indicate that the power spectrum of the daily runoff time series in Kaidu River Basin is continuous and it decreases exponentially with the increase of frequency. Therefore, from a qualitative perspective, it shows that the daily time series in Kaidu River Basin have chaotic characteristics. The maximum Lyapunov index of the daily time series is 0<λ max =0.0097<1, also indicating chaotic characteristics from the quantitative view. The correlation coefficient and the relative root mean square errors (RRMSE) obtained by the simulation are 0.9376 and 0.2390 respectively, which suggests a satisfactory simulation result of the Volterra adaptive model. In addition, graphical comparison also indicates that the Volterra adaptive model can simulate the variation pattern of the daily runoff time series well. In detail, the proportion of points with a relative error between -10% and +10% reaches 43.65% , between -20% and + 20% accounts for 70.67% and between -50% and + 50% is only 3.26%. However, the simulation result is not accurate when the daily runoff values show dramatic changes, which can be seen from the simulated results.
%K Daily runoff time series
%K Phase space reconstruction
%K Chaos theory
%K Maximum Lyapunov index
%K Volterra adaptive model<br>日径流时间序列
%K 相空间重构
%K 混沌理论
%K 最大Lyapunov指数
%K Volterra自适应模型
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=B5EDD921F3D863E289B22F36E70174A7007B5F5E43D63598017D41BB67247657&cid=B47B31F6349F979B&jid=9DEEAF23637E6E9539AD99BE6ABAB2B3&aid=759CCD45607BE0D90A27B9E19A348565&yid=99E9153A83D4CB11&vid=339D79302DF62549&iid=E158A972A605785F&sid=0636354D8CF77519&eid=7004BE6E41AAF52C&journal_id=1007-7588&journal_name=资源科学&referenced_num=0&reference_num=26