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| 开都河日径流时间序列混沌分析与模拟 | |
| 引用本文： | 胡增运,袁山林,吉力力·阿不都外力,李兰海,刘英.开都河日径流时间序列混沌分析与模拟[J].资源科学,2012,34(4):644-651. |
| 作者姓名： | 胡增运 袁山林 吉力力·阿不都外力 李兰海 刘英 |
| 作者单位： | 1. 中国科学院新疆生态与地理研究所,荒漠与绿洲生态国家重点实验室,乌鲁木齐830011／中国科学院新疆生态与地理研究所,新疆水循环与水利用自治区重点实验室,乌鲁木齐830011 2. 浙江财经学院,杭州,310018 3. 中国科学院新疆生态与地理研究所,荒漠与绿洲生态国家重点实验室,乌鲁木齐830011 |
| 基金项目： | 中科院知识创新工程重要方向项目(编号:KZCX2-YW-334,KZCX2-YW-GJ04);国家自然科学基金项目:"塔河干流生态水文过程及其对气候波动的多尺度效应"(编号:40871027);中国科学院"西部之光"西部博士资助项目(编号:XBBS201005). |
| 摘 要： | 本文利用相空间重构技术和混沌理论讨论了开都河日径流的混沌性质。通过日径流时间序列的功率谱分析,从定性角度讨论了日径流时间序列的混沌特征。进一步根据互信息量法得到相空间重构的延时,再根据Cao方法得到相空间重构的嵌入维数。利用Matlab软件计算得到相空间重构的延时和最佳嵌入维数分别为τ=6,m=14。这样将一维的开都河日径流时间序列重构成14维的相空间。通过最小数据量法计算出开都河日径流时间序列最大Lyapunov指数。利用最大Lyapunov指数对开都河日径流时间序列进行定量混沌分析。最后通过二阶Volterra自适应一步模型进行模拟。结果表明：开都河日径流时间序列的功率谱是连续的,功率谱呈现随频率增高而以指数方式递减趋势,区别于具有离散尖峰谱特征的周期时间序列和具有连续的、频率和振幅不相关谱特征的随机时间序列。这从定性角度表明开都河日径流时间序列具有混沌特征。通过计算得到开都河日径流时间序列的最大Lyapunov指数0〈λmax=0.0097〈1,从定量角度表明开都河日径流时间序列具有较弱的混沌特征。利用二阶Volterra自适应一步模型模拟得到相关系数和相对均方根误差分别0.9376和0.2390。这说明利用Volterra自适应模型模拟效果较好。 |
| 关 键 词： | 日径流时间序列 相空间重构 混沌理论 最大Lyapunov指数 Volterra自适应模型 |
| 修稿时间： | 3/1/2012 12:00:00 AM |
Chaotic Analysis and Simulation of Time Series of Daily Runoff in the Kaidu River Basin |
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| HU Zengyun,YUAN Shanlin,JI lili Abduweli,LI Lanhai and LIU Ying.Chaotic Analysis and Simulation of Time Series of Daily Runoff in the Kaidu River Basin[J].Resources Science,2012,34(4):644-651. | |
| Authors: | HU Zengyun YUAN Shanlin JI lili Abduweli LI Lanhai and LIU Ying |
| Institution: | State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumq 830011, China; Xinjiang Key Laboratory of Water Cycle and Utilization in Arid Zone, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China;Zhejiang University of Finance and Economics, Hangzhou 310018, China;State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumq 830011, China; Xinjiang Key Laboratory of Water Cycle and Utilization in Arid Zone, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China;State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumq 830011, China; Xinjiang Key Laboratory of Water Cycle and Utilization in Arid Zone, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China;State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumq 830011, China |
| Abstract: | 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. |
| Keywords: | Daily runoff time series Phase space reconstruction Chaos theory Maximum Lyapunov index Volterra adaptive model |
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