三峡流域径流特性分析及预测研究
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摘要
水文系统是一个复杂的高度非线性系统，其中，径流的变化对整个系统的演化起主导作用，并会对资源环境和区域经济产生重大影响。由于受气象、自然地理、流域特性等多因素的综合影响，三峡流域径流的变化具有多种不确定性，表现出非线性、多时间尺度性和混沌等特性，而受流域水文过程观测资料的限制以及对水文过程认识程度的局限，目前还难以完全用数学和物理方法来准确地描述和刻画其完整的演化过程。以前主要用传统研究方法和手段或基于单个水文站来对流域径流的演化规律进行分析和预测，从线性角度或近似为线性问题去研究本质上是非线性的水文时空变化问题，这必将引发许多无法妥善解决的困难。为了摆脱这种困境，需要不断将新的理论和方法引入到水科学研究中，通过各种方法的有机结合，从流域可变时空尺度的角度来对系统进行分析和研究。
在总结吸收前人研究成果的基础上，本文运用小波、混沌、支持向量机等现代分析及预测理论，并结合传统的理论分析方法，对三峡流域径流的周期、趋势、相关性和混沌性等演化特性进行了深入研究，在此基础上建立了基于小波分析和支持向量回归的径流多尺度耦合预测模型，构建了一种中长期径流区间预测的混沌时间序列方法。研究成果已成功应用到三峡梯调工程实践，为今后长江上游水资源管理的政策制定者、研究人员以及公众提供了未来径流变化的背景。概括起来，研究工作取得了以下主要成果：
通过小波分析，揭示三峡流域径流系统的周期演化规律和趋势变化特征，发现三峡流域年平均径流在长期的变化中主要存在30年左右的长周期变化，12～18年左右的年代周期变化和3～8年的年际周期变化特点，且总体呈现越来越明显的减少趋势。它们主导着年平均径流长期变化的特性。另外，时间尺度不同，径流处的丰枯阶段不同，从各个站年平均径流变化的主周期来看，2006年后寸滩站处于丰水期，万县站和宜昌站分别在在2003年和2004年后处于枯水期。
考虑到噪声对径流分析的影响以及传统消噪技术在对径流消噪处理中存在的不足，本文引入小波理论对三峡流域径流进行了消噪处理。通过对消噪前后三峡流域各站的年径流变化过程进行相关性分析，研究其时间序列自身的相关性随时间的推移而变化的特征。结果表明，三峡流域各站年径流时间序列自相关性在长期的变化过程中均不明显，但消噪后都凸显出一定的自相关性，并且随着时移的增加呈波动减弱。
针对三峡流域径流系统的变化存在多时间尺度结构和局部化的特点，本文利用小波方法对各站径流时间序列进行了分解，运用互相关分析方法揭示了在不同的尺度下各站径流时间序列之间的相互关系，并对其相关性进行了检验。结果显示，在不同时间尺度下，三峡流域任意两个站点年径流时间序列的互相关性表现差别较大，主要是随着时移改变表现出明显的正或负的互相关性。就总体而言，序列之间互相关性随时间尺度的增大而增强，随时移的扩大而减弱或出现较大负相关。
通过重建三峡流域径流动力系统相空间并进行系统混沌特性辨识，发现各站的最大Lyapunov指数均大于零，表明三峡流域的径流序列具有混沌特性。该结论经饱和关联维数法和Cao方法得到了进一步证实。此外，还发现各站径流时间序列的状态空间维数沿程逐渐增大，对应的饱和关联维数也沿程呈增大趋势。这说明受区间来水和水库调节的影响，三峡流域沿程径流组合的特性越来越复杂。
将不确定性和确定性的分析方法有机的结合起来，扬长避短，是目前建立水文分析与预测模型发展的一种趋势。本文将多尺度分析理论中的Daubechies小波和Mallat算法与支持向量回归建模方法相结合，建立了径流序列的多尺度耦合预测模型，并通过实验证明，与传统的单一统计建模方法相比，耦合模型预测精度高，能较好的反映径流时间序列变化的规律，且概念清晰，结构严谨，具有一定的可操作性，为研究水文水资源时间序列的演变规律提供了一条新的途径。
根据径流变化的混沌特性，同时为了避免混沌预测方法中存在的延迟时间、嵌入维数以及相似数据提取方法等多种不确定因素带来的误差，从区间预测的角度提出了一种中长期径流区间预测的混沌时间序列方法。为此，首先对径流时间序列进行相空间重构，并在相空间中通过聚类算法寻找当前时刻相点的相似状态，根据其预测结果来确定未来径流的取值区间，最后通过实验研究，验证了该方法的有效性和可行性。
Water resources system and hydro-environment is a nonlinear energy-system with vast, complicated, dynamic characteristics, in which the variance of runoff is taken as its main factor, for its changes dominants the whole system's changing trend , and may greatly affect the resources, environment and regional economy. Due to the impacts caused by many factors such as climate, geography, characteristic of the basins, the changing trend of flow in Three Gorges Region takes on a great deal of uncertainty featuring nonlinear, multi-timescale and chaos. In addition, there still exist many limits that the hydrology process is not clear and the datum which affect the hydrology process are inadequate. Therefore, mathematics physics method has difficulty in clearly describing each hydrology process till now. In the past, researchers mainly studied the evolvement characteristic of the runoff using the traditional method or based on a single hydrology station and then make analysis and forecast, however, they're hard to obtain satisfactory results and also facing many difficulties. To get rid of this problem, new theories and methods are needed to be continuously introduced to the researches on water resource, besides, various methods can be properly combined to research on the whole basin systematically.
We sum up the advantages the preceding results, on this basis, modern new theories, such as wavelet transformation, chaos and support vector machine, and their combination with traditional methods are introduced to make a profound study on the long-term variant characteristic of runoff of Three Gorges, such as period, trend, relativity and chaos etc. Based on the analysis above, a new mufti-time-scale hybrid model for runoff series prediction is proposed with the support vector machine and wavelet, and then the runoff interval forecast models and its solving methods are studied by using clustering algorithm and chaotic time series method. The results provide the future annual runoff process for the water resources policy makers, researchers and the public. Generally speaking, we conclude the following primary findings:
Through wavelet transform, we made an analysis on the characteristic of period and its changing trend using the natural annual runoff time series in the Three Gorges basin in mufti-time scales. The results demonstrated that the annual runoff time series has a period of about 30 years' in long term variety, a middle-term period of 12～18 years and a short term period of 3~8 years, and has a more and more obvious decreasing tendency on the whole. In addition, the flood and dry periods of annual runoff differ with different scales. Seen from the first main period of each station, it's found that Cuntan station enters flood season after 2006, Wanxian station, Yichang Station enter dry season after 2003 and 2004, respectively.
Considering the influence of noise and the disadvantages of traditional noise eliminating technologies erenow, the wavelet theory is applied, which not only de-noises well, but also retains the effective composition in the original signal. Based on the correlation analysis of the natural annual runoff time series and the processed series in the Three Gorges basin, the characteristic of self correlation which change with time are probed. In the long-term change, natural runoff time serial itself have no self correlation in the Three Gorges basin; but after wavelet de-noising, runoff time serial of there have certain characteristic of self correlation, which turns smaller as the time increases.
Considering that the variety of the hydropower and water resource system in time domain has a multi-layer structure and characteristic of locality, we make time series decomposition using velvet transforming method in different time scales and analyses their mutual correlation with mutual correlation analysis method and verifies its correctness. The result demonstrated that the mutual correlations of annual runoff time serials in any two stations between Cuntan station, Wanxian station and Yichang station were totally different in different time scales, which manifested a correlation, or negative, or independent, with positive as its main trend with the changing of the dimension. With the increase of the dimension, the mutual correlation strengthens continuously, but weakens or it appears a great negative correlation as the time increases.
Based on the reconstruction of the phase space of runoff for the Three Gorges basin, it is found that the maximum Lyapunov exponent of each station's runoff serial are larger than zero, which means that the runoff of each station has chaos characteristic, and it has been further verified by saturated correlation dimension method and Cao method. In addition, it is also found that the saturation correlation dimension turns larger from upper stream to downstream, which is caused because of the joining of branches, the section raining along the river and the regulation of reservoir.
In building a hybrid water resources model, there is a trend to combine certain and uncertain analysis methods probably in recent times. We proposed a new hybrid time serial wavelet prediction model ,which combines the Daubechies's wavelet in the multi time scales theory, and the Mallat's algorithm with support vector machine with the traditional support vector machine(SVM) modeling method. Compared to the traditional methods based on support vector machine and chaos model, the hybrid model has a higher prediction precision and can better reflect the changing characteristic of runoff, as well as having advantages of clear concept, integrated structure, easy operated, thus make it a effective approach to study the evolving principle of the runoff time series. The results have shown that the new model is meaningful and feasible.
In order to avoid the error caused by several uncertain factors such as embedding dimension, time delay and similar states extracted method, we proposed a chaotic time series method for long-term runoff interval forecasting based on the chaotic characteristic of runoff. First, the phase space of runoff time series is reconstructed and similar states of current phase point are searched by the clustering algorithm, based on which the interval values of the future are determined. Finally, we verified its feasibility and effectiveness by applying it to monthly runoff forecasting.
在总结吸收前人研究成果的基础上，本文运用小波、混沌、支持向量机等现代分析及预测理论，并结合传统的理论分析方法，对三峡流域径流的周期、趋势、相关性和混沌性等演化特性进行了深入研究，在此基础上建立了基于小波分析和支持向量回归的径流多尺度耦合预测模型，构建了一种中长期径流区间预测的混沌时间序列方法。研究成果已成功应用到三峡梯调工程实践，为今后长江上游水资源管理的政策制定者、研究人员以及公众提供了未来径流变化的背景。概括起来，研究工作取得了以下主要成果：
通过小波分析，揭示三峡流域径流系统的周期演化规律和趋势变化特征，发现三峡流域年平均径流在长期的变化中主要存在30年左右的长周期变化，12～18年左右的年代周期变化和3～8年的年际周期变化特点，且总体呈现越来越明显的减少趋势。它们主导着年平均径流长期变化的特性。另外，时间尺度不同，径流处的丰枯阶段不同，从各个站年平均径流变化的主周期来看，2006年后寸滩站处于丰水期，万县站和宜昌站分别在在2003年和2004年后处于枯水期。
考虑到噪声对径流分析的影响以及传统消噪技术在对径流消噪处理中存在的不足，本文引入小波理论对三峡流域径流进行了消噪处理。通过对消噪前后三峡流域各站的年径流变化过程进行相关性分析，研究其时间序列自身的相关性随时间的推移而变化的特征。结果表明，三峡流域各站年径流时间序列自相关性在长期的变化过程中均不明显，但消噪后都凸显出一定的自相关性，并且随着时移的增加呈波动减弱。
针对三峡流域径流系统的变化存在多时间尺度结构和局部化的特点，本文利用小波方法对各站径流时间序列进行了分解，运用互相关分析方法揭示了在不同的尺度下各站径流时间序列之间的相互关系，并对其相关性进行了检验。结果显示，在不同时间尺度下，三峡流域任意两个站点年径流时间序列的互相关性表现差别较大，主要是随着时移改变表现出明显的正或负的互相关性。就总体而言，序列之间互相关性随时间尺度的增大而增强，随时移的扩大而减弱或出现较大负相关。
通过重建三峡流域径流动力系统相空间并进行系统混沌特性辨识，发现各站的最大Lyapunov指数均大于零，表明三峡流域的径流序列具有混沌特性。该结论经饱和关联维数法和Cao方法得到了进一步证实。此外，还发现各站径流时间序列的状态空间维数沿程逐渐增大，对应的饱和关联维数也沿程呈增大趋势。这说明受区间来水和水库调节的影响，三峡流域沿程径流组合的特性越来越复杂。
将不确定性和确定性的分析方法有机的结合起来，扬长避短，是目前建立水文分析与预测模型发展的一种趋势。本文将多尺度分析理论中的Daubechies小波和Mallat算法与支持向量回归建模方法相结合，建立了径流序列的多尺度耦合预测模型，并通过实验证明，与传统的单一统计建模方法相比，耦合模型预测精度高，能较好的反映径流时间序列变化的规律，且概念清晰，结构严谨，具有一定的可操作性，为研究水文水资源时间序列的演变规律提供了一条新的途径。
根据径流变化的混沌特性，同时为了避免混沌预测方法中存在的延迟时间、嵌入维数以及相似数据提取方法等多种不确定因素带来的误差，从区间预测的角度提出了一种中长期径流区间预测的混沌时间序列方法。为此，首先对径流时间序列进行相空间重构，并在相空间中通过聚类算法寻找当前时刻相点的相似状态，根据其预测结果来确定未来径流的取值区间，最后通过实验研究，验证了该方法的有效性和可行性。
Water resources system and hydro-environment is a nonlinear energy-system with vast, complicated, dynamic characteristics, in which the variance of runoff is taken as its main factor, for its changes dominants the whole system's changing trend , and may greatly affect the resources, environment and regional economy. Due to the impacts caused by many factors such as climate, geography, characteristic of the basins, the changing trend of flow in Three Gorges Region takes on a great deal of uncertainty featuring nonlinear, multi-timescale and chaos. In addition, there still exist many limits that the hydrology process is not clear and the datum which affect the hydrology process are inadequate. Therefore, mathematics physics method has difficulty in clearly describing each hydrology process till now. In the past, researchers mainly studied the evolvement characteristic of the runoff using the traditional method or based on a single hydrology station and then make analysis and forecast, however, they're hard to obtain satisfactory results and also facing many difficulties. To get rid of this problem, new theories and methods are needed to be continuously introduced to the researches on water resource, besides, various methods can be properly combined to research on the whole basin systematically.
We sum up the advantages the preceding results, on this basis, modern new theories, such as wavelet transformation, chaos and support vector machine, and their combination with traditional methods are introduced to make a profound study on the long-term variant characteristic of runoff of Three Gorges, such as period, trend, relativity and chaos etc. Based on the analysis above, a new mufti-time-scale hybrid model for runoff series prediction is proposed with the support vector machine and wavelet, and then the runoff interval forecast models and its solving methods are studied by using clustering algorithm and chaotic time series method. The results provide the future annual runoff process for the water resources policy makers, researchers and the public. Generally speaking, we conclude the following primary findings:
Through wavelet transform, we made an analysis on the characteristic of period and its changing trend using the natural annual runoff time series in the Three Gorges basin in mufti-time scales. The results demonstrated that the annual runoff time series has a period of about 30 years' in long term variety, a middle-term period of 12～18 years and a short term period of 3~8 years, and has a more and more obvious decreasing tendency on the whole. In addition, the flood and dry periods of annual runoff differ with different scales. Seen from the first main period of each station, it's found that Cuntan station enters flood season after 2006, Wanxian station, Yichang Station enter dry season after 2003 and 2004, respectively.
Considering the influence of noise and the disadvantages of traditional noise eliminating technologies erenow, the wavelet theory is applied, which not only de-noises well, but also retains the effective composition in the original signal. Based on the correlation analysis of the natural annual runoff time series and the processed series in the Three Gorges basin, the characteristic of self correlation which change with time are probed. In the long-term change, natural runoff time serial itself have no self correlation in the Three Gorges basin; but after wavelet de-noising, runoff time serial of there have certain characteristic of self correlation, which turns smaller as the time increases.
Considering that the variety of the hydropower and water resource system in time domain has a multi-layer structure and characteristic of locality, we make time series decomposition using velvet transforming method in different time scales and analyses their mutual correlation with mutual correlation analysis method and verifies its correctness. The result demonstrated that the mutual correlations of annual runoff time serials in any two stations between Cuntan station, Wanxian station and Yichang station were totally different in different time scales, which manifested a correlation, or negative, or independent, with positive as its main trend with the changing of the dimension. With the increase of the dimension, the mutual correlation strengthens continuously, but weakens or it appears a great negative correlation as the time increases.
Based on the reconstruction of the phase space of runoff for the Three Gorges basin, it is found that the maximum Lyapunov exponent of each station's runoff serial are larger than zero, which means that the runoff of each station has chaos characteristic, and it has been further verified by saturated correlation dimension method and Cao method. In addition, it is also found that the saturation correlation dimension turns larger from upper stream to downstream, which is caused because of the joining of branches, the section raining along the river and the regulation of reservoir.
In building a hybrid water resources model, there is a trend to combine certain and uncertain analysis methods probably in recent times. We proposed a new hybrid time serial wavelet prediction model ,which combines the Daubechies's wavelet in the multi time scales theory, and the Mallat's algorithm with support vector machine with the traditional support vector machine(SVM) modeling method. Compared to the traditional methods based on support vector machine and chaos model, the hybrid model has a higher prediction precision and can better reflect the changing characteristic of runoff, as well as having advantages of clear concept, integrated structure, easy operated, thus make it a effective approach to study the evolving principle of the runoff time series. The results have shown that the new model is meaningful and feasible.
In order to avoid the error caused by several uncertain factors such as embedding dimension, time delay and similar states extracted method, we proposed a chaotic time series method for long-term runoff interval forecasting based on the chaotic characteristic of runoff. First, the phase space of runoff time series is reconstructed and similar states of current phase point are searched by the clustering algorithm, based on which the interval values of the future are determined. Finally, we verified its feasibility and effectiveness by applying it to monthly runoff forecasting.
引文
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