河川径流时间序列的分形特征研究
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摘要
河川径流是一种非线性时间序列,对其进行合理正确描述和规律探索直接关系到水资源高效开发利用。本文针对径流演变特征,基于分形等非线性理论,对河川径流演变的若干非线性特征进行了提取、比较、分析,以及建模、计算等工作,主要研究成果有:
(1)河川径流时间序列基本统计特征研究。引入柯尔莫哥罗夫-斯米尔诺夫(Kolmogorov-Smirnov)对径流波动进行了随机正态性检验,结果表明其分布的形状与对称形式与正态分布型的偏离程度均存在显著差异;同时,通过其频数分布说明研究对象具有“尖峰厚尾”的分形分布特征。
(2)河川径流非线性识别。利用双谱分析对河川径流时间序列数据进行了定性分析,分析结果说明黄河、长江干流径流时间序列数据结构具有非线性特征。对于非对称系统,双谱完全可表征系统的非线性特性。所以总体来看,用高阶累积量研究系统的非线性是一个极为精确和有效的方法。
(3)河川径流的长期相关性及维数研究。在对时间序列长期相关性评述的基础上,提出了一种基于不对称周期模型的非趋势波动分析方法,识别了黄河、长江干流主要水文站月径流序列进行相关性分析以及标度不变性分析。所得结论为:黄河及长江干流的月径流序列存在明显的长程相关性,标度指数均大于0.5,且黄河干流相关性程度高于长江干流。各站月径流序列在年内周期普遍存在上升慢、下降快的趋势特点,而且随着集水面积的增大,序列相关性增强,表现出明显的累积效应,揭示越大尺度的水文系统,越趋于稳定。根据标度指数,计算了流域分形维数,进一步验证了河川径流所具有的自相似性与标度不变性。
(4)径流演变的长记忆性分析。分析与了解径流结构、判断径流演变趋势以及长记忆性对水文系统与未来变化的影响等方面具有重要的作用,基于此,本文提出一种基于Liu变换的径流序列分解方法,运用修正R/S分析对分解前后的序列进行长记忆性检验。结果表明:径流波动突变的原因与降水、气候变化有着不可分割的关系。同时,只包含长记忆的序列,有效证实了径流序列波动长记忆性的存在,而且其产生原因可以由结构转换的持续性作出合理解释,进一步说明在实证之前进行序列分解是非常有必要的。
(5)河川径流多重分形研究。与单分形相比,多标度分形更能刻画径流系统演变过程中的不均匀性。本文采用多重分形消除趋势波动分析法(简称MF-DFA)对径流的多重分形性进行分析,并探讨多重分形形成的原因。所得到的结论为:黄河、长江干流径流序列均呈现出明显的多重分形,且多重分形是由其内在的长期相关性和厚尾分布共同作用的结果,这为深化水系发育演化规律的定量研究开辟了一条新途径。
(6)河川径流预测。针对径流非线性特征,建立了最近邻域混沌预测模型,对黄河、长江干流径流过程进行了预测,得到了满足精度要求的预测结果,并利用该模型能够有效跟踪径流系统中相空间里的吸引子、充分扑捉历史数据中所隐含的有用信息这一特点,进一步通过增加邻近点数来发现预测均方误差的变化,对预测效果进行了检验,结果证实这一方法真实地反映了河川径流变化的总体趋势,这同时为判断时间序列数据的非线性提供了一种新方法。
Stream flows are sorts of nonlinear time series, description and exploration exactly about which have straight relations with water resources exploitation and utilization efficiently. Based on fractal and other nonlinear theories, aimed at the characteristics of stream flow evolvement, some works have be done such as distilling, comparing, analyzing, modeling and computing on certain nonlinear characteristics about stream flow evolvement. The main results of this paper are as follows:
(1) Basis statistic characteristics of the stream flow time series are analyzed. Kolmogorov-Smirnov is introduced to test random normal nature of the stream flow fluctuation. The results indicate that the distributing forms have distinct difference with the departure degree about normal school. Through frequency distributing, stream flows are proved having the fractal distributing characteristic of“pinnacle and large trail”.
(2) Stream flow nonlinearity is identified through Bispectrum analysis. The results shows that the stream flow time series of the Yellow River and the Yangtse River are nonlinearity. For non-symetry systems, Bispectrum can token nonlinear characteristics completely. So high steps accumulated measures are kinds of exact and effective method to study systemetic nonlinearity.
(3) Long-range relativity and dimensions about the stream flows are analyzed. Based on time series long relativities, detrended fluctuation analysis based on certain non-symmetry cycle models is advanced to identify the relativity and index fixity of the months flow time series in the Yellow River and the Yangtse River main streams. The results indicate that the two main streams have long-range relativities and the indexes are larger than 0.5 and even the degree in the Yellow River is higher than the Yangtse River. Months flow time series of every hydrological station has the characteristic of slow raise, quick fall in annual cycle. Larger the catchment areas are, stranger the relativity is. So the long-range relativity shows clear cumulated domino offect. Larger the scales of the hydrology system are, higher stability it is. Then according to the index, the fractal dimensions of the object are calculated and the results validate the stream flow is of comparability and index fixty.
(4) Long memory about the stream flows evolution is researched. To analyze, understand flow structure, and estimate the trend and the long memory has important effects on hydrology system and its future movement. So a kind of flow decomposes analysis based on Liu switch has been put forward and then R/S is used to test the long memory of the fore-and-aft decomposed time series. The results indicate that the change of the stream flow has large relations with precipitation and climate changes. At the same time, long memory series have been proved the long memory is being in the stream flow fluctuation, which can be explained through the durative of structure switches in reason and deeply makes clear that it is very important to structure decomposing before series analysis.
(5) Multi-fractal characteristics of the stream flow are analyzed. Compared to single fractal, multi-fractal is better to depict asymmetry in the process of the stream flow evolution. MF-DFA is used to analyze the multi-fractal characteristics in the stream flow and the formation is discussed. The conclusion shows that the flow time series in the Yellow River and the Yangtse River main streams present obvious multi-fractal characteristics, which is the outcomes of long relativities and the large trails. It breaks a new path for quantitive analysis on deepen water system evolution rules.
(6) Aimed at the stream flow nonlinearity, the nearest adjacent chaos forecast model has been established to analyze the flow process in the Yellow River and the Yangtse River main streams and the satisfied precision is received. Then based on the model tracking the attracted dot in phase-spaces efficiently and catching useful information in the original dates well, the average square errors change is found through adding adjacent dots deeply to test the forecast effects. The results indicate that the method can reflects the general trend of the stream flow truly, which provides a new method to estimate the nonlinearity of time series.
(1)河川径流时间序列基本统计特征研究。引入柯尔莫哥罗夫-斯米尔诺夫(Kolmogorov-Smirnov)对径流波动进行了随机正态性检验,结果表明其分布的形状与对称形式与正态分布型的偏离程度均存在显著差异;同时,通过其频数分布说明研究对象具有“尖峰厚尾”的分形分布特征。
(2)河川径流非线性识别。利用双谱分析对河川径流时间序列数据进行了定性分析,分析结果说明黄河、长江干流径流时间序列数据结构具有非线性特征。对于非对称系统,双谱完全可表征系统的非线性特性。所以总体来看,用高阶累积量研究系统的非线性是一个极为精确和有效的方法。
(3)河川径流的长期相关性及维数研究。在对时间序列长期相关性评述的基础上,提出了一种基于不对称周期模型的非趋势波动分析方法,识别了黄河、长江干流主要水文站月径流序列进行相关性分析以及标度不变性分析。所得结论为:黄河及长江干流的月径流序列存在明显的长程相关性,标度指数均大于0.5,且黄河干流相关性程度高于长江干流。各站月径流序列在年内周期普遍存在上升慢、下降快的趋势特点,而且随着集水面积的增大,序列相关性增强,表现出明显的累积效应,揭示越大尺度的水文系统,越趋于稳定。根据标度指数,计算了流域分形维数,进一步验证了河川径流所具有的自相似性与标度不变性。
(4)径流演变的长记忆性分析。分析与了解径流结构、判断径流演变趋势以及长记忆性对水文系统与未来变化的影响等方面具有重要的作用,基于此,本文提出一种基于Liu变换的径流序列分解方法,运用修正R/S分析对分解前后的序列进行长记忆性检验。结果表明:径流波动突变的原因与降水、气候变化有着不可分割的关系。同时,只包含长记忆的序列,有效证实了径流序列波动长记忆性的存在,而且其产生原因可以由结构转换的持续性作出合理解释,进一步说明在实证之前进行序列分解是非常有必要的。
(5)河川径流多重分形研究。与单分形相比,多标度分形更能刻画径流系统演变过程中的不均匀性。本文采用多重分形消除趋势波动分析法(简称MF-DFA)对径流的多重分形性进行分析,并探讨多重分形形成的原因。所得到的结论为:黄河、长江干流径流序列均呈现出明显的多重分形,且多重分形是由其内在的长期相关性和厚尾分布共同作用的结果,这为深化水系发育演化规律的定量研究开辟了一条新途径。
(6)河川径流预测。针对径流非线性特征,建立了最近邻域混沌预测模型,对黄河、长江干流径流过程进行了预测,得到了满足精度要求的预测结果,并利用该模型能够有效跟踪径流系统中相空间里的吸引子、充分扑捉历史数据中所隐含的有用信息这一特点,进一步通过增加邻近点数来发现预测均方误差的变化,对预测效果进行了检验,结果证实这一方法真实地反映了河川径流变化的总体趋势,这同时为判断时间序列数据的非线性提供了一种新方法。
Stream flows are sorts of nonlinear time series, description and exploration exactly about which have straight relations with water resources exploitation and utilization efficiently. Based on fractal and other nonlinear theories, aimed at the characteristics of stream flow evolvement, some works have be done such as distilling, comparing, analyzing, modeling and computing on certain nonlinear characteristics about stream flow evolvement. The main results of this paper are as follows:
(1) Basis statistic characteristics of the stream flow time series are analyzed. Kolmogorov-Smirnov is introduced to test random normal nature of the stream flow fluctuation. The results indicate that the distributing forms have distinct difference with the departure degree about normal school. Through frequency distributing, stream flows are proved having the fractal distributing characteristic of“pinnacle and large trail”.
(2) Stream flow nonlinearity is identified through Bispectrum analysis. The results shows that the stream flow time series of the Yellow River and the Yangtse River are nonlinearity. For non-symetry systems, Bispectrum can token nonlinear characteristics completely. So high steps accumulated measures are kinds of exact and effective method to study systemetic nonlinearity.
(3) Long-range relativity and dimensions about the stream flows are analyzed. Based on time series long relativities, detrended fluctuation analysis based on certain non-symmetry cycle models is advanced to identify the relativity and index fixity of the months flow time series in the Yellow River and the Yangtse River main streams. The results indicate that the two main streams have long-range relativities and the indexes are larger than 0.5 and even the degree in the Yellow River is higher than the Yangtse River. Months flow time series of every hydrological station has the characteristic of slow raise, quick fall in annual cycle. Larger the catchment areas are, stranger the relativity is. So the long-range relativity shows clear cumulated domino offect. Larger the scales of the hydrology system are, higher stability it is. Then according to the index, the fractal dimensions of the object are calculated and the results validate the stream flow is of comparability and index fixty.
(4) Long memory about the stream flows evolution is researched. To analyze, understand flow structure, and estimate the trend and the long memory has important effects on hydrology system and its future movement. So a kind of flow decomposes analysis based on Liu switch has been put forward and then R/S is used to test the long memory of the fore-and-aft decomposed time series. The results indicate that the change of the stream flow has large relations with precipitation and climate changes. At the same time, long memory series have been proved the long memory is being in the stream flow fluctuation, which can be explained through the durative of structure switches in reason and deeply makes clear that it is very important to structure decomposing before series analysis.
(5) Multi-fractal characteristics of the stream flow are analyzed. Compared to single fractal, multi-fractal is better to depict asymmetry in the process of the stream flow evolution. MF-DFA is used to analyze the multi-fractal characteristics in the stream flow and the formation is discussed. The conclusion shows that the flow time series in the Yellow River and the Yangtse River main streams present obvious multi-fractal characteristics, which is the outcomes of long relativities and the large trails. It breaks a new path for quantitive analysis on deepen water system evolution rules.
(6) Aimed at the stream flow nonlinearity, the nearest adjacent chaos forecast model has been established to analyze the flow process in the Yellow River and the Yangtse River main streams and the satisfied precision is received. Then based on the model tracking the attracted dot in phase-spaces efficiently and catching useful information in the original dates well, the average square errors change is found through adding adjacent dots deeply to test the forecast effects. The results indicate that the method can reflects the general trend of the stream flow truly, which provides a new method to estimate the nonlinearity of time series.
引文
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