塔里木河流域气候—水文过程的复杂性与非线性研究
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摘要
全球暖化现象正在世界各地以加速的节拍在发展,而伴随全球暖化的结果之一就是全球气候及水文循环正在急剧的改变,气候-水文过程因气温的上升及气候极端变化而有明显的调整。塔里木河流域作为一个干旱区典型,是气候水文变化的敏感区域,许多研究人员对其已经展开了大量的研究和讨论。对气候-水文过程的特征及其随时间演变的规律和内在动力学机制的研究,将有助于制定新的环保治理措施和发展更有效气候-水文预测预报方法,从而减缓气候-水文环境的恶化。
气候-水文系统由多个子系统组成,并受到多圈层、多要素、多尺度的共同作用,子系统之间一种或多种方式发生非线性的内部或者外部的相互作用,导致它们不仅在时间上而且在空间上产生多种复杂形式的关联结构,形成了外有压迫、内有非线性耗散的复杂巨大系统,整体表现出复杂性。其影响因素有很多,例如,人类活动、地理位置、下垫面复杂的特征等等。但这些因素不是相互独立无关的,而是在各种时空尺度内产生复杂的非线性相互作用,从而使得塔里木河流域气候-水文过程的时间演化过程呈现出内在非线性外在复杂性的特征。
针对上述问题,本文引入分形理论、混沌理论、复杂网络理论等并结合GIS技术对塔里木河流域的气候-水文过的复杂性与非线性特征进行了系统的定性与定量分析；深入研究了气候-水文因子某些复杂的时间演变过程和动力学机制；最后分析了气候-水文过程的临界自组织行为,对其存在的复杂性与非线性进行初步解释。
本文主要的研究工作及其结论如下：
1.首先应用重标极差法(R/S分析)、消除趋势波动分析法(DFA分析)以及谱分析法对日平均温度、日降水量、日平均相对湿度、日蒸发量和开都河日径流量序列进行分析,研究其长期持续性特征。结果表明,五个因子时间序列在较短的时间尺度上(约一年),具有明显的标度不变性,均表现出相类似的较高的长记忆性；而五个序列而在较长的时间尺度上(大于一年),不同因子时间尺度上的幂律特征存在着一些明显的差异。然后,借助消除趋势互相关性分析(Detrended Cross-Correlation Analysis, DCCA)揭示五个因子之间的长程互相性。结果发现,F2(S)与s的双对数曲线存在两个甚至三个无标度区间。最后在GIS空间分析技术支撑下,应用联合克利金插值法,分析研究了塔里木河流域气候-水文过程的长记忆强度的空间分布特征。
2.根据混沌理论,对日平均温度、日降水量、日平均相对湿度、日蒸发量和开都河日径流量序列通过相空间重构,应用Rosenstein算法及G-P算法,分别计算了它们的序列的关联维数D、最大Lyapunov指数λ1以及Kolmogorov熵K等特征量。结果表明五个因子时间序列中存在明显的混沌特性,是非线性混沌动力系统演化的结果；塔里木河流域的气候-水文过程的变化同时具有确定性和随机性。最后在GIS空间分析技术支撑下,应用地统计理论,通过三个特征量分析了塔里木河流域的混沌特征和复杂度的分布。我们发现在气候变化复杂、具有径流、海拔较高的区域的值较大,混沌特性较强,复杂度较高,而受气候-水文过程影响较小的沙漠腹地区域的值较小,混沌特征较弱,复杂度较低,趋势明显。另外,通过关联维数D我们知道,D值越小(大),系统的层次越高(低),趋势越明显(不明显)。通过最大Lyapunov指数λ1,我们还知道五个因子的最大可预报尺度差异显著,低值地区最大可预报时间较长,高值区域较短；气候-水文因子系统的蝴蝶效应强弱程度表现为日平均相对湿度>日平均温度>日降水量≈日蒸发量,年径流量系统蝴蝶效应的平均强弱程度表现为和田河>叶尔羌河>阿克苏河≈开都河。
3.应用两种多重分形方法(多重分形盒维数)对各气候-水文因子时间尺度和强度尺度上的多重分形结构进行分析。多重分形盒维数的分析表明,各因子在整个时间尺度上具有完全不同的多重分形特征,这些特征可以用三个具有明确物理意义的参数(B,Aa和△f)进行定量表征。进一步,本文将五个时间序列分为5个或者4个年代,分析了各年代因子的多重分形特征的变化,并结合塔里木河流域的气候水文变化进行了分析。最后在GIS空间分析技术支撑下,应用联合克利金插值法,分析研究了塔里木河流域气候-水文过程的多重分形强度的空间分布特征。
4.根据粗粒化方法,将塔里木河流域的逐日平均温度、日降水量、日平均相对湿度、日蒸发量和开都河日径流量序列转化为由5个特征字符{R,r,e,d, D}构成的气候-水文因子符号序列。以符号序列中的125种3字串组成的温度、降水量、相对湿度、蒸发量、径流量的波动模态为网络的节点(即连续3d的因子波动组合),并按照时间顺序连边,构建有向加权的温度波动网络(TFN)、降水波动网络(PFN)、湿度波动网络(HFN)、蒸发波动网络(EFN)、径流波动网络(RFN)进而将五个因子的波动模态间的相互作用等综合信息蕴含于网络的拓扑结构之中。计算三种网络的度与度分布、聚群系数、最短平均路径长度等动力学统计量,从网络的角度对比研究五种序列内秉性质的差异,体现了五种气候-水文因子变化的复杂性。结果表明,五种因子波动网络均表现出很强的集聚性和较短的最小平均路径长度；TFN和RFN的度分布分别服从三段和双段幂律分布,是具有无标度特性的小世界网络；PFN、HFN和EFN兼具有无标度特性和小世界效应,既是无标度网络又是小世界网络。我们还发现在五种因子波动网络中,一些顶点的顶点度异常高,以这些顶点为代表的温度波动模态发生概率较大,例如,TFN中的节点RRR、dRR、ReR....。在TFN、HFN、EFN和RFN、PFN的重要节点中分别大都包含了R、r和r、e两种符号,这说明塔里木河流域的气候-水文过程的波动主要以上升为主,前三个因子比后两者上升的稍快。五个因子波动网络部分节点的介中向心性能力较强,4.5%(3.2%、3.2%、0.8%、3.2%)的节点承担了网络19.71%(19.71%、13.64%、3.4%、13.88%)的中介中心性功能,这些具有拓扑统计重要性的节点对于理解五个气候-水文因子波动的内在规律和波动信息的传递等有一定指导意义。根据5种顶点的平均度在塔里木河流域23个气象台站中的排行分布,将它们的主要作用区域依次定义为：一级度带、二级度带和三级度带。平均度、相似系数、最短平均路径长度和平均集群系数分布存在一定的区域特征,为通过复杂性来研究气候-水文变化的区域特征提供了理论基础。
5.首先,五个气候-水文因子的强度-频度关系说明极端气候-水文事件与小因子值变化事件的过程均可归因于同一种动力学机制。然后,建立具有自身衰减因子的数值沙堆模型对气候-水文演变过程进行模拟。模型中仅仅通过改因子值的衰减系数,其结果就可以很好地解释五种气候-水文因子实际的强度-频度关系。模型研究的结果表明,因子自身的临界自组织行为是气候-水文过程时间演化的动力学根源,正是气候-水文因子自身的自组织临界性导致了其时间演变中存在幂律关系。
Global warming has currently accelerating in the troposphere and one of the consequences that derived from climate change is the chaotic variations of weather and water cycle on the earth surface. Extreme weather events have been observed all over the world, particularly for the pattern and intensity of climatological-hydrologic-al process. The Tarim River Basin, a typical arid area, is a sensitive area of climatological-hydrological change; many researchers have launched a lot of research and discussion about it. It seems evident that the understanding of the complex dynamic characteristics of climatological-hydrological process can contribute to developing advanced techniques for climatological-hydrological forecasting. The accurate forecast can help to develop effective warning strategies to reduce impacts on climatological-hydrological environment.
Climatological-hydrological system is composed by several subsystems, and by the interaction of multi spheres, multi factors, multi scale. One or more ways can be internal or external interaction among subsystems, which result in interaction structure of more complex form not only in the time, but also in the space. The results form complex-huge system with oppression outside and nonlinear dissipative inside, and the whole show its complexity. There are many influence factors of climatological-hydrological system, for example, human activities, geographical location, complex surface characteristics and so on. But these factors are not independent of each other, but there are nonlinear interactions at various spatial and temporal scales. These reasons result in which the time evolution process of climatological-hydrological process shows inherent nonlinear and external complex characteristics.
For the above question, the author has introduced the fractal theory, chaos theory, complex network theory and GIS technology to study complexity and nonlinear characteristics of regional climatological-hydrological process. On this basis, the authorinvestigates the temporal evolution dynamics of the process further. At last, the author sets up the self-organized critical theory of regionalclimatological-hydrological factors, and interprets the fractal structure of regional climatological-hydrological process.
The main works and conclusions in this study are as follows:
1. Firstly, the long memory and scaling properties of average daily temperature, precipitation, relative humidity, evaporation and daily runoff of Kaidu River are investigatedby rescaled range analysis (R/S), detrended fluctuation analysis (DFA) and spectral analysis. The results show that the temporal scaling behaviors in the five series all exhibit two different power laws. In shorter temporal scaling, all series indicate thesimilar persistence corresponding to the annual cycle. However in longer temporalscaling, the trends are different for the five series, which reflect the different inherentdynamic nature of various climatological-hydrological factor series. The fluctuations of Hurst exponent, DFA exponent and power spectrum exponent with increasing the threshold magnitude are analyzed. Secondly, long-range cross correlations between each pair of five indices are revealed by the Detrended Cross-Correlation Analysis method (DCCA). We find that the double logarithm curve F2(s)～s two or even three scale-invariant regions are presented. Lastly, Supported by the GIS technical and based on the CoKriging method, the space distribution for the degree of long memory for climatological-hydrological process in Tarim River Basin is analyzed.
2. According to chaos theory, through reconstructing the phase-space for the series of average daily temperature, precipitation, relative humidity, evaporation and daily runoff of Kaidu River in Tarim River Basin, and calculates their three characteristic quantities, including the maximum Lyapunov exponent λ1, Kolmogorov entropy K and the correlation dimension D, with Rosenstein and G-P algorithm respectively. All results show obvious chaotic and fractal characteristics in the five series, which are the result of the evolution of non-linear chaotic dynamic system. The climatological-hydrological process in the Tarim River basin also has deterministic and stochastic characteristic. Supported by the GIS technical and based on the CoKriging method, the space distribution for the degree of chaotic and complexity for climatological-hydrological process in Tarim River Basin is analyzed. We find that the bigger for the values of three characteristic quantities is, the stronger the chaotic and complexity are in region with complicated climate change is, runoff and higher altitudes. However, the values of three characteristic quantities are smaller in desert hinterland, which the chaotic and complexity is weaker. Furthermore, the lower (higher) the correlation dimension D, the higher (lower) the level of the system, and the more obvious (less obvious) the trend. The different the maximum Lyapunov exponent λ1indicate that there are significant differences for five series in the the maximum forecasting scale. Specifically, the bigger λ1, the longer the scale is and the smaller λ1, the shorter the scale is. And the average degree of butterfly effect of climatological-hydrological factor system shows average daily relative humidity> average daily temperature>daily precipitationdaily evaporation, as for annual runoff, Hotan River>Yerqiang River>Akesu River(?)Kaidu River.
3. Multi-fractal methods (multi-fractal box counting method) has been applied to analyze the five climatological-hydrological factor series. It shows that the method can not only identify the scaling invariance but also explain the scaling behavior of the probability distributions in the factor time series. Multifractal characteristics of the five factor series can be described by three multi-fractal parameters, namely B,△α and△f. Further, multifractal characteristics changes of every age are analyzed, combining with the climate and hydrological changes of the Tarim River basin. Lastly, Supported by the GIS technical and based on the CoKriging method, the space distribution for the degree of multifractality of climatological-hydrological process in Tarim River Basin is analyzed. 4. To analyze the dynamics of the climatological-hydrological process in Tarim River Basin, using homogenous partition of coarse graining process, the series of average daily temperature, precipitation, relative humidity, evaporation and daily runoff of Kaidu River is transformed into symbolic sequences consisting of5characters{R, r, e, d, D}. The vertices of the Temperature fluctuant network (TFN), Precipitation fluctuant network (PFN), Relative humidity fluctuant network (HFN), Evaporation fluctuant network (EFN) and Runoff fluctuant network (RFN) are1253-symbol strings (i.e.,125fluctuation patterns in durations of3days), respectively, linked in the networks'topology by time series. They contain integrated information about interconnections and interactions between fluctuation patterns of temperature, precipitation, relative humidity, evaporation and runoff in networks'topology. We calculate the dynamical statistics of the degrees and the distribution of degrees, clustering coefficient and the shortest path length, and compared the difference of these five series from the view point of network. The result shows that the five factor fluctuant networks have good clustering characteristic with obvious characteristic of community structure and shorter average path length. TFN and RFN are scale-free and small-world network with degree distribution obeying a three and double power law, respectively, and with obvious characteristic of local community structure. PFN, HFN and EFN are also scale-free and small-world networks with obvious characteristic of scale-free and small-world effect.
We also find some vertices' degrees are remarkably high, for example, there are more RRR, dRR, ReR..., which shows these occurrence probabilities of the climatological-hydrological factor fluctuation represented by these5nodes, is greater. Furthermore, the main vertices of each one of TFN, HFN and EFN generally contain the2characters R and r, and the main vertices of both RFN and PFN generally contain r and e, which shows that all the five factors are is mainly ascending, however, the temperature, relative humidity and evaporation are rising faster than the precipitation and runoff of Kaidu river. Futher, some vertices in the five factor fluctuant network have high betweenness centrality (BC),4%,3.2%,3.2%,0.8%and3.2%of vertices bear19.71%,19.71%,13.64%,3.4%and13.88%of betweenness centrality of networks, respectively, these vertices of importance in topological statistics are helpful to understanding the inherent law and information transmission.
Lastly, supported by the GIS technical and based on the Geostatistics theory, the space distribution for the degree of complexty by the average daily temperature, precipitation, relative humidity, evaporation fluctuant networks of climatological-hydrological process in Tarim River Basin is analyzed. From the distribution graph of the average degree of these5nodes in all the23meteorological stations, we define them by the symbols as the Tarim River Basin wide model, the first-level-degree area, the second-level-degree area and the third-level-degree area. The distribution of the average degree, similarity coefficient, cluster coefficient and average shortest path have a regional characteristics, which provide us with the feasibility for analyzing the regional climatological-hydrological characteristics intheory.
5. Firstly, the frequency-intensity distribution of five climatological-hydrological factors suggest there are inherent dynamical connection between small factor change and extreme weather events. Then, a numerical sandpile model with decay coefficient is constructed to revealinherent dynamic mechanism of climatological-hydrological process revolution. In this model, changing the number value of decaycoefficient, the frequency-intensity distribution of various factor values can be simulated. And all results are consistent with the actual data very well. Simulating computation shows that the factors act as dynamically self-organized systems and it is the self-organized criticality of the climatological-hydrological processes that results in the temporal variation of the processes.
气候-水文系统由多个子系统组成,并受到多圈层、多要素、多尺度的共同作用,子系统之间一种或多种方式发生非线性的内部或者外部的相互作用,导致它们不仅在时间上而且在空间上产生多种复杂形式的关联结构,形成了外有压迫、内有非线性耗散的复杂巨大系统,整体表现出复杂性。其影响因素有很多,例如,人类活动、地理位置、下垫面复杂的特征等等。但这些因素不是相互独立无关的,而是在各种时空尺度内产生复杂的非线性相互作用,从而使得塔里木河流域气候-水文过程的时间演化过程呈现出内在非线性外在复杂性的特征。
针对上述问题,本文引入分形理论、混沌理论、复杂网络理论等并结合GIS技术对塔里木河流域的气候-水文过的复杂性与非线性特征进行了系统的定性与定量分析；深入研究了气候-水文因子某些复杂的时间演变过程和动力学机制；最后分析了气候-水文过程的临界自组织行为,对其存在的复杂性与非线性进行初步解释。
本文主要的研究工作及其结论如下：
1.首先应用重标极差法(R/S分析)、消除趋势波动分析法(DFA分析)以及谱分析法对日平均温度、日降水量、日平均相对湿度、日蒸发量和开都河日径流量序列进行分析,研究其长期持续性特征。结果表明,五个因子时间序列在较短的时间尺度上(约一年),具有明显的标度不变性,均表现出相类似的较高的长记忆性；而五个序列而在较长的时间尺度上(大于一年),不同因子时间尺度上的幂律特征存在着一些明显的差异。然后,借助消除趋势互相关性分析(Detrended Cross-Correlation Analysis, DCCA)揭示五个因子之间的长程互相性。结果发现,F2(S)与s的双对数曲线存在两个甚至三个无标度区间。最后在GIS空间分析技术支撑下,应用联合克利金插值法,分析研究了塔里木河流域气候-水文过程的长记忆强度的空间分布特征。
2.根据混沌理论,对日平均温度、日降水量、日平均相对湿度、日蒸发量和开都河日径流量序列通过相空间重构,应用Rosenstein算法及G-P算法,分别计算了它们的序列的关联维数D、最大Lyapunov指数λ1以及Kolmogorov熵K等特征量。结果表明五个因子时间序列中存在明显的混沌特性,是非线性混沌动力系统演化的结果；塔里木河流域的气候-水文过程的变化同时具有确定性和随机性。最后在GIS空间分析技术支撑下,应用地统计理论,通过三个特征量分析了塔里木河流域的混沌特征和复杂度的分布。我们发现在气候变化复杂、具有径流、海拔较高的区域的值较大,混沌特性较强,复杂度较高,而受气候-水文过程影响较小的沙漠腹地区域的值较小,混沌特征较弱,复杂度较低,趋势明显。另外,通过关联维数D我们知道,D值越小(大),系统的层次越高(低),趋势越明显(不明显)。通过最大Lyapunov指数λ1,我们还知道五个因子的最大可预报尺度差异显著,低值地区最大可预报时间较长,高值区域较短；气候-水文因子系统的蝴蝶效应强弱程度表现为日平均相对湿度>日平均温度>日降水量≈日蒸发量,年径流量系统蝴蝶效应的平均强弱程度表现为和田河>叶尔羌河>阿克苏河≈开都河。
3.应用两种多重分形方法(多重分形盒维数)对各气候-水文因子时间尺度和强度尺度上的多重分形结构进行分析。多重分形盒维数的分析表明,各因子在整个时间尺度上具有完全不同的多重分形特征,这些特征可以用三个具有明确物理意义的参数(B,Aa和△f)进行定量表征。进一步,本文将五个时间序列分为5个或者4个年代,分析了各年代因子的多重分形特征的变化,并结合塔里木河流域的气候水文变化进行了分析。最后在GIS空间分析技术支撑下,应用联合克利金插值法,分析研究了塔里木河流域气候-水文过程的多重分形强度的空间分布特征。
4.根据粗粒化方法,将塔里木河流域的逐日平均温度、日降水量、日平均相对湿度、日蒸发量和开都河日径流量序列转化为由5个特征字符{R,r,e,d, D}构成的气候-水文因子符号序列。以符号序列中的125种3字串组成的温度、降水量、相对湿度、蒸发量、径流量的波动模态为网络的节点(即连续3d的因子波动组合),并按照时间顺序连边,构建有向加权的温度波动网络(TFN)、降水波动网络(PFN)、湿度波动网络(HFN)、蒸发波动网络(EFN)、径流波动网络(RFN)进而将五个因子的波动模态间的相互作用等综合信息蕴含于网络的拓扑结构之中。计算三种网络的度与度分布、聚群系数、最短平均路径长度等动力学统计量,从网络的角度对比研究五种序列内秉性质的差异,体现了五种气候-水文因子变化的复杂性。结果表明,五种因子波动网络均表现出很强的集聚性和较短的最小平均路径长度；TFN和RFN的度分布分别服从三段和双段幂律分布,是具有无标度特性的小世界网络；PFN、HFN和EFN兼具有无标度特性和小世界效应,既是无标度网络又是小世界网络。我们还发现在五种因子波动网络中,一些顶点的顶点度异常高,以这些顶点为代表的温度波动模态发生概率较大,例如,TFN中的节点RRR、dRR、ReR....。在TFN、HFN、EFN和RFN、PFN的重要节点中分别大都包含了R、r和r、e两种符号,这说明塔里木河流域的气候-水文过程的波动主要以上升为主,前三个因子比后两者上升的稍快。五个因子波动网络部分节点的介中向心性能力较强,4.5%(3.2%、3.2%、0.8%、3.2%)的节点承担了网络19.71%(19.71%、13.64%、3.4%、13.88%)的中介中心性功能,这些具有拓扑统计重要性的节点对于理解五个气候-水文因子波动的内在规律和波动信息的传递等有一定指导意义。根据5种顶点的平均度在塔里木河流域23个气象台站中的排行分布,将它们的主要作用区域依次定义为：一级度带、二级度带和三级度带。平均度、相似系数、最短平均路径长度和平均集群系数分布存在一定的区域特征,为通过复杂性来研究气候-水文变化的区域特征提供了理论基础。
5.首先,五个气候-水文因子的强度-频度关系说明极端气候-水文事件与小因子值变化事件的过程均可归因于同一种动力学机制。然后,建立具有自身衰减因子的数值沙堆模型对气候-水文演变过程进行模拟。模型中仅仅通过改因子值的衰减系数,其结果就可以很好地解释五种气候-水文因子实际的强度-频度关系。模型研究的结果表明,因子自身的临界自组织行为是气候-水文过程时间演化的动力学根源,正是气候-水文因子自身的自组织临界性导致了其时间演变中存在幂律关系。
Global warming has currently accelerating in the troposphere and one of the consequences that derived from climate change is the chaotic variations of weather and water cycle on the earth surface. Extreme weather events have been observed all over the world, particularly for the pattern and intensity of climatological-hydrologic-al process. The Tarim River Basin, a typical arid area, is a sensitive area of climatological-hydrological change; many researchers have launched a lot of research and discussion about it. It seems evident that the understanding of the complex dynamic characteristics of climatological-hydrological process can contribute to developing advanced techniques for climatological-hydrological forecasting. The accurate forecast can help to develop effective warning strategies to reduce impacts on climatological-hydrological environment.
Climatological-hydrological system is composed by several subsystems, and by the interaction of multi spheres, multi factors, multi scale. One or more ways can be internal or external interaction among subsystems, which result in interaction structure of more complex form not only in the time, but also in the space. The results form complex-huge system with oppression outside and nonlinear dissipative inside, and the whole show its complexity. There are many influence factors of climatological-hydrological system, for example, human activities, geographical location, complex surface characteristics and so on. But these factors are not independent of each other, but there are nonlinear interactions at various spatial and temporal scales. These reasons result in which the time evolution process of climatological-hydrological process shows inherent nonlinear and external complex characteristics.
For the above question, the author has introduced the fractal theory, chaos theory, complex network theory and GIS technology to study complexity and nonlinear characteristics of regional climatological-hydrological process. On this basis, the authorinvestigates the temporal evolution dynamics of the process further. At last, the author sets up the self-organized critical theory of regionalclimatological-hydrological factors, and interprets the fractal structure of regional climatological-hydrological process.
The main works and conclusions in this study are as follows:
1. Firstly, the long memory and scaling properties of average daily temperature, precipitation, relative humidity, evaporation and daily runoff of Kaidu River are investigatedby rescaled range analysis (R/S), detrended fluctuation analysis (DFA) and spectral analysis. The results show that the temporal scaling behaviors in the five series all exhibit two different power laws. In shorter temporal scaling, all series indicate thesimilar persistence corresponding to the annual cycle. However in longer temporalscaling, the trends are different for the five series, which reflect the different inherentdynamic nature of various climatological-hydrological factor series. The fluctuations of Hurst exponent, DFA exponent and power spectrum exponent with increasing the threshold magnitude are analyzed. Secondly, long-range cross correlations between each pair of five indices are revealed by the Detrended Cross-Correlation Analysis method (DCCA). We find that the double logarithm curve F2(s)～s two or even three scale-invariant regions are presented. Lastly, Supported by the GIS technical and based on the CoKriging method, the space distribution for the degree of long memory for climatological-hydrological process in Tarim River Basin is analyzed.
2. According to chaos theory, through reconstructing the phase-space for the series of average daily temperature, precipitation, relative humidity, evaporation and daily runoff of Kaidu River in Tarim River Basin, and calculates their three characteristic quantities, including the maximum Lyapunov exponent λ1, Kolmogorov entropy K and the correlation dimension D, with Rosenstein and G-P algorithm respectively. All results show obvious chaotic and fractal characteristics in the five series, which are the result of the evolution of non-linear chaotic dynamic system. The climatological-hydrological process in the Tarim River basin also has deterministic and stochastic characteristic. Supported by the GIS technical and based on the CoKriging method, the space distribution for the degree of chaotic and complexity for climatological-hydrological process in Tarim River Basin is analyzed. We find that the bigger for the values of three characteristic quantities is, the stronger the chaotic and complexity are in region with complicated climate change is, runoff and higher altitudes. However, the values of three characteristic quantities are smaller in desert hinterland, which the chaotic and complexity is weaker. Furthermore, the lower (higher) the correlation dimension D, the higher (lower) the level of the system, and the more obvious (less obvious) the trend. The different the maximum Lyapunov exponent λ1indicate that there are significant differences for five series in the the maximum forecasting scale. Specifically, the bigger λ1, the longer the scale is and the smaller λ1, the shorter the scale is. And the average degree of butterfly effect of climatological-hydrological factor system shows average daily relative humidity> average daily temperature>daily precipitationdaily evaporation, as for annual runoff, Hotan River>Yerqiang River>Akesu River(?)Kaidu River.
3. Multi-fractal methods (multi-fractal box counting method) has been applied to analyze the five climatological-hydrological factor series. It shows that the method can not only identify the scaling invariance but also explain the scaling behavior of the probability distributions in the factor time series. Multifractal characteristics of the five factor series can be described by three multi-fractal parameters, namely B,△α and△f. Further, multifractal characteristics changes of every age are analyzed, combining with the climate and hydrological changes of the Tarim River basin. Lastly, Supported by the GIS technical and based on the CoKriging method, the space distribution for the degree of multifractality of climatological-hydrological process in Tarim River Basin is analyzed. 4. To analyze the dynamics of the climatological-hydrological process in Tarim River Basin, using homogenous partition of coarse graining process, the series of average daily temperature, precipitation, relative humidity, evaporation and daily runoff of Kaidu River is transformed into symbolic sequences consisting of5characters{R, r, e, d, D}. The vertices of the Temperature fluctuant network (TFN), Precipitation fluctuant network (PFN), Relative humidity fluctuant network (HFN), Evaporation fluctuant network (EFN) and Runoff fluctuant network (RFN) are1253-symbol strings (i.e.,125fluctuation patterns in durations of3days), respectively, linked in the networks'topology by time series. They contain integrated information about interconnections and interactions between fluctuation patterns of temperature, precipitation, relative humidity, evaporation and runoff in networks'topology. We calculate the dynamical statistics of the degrees and the distribution of degrees, clustering coefficient and the shortest path length, and compared the difference of these five series from the view point of network. The result shows that the five factor fluctuant networks have good clustering characteristic with obvious characteristic of community structure and shorter average path length. TFN and RFN are scale-free and small-world network with degree distribution obeying a three and double power law, respectively, and with obvious characteristic of local community structure. PFN, HFN and EFN are also scale-free and small-world networks with obvious characteristic of scale-free and small-world effect.
We also find some vertices' degrees are remarkably high, for example, there are more RRR, dRR, ReR..., which shows these occurrence probabilities of the climatological-hydrological factor fluctuation represented by these5nodes, is greater. Furthermore, the main vertices of each one of TFN, HFN and EFN generally contain the2characters R and r, and the main vertices of both RFN and PFN generally contain r and e, which shows that all the five factors are is mainly ascending, however, the temperature, relative humidity and evaporation are rising faster than the precipitation and runoff of Kaidu river. Futher, some vertices in the five factor fluctuant network have high betweenness centrality (BC),4%,3.2%,3.2%,0.8%and3.2%of vertices bear19.71%,19.71%,13.64%,3.4%and13.88%of betweenness centrality of networks, respectively, these vertices of importance in topological statistics are helpful to understanding the inherent law and information transmission.
Lastly, supported by the GIS technical and based on the Geostatistics theory, the space distribution for the degree of complexty by the average daily temperature, precipitation, relative humidity, evaporation fluctuant networks of climatological-hydrological process in Tarim River Basin is analyzed. From the distribution graph of the average degree of these5nodes in all the23meteorological stations, we define them by the symbols as the Tarim River Basin wide model, the first-level-degree area, the second-level-degree area and the third-level-degree area. The distribution of the average degree, similarity coefficient, cluster coefficient and average shortest path have a regional characteristics, which provide us with the feasibility for analyzing the regional climatological-hydrological characteristics intheory.
5. Firstly, the frequency-intensity distribution of five climatological-hydrological factors suggest there are inherent dynamical connection between small factor change and extreme weather events. Then, a numerical sandpile model with decay coefficient is constructed to revealinherent dynamic mechanism of climatological-hydrological process revolution. In this model, changing the number value of decaycoefficient, the frequency-intensity distribution of various factor values can be simulated. And all results are consistent with the actual data very well. Simulating computation shows that the factors act as dynamically self-organized systems and it is the self-organized criticality of the climatological-hydrological processes that results in the temporal variation of the processes.
引文
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