黄河健康状况评判方法的探讨

黄河健康状况评判方法的探讨
王煜
（黄河勘测规划设计有限公司河南郑州，邮编450003）
摘要：河流系统是一个耗散结构，因此评价河流健康状况可以从系统的观点出发进行探讨研究。

本文应用系统论和信息论的有关概念和理论，提出了基于系统有序度熵的河流健康评价方法，导出了综合考虑河流系统多个子系统（健康目标）的河流健康指标的数学表达。

以黄河为例，分析提出了黄河健康因子，研究了各健康因子的阈值范围，评价了黄河现状的健康状况。

关键词：河流；健康；熵；评价
1 引言
河流和人类的文明进程密不可分，从某种意义上说，人类是依附于河流而成长和发展的，无数古代文明和现代文明都可以证明这一点。

人类文明的进步一方面受益于河流，一方面也影响着河流，随着文明的进程，人类越来越多地需要水资源支撑其自身的发展，在某个时间点，甚至已经超过了河流所能够承载的负荷，河流本身的健康就会受到影响。

以黄河来说，由于人类耗水量超过了流域水资源承载能力，导致一系列社会经济和生态问题，主要包括：主槽严重萎缩、二级悬河加剧，水资源紧缺供需矛盾日益突出、河道断流频繁，多数河段水质恶化，河流生态系统退化。

如何评价河流的健康状况，以更好地实现人水和谐，这是本文研究探讨的内容。

众所周知，河流系统是一个耗散结构，因此评价河流健康状况可以从系统的观点出发进行探讨研究。

本文应用系统论和信息论的有关概念和理论，提出了基于系统有序度熵的河流健康评价方法，导出了综合考虑河流系统多个子系统（健康目标）的河流健康指标的数学表达。

以黄河为例，分析提出了黄河健康因子（序参量组），研究了各健康因子的阈值范围，评价了黄河现状的健康状况。

2 基于系统有序度熵的河流健康评判方法
本文应用系统论、信息论、水资源临界调控理论的思想[1]，进行河流健康的评价，提出基于系统有序度熵的河流健康评判方法，提出了河流健康指标的数学表达。

2.1 熵和耗散结构[2～5]
约140年前，德国物理学家克劳修斯（R.Clausius）把可逆过程中要作物质吸收的热与温度之比值称为熵（Entropie），用符号S表示，后来熵引申为描述信息的一种量化指标。

耗散结构理论认为：一个远离平衡态的非线性的开放系统（不管是物理的、化学的、生物的
乃至社会的、经济的系统）通过不断地与外界交换物质、能量和信息，系统中存在有非线性动力过程和正负反馈机制，在系统内部某个参量的变化达到一定的阈值时，通过涨落及负熵的增加，系统可能发生突变即非平衡相变，由原来的混沌无序状态转变为一种在时间上、空间上或功能上新的有序的耗散结构。

2.2 耗散结构系统演变的评判方法
对于河流系统等耗散结构，系统的相变结果不一定都走向新的有序，也可能走向无序，因此，为了把握系统协调的程度，以促使系统向更加有序的方向转化，引入有序度这一概念来衡量协同作用[3]。

考虑系统具有K 个子系统，各子系统以序参量组j e 来表达，j ＝1,…,K ，1≥K 。

设j e 子系统演变过程中的序参量变量为)(21jK j j j e e e e ，，=,ji e 有序度定义为)(e U ji j ，且[]10)(e U ji j ，∈。

ji e 的取值应在临界阈值区间，如i ji i e αβ≤≤。

假定)1(21p m e e e jm j j ≤≤ ，
， 在阈值区间的取值越大，则有序程度越高，其取值越小，有序程度越低；假定)(21n p m e e e jp jm jm ≤≤++ ，，在临界阈值区间的取值越大，其有序程度越低，取值越小，有序程度越高；假定jn jp jp e e e ，，21++在临界阈值区间越接近某一值c ，有序程度越高。

这样，j e 序参量变量ji e 的有序度)(e U ji j 为：
⎪⎪⎪⎩⎪⎪⎪⎨⎧+∈---+∈--∈--=]
,1[1],1[],1[)(n p i c e p m i e m i e e U ji ji ji ji
ji ji ji ji
ji ji ji ji j βαβααβαβ （1） 式中，)(e U ji j 为序参量变量ji e 的有序度，i β和i α分别为ji e 的最小和最大临界阈值。

由上式可知，若序参量变量ji e 的有序度值[]10)(e U ji j ，∈，则序参量变量在临界阈值区间，且其值越大，ji e 对j e 有序的贡献越大。

相反，若[]10)(e U ji j ，∉，说明ji e 不在合理阈值区间，需进行调节。

从总体上看，序参量变量ji e 对j e 有序程度的总贡献可通过)(e U ji j 的集成来实现，如下式所示：
1,0),()(11=≥=∑∑==n i i i ji j n i i
j j e U e U λλλ （2）
)(e U j j 为序参量组j e 的有序度，[]10)(e U j j ，
∈。

)(e U j j 越大，说明j e 对整个系统有序的贡献越大，系统有序的程度就越高，反之则越低。

i λ为序参量变量ji e 的权系数，它的确定既应考虑到系统的实际运行情况，又应能够反映系统在一定时期内的发展目标。

考虑系统的多个序参量组j e （j ＝1，…，K ），根据信息熵的定义，利用j e 的有序度)(e U j j ，提出系统有序度熵Y S ，以此来评价系统演化的状态。

河流系统有序度熵越小，表明河流系统相对越健康。

K e U K e U S j j K j j j Y )
(1ln )(11---=∑= （3）
2.3 河流健康指数
根据上述河流系统有序度熵Y S ，提出河流健康指数。

首先，定义河流系统各序参量变量的有序度阈值为中值情况下的河流为中等健康程度，此情况下：
)(e U ji j ＝2
1 （j ＝1，…，K ；i=1，…，n ） （4） )(e U j j ＝2
1 （j ＝1，…，K ） （5） 将（4）和（5）式带入式（3），获得河流中等健康程度的系统有序度熵Y S ，定义为YM S ：
K S YM 2ln 2
1= （6） 将河流中等健康程度对应的有序度熵YM S 和河流系统有序度熵Y S 的比值，作为河流健康指数H I ，即：
H I ＝Y
YM S S （7） 将（5）式和（6）式带入上式，得到河流健康指标H I
K e U K e U K I j j K j j j H )(1ln )(122ln 1
---=∑= （8） 根据上述定义可知，H I ＝1时表示河流为中等健康状态；H I <1时表示河流为亚健康或者非健康状态；H I >1时表示河流为基本健康或者健康状态，据此可以评价河流健康的状态。

应用河流健康指数还可以评价采取治理和调控措施后河流健康的演变方向。

如果调控后河流健康指数大于治理前河流健康指数，表示调控措施利于河流健康，河流系统向健康方向转化，调控措施合理；如果治理后河流健康指数小于治理前河流健康指数，表明调控措施不利于河流健康，河流系统健康向不利的方向发展，调控措施不合理。

2.4 河流健康评价的关键问题
按照（8）式可以评价河流的健康程度，评价的关键问题包括：系统序参量选择，分析评价河流系统的特点、开发利用目标、存在主要问题，提出所需要评价的子系统（序参量分组），再进行各子系统量化指标的选择，即序参量变量)(21jK j j j e e e e ，，=的确定；序参量合理阈值的确定，序参量变量合理阈值的确定就是合理确定序参量目标值和变化范围，即确定每个序参量变量ji e 的阈值范围i ji i e αβ≤≤，阈值需要根据河流情况和开发治理规划确定；河流健康指数的计算和调控措施对河流健康的影响分析。

3 黄河健康生命评价的探讨
在分析黄河的水沙特点、存在问题和治理目标的基础上，按照科学、独立、客观、可操作的原则，参考有关研究成果[2]，提出河流形态、河流水生态、河流水环境、河流对人类的支撑和河流对洪水的容纳等5个序参量分组，并用16个序参量变量表达，通过研究提出各序参量变量阈值的研究成果，见表1。

当然，限于问题的复杂性和指标获取的可能性，本文提出的序参量分组和各序参量变量阈值仅仅是探讨性和初步的，需要开展更深入的工作以使指标选择更加科学和全面。

以2000年为代表，评价黄河现状的健康状况。

2000年为黄河特别枯水年份，利津断面全年实际来水仅48亿m ，其中非汛期入海水量仅31亿m3，汛期仅17亿m 3，非汛期最小流量为30m 3/s,下游平滩流量约2200m 3/s ；河口镇断面全年实际来水140亿m 3，其中非汛期94亿m 3，汛期46亿m 3，最小日流量31m 3/s ；宁蒙河段平滩流量为1000 m 3/s 左右；上游河段水质为三类～四类，中下游河段基本为四类；流域国民经济耗用地表水290亿m 3，地下水130亿m 3；宁蒙河段防洪能力为5900m 3/s ，下游防洪能力22000 m 3/s 。

根据上述提出的5个序参量组的16个序参量变量2000年实际值（表1中c 栏）及其各自的阈值（表1中b 栏），应用（1）式，计算各序参量变量ji e 的有序度)(e U ji j ，结果见表1中d 栏；应用（2）式，并认为各序参量变量的权系数i λ相等，可以得到各序参量组的有序度)(e U j j ，见表1中e 栏；最后应用（8）式，式中K ＝5，可以得到2000年黄河健康指数H I ＝0.95，说明现状黄河处于非健康状态。

对于黄河这条高度开发和人工干预的河流，河流非健康状态的根本原因是人类耗用的水资源量超过了河流水资源的承载能力，造成河流维持其生命的所需用水量（如输沙用水、非汛
期生态用水等）被人类挤占，水沙关系不协调，因此重塑黄河健康、维持黄河健康生命的重要措施是实施跨流域调水以及流域和谐水沙关系的塑造。

4 结语
河流健康生命理论是一个崭新的理论，河流健康因子选择和综合评价方法本身就是一个复杂的
I 科学问题，本文仅从系统熵的角度进行了一些有益的探索，取得了一些认识，现状黄河健康指标
H 为0.95，处于非健康状态。

但是，仍有许多问题需要进一步的研究和探索，一方面需要研究健康因子及其阈值的动态特征和健康指标的演变特征等等，还需要不断研究探索新的方法，另一方面需要研究河流健康生命和流域开发治理的关系，以更好地为流域开发治理提供技术支撑。

表1 黄河健康生命评价指标
注：部分阈值代表了黄河水沙关系极其恶劣的情况。

参考文献
[1] 黄委会，黄河流域水资源多维临界调控研究报告[R]，2005年
[2] 黄委会，维持黄河健康生命理论体系框架[R]，2005年
[3] 哈肯H，高等协同学[M]，郭治安译，北京：科学出版社，1998
[4] 朱稼兴，信息和熵[J]，北京航天航空大学学报，1995 21（2）
[5] 畅建霞，黄河水资源多维临界调控研究[R]，西安理工大学博士论文
Study on River Health Evaluation Method
Wang Yu
(Yellow River Engineering Consulting Co., Ltd. Zhengzhou, Henan, 450003)
Abstract: Since River system is of dissipative structure, the evaluation of river health can be studied from point of the systematic view. With application of system and information theories, this paper presents a method to evaluate the river health based on system order degree entropy. The River Health Index is educed with consideration of multiple subsystems or health targets of the river. An example of Yellow River is given, in which the river health factors and its threshold parameters are put forward, and the current health situation are evaluated.
Keywords: river, health, entropy, evaluation
1 Introduction
River is closely related with human civilization course. In a certain meaning, human growth and development relies on river, and this can be proved by countless ancient and modern civilization. Human civilization progress can receive benefit from river on one hand and can bring about impact on river on the other hand. In the civilization course, human needs more and more water resources to support his development, the need even surpasses the bearing capacity of river at a certain time, and the health of river itself will be impacted consequently. Yellow River can be taken as an example. Since water consumption by human surpasses the bearing capacity of basin water resources, a series of social, economic and ecologic problems have appeared. For instances, main channel shrinks greatly, secondary suspended river is sped up, contradiction between water resources supply and demand is getting prominent, frequent zero-flows appear in river channel, water quality is worsened in most river sections, and river ecosystem deteriorates.
This study focuses on how to evaluate river health for the purpose of realizing the harmony between human and the nature. It is known that river system is a dissipative structure, and the evaluation of river health can be studied from point of the systematic view. With application of system and information theories, this paper presents a method to evaluate the river health based on system order degree entropy. The River Health Index is educed with consideration of multiple subsystems or health targets of the river. An example of Yellow River is given, in which the river health factors and its threshold parameters are put forward, and the current health situation are evaluated.
2 Method to Evaluate River Health Based on System Order Degree Entropy
With application of system theory，information theory and water resources critical controlling theory, a method to evaluate the river health based on system order degree entropy is presented and River Health Index is educed in this paper to evaluate the river health.
2.1 Entropy and Dissipative Structure [2～5]
About 140 years ago, R.Clausius, a German physical scientist, defined the ratio of heat and temperature for material absorption in reversible process as Entropie which is referred as S, and entropy is further interpreted as a quantized index for information description later on.
According to dissipative structure theory, a non-linear open system (whether physical or chemical or ecologic or even social or economic system) far away from equilibrium state has a non-linear power process and positive and negative feedback mechanism through continuous exchanges of material, energy and information with the outside; when a parameter change in the system reaches a certain threshold, the system may have a sudden change, e.g., non-equilibrium phase change after fluctuation and negative entropy increase, being turned into a orderly new dissipative structure in time, space or function from the original disorderly state.
2.2 Method to Evaluate Dissipative Structure Evolution
For dissipative structures including river system, etc., not all system phase changes can result in a new ordered state, some may result in a disordered state. Consequently, a concept, i.e. order degree, is recommended to judge the coordination function so as to control the system coordination degree for a promotion of a better system order [3]. Since the system has k subsystems, each subsystem is referred as order parameter group j e , i.e., j ＝1,…, K, 1≥K . Supposing order parameter variable is )(21jK j j j e e e e ，，= in evolution of subsystem j e , the order degree of ji e is defined as )(e U ji j , and []10)(e U ji j ，∈.
ji e values shall be in the critical threshold limit, e.g., i ji i e αβ≤≤. Supposing )1(21p m e e e jm j j ≤≤ ，， are bigger values in threshold limit, the order degree will be higher, and vice versa. Supposing )(21n p m e e e jp jm jm ≤≤++ ，， are bigger values in the critical threshold limit, the order degree will be lower, and vice versa. Supposing jn jp jp e e e ，，21++ are closer to a certain value c in the critical threshold, the order degree will be higher. Therefore, order degree )(e U ji j for parameter variable ji e of order j e will be as follows:
⎪⎪⎪⎩⎪⎪⎪⎨⎧+∈---+∈--∈--=]
,1[1],1[],1[)(n p i c e p m i e m i e e U ji ji ji ji
ji ji ji ji
ji ji ji ji j βαβααβαβ (1） in which: )(e U ji j is order degree for order parameter variable ji e , i β and i α are minimum and maximum critical thresholds for ji e respectively.
The above Equation (1) shows: in case of order degree value for order parameter variable ji e is []10)(e U ji j ，∈, the order parameter variable will be in the critical threshold limit, and the bigger the value is, the greater contribution will be presented to order degree j e by ji e . Otherwise, in case of
[]10)(e U ji j ，∉, it means that ji e is not in the reasonable threshold limit and shall be adjusted. In general, the total contribution presented by order parameter variable ji e to order degree j e can be realized through integration of )(e U ji j as follows:
1,0),()(11=≥=∑∑==n i i i ji j n i i
j j e U e U λλλ （2）
)(e U j j is the order degree for order parameter group j e , []10)(e U j j ，
∈. The bigger )(e U j j is, the greater contribution will be presented by j e to the whole system order degree and the higher order degree the system will be in, and vice versa. i λ is the weight coefficient for order parameter variable ji e , the actual operation shall be taken into consideration and the development aim of the system in a certain period shall be reflected when i λ is determined.
Since a system has multiple order parameter groups j e （j ＝1，
…，K ）, system order degree entropy Y S is presented to evaluate the state of system evolution according to the definition of information entropy and with the application of order degree )(e U j j of j e . The smaller the river system order degree entropy is, the more healthy the river system will be.
K e U K e U S j j K j j j Y )
(1ln )(11---=∑= （3）
2.3 River Health Index
River health index is presented based on the above river system order degree Y S . First, a river will be in the middle health degree if the order degree threshold of each order parameter variable in the river system is defined as mid-value. In such cases:
)(e U ji j ＝2
1 （j ＝1，…，K ；i=1，…，n ） （4） )(e U j j ＝2
1 （j ＝1，…，K ） （5） System order degree entropy Y S for river in middle health degree can be obtained upon the substitution of Equations (4) and (5) in Equation (3), and it can be defined as YM S :
K S YM 2ln 2
1= （6） The ratio of the order degree YM S corresponding to river’s middle health degree and the order degree entropy of river system is taken as the river health index H I , i.e.:
H I ＝Y
YM S S （7） River health index H I can be obtained upon the substitution of Equations (5) and (6) in the above equation.
K e U K e U K I j j K j j j H )(1ln )(122ln 1
---=∑= （8） It can be seen from the above definitions that the river will be in middle health state in case of H I ＝1, the river will be in sub-health or non-health state in case of H I <1, and the river will be in basic health or health state in case of H I >1, in accordance with which river health can be evaluated.
River health index can also be adopted to evaluate the evolution orientation of river health after treatment and controlling measures are taken. If the river health index after treatment and controlling is bigger than the index before treatment and controlling, it means that the measures are favorable for river health, the river system is on the way of health and the controlling measures are reasonable. If the river health index after treatment and controlling is smaller than the index before treatment and controlling, it means that the measures are unfavorable for river health, the river system is on the way of non-health and the controlling measures are unreasonable.
2.4 Key Problems in River Health Evaluation
River health degree can be evaluated based on Equation (8), and the key problems to be evaluated include: selection of system order parameter, analysis and evaluation of characters, development aim and main existing problems of river system, presenting of subsystem (order parameter groups) to be evaluated, and selection of quantized index for each subsystem, i.e., determination of order parameter variable )(21jK j j j e e e e ，，=; determination of reasonable threshold for order parameter, which is to determine target value and variation range, i.e., determination of threshold limit i ji i e αβ≤≤ of each order parameter variable ji e , threshold being determined according to river situation and development planning; calculation of river health index and analysis of impact from controlling measures on river health. 3 Study on Evaluating Healthy Life of Yellow River
Based on the analysis of Yellow River water-sediment characters, existing problems and treatment aim, in accordance with the scientific, independent, objective and operational principle, and with reference of the related study results [2], 5 order parameter groups are presented, including river state, river aquatic ecosystem, river water environment, supporting for human from river, and flood acceptance by river, and with application of 16 order parameter variables, study results of thresholds for each order parameter are presented, shown as Table 1. Limited by the problem complication and possibility for index obtaining, the order parameter groups and variable threshold for each parameter group presented in this paper are only the preliminary ones from study, and more work are required to make the index selection more scientific and comprehensive.
With the yea 2000 as a representative, Yellow River health is evaluated. The year 2000 is an extraordinary low flow year for Yellow River. The actual inflow at Lijin Section is only 4.8 billion m 3 in the whole year, in which the water volume into sea is only 3.1 billion m 3 in non-flood season and 1.7 billion m 3 in flood season, the minimum discharge in non-flood season is 30m 3/s, the downstream over-channel discharge is about 2200m 3/s. The actual inflow at Hekouzheng Section is 14 billion m 3 in the whole year, in which the inflow is 9.4 billion m 3 in non-flood season and 4.6 billion m 3 in flood season, the minimum daily discharge is 31m 3/s. The over-channel discharge in Ningmeng Section is about 1000m 3/s. The water quality is in Grade III ~ Grade IV in upper reach and basically in Grade IV in middle and lower reaches. The surface water consumed and used for national economy in the basin is 29 billion m 3 and the groundwater is 13 billion m 3. The flood control capacity is 5900m 3/s in Ningmeng Section and 22000m 3/s in lower reach.
Based on the actual values in 2000 for the 16 order parameter variables in the above 5 order parameter groups (column c in Table 1) and the threshold for each of them (column b in Table 1), the order degree )(e U ji j for each order parameter variable ji e is calculated with the application of Equation (1) and the result is shown in column d in Table 1; the order degree )(e U j j for each order parameter group can be obtained with the application of Equation (2) and with the idea of the same weight coefficient
i
for each order parameter variable, and the result is shown in column e in Table 1; finally, Yellow River health index H I ＝0.95 in 2000 can be obtained with the application of Equation (8) with k ＝5, this shows that the current Yellow River is in non-health state. For Yellow River which is highly developed and is artificially intervened, the reason for the non-health state is that the consumed and used water resources surpasses the bearing capacity of river water resources, and the water volume for keeping the river healthy life (water for sediment transmission, water for ecosystem in non-flood season, etc.) is used up by human, water-sediment relationship is not proper. Therefore, the important measure to recover Yellow River health and to keep the healthy life of Yellow River is to carry out basin-to-basin water diversion and mold a harmonious water-sediment relationship. 4 Conclusions
Theory of river healthy life is a new theory, and selection and evaluation of river health factors is a complicated scientific problem. In this paper, some study has been carried out only from the view of system entropy, the study shows the current Yellow River health index H I is 0.95, indicating that Yellow River is in non-health state. However, further research and study on many problems are required. On one hand, study shall be conducted on health factor, dynamic character of threshold, and evolution character of health index, etc., as well as on new method. On the other hand, research and study on the relationship between healthy life of river and basin development and treatment shall be carried out in order to provide technical support for basin development and treatment.
Note: Part of threshold represent the water-sediment relationship of Yellow River and the worsening state.
References
[1] YRCC, Study on Multi-dimension Critical Controlling of Yellow River Basin Water Resources [R], 2005
[2] YRCC, Theory for Keeping Healthy Life of Yellow River [R], 2005
[3] Haken H, Advanced Synergetics, translated by Gao Zhian, Beijing: Science Press, 1998
[4] Zhu Jiaxing, Information and Entropy [J], Journal of Beihang University, 1995 21(2)
[5]Chang Jianxia, Study on Multi-dimension Critical Controlling of Yellow River Water Resources [R], Doctoral Thesis, Xi’an University of Technology。