Journal of Geographical Sciences 13, 1 (2003) 112-122 ISSN: 1009-637X www.geog.com.cn

Theory and model of water resources complex adaptive allocation system ZHA O Jianshi, WANG Zhongfing, WENG Wenbin (Institute of Hydrology & Water Resources, Tsinghua University, Beijing 100084, China)

Abstract: Complex adaptive system theory is a new and important embranchment of system science, which provides a new thought to research water resources allocation system. Based on the analysis of complexity and complex adaptive mechanism of water resources allocation system, a fire-new analysis model is presented in this paper. With the description of dynamical mechanism of system, behavior characters of agents and the evaluation method of system status, an integrity research system is built to analyse the evolvement role of water resources allocation system. And a brief research for the impact of water resources allocation in beneficial regions of the Water Transfer from South to North China Project is conducted. Key words: water resources allocation; complex adaptive system; complex giant system CLC number: P349; P91

Water resources allocation is an important problem of social sustainable development. The allocation of water resources relates to a complex and huge system which contains society, economy, environment and water circle. The system is impacted not only with the natural factor, but also with society, economy, culture, tradition and so on. The factors of the system are various and of complex relationship. The characters of the system are deferent between macro-class and micro-class. So water resources allocation should be researched synthetically and homeostatically with the theory and method of system science based on the time finity and reproducible ability of water resources.

At present, the primary theories and methods of system science applied to research on water resources allocation are system dynamics (Gao and Liu, multi-object analysis (Xu et al., 1997; Wong et al., 1995; achievements are outstanding and abundant, there still exist be described clearly. The one is how to relate the behaviors the whole system. The other is how to explain relationship and the inevitability of the system.

System science is the basic theory and method of water

1996; Su and Liu, 1997) and Cai, 1997). Although the research

two problems which are difficult to of individual and the evolvement of of the chanciness of various factors

resource allocation research, so the key of the two problems should be quested from the new theory and new method of system science. Since the 1980s, the rise of nonlinear science (Zhu, 1992) and complexity study brings system science to a new period, especially the present of complex adaptive system (CAS) theory (Holland, 1998) in 1994, which is a new breakthrough of complex system study. With the penetration of complex system study, although there are many debates in mechanism of the form of complex system and complexity, it is accepted that reductionism theory and method is difficult to adapt the demand of complex system study. In April of 1994, Science magazine presented a special article entitled "Exceeding Reductionism Theory", for which eight scientists were invited to write the process of complex system study in physics, chemistry, biology, economy, environment and neurology. While there are different theories and methods in complex system study, the direction of the study is mostly consistent, that is exceeding the Reductionism Theory.

Received date: 2002-06-24 Accepted date: 2002-09-10 Foundation item: National "973" Project, No.G1999043607 Author: Zhao Jianshi (1975-), Ph.D., specialized in water resources allocation and planning.

E-mail: zhj sh98@mails.tsinghua.edu.cn

Theory and model of water resources complex adaptive allocation system 113

As a field based on system science theory, the study of water resources allocation system (WRAS) should absorb new theory and method of system science to develop itself. For WRAS contains various factors and subsystems, it should be researched with the method of "Hall for Workshop of Meta-synthetic Engineering" (Qian et al., 1990). A model named Water Resources Complex Adaptive Allocation System Model (WRCAASM) is presented based on the application of CAS theory in this paper, which aims to solve the two problems ahead effectively with quantitative analysis.

1 The theoretic analysis of water resources complex adaptive allocation system

The complexity of WRAS is shown in the following ways: (1) the units of system are multiplayer and cosmically; (2) there are various nonlinear relationships among the units of system subsystems; (3) the openness of WRAS induces the complexity of system evolvement; (4) the spatial structure of WRAS is complex; and (5) the complexity of WRAS is formed with synthetical action of the factors ahead.

The complexity of WRAS determines that it has to be analyzed and researched with the theory and method resolving complex problem, CAS is such a theory which can be used to analyze and research complex system effectively. 1.1 Complex adaptive character analysis of WRAS The core of CAS theory can be generalized that adaptability brings up complexity. The complexity of macro system comes down to the behaviors of micro individual in the theory. The basic thought of theory is as follows. The members of the system are called adaptive agent. Every kind of agent has its structure and lots of behaviors. The adaptability of the agent refers to that it can interact with other agents and the environment of the system. During the period of sustaining interaction, agents can modify its structure and behaviors according to the changes of other agents and the environment of the system. In this way, the agent studies and accumulates experience. So it can modify its structure and behaviors to new states for adapting to the changes according to the experience. The evolvement or anagenesis of macro system, including the birth, polarization and variety of new layers, and the appearance of new, aggregation, bigger agents, derives from this base. Based on the theory of self-organization and synergetics, CAS theory considers that the units of the system are self-aimed, initiative and active agents, which is a great progress of conception of complex system study.

Surrounding the core concept of "adaptive agent", the CAS theory advocates some system evolution related concepts which include: aggregation, nonlinearity, flow, diversity, tagging, internal model, and building blocks, etc.

The "adaptive agent" is capable of initiative and self-study mechanism. Adaptive agents among WRAS, such as irrigation districts, enterprises, community societies and ecology zones, have the power of initiative and evolution, which contributes to reaching the status of fair competition-the survival of the fittest, in both the system of water resources utilization and the adaptive agent itself.

The main momentum for systems evolution is reciprocity between two adaptive agents, or between adaptive agent and the environment. The competition relationship among adaptive agents, the changes of adaptive agents and environment, will lead to nonlinear inflexion of such reciprocity, promoting the steady evolution of the mechanism of water resources utilization. This paper abstracts the resultant force of three kinds of systems-geographic gravitation, interest gravitation and policy gravitation-from the momentum of WRAS evolution.

As we believe, there are organic relations between macrocosm and microcosm. The variances of individuals serve as the foundation for those of wholeness. Simultaneously the integer has the "emergent property". All kinds of variances of adaptive agents in WRAS can cause the variance of the whole system. For example, the improvement of water saving may lead to the transfer of water supply from imbalance to balance.

114 Zhao Jianshi, Wang Zhongjing, Weng Wenbin

Chanciness and inevitability are opposite and conforming. Uncertainty of WRAS (Chanciness) can be divided into two sides: the uncertainty of natural world and that of society. The uncertainty of nature mainly results from stochastic process of meteorology. And the uncertainty of society results from the uncertainty of factors as future population, water demand per capita, economic development, irrigation regulation, priority of water utilization, etc. The paper focuses the innovative research on the latter part, and bring stochastic process into the evolution of adaptive agent. Through analyzing the genetic arithmetic based and classified study, as well as the selection of different adaptive agents, we try to establish the relationship between the Chanciness of microcosm and the inevitability of macrocosm. 1.2 The dynamical analysis of the WRAS' evolution Two obvious factors cause the evolution of WRAS: one is the change of environment upon which the WRAS depends, such as population growth, climate inflexion and affiux-efflux of local water resources. These are extrinsic factors or the evolution. The other is the intrinsic factor for such evolution, namely the reciprocity among the adaptive agents in system. This reciprocity drives the evolution of system through materials flow, energy flow and information flow within WRAS. All flows relating to the momentums of system evolution comprise many vital factors, such as water resources quantity flow in materials flow, currency flow in energy flow, the information of water resources allocation and the policy, regulation information in information flow. The evolution is accomplished by these flows. And finally the transition of status of the water resources allocation and the system is reached.

In order to facilitate the dynamical analysis of the WRAS' evolution, we use the concept of "water resources potential energy". Based on the general definition of potential energy, the force driving the movement of matter points to the low place with lower potential energy from the place with higher potential energy. So in our WRAS, on both spatial and temporal scales, the driving force of water resources should parallel the gradient of water resources potential energy. Followed by the above concepts, the potential energy of water resources can be formulated as:

d n = f (dG, dF, dM) (1) where dH is the variation of the potential energy of water resources; and dG is the variation of the geographical potential energy of water resources. The nearer to the source and the more convenient for channeling off water, the lower the geographical potential energy is. dF is the increase or decrease of the "interest potential energy" of water resources. The higher the price submitted by the water resources market, the lower the interest energy is. dM is the variation of management potential energy of water resources. The greater disparity of water quantity between real use and that stipulated by laws and regulations, the lower the management PE of water resources is.

Seen from formulation (1), the direction of water resources movement depends on the composition of three forces: geographical force, interest force and management force. The

] / Lack of water resources ] . / caused by the changing of ~ ' ~ system environment ] \

Incoming of water resources reduced or interrupted ]

Potential energy of water resources increased ]

Study and e v o l v e m e n t ~ Potential energy of water mechanism of agents / T ] resources reduced

Incoming of water resources

Study and evolvement ~ Lack of water mechanism of agents resources relaxed

Figure 1 Dynamical mechanism of water resources allocation system

Theory and model of water resources complex adaptive allocation system 115

mechanism of initiation for the composite force is intricate. It is very hard to be expressed by mathematical method. It can only be demonstrated by various reciprocities among adaptive agents of WRCAASM model.

In the WRCCASM model, the three forces impel the exchange of materials, energy and information through self-study of adaptive agents and feedback procedure caused by evolution mechanism. In WRAS, water quantity plays as one of the significant influencing factors in main adaptive agents. These agents are sensitive to the variation of water resources amount, producing feedback to system by adjusting their status quickly. The principle of this feedback is showed in Figure 1.

2 The frame of WRCAASM

The basic idea of WRCAASM is expressed as follows. It is comprised of adaptive agents with self-study capability as basic elements, and constructed upon social and economic frames. It researches the macro evolution rules based on micro prospect, through simulating both behaviors related to water resources utilization, and the development models of society and economy with the water resources allocation model under certain water conditions. Because of undivided relationship between the WRAS and macro-economy system, our model would use ASPEN model for reference when describing economic system. ASPEN is a simulation model of US micro-economy, developed by US Sandia lab. Our model also integrates the simulating frames of WRAS with the economy system.

Adaptive agents are basic elements for WRCAASM. Agents in this model can be divided into three areas: agents for social production, social administration and ecology. In agents of social production, they include individuals in each chain of economic production: producers- agriculture enterprises, light industry, heavy industry and estate enterprises; consumers-urban and rural families; service provider-banks and service enterprises. Social administration mainly includes administrative departments of each level, who execute the supervision and administration of social production, water resources, ecology and environment. Agents for ecology and environment include vegetation and water environment.

The above pattems simulate the real society through production trade market, service trade market, water resources allocation market, loan market and policy.

In the model every agent exchanges materials, energy and information with other agents and environment, based on the self-study mechanism and behavior model. All of individual's behaviors constitute the behavior of the system. And accumulation of this behavior results in evolution of the system. That is the core idea of WACRRSM. The following tries to constitute the frame of WRCAASM based on the self-study mechanism and behavior model. 2.1 Self-study mechanism of adaptive agent The adaptive agent in WRCAASM model adopts classified study mechanism depending on genetic arithmetic. Such mechanism is elaborated through an example of identifying the quantity of conducted water in a given irrigation district.

Our model applies the method of Long-term Average in precipitation and runoff simulation, and only simulates the uncertainty in production because of the complexity of simulation of climate and hydrology. Guided by the above assumption, we need to compare the following two trends of this year with those of last year before every irrigation practice: (1) Does the water price of irrigation district ascend or descend; (2) Is the irrigation level in the district higher or lower than perennially average value. Based on judgment of the above two trends there are 3*3=9 kinds of states of district, correspondingly, because there are three kinds of states of every trend. As irrigation takes place many times among the growth of crop, each of all irrigated crops has 32n kinds of states (n is the irrigating times).

Genetic arithmetic based classified study mechanism endows every state with a probability vector (PD, PI, PC), among which PD is the probability of added irrigated water compared with

116 Zhao Jianshi, Wang Zhongjing, Weng Wenbin

last year; PI is the possibility of invariable irrigated water; PC is the decreased irrigated water. Every given range for variation of water is a constant.

Before every irrigation, the state is decided after the judgment. Then variance of irrigated water is determined stochastically by probability vector corresponding to the states. For example, at certain time, state 4 corresponds to the probability vector (0.3,0.5,0.2). We assume to adopt stochastically the measurement of increasing water amount after the district is in state 4. If the later facts verify that that measurement leads to the decreasing of planting profits, probability would be adjusted to (0.2,0.55,0.25) as response to errors, which reduces the value of certain probability to the state. When the irrigation district inters into the same state, the probability of adding irrigated water decreases. 2.2 Behavior pattern of adaptive agents 2.2.1 The urban family The urban family is an important component of the model. For an urban family the salary income from work is the main financial source. The work includes light industry, heavy industry and estate enterprises, banks, service enterprises and administrative departments. If the urban family is unemployed, the government will pay the minimum guarantee of living, which is determined by the number of family members. Also the family members will join the labor market to compete for new jobs. The aged citizen will receive pension. Income of a family also includes interest of saving. The family pays taxes under single taxation, according to the total income.

The consumption of families includes several parts: water, food, non-durable products, housing, transportation, traveling, etc. In model of WRCAASM, we make presumption to urban family consumption as:

The water demand of family per day can be described as: = w0 + op(w) (2)

where IVy is the total water demand of the family; W0 is the essential amount of water demand; p (w) is the marketing price (determined by administration); a and b are parameters. After the water demand of family is prescribed, it can buy additional water from administration through water resources allocation market with the price ofp(w).

Food demand per day can be estimated by the number of a family. Once the demand is determined, the family will purchase them from a suitable company. The searching process of such company could be the following: First, each food company offers unit price of his products. Then the family refers to these price lists to make a decision. Supposing company c gives a quoted price ofp(c), the probability for the family to purchase from c is:

p = k c ~ (3) where p is the probability of purchase; e is food price; q is a given parameter; and k is a constant standardizing the probability vector. This equation means that the lower the price of c compared to those of other companies, the more possible the purchase of family from company £ .

The family's purchase of other non-durable products and other service is decided in the same way. While the calculation of the demand varies:

demand amount = r* (family income-payment for food)/average price of products where r is a constant for proportional purpose.

The family's demand of housing is based on the following. At the beginning, every family owns its housing or rents house from estate enterprises. If he chooses renting, the family would pay rent in proportion to his income. Meanwhile the family would hold desire of purchasing house every day with a certain probability. Those who own housing would hold desire of improving house condition with a certain probability.

In addition to the above consumption, the family holds a certain amount of cash every day. And the rest of income is saved into bank. After each interval, the family would choose new banks judged by a given probability. The probability of selection of banks is related to their total estates.

Theory and model of water resources complex adaptive allocation system 117

2.2.2 The rural family The rural family is the important component of the model with largest number. For a rural family the salary income from work is also the main financial source. The work is mainly in irrigation district. The rest of labor force enters into urban labor force market, competing with urban labor force in sectors of light industry, heavy industry, estate enterprises, banks, service enterprises and administrative departments. If the urban family is unemployed, the government will pay the minimum guarantee of living, which is determined by the number of family members. Also the family member will join the labor market to compete for new jobs. The aged citizen will receive pension. Income of family also includes interest of saving. The family pays taxes under single taxation, according to the total income.

The consumption of rural family is similar to urban family in their components and models. But they have different parameters and water prices. Besides, unlike the urban family, the rural family's demand for housing is determined as follows: At the beginning, each family owns house. They would hold desire of improving housing conditions with a certain probability. The housing consumers choose the estate enterprises by prices for purchasing houses (because only the construction cost is considered, its price is lower than the city's). And rural family choose loan by loan interest.

In addition to the above consumption, the family holds certain amount of cash every day. And the rest of income is saved into bank. After each interval, family would choose new banks judged by a given probability. The probability of selection of banks is related to their total estates. 2.2.3 Irrigation district The land in irrigation district comprises irrigated land and non-irrigat- ed land. The production function of irrigation district can be formulated as:

Y = k x S n x Y n + S r ( W T ~ ,Ai x f f (4) • = " WT,~ "

where Y is the output of irrigation district; k is given parameter; Sn is the area of non-irrigated region; Yn is the unit output of non-irrigated region; Sr is the area of irrigated region; n is the number of periods in irrigation; Yoz is the potential output of crops; and ,~i is the sensitivity index of water scarcity in period L representing the extent of output loss caused by water scarcity. The greater the A~, the greater the loss rate is. WT~ is the actual amount of irrigated water in period I; WT,~ is the potential amount of water for irrigation; L is the number of labor; and a is given parameter.

The irrigation district can adjust the output of crops through altering the areas of two lands (irrigated and non-irrigated), water amount, and number of labor. Every year the managers of irrigation may apply the loan for developing areas of irrigated and non-irrigated regions. The irrigation district decides whether to apply loan or not by weighing both increased yield and reconstruction cost. Once the reconstruction of a district is decided, the district needs to join the products market to purchase a certain number of light industry products or heavy industry products. The irrigation districts determine the amount of water for irrigation according to irrigation regulation every year. Besides, district can hire or dismiss the labor. The above three decisions are based on classified study mechanism of genetic arithmetic.

All crops produced by irrigation district enter into the market, of which the prices are decided by mechanism of classified study, and the volumes of sale are decided by the market.

In our model, the employee of district has the same level of wage. At last the irrigation district should pay profit tax based on profit, and pay social insurance tax based on average wage level. 2.2.4 Enterprises Enterprises in the model include light industry, heavy industry, estate corporation and service corporation. They have the same behavior pattern. They perform manufacture based on capital, resources and labor force. The product function of these enterprises can be formulated as:

y = kM~WbL c (5)

118 Zhao Jianshi, Wang Zhongjing, Weng Wenbin

where y is the daily output of one enterprise; k is the number of machines owned by that enterprise; W is amount of water used in production; L is the number of employee in the enterprise; k, a, b and c are given parameters, varying with different enterprises.

The enterprise can adjust output through altering the value of K or L. Each year the enterprise can apply business loan to purchase new machines. It decides whether to apply loan by weighing increased output and the cost of purchasing machines and cost of loan. Besides, the enterprise determines water amount for production daily. And it will dismiss or hire more employees. It compares the current average demand for its products with the stocks. If the balance between these two items is under a given constant, the enterprise will increase the water amount and hire new employee. If such balance surpasses the constant, the enterprise will reduce the water amount and dismiss its employees. When the water amount and labor force in production are decided, the enterprise enters into relevant market to sale its products based on price, sale volume and profit of the products and the average price of the market, which applies classified study method based on genetic arithmetic in determining product price in the market.

In our model, the employee of the enterprise has the same salary level. At last the enterprise should pay profit tax based on profit, and pay social insurance tax based on average salary level. 2.2.5 Banks The adaptive agent of bank in the model accomplishes three functions: managing family saving, providing loan, and hiring a small number of employees.

The interest of family saving is determined by the government. The family will choose the new bank of saving after each interval. The probability of being selected for the bank is related to the bank's total capital.

The interest of loans consists of two parts during the bank's processing of loan: one is decided by the default value of bank interest, the other is decided by classified study mechanism based on genetic arithmetic. Once the application of loan is received, the bank will review the following: a) whether loan is much higher than the applicant's income; b) whether current loan interest is much higher; c) whether an applicant has applied loan and has not paid it off. If any of these conditions is filled, the application will be denied.

At last, the bank hires a few employees, the number of which is related to its total capital. The bank pays income tax and social insurance to the government. 2.2.6 Vegetation In order to simulate the function of vegetation in the sustainable social development and value this function, our model takes the vegetation as a virtual adaptive agent with yielding function. Its input is water resources. And its output is area of vegetation. And the production function is:

Pa = a W b (6) where Pa is area of vegetation; W is water amount; a and b are given parameters. When the government tries to value its benefit, the transition relationship between vegetation area and currency can be established as to decide precisely the water resources for ecology prosperity. 2.2.7 Water environment Water environment in the model is simulated by the agent that can bring accessional benefits. Wastewater of water environment is made up of different water consumers in a certain proportion. Firstly this wastewater should be processed by wastewater treatment plants. The treated water becomes usable water resources, and untreated waste brings negative influence on water environment. The production function is:

P~ = - a W b (7) where Pw is the benefit of water environment; W is wastewater; a and b are given parameters. The government decides if new wastewater treatment plants should be built based on balancing its benefit and cost. 2.2.8 The government The role of government in the model is very important as a system ad- ministrator, whose function could be epitomized as the following:

Every day, the government recruits all kinds of taxation from families, enterprises and banks. Meanwhile it pays kinds of subsidies and pensions to unemployed people and retirees.

Every day the government reviews the following trends: 1) current relationship of demand

Theory and model of water resources complex adaptive allocation system 119

and supply in all products; 2) the proportion of citizen's net income in total output; 3) the margin between the loan and the deposit in the bank; and 4) the margin between the income and expenditure of the government. Based on the above trends, the government determines all tax rates and defaulted loan interest of banks through classified study mechanism in order to simulate the government's tendency of extension and the policy of currency contraction.

The government decides the water amount for ecological use and all water prices, including water for urban life, rural life and production. The following tendencies of every kind of water's changing should be taken into account when deciding the price of water resources: 1) the relationship between demand and supply of the given sort of water resources; 2) the marginal utility of the given sort of water resources; and 3) the tendency of increasing or decreasing of total amount for that given water resources.

After every interval, the government decides whether to build new water conservancy projects through classified study mechanism, which is based on the judgment to altering tendencies of the following values: 1) the margin between the total demand of and current supply of water; 2) the ratio of engineering cost to the profit of accessional water supply; and 3) the ration of engineering cost to the government's income.

After every interval, the government decides whether to build new wastewater treatment plants through classified study mechanism, which is based on the judgment to altering tendencies of the following values: 1) the inflexion of rate of treated water; 2) the ration of construction cost to expected benefit; and 3) the ratio of construction to government income.

In the model water conservancy projects and wastewater treatment plants have special functions, while they are not agents with ability of study and adaptation.

Besides the government employs a certain number of officials. 2.3 The evaluation of WRAS states The most basic character of CAS theory in describing problems is evolution of the system and the study ability of adaptive agents. During the development of systems science, entropy is applied to analyze the evolution direction of the system. The system in which entropy increases is called retrogressed system. The degree of chaos and disorder enhances along with the increasing of entropy. The system in which entropy decreases is called evolutive system. The system's degree of chaos and disorder reduces along with the decreasing of entropy. From the view of history of water resources utilization, human evolves from the status of living beside the water area to the status of channeling water for utilization. Finally they reach to the capability of building large water conservancy projects and establish the system of water resources allocation, in which the order continually increases to form a typical evolutive system. It is crucial to define the entropy of WRAS fin order to evaluate the system's general state and its controllable boundary conditions (engineering projects, policies, measures, etc.).

The conception of entropy is presented by Clsusius in the research of thermodynamics. The explicit definition was given by Boltzmannn as follows:

S = kB In W (8) where kB is Boltzmann constant; and W is the number of microcosmic states of system in a certain macrocosmic state.

In fact, the evolvement of WRAS is tightly related with the development of productivity and the evolvement of society. So the entropy of water resources allocation system is defined as follows in this paper.

The social welfare efficiency of water resources is defined at first. B(t) = f (F(t), P(t), R(t), E(t)) / W(t) (9)

where t is variable of time; F(t) is economy; P(t) is population; R(t) is resources; E(t) is environment; f (F(t), P(t), R(t), E(t)) is the value of social welfare; W(t) is total amount of water resources which can be allocated; and B(t) is the social welfare efficiency of water resources.

The entropy of WRAS is defined as follows. S(t) = -k In B(t) (10)

120 Zhao Jianshi, Wang Zhongjing, Weng Wenbin

where k is proportion factor; and S(t) is the entropy of WRAS. 2.4 Operational mode and characters of WRCAASM The model should be initialized before it runs. The quantity of agents, the original states, boundary conditions and the parameters of agent behaviors in the system, all this should be confirmed in this process. The model reaches a relatively steady state after the process. Based on all parameters of this relatively steady state, the model could run with a period of simulating specified.

During the operation of the model, the behaviors of agents occur in a specified order. In principle, when a behavior involves several agents of the same kind, a stochastic dispatch algorithm would be provided in the model so that the phenomena of differentiation could be avoided because of the order of occurrence. After the simulating calculation of the model, the macrocosmic characters of economy system and water resources can be calculated with the superposition of the behavior results of microcosmic agents. Using the index and calculating method of system evaluation, the analysis and evaluation for the evolvement tracks and states of the system could be conducted, and the analysis conclusion of various schemes could be drawn. The flow of system operation is shown as Figure 2.

Compared with the traditional method of system dynamics and multi-object analysis, the characters of WRCAASM are as follows. First, WRAS is studied based on the behaviors microcosmic agents. The macrocosmic characters of system are explained as the emergent property of agents' behaviors, which simulates the evolvement of system more scientifically. Second, the agents in the model have the ability of study and adaptation, every kind of agents has their own optimal objects, which makes the system have the characters of multi-object optimization. Third, most of the relationships in system are described with nonlinear equation, which can reflect the relationship between quantitative change and qualitative change more efficiently. Fourth, part of chanciness in system is described with the study mechanism of agents based on genetic arithmetic. The inevitability of system is shown as the macrocosmic dynamical characters. They are associated well in the model.

I Model Initialization I

l Initializing the Quantit3~ Initializing the Initializing the Initializing the ] t I I of Agents ] ] OriginalStates or Boundary Paramet . . . . fAgent] ~!1 / ] System Conditions Behaviors I t~ i i i

-EL Simulation with WRCAASM Integrating Society. Economy, Water Resource l

Ecosystem and Environment [

+ / Evolvio T ck Regio. States I

Society, Economy, Water Resource, Ecosystem / I and Environment) J l

Analysis Result of Macrocosmic and Microcosmic States of System

I Conclusions, Advises or Decisions

Evaluation of System States and Sustainable

Developing for the Region

Criterion, Index i and Method of i

Evaluation

Figure 2 The flow of WRCAASM operation

Theory and model of water resources complex adaptive allocation system 121

3 Calculating sample of WRCAASM

After the foundation of WRCAASM, the beneficial region of the Water Transfer from South to North China Project is simulated to analyse the impact of different amounts of diversion water. In WRCAASM, the developing mode of society and economy is interrelated tightly with the utilizing condition of water resources. So society and economy will be in deferent developing mode within the deferent utilizing condition of water resources. In the criterion contrast scheme, the parameters of model are initialized based on the society and economy statistics data of the region in 2000, and the total amount of diversion water is 10.324 billion m 3. In this condition, the model is run to analyse the evolution of the region from the year 2000 to 2030. Because the project involves the benefits of many-sided and the final diversion scheme is not confirmed, according to the calculation and contrast between the deferent amounts of diversion water, on one hand, the impact of the deferent amount of diversion water in the region can be studied. On the other hand, all diversion schemes can be contrasted comprehensively.

Based on the criterion contrast scheme F103, in the same condition of other boundary, the serial numbers and the diversion amount of other contrast schemes are shown in Table I.

According to the calculating result of the

80000 model, the relationship 7oooo between diversion amount ~ 60000 and GDP in the region is ~, 5oooo shown in Figure 3, the % 40000 30000 relationship between ~ 2oooo diversion amount and the ~ 10ooo

o total yield of food crops is shown in Figure 4.

From the changing tendency of total GDP, it is shown that the efficiency would be down with the increasing of diversion amount. The reason is that water is a restricting factor of the development of 1000o society and economy when the diversion amount is 8000 small. It would be more ~ 6000 efficient with more scarcity. _~ 40oo With the increasing of .~ diversion amount, it would 2000 not be the restricting factor

0 when the total amount of water resources can reach the requirements of social and economic development. So the efficiency would be down

Table 1 Serial numbers and diversion amount of schemes

Serials number F40 F50 F60 F70 F80 F90

Diversion amount (108 m 3) 40 50 60 70 80 90 Serials number F103 F l l 0 F120 F130 F140 F150 Diversion amount (108m 3) 103 110 120 130 140 150

I ""m-- GDP of 2030 ,I, GDP of 2010

Y , , , , , J , J L , L , , i , I , , , , J i ,

40 50 60 70 80 90 103 110 120 130 140 150

diversion amount (10 8 m 3)

Figure 3 Relationship between diversion amount and GDP in the region

¢ food crops yields of 20 10

+ Rxxt crolz yields of 2030

I I I I I I I I I I I

40 50 60 70 80 90 103 110 120 130 140 150 di~rsion arnmnt (1~ m 3)

Figure 4 Relationship between diversion amount and total yield of food crops

122 Zhao Jianshi, Wang Zhongjing, Weng Wenbin

after that time. From the changing of total yield of food corps, it is shown that the yield would increase

more rapidly when the diversion amount is between 6 and 11 billion mL In this case, most of the diversion water is used by living and industrical production, which restricts the development of agriculture because less water is used by the planting of food crops.

4 Summary

The theory of water resources complex adaptive allocation system is established according to the analysis o f its characters in this paper, and a model named WRCAASM is built. The structure, study mechanics, behavior mode and relationship o f agents are described qualitatively and quantitatively, so the primary simulating calculation and analysis o f WRAS can be done by the model. WRCAASM explains the inherence relationship between units and macro system, chanciness and inevitability from the mechanics of system. The model sets up a bridge linking micrograph and macrograph, so it can disclose the internal reasons and dynamic power that make WRAS evolve continually.

Otherwise, there are a few deficiencies in WRCAASM. The theory of model is not perfect, and the model is not entire. There is irrationality in parts of the model. All of these should be verified and proved in practice.

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