A System Dynamics Approach to Urban Water Demand
---A Case Study of Tianjin *
Xuehua Zhang Hongwei Zhang
School of Environmental Science and Engineering Department of Environmental System Analysis
Tianjin University Tianjin Polytechnic University
Tianjin China 300072 Tianjin China 300160
Department of Environmental System Analysis
Tianjin Polytechnic University
Tianjin China 300160
A system dynamics (SD) approach to urban water demand forecasting was developed based on the
analysis of urban water resources system, which was characterized by multi-feedback and
nonlinear interactions amongst system elements. As an example, Tianjin water resources system
dynamic model was set up to forecast water resources demand of the planning years. The practical
verification showed forecasting relative error was lower than 10%. Furthermore, through
comparing and analyzing the simulation results in different development modes framed in this
paper, the forecasting results of the water resources demand of Tianjin was achieved in
sustainable utilization of water resources strategy.
Keywords: system dynamics; water resources demand forecasting; nonlinearity
Population growth and economic expansion have been increasingly stimulating the demands for water supplies, which results in serious water shortage and water quality degradation in many cities of China. Effective plan of sustainable utilization of water resources has been one of the major concerns with regard to sustainable urban economic development. Correct forecasting of water resources demand is the key to water resources plan and waterworks building. A better understanding of the significant contribution to urban water resources supply-demand balance and of the water resources system reacts to certain policy is necessary for water demand forecasting. System dynamics (SD) was considered to be an appropriate method to illustrate the complex dynamics and analyze the relative implications of
[1-5] regulatory policies and have been applied to global scale and national and regional scales systems’ research. Liu
 used the SD approach to solve the urban water demand problem with focus on population factors. This paper
develops a system dynamics model which takes population, economy, environment, and policy factors into account to forecast and analyze the water resources’ supply and demand of a city.
2 Methodology SD, proposed by Forrester , aims at solving the simulating problems of large-scale systems by integrating system
* Supported by: National Natural Science Foundation of China (No.50578108), Ph.D. Programs Foundation of Ministry of Education of China (No. 20050056016), National Key Program for Basic Research (―973‖ program, No. 2007CB407306-1), Science and
Technology Development Foundation of Tianjin (No. 033113811 and No. 05YFSYSF032), Educational Commission of Hebei Province of China (No. 2008324), and Tianjin Social Key Foundation (No. tjyy08-01-078).
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theory, cybernetics, information theory, decision-making theory, and computer technology. SD method consists of dynamic simulation models embracing information feedback that governs interactions in a target system. Through simulating the development trends of the system and identifying the interrelations and information feedback relations among each factor of the system, the SD model can obtain more detailed information, which will be helpful to exploring the hidden mechanism and thus improving the performance of the total system.
2.1 Basic concepts of SD
The SD model takes certain steps along the time axis in the simulation process. At the end of each step, the system variables denoting the state of the system are updated to represent the consequences resulting from the previous simulation step. Initial conditions are needed for the first time step. Variables representing flows of information and initials, arising as results of system activities and producing the related consequences are named as level variables and rate variables respectively. Auxiliary variable means the detailed steps by which information associated with current levels are transformed into rates to bring about future changes.
2.2. Procedures for applying SD model to water resources planning
.2.1 Construction of SD model 2
The first step of the procedures is to construct SD model through analyses of the total system, and identifying the model validity by historical examination and sensitivity analysis. Accordingly, parameters and relevance can be modified and confirmed.
2.2.2 History examination
History examination is to check the error between simulation and reality. The requirement that SD model could be used in real system is the errors of the main forecasting level variables can be accepted.
2.2.3 Sensitivity analyses
Another requirement is that the target system responds in lower degree sensitivity to most of the parameters through a series of sensitivity analyses conducted to examine the system’s responses to variations of input parameters
and/or their combinations. A concept of sensitivity degree is defined as follows: X Q(t )(t ) (1) S Q X Q (t )(t )
where t is time; Q(t) denotes system state at time t; X(t) represents system parameter affecting the system state at time t;
SQ is sensitivity degree of state Q to parameter X; and ?Q (t) and ?X (t) denote increments of state Q and parameter
X at time t, respectively.
For the n state variables (Q1？ Q2？…？Qn), the general sensitivity degree of a parameter at time t can be defined
as follows: n 1 S S(2) Q in i 1
Where n denotes the number of state variables; S is sensitivity degree of state Q; S is general sensitivity degree ofiQ i
the n states to the parameter X.
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2.2.4 Identifying the strategic important parameter variable
The important parameters and variables (IPV) of the system relative to water resources demand could be determined by analyzing, sensitivity and running the SD model based on the current situations (termed as the base running, TBR) as well as on the strategies of the master plan (termed as master plan running, MPR). Since it is possible to distinguish the variables with significant differences during the original running and master plan running periods, the strategic important parameters and variables (SIPV) within the IPV could be determined.
2.2.5 Applying SD model to urban water demand forecasting
Based on the IPV, experiences of researchers and comments of decision-makers, different scenarios for the SD model running were designed, thus the optimal mode, which could achieve the coordinated development of the society, economy and environment, and particularly, realize the water resources supply-demand balance, could be decided by comparing and analyzing different option simulation results, while the urban water resources demand could be obtained from simulation results.
3 The case study of Tianjin
Tianjin, a municipality directly under the central government of China, is located at latitude 38?34′–40?15′N and
2longitude 116?43′–118?4′E, covers an area of 11 919.70 km, and is 189 km long from the south to the north and 117
km wide from the east to the west. The annual rainfall is about 550 mm to 680 mm, 75% of which is concentrated in
3June, July and August. The water resource per capita in Tianjin is 160 m/a, which is only about 7% of the average level
in China. The total population of Tianjin in 2005 was 10.43 million, with the gross domestic product (GDP) being 369.762 billion RMB and the GDP per capita 35 783 RMB.
3.1 Construction of Tianjin SD model
The Tianjin SD (TJSD) model was developed through the examination of interactions among a number of system components, the production of flow diagrams that link different subsystems, and the formulation of SD modeling equations using a professional dynamo compatible language.
The model includes EWDDLPCOPEWDDLPCC TFWUPC RCPCHUA FRCPCHUSA four major subsystems, i.e.,TOWUP EWDDLOP TEWDDLPCC WUPC OWUP population subsystem, MEUR PCLA EWDDL CTGSREWDDLC AP ACPCHUA NAPUReconomic subsystem, GL URF EFPCHUA BUAGBCR
especially in water Fig. 1 Flow chart of Tianjin
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resources supply and demand area. In Fig.1, the entire variable’s and parameter’s name are from the first letter of the
meaning word, for example, ―TP‖ means ―total population‖, ―TWD‖ means ―total water demand‖, ―WRSDBI ‖ means
―water resources supply and demand balance index‖, etc.
3.1.2 Central equation of TJSD
The flow diagram can only show the logic connection and systematic structure among factors, the quantitative relations among factors need be described by SD equations. TJSD model consists of more than a hundred equations, in
which the central equations are in reference .
3.1.3 SD model validity in nonlinear system
In order to make the flow diagram clear and easy to understand, the above central equations don’t include all the
delay feedback details of the target system although they are also components of TJSD model. To improve this absence as well as to improve SD model validity in nonlinear system, a water resources subsystem delay feedback circle (in Fig.1 with bold and underlined signs)—— water supply capacity buildings —— is introduced as an example in the
Fig.2 is water supply capacity building flow chart which is a piece of water resources subsystem SD diagram detail which included two simple first-order delay feedbacks.
Plan t ime, Pt—— Plan for t ransfer water from ot her area, Wr(t) Water demand, Wd --- - + Delay t ime, DtD elay flow, ;D f(t)
Water transfer p roject building, Wbr(t) +
Wat er sup p ly
cap acity , Ws(t)
Fig. 2 Water supply capacity flow of TJSD
Plan for water transfer from other area (Wr(t))？in which there is had a first-order delay, is shown as the basic
divided differences formula，Wr (t) (Wd Ws(t))/ Pt .
Due to delay time to implement from the confirmation of water transfer scheme to water supply formation, water transfer project building (Wbr(t)) can be expressed as a simple first-order master delay function:
Wbr (t )Df (t )/ Dt .
333As known, the initialization of Df (t) is A m, initialization of Ws (t) is B m, Wd = C m, Pt = a, Dt = b. According
to the above conditions Eq. (3) can be established:
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