Analysis of the ultimate water resources carrying capacity in Yancheng , China

Unreasonable development and utilization of resources has caused serious environmental problems, especially water shortage and water pollution. Determining the largest population size and economic scale that water resources can support without destroying the ecological environment in a region, that is, ultimate water resources carrying capacity (UWRCC), helps to realize the sustainable utilization of water resources. UWRCC is a variable value which is easily affected by natural conditions, technical level and economic status. This study proposes a UWRCC research method that combines multi-objective optimization and scenario analysis. This method draws a diagram of UWRCC result sets based on multi-scenario UWRCC calculation, through which UWRCC values under different specific technical and economic levels are easily and quickly obtained. This method has been applied to Yancheng in this study and the quantitative relationship between technical level, economic level and UWRCC of Yancheng was analyzed. Taking Yancheng as the research area, this study analyzes the quantitative relationship between the technical level, economic level and UWRCC of Yancheng. The results show that according to existing government planning, Yancheng’s water resources will be sufficient to support socioeconomic development. But the districts of Yandu, Tinghu, and Binghai will experience population and gross domestic product overloading in future years. In addition, a diagram of the UWRCC sets of Yancheng was obtained and it provides a reference for local water resources management.


INTRODUCTION
Since the 20th century, the global population has expanded rapidly and now exceeds 7.5 billion (7.5 × 10 9 ). (Chen et al. ). With the development of technology and the economy, the living standard of human beings has been greatly improved. However, with the accompanying unreasonable exploitation and utilization of resources, the ecological environment has been seriously damaged. Major problems, including environmental pollution (Wang et al. ), ecological degradation (Shen et al. ), and resource shortages (Li et al. ) have gradually emerged. As an important part of natural resources, water is also confronted with over-exploitation (Liao et al. ). To ensure water security and to promote sustainable development of the social economy, scholars have conducted a wide range of research covering rational utilization and protection of water resources, and have gradually formed the concept of water resources carrying capacity (WRCC).
Until now, a major achievement of WRCC is the evaluation of water resources carrying status (WRCS) (Chi et al. ). WRCS refers to the overall status of the water resources system, the socioeconomic system and the ecological system in a particular region (Yang et al. ). It is evaluated by a comprehensive assessment system, which includes the degree of water resources development and utilization, the degree of social and economic development, region. These achievements provide scientific guidance for water resources management. However, UWRCC is a specific value under given economic and technical conditions. Indicators used to characterize economic and technical conditions, such as per capita GDP, water supply capacity of water conservancy projects, water use efficiency and sewage treatment level, will change during the development of a region, resulting in continuous dynamic changes of UWRCC. Therefore, instead of employing a single value, the UWRCC result sets under different economic and technical levels can provide better reference for the determination of regional development goals in the future.
Yancheng is located on the east coast of China. It is one of the major cities involved in the 'Great Development Strategy of Jiangsu Coast' and is under a plan to further expand its socioeconomic scale. However, as agriculture is the leading industry in Yancheng, accounting for 80% of the total water consumption in 2015, the water use efficiency of Yancheng is relatively low and the contradiction between water supply and demand is relatively sharp.
To achieve the goal of sustainable development, it is necessary to analyze the rationality of the planned socioeconomic scale and to put forward suggestions on the socioeconomic development of Yancheng from the perspective of water resources utilization.

Framework of the study
This study is divided into four steps, as is shown in Figure 1.
The first step is identifying major influence factors for UWRCC for the study area. The second step is constructing the UWRCC calculation model. The third step is setting computing scenarios and calculating. The last step is analyzing the UWRCC results and drawing a diagram of the UWRCC result sets.

Analysis of influencing factors of UWRCC
The main influencing factors of UWRCC are divided into three categories: natural conditions, technical level, and economic status, as is shown in Figure 2. Natural conditions mainly include precipitation, underlying surface, and the number of rivers, and channel morphology, determining the carrying capacity of the carrying subject. In this study, natural conditions are specifically reflected in the amount of water resources and the self-purification capacity of the rivers. The amount of water resources affects the amount of available water supply in a region which refers to the maximum

Model description
As is shown in Figure 3, the UWRCC model constructed in this study is a multi-objective optimization model. To realize the optimal allocation of water resources in space, an intact   includes three sub-constraints: industrial structure constraint, food supply constraint and economic level constraint. Industrial structure constraint is used to ensure that the calculated industrial structure of each calculation unit is reasonable.
Food supply constraint is used to guarantee that local grain production meets the demand of the residents in each calculation unit. Economic level constraint refers to a requirement that GDP per capita is reaches a certain level to ensure the fine economic condition of residents in each calculation unit.

Mathematical expressions
Water use of domestic sources W domestic k , water use of primary industry W 1 k , water use of secondary industry W 2 k , and water use of tertiary industry W 3 k in the calculation unit k are decision variables of the model.

Objectives
①Maximum sum of GDP scale of each calculation unit. (GDP k ). The objective is expressed by equation (1) and the GDP scale in each unit is calculated by equation (2).
where K is the number of calculation units, W ik is the water use of the industry i in unit k, w use pergdp ik is the per-10,000-yuan-GDP water use of the industry i in unit k.
②Maximum sum of population size of each calculation unit (POP k ). The objective is expressed by equation (3) and population size of each unit is calculated by equation (4).
where W domestic k is the domestic water use in unit k, w use urban k is the urban domestic water use per capita in unit k, r urban k is the urbanization rate of the unit k, and w use rural k is the rural domestic water use per capita in unit k.

Constraints
① Water quantity constraint. This constraint is that the sum of domestic water use, production water use and ecoenvironmental water use (W environ k ) must be less than the available water supply in each calculation unit. The water quantity constraint is expressed by equation (5). The available water supply includes the available local water supply (W avail local k ) and the available transit water supply (W avail transit k ). The sum of the available transit water supply in each calculation unit is less than the total amount of available transit water supply in the region (W avail t), which is expressed by equation (6). Ecoenvironmental water use of each calculation unit is calculated by equation (7), which is the sum of environmental sanitation water use (W san k ) and landscape plant water use where W 1 k is the water use of primary industry in unit k, W 2 k is the water use of secondary industry in unit k, W 3 k is the water use of tertiary industry in unit k, W environ k is the ecoenvironmental water use in unit k, W avail local k is the available local water supply in unit k, W avail transit k is the available transit water supply in unit k, W avail t is the total amount of available transit water supply in the region, W san k is the environmental sanitation water use in unit k, W lan k is the landscape plant water use in in unit k, w use san k is the environmental sanitation water use per capita in unit k, area lan k is the landscape plants area in unit k, and w use lan k is the landscape plants water use per unit area in unit k.
②Water quality constraint. This constraint is that pollutant emissions of COD and NH 3 -N must be less than the water environmental capacity of rivers for each calculation unit.
Because of the same calculation process, the study uses COD as an example to illustrate its specific mathematical expression. The constraint is expressed by equation (8).
The pollutant emissions of COD in unit k (COD k ) is calculated by equation (9). The pollutant sources are divided into point source and non-point source. The pollutant emissions from point source, that is domestic source (COD domestic k ), secondary industry source (COD production 2 k ) and tertiary industry source (COD production 3 k ), are calculated by equations (10), (12), (13), respectively. The pollutant emissions from non-point source, that is agriculture source (COD production 1 k ), are calculated by equation (11).
The water environmental capacity of COD of unit k (COD environ capa k ) is calculated by one-dimensional hydrodynamic model.
where COD k is the pollutant emissions of COD in unit k, COD environ capa k is the water environmental capacity of COD of unit k, and COD domestic k , COD production 1 k , COD production 2 k , COD production 3 k are the pollutant emissions from domestic, agriculture, secondary industry, tertiary industry in unit k, respectively. r pollinriver3 k is the proportion of domestic and tertiary industry water that goes into the rivers after consumption and treatment in unit k, r poll concen cod k is the COD concentration of domestic and tertiary industry tail water in unit k, gdp perarea k is the output value per unit area of agricultural planting in unit k, poll cod is the COD emissions per unit area of agricultural planting in unit k, r pollinriver1 cod k is the proportion of COD produced by agricultural planting that goes into the rivers in unit k, r pollinriver2 k is the proportion of the secondary industry water that goes into the rivers after consumption and treatment in unit k, r poll in concen cod k is the COD concentration of the secondary industry tail water in unit k.
③Socioeconomic constraint. This constraint includes three aspects: industrial structure constraint, food supply constraint and economic level constraint.
The industrial structure constraint is expressed by equation (14). The upper limit (r ind max ik ) and lower limit (r ind max ik ) of the proportion of industry i in GDP in unit k are determined by actual values in previous years, and the proportion of industry i in unit k (r ind cal ik ) is calculated by formula (15).
r ind min ik r ind cal ik r ind max ik (14) The food supply constraint is expressed by equation (16), which refers to grain production (food cal k ) being larger than food demand (food demand k ) in unit k. The grain production is calculated by equation (17) and the food demand is calculated by equation (18). However, because the cultivated land of unit k (cultiarea k ) is limited, the maximum grain production, that is the planting area (plantarea cal k ), is constrained, which is expressed by equation (19). The planting area is calculated by equation (20).
food cal k ! food demand k (16) where food cal k is the grain production in unit k, food demand k is the food demand in unit k, food perarea k is the grain yield per unit area in unit k, food demcapital is the food demand per capita, plantarea cal k is the planting area in unit k, cultiarea k is the cultivated land area of unit k, and index multicrop is the multiple cropping index, which refers to the average planting times on the same cultivated land in one year.
The economic level constraint refers to GDP per capita (GDP percapti cal k ) which is required to reach a certain level (GDP percapti k ) to ensure the fine economic conditions of residents in each calculation unit, which is expressed by equation (21). The GDP per capita is calculated by equation (22).
where GDP percapti cal k is the calculated GDP per capita in unit k, and GDP percapti k is the required value of the GDP per capita in unit k.

Model solution
As is shown in Figure 4, a genetic algorithm (GA) is used to solve the UWRCC model (Chang et al. ). Specifically, the first step is to generate the initial population of the aforementioned decision variables. The initial population size is 40. The second step is to construct the fitness function, which is expressed by formula (23): where F(x) is the fitness function and ρ m is the weight of the objective m. In this study, the objectives in the model are  Figure 5.

Construction of computing scenarios
To make the calculated UWRCC meet the concept of longterm and stable support, the available water supply in an extremely dry year (after frequency analysis of long series data of annual water resources using the P-III distribution curve, the water quantities of an extremely dry year correspond to the 90% frequency on the P-III distribution curve) of Yancheng was selected as the water quantity input of the model. To compare the influence of different economic levels and technical levels on the UWRCC results, different computing scenarios were set in this study. The influencing factors of technical level included three types of water supply capacity of water conservancy projects, water use efficiency and sewage treatment level. In this study, water supply capacity was not considered in scenario analysis because the water supply capacity of water conservancy projects exceeds the amount of water resources in Yancheng. The technical level in this study was considered from two aspects: water use efficiency and sewage treatment level. It was characterized by a series of parameters and they could also be divided into four grades: basic, medium, relatively high, and high. They referred to the level that   Table 2.

RESULTS
The UWRCC results of 16 computing scenarios for Yancheng are shown in  Planning' (Yancheng Government, undated). When r >1, the region is in an overloaded state and when r 1, the region is in a sustainable state. Technical Per-10,000-yuan-GDP water use of the primary industry (m 3 /10 4 yuan) 250 200 135 80 Per-10,000-yuan-GDP water use of the secondary industry (m 3 /10 4 yuan) 20 16 12 8 Per-10,000-yuan-GDP water use of the tertiary industry (m 3 /10 4 yuan) 5 4 2.5 1.5 Urban domestic water use per capita (  Note: POP refers to the maximum population size; its unit is 10 4 persons. GDP refers to the maximum GDP scale, its unit is 10 8 yuan.
The WRCD calculation results are shown in Figure 6. Two characteristics of the diagram need to be noted.
First, with the increase in per capita GDP, the curves in the diagram show a downward trend. This means that with the increase of regional economic demand, the population size that water resources can carry will gradually decrease. This is due to the competition relationship between domestic water use and production water use. If we assume that the population of a region is X, the per capita GDP is Y 1 , the domestic water use per capita is D d , and the per-10,000-yuan-GDP water use is D e , then, the total water use of the social economy Z 1 can be expressed by Formula (25). When calculating the UWRCC in this study, the value of Z 1 is set as the maximum available socioeconomic water supply, which is a constant. When the technical level, namely the water use efficiency indicators D d and D e , are also constants, the increase in the economic level, that is, the per capita GDP Y 1 , will inevitably lead to a decrease in the population size X. The second characteristic to be noted is that the higher the technical level is, the higher the position of the corre- Certainly, the diagram can be further refined from the following two aspects: firstly, for each technical level, more economic level scenarios can be set up to increase the point density to better fit the curve, so as to make the fitting results more credible; secondly, more technical level scenarios can be added to increase the number of curves and expand the applicability of the diagram.

Applicability and limitations
The method proposed in the study seeks the largest socio- and water environment capacity, which need lots of preliminary work. The second is that, before applying the scenario analysis method, it is necessary to identify the major factors of UWRCC to reduce calculation.
The UWRCC research can be improved in the future as follows. Firstly, the calculation step length in the model is one year, which does not take into account the uneven distribution of precipitation (Zhan et al. ) and socioeconomic water demand during the year. Especially for grain planting, there are some differences in the water demand in different periods of the planting cycle (Cao et al. ). In later research, the calculation step length could be set as a month to reflect the above influence. Secondly, the water exchange brought by grain trade between regions is not considered. Yancheng is the main grain base of Jiangsu Province, whose production fully meets the local grain demand, so its impact is not considered. In regions with high socioeconomic development and dominated by industry and services, local grain yield is low.