Conception and evaluation methodology of water resources carrying capacity based on three-level analysis

In supply-oriented water development, water is a rigid constraint on sustainable development in many parts of the world, especially in arid and semi-arid areas. The water resources carrying capacity (WRCC) concept represents the maximum socio-economic scale that can be supported by water exploitation without causing an irreversible impact on the ecosystem. In this paper, three-level framework is put forward to illustrate and quantitatively evaluate the WRCC. The first level is the principal body, which focuses on the study of water resources systems. The second level is the carried object, including the socio-economic system, water ecological system, and environment system. The third level is the coupling of the principal body and carried object to calculate the WRCC. This three-level WRCC model was applied to the load conditions of the Shiyang River Basin (SRB). The results show that the SRB is overloaded, and only 1.99 million people can be carried at the modern carrying level. The WRCC could be increased by optimizing industrial structures and improving water efficiency. This method provides a tool to help policymakers develop sustainable approaches to environmental management and planning.


INTRODUCTION
Water is a basic natural resource that cannot be separated from human survival and development. Societal development, progress in science and technology, and the continuous improvement in living standards has increased people's demand for water resources both qualitatively and quantitatively. Owing to the overuse and misuse of natural resources, resource scarcity has become increasingly severe and threatens China's sustainable socio-economic development (Varis & Vakkilainen ). Especially in inland arid areas, runoff water resources should support not only the socio-economic development of oases but also the fragile ecological environment. Previous studies have focused on how to use water resources more efficiently based on the concept of sustainability, and the water resources carrying capacity (WRCC) concept has been used to appraise the reasonable and possible scales of socio-economic activities in specific given level of consumption without degrading the environment and therefore reducing the future carrying capacity (Abernethy ). The WRCC was proposed as a concept for water resources planning, development, and management. Most research on the WRCC has focused on providing analytical tools to consider the tradeoffs among water resources development, socio-economic sustainable development, and environmental and ecological protection to present suggestions for future regional planning (Jia et al. ).
Hadwen & Palmer () considered the carrying capacity when studying how to control the population of reindeer introduced into Alaska. Pulliam & Haddad () introduced the concept of the carrying capacity for human populations when studying sustainability and showed the relationship between population growth and ecology.
Water resources are an important component of ecosystems, but there have been few studies on the carrying capacity of individual water systems. With increasing problems regarding water resources, the WRCC has become the subject of interest as a basic attribute of natural resources (Carter & Howe ).
Recently, more researchers have recognized the importance of the WRCC as a concept and have applied it to analyzing rational patterns of development. More research attention has been given to developing quantitative evaluation methods, such as the comprehensive evaluation model (Wang ), the set pair analysis method (Zhang & Li ), the system dynamics evaluation method (Feng et al. ), and variable fuzzy evaluation (Gong & Jin ). These methods were proposed from different aspects of the WRCC, according to the characteristics of the WRCC. But these methods cannot effectively study the feedback relationship between social and economic development and the WRCC.
Sustainable human-water coexistence requires the reasonable and consistent development of human society, healthy water ecosystems, and a coordinated interaction between humans and water (Ding et al. ). The WRCC is a comprehensive concept that is related to various variables. It is not easy or even possible to consider all influencing factors. Therefore, more sophisticated techniques and new analytical methods are needed to improve the computational process, especially regarding the description and analysis of rational water allocation to different users. This paper defines the WRCC by summarizing previous studies and discusses relevant influence factors before presenting a concrete computational method for its assessment based on the human-water harmony theory.

Principal body
The principal body focuses on the study of water resources systems and evaluates the valid water resources. Valid water resources refer to water with sufficient quantity and quality to meet demand. Low-quality water is not a valid water resource and is therefore not part of the calculation of the WRCC. As a society must be able to control and exploit valid water resources, floods are not valid water resources. For sustainable development, a suitable water ecological environment and a suitable habitat environment are imperative. Therefore, a certain amount of water is reserved for ecological environmental needs. So the ecological environment water requirements are also not valid water resources.

Carried objects
Carried objects include both natural and artificial systems directly or indirectly related to water, such as humans and other creatures living in the basin, natural or cultivated plants, and industries. For water planning and management, human systems are generally considered to be a carried object because they are controllable factors. The most basic indices for assessing the scale of an artificial system are the population and economic level (Yuan et al. ).
Therefore, an index that represents these two aspects can be used to assess the carrying capacity.
The concept of carried objects is related to the level of social development. The level of social development determines the productive and technological levels, of which the technological level is an important factor that influences the water consumption per unit production value. From a macroscopic view, the total water demand depends on the total economy and water consumption per unit productive value. The carried body of an artificial system is always located at some objective level that can be used to ascertain the scale of the carried body under the limitations of a definite principal body (e.g., valid water resources).

Carrying level
Both the valid water resources and social productive level are determinants for the WRCC, but both of these factors will change with socio-economic development. Therefore, to calculate the WRCC in a region, the carrying level must be determined first, to determine the valid water resources and water use efficiency. When the carrying level is determined, the water resource utilization capacity, the socio-economic level and the intensity and efficiency of water consumption can be determined. The socio-economic level is quantified by the gross domestic product (GDP) per capita, which is the key factor for calculating the amount of bearable population under a specific GDP. The level of social development basically determines different values for the water consumption per capita, where the WRCC can be computed under specific conditions for the water resources. Therefore, the carrying level is a precondition of the carrying capacity.
Fundamentally, the carrying level includes living standards, the level of economic development, and the objectives of ecological and environmental protection.
When a certain carrying level is determined, the water norm, water efficiency, and ecological environmental water requirements will be determined accordingly. Although there is a competitive relationship between socio-economic and human water use, this does not affect human living conditions. Among the various influences on the carrying level, the population and economic development are the most decisive factors. These two factors represent the level of water demand from different sectors. Generally, higher living standards mean higher consumption of materials and energy, which results in a greater demand for water. However, it also represents a more developed society with higher efficiency and better management, which lowers the water consumption of per unit product. The same living standard or GDP per capita can represent different industrial structures. A higher carrying level increases the water demand despite the higher water utilization efficiency, although specific conditions differ and depend on the pattern and structure of the society and economy.
Steps of the model Based on the above definitions of the WRCC and its related parameters, the following three-level approach is proposed for quantitatively analyzing the water carrying capacity of a specific area. The first level is the principal body (i.e., valid water resources and their variability). This represents the natural attributes of water and the capacity to support socio-economic development. The second level is the object (i.e., the scale of the society and economy). This is expressed by the population and GDP. The third level is the bridge between the principal body and object (i.e., the rational water allocation from valid water resources to water users at a specific water utilization efficiency). The framework of the approach is illustrated in Figure 1.

Determining the carrying level
The carrying level is the most important factor for ascertaining the WRCC. The general criterion for classifying social development is identifying the GDP per capita. Development trends can be determined from economic predictions and population projections. The predicted economic development is the bedrock for setting the threshold value in future planning. The approximate trends of industrial changes are also available for macroscopic economic planning. The predicted economic growth curve can be used to determine the industrial structure and comprehensive water utilization efficiency at critical points (i.e., the carrying level). Based on the above analysis for the carrying level, the comprehensive water consumption per unit production can eventually be determined.
The carrying level can be classified into four levels based on the widely accepted Engel rule and living standard criteria put forward by the World Bank, as presented in Table 1. The critical value of the GDP per capita is an analytic result integrated with the realistic economic situation for China. Therefore, four critical values are chosen to estimate the WRCC. The economic status can be used to analyze the total production value and water utilization efficiency for calculating the WRCC.
The first-level calculation The total valid water resources represents the amount of water technically and economically usable considering ecological and environmental demands, including both surface water and groundwater. The valid water resources of a specific area can be calculated from the total water resources by subtracting the necessary ecological water demand and unmanageable floods: where W v is the valid water resources, W g is exploitable groundwater. W s is the surface water resources, W e is the ecological water demand; considering different ecological conditions, it can be taken from the minimum to the maximum ecological environment water consumption to adjust the competition between the ecological environment and other water users. W f is uncontrollable floods. All variables are average annual values.
For the calculation of valid water resources, the major part is supplied to production sectors, which include irrigation, industries, and services. The domestic water demand should also be considered, although its amount is relatively small. The domestic water demand is obtained according to the projected population and water norm indicators at different carrying levels: where W do is the domestic water demand; P fo is the initial estimated population, which during the calculation process, will be optimized to the carrying population P; and E do is normal domestic use. Domestic water users  In general, the agriculture water consumption per unit GDP is much higher than that of other industries. If agriculture is also taken into comprehensive water consumption per unit GDP, the effect of other industries can be obscured.
To reduce this adverse effect, the agricultural water demand at different carrying levels is calculated separately by the irrigated area and irrigation norm: where the W ar is the agricultural water demand, A is the irrigation area, and E ar is the amount of irrigation water per hectare per year. Thus, the valid water resources for production enterprises (i.e., the available economic scale calculated for a certain carrying level) is the surplus when the estimated domestic water demand and agricultural water demand are subtracted from the total valid water resources: where the W ec is the valid water resource for secondary and tertiary industries.

The second-level calculation
With the valid water resources and carrying level, it is feasible to compare and calculate the indices of the WRCC; that is, the bearable population and economic scale. The comprehensive water consumption per unit GDP can be obtained according to the industrial development scale, industrial structure, and water norm indicators at different carrying levels. The agricultural water demand is deducted in advance when calculating the amount of water available, so the comprehensive water consumption per unit GDP only needs to consider secondary and tertiary industries: where C u is the comprehensive water consumption per unit GDP (except agriculture) at a given carrying level, GDP i is the industrial added value of different sectors, mainly including secondary and tertiary industries. k i is the industrial added value as a percentage of GDP (except agriculture), and E i is the norm of water consumption for given industry.
i represents different sectors.
The added value of different industries is predicted according to their respective development trends. Therefore, it is not completely independent and is limited by the historical proportional structure. Some unreasonable phenomena are expected in the process of extension, and the industrial structure can be adjusted: where GDP i,fo is the initial forecast added value of different industries. GDP agr,fo is the initial forecast added value of agriculture. β i and β ag are the adjustment factor, which can control the changing industry added value. When the carrying level is determined, the initial projections of population and GDP per capita are fixed, so the initial forecasted total GDP is also a fixed value. When adjusting the industrial structure, it should satisfy the following constraint: k i can be obtained using Equation (8): where k i is not the industrial added value as a proportion of the total GDP, but a proportion of the sum of the secondary and tertiary added values.

The third-level calculation
The total bearable GDP at a certain level can be calculated by comparing the comprehensive water consumption per unit production and total available valid water resources: where E t is the bearable economic scale at a certain carrying level, W ec is the valid water resources for secondary industry and tertiary industry and K s&t is the secondary and tertiary industrial added values as the percentage of GDP.
With the estimated total economic scale, the bearable population can be determined from the average GDP per capita at that carrying level: where P is the bearable population scale at a certain carrying level and V p is the average GDP per capita (with agriculture not included) at a given carrying level. Given the total economic scale and average GDP per capita, the other index for the WRCC (i.e., the bearable population) can be determined. When the carrying population is determined, the carrying capacity condition can be determined according to the water carrying index: where δ is the water carrying index. When δ is greater than 1, the predicted population is within the carrying range; when it is less than 1, the predicted population exceeds the carrying capacity. P fo is the initial forecast population and P is the bearable population.
Finally, the estimated water demands should be checked against the domestic water needs from the calculated bearable population. If there is a large difference, the estimated population should be estimated again, and the whole process should be performed again. For example, if the water demand from the calculated bearable population is much higher than the estimated water demand for domestic users, this means that the estimated water resources for domestic users are too low. Hence, the estimated water demand subtracted from the total valid water resources should be increased or vice versa. When the forecasted population is changed, the forecasted GDP should change, and the water demand for agriculture should also be revised proportionally: where W ar is the revised agricultural water consumption.
P ca , P fo are the revised and initial population respectively.
W fo is the initial forecast of agricultural water demand.
After the necessary calibration and iterative checking of the pre-allocation to the domestic water demand, a rational WRCC representing the total economic scale and population can be obtained.

Study area
The Shiyang River Basin (SRB) is an essential part of the Silk Road. The river flows through the eastern Hexi Corridor in northwest China, and the basin is a typical arid inland region.
As shown in Figure   CNY. The SRB is predicted to reach the modernized carrying level in 2096 when the per capita GDP will be 74,520 CNY.
According to the GDP growth curve in Figure 4, the national economy will grow very slowly from 1996 to 2096 with an average GDP per capita growth rate of only 3.2%.

Calculating valid water resources
The surface water resources in the SRB are mainly generated in the Qilian Mountains. The runoff generation area    Table 3.

Determining social and economic indicators
Equation (5)   it is reduced to 10.5 m 3 /10,000 CNY. As the carrying level increases, the water norm of various industries decreases,  and the water efficiency increases; therefore, the comprehensive water consumption per unit GDP decreases.

Analysis of preliminary carrying conditions
The first step to calculating the carrying capacity was to determine whether the water demand at the predicted carrying level could be guaranteed to be met. The population could be predicted based on population development rate.
Then, the amount of domestic water demand at different carrying levels was determined from the projected population and norm for the per capita domestic water use. As indicated in Table 5, the predicted socio-economic development caused the total water demand to exceed the valid water resources. This implies that the SRB will be over-  When the carrying level was increased, the per capita GDP and water use efficiency increased, which had an opposite effect on the carrying capacity. From the basic subsistence to the well-off carrying levels, the per capita GDP growth was more significant than water efficiency improvement, so the bearable population decreased. However, from the well-off to the modernized carrying level, the water efficiency improvement was more significant than the per capita GDP growth, so the bearable population increased.   industries. A suitable proportion of domestic water consumption to the total water consumption was calculated to be 0.03-0.34 from the basic subsistence to the modernized carrying levels. Although the bearable population on the basic subsistence carrying level is more than when for the well off owing to its poorer living conditions, the domestic water consumption is relatively small. The consumption of water for agriculture will continue to decline but will fall less and less as the carrying level increases. However, it is still the lar- Therefore, when calculating the carrying capacity of water resources, it is necessary to guarantee a suitable environment with a pre-set ecological water demand. In order to analyze the relationship between the ecological environment water consumption and the WRCC, the change in the carrying capacity can be analyzed by adjusting the size of the reserved ecological water volume. In this study, the predicted water demand for the ecological environment is taken as the maximum water reserve, and the proportion of water demand for the ecological environment is considered to change the water reserve for the ecological environment. Table 7 shows that with a reduction in the proportion of eco-environment water consumption, the bearable population and bearable GDP will increase accordingly in the study area, but they are disproportionate. At the modern carrying level, when eco-environment water is reduced by 50%, the population carrying level can increase by only 20%.
Although the ecological environment has been severely damaged, the resulting population benefits are not obvious.
Compression of the eco-environment water is not a sustainable development method and is not recommended.

Relationship between industrial structure and WRCC
According to Equation (5), the comprehensive water consumption per unit GDP is greatly influenced by the industrial structure. Therefore, at the same carrying level, adjusting the industrial structure will have a major impact on the WRCC. The industrial structure at the carrying level year is predicted based on historical data. The GDP increment of different industries is not completely independent, and they are constrained by the current economic structure. By adjusting the predicted industrial structure, we analyze the corresponding load-carrying capacity changes and determine the impact of the industrial structure on the carrying capacity. Zhang et al. () pointed out that agriculture is a significant factor to solve the gap between supply and demand in northwest China. Therefore, this study mainly focuses on the active adjustment of agricultural factors, while other industries are passively adjusted according to the predicted structure. When the proportion of agriculture in the industrial structure is reduced, qualitative analysis will lead to a reduction in agricultural water consumption, and hence, the amount of water available for other industries will increase. According to Equation (7), the relationship between the industrial structure and the carrying capacity is quantitatively analyzed using β i . The horizontal coordinate of Figure 5 is the agriculture industrial structural adjustment coefficient; when this value gradually increases, it implies that agriculture accounts for an increase in the proportion of the industrial structure. When the value of the adjustment coefficient is negative, it means the adjusted agricultural proportion of total GDP is lower than the predicted structure, but on the contrary, the adjusted agricultural proportion of total GDP is higher than the predicted structure. The main longitudinal coordinate is the load-carrying population, and the secondary vertical coordinate is the load-bearing GDP. Figure 5 shows that the larger the proportion of agriculture in the industry structure, the smaller the population and GDP that can be carried on the same carrying level year.
Therefore, industrial structural optimization can be considered if the WRCC of a region needs to be increased.
When β agriculture changes from 0.2 to À0.2, the variation in the carrying capacity in higher carrying level years is smaller than that in lower carrying level years. Optimizing the industrial structure can increase the regional WRCC in the low carrying level years. In the high carrying level years, the industrial structure is already sufficiently optimized. It is more difficult to adjust the industrial structure, and it has less potential to increase the WRCC. The projected population at the modernized carrying level is 3.25 million; and agricultural water will need to be compressed by 80% to carry this population. This proportion will lead to the total destruction of agricultural production and will not guarantee effective food production. Therefore, the population size must be controlled, or water diversion projects need to be considered to increase the amount of water available.

DISCUSSION
Many studies have considered how to calculate the WRCC.  ing to the predicted development trend, the total water demand will exceed the amount of water resources available, and the SRB is already overloaded. Optimizing the industrial structure and improving water efficiency would increase the carrying capacity. However, even with improved efficiency, the population is still above the WRCC.
Through qualitative and quantitative analysis of the regional WRCC under the influence of various factors, the following measures can be considered to improve the regional WRCC: (1) Restructuring of socio-economic development: The structure of socio-economic development needs to be matched with the local water resources conditions.
The WRCC is related not only to the GDP but also to the economic structure. For regions with poor water resources, appropriate policies are needed to guide the development of low-water-consuming industries. The water resources in the SRB do not match the current socio-economic structure, which will leads to serious ecological environment problems. Therefore, it is necessary to gradually reduce the proportion of agricultural development and develop other industries with higher added value.
(2) Improving the water efficiency: Improving the water efficiency can increase the bearable population and GDP. (3) Improving water resource utilization: To maximize water resource utilization, the complementary use of surface water, groundwater resources and unconventional water sources is essential. The utilization of water resources requires full consideration of the water needs of the ecological environment, to ensure the sustainable development of water resources. In addition, a greater degree of inter-basin water transfer is required to achieve sustainable water resource utilization, especially in dry areas.
(4) Ensuring good water quality: Water quality is also a determinant of carrying capacity, and only qualified water can be regarded as the valid water resources. Therefore, while developing the social economy, sewage treatment capacity building should be strengthened.
The results of the model for the SRB are satisfactory and should help policymakers to develop sustainable approaches to environmental management and planning.
The three-level WRCC analysis method can not only be used for the overall basin, but also could also be used to evaluate the differences in water carrying conditions between different regions within a basin or city. In future work, it will be necessary to normalize and simplify the method, and create a visual model with information technology tools to makes the calculation of the WRCC more convenient and universal.