An analytical method of regional water resources carrying capacity in karst area – a case study in Guizhou province, China

Available freshwater resource is limited in a particular time and space. However, the uneven temporal and spatial distributions and the unreasonable development and utilization of water resources have led to the increasingly severe water resources shortage and pollution around the world. The key of the sustainable development of human society is to restrict human activities within the carrying capacities of resource, environment and ecology. Therefore, the concept of carrying capacity has been gradually accepted by people and applied in related fields, and the studies on regional water carrying capacity have also emerged in response to such circumstance (Joeres et al. 1981; National Research Council 2002).

Regional water carrying capacity is a combination of the concept of carrying capacity and the water resources field. The regional water carrying capacity is defined by taking the definition of resource carrying capacity defined by AO and UNESCO for reference Falkenmark & Lundqvist (1998). However, a unified understanding on the definition of regional water carrying capacity has not yet been reached currently. The authors consent to the definition of regional water carrying capacity proposed by Xu Youpeng. Xu believed that regional water carrying capacity refers to the maximum ability of supplying water to industrial and agricultural production, people's living and ecological environment protection at given economic and technological level and social production conditions (Xu 1998). Existing theoretical studies on the regional water resources carrying capacity mainly target to special water resources problems. For example, Joardor et al. carried out relevant investigations on the carrying capacity of urban water resources in terms of water supply and incorporated regional water carrying capacity into the urban development planning (Hrlich 1996). Rijiberman. J et al. applied the carrying capacity as the evaluation standard for guaranteeing the security of urban water resources in their investigation of the evaluation and management system of urban water resources (Rijsberman & van de Ven 2000). Harris studied the regional water carrying capacity in the field of agricultural production particularly, and applied it as the benchmark for evaluating the potentiality of regional development (Harris 1999). However, existing studies on water resources carrying capacity are absent of comprehensive evaluation in larger regions, and the selected driving factors of carrying capacity are incomprehensive and non-representative. In view of above conditions, the typical karst area in China – Guizhou province was applied as the research area. Meanwhile, twelve indexes were selected in terms of water supply, water demand and social economy to establish the evaluation index system of water resources carrying capacity in a larger region. Additionally, based on the standardized index data, analysis hierarchy process (AHP) was utilized to construct the evaluation model of regional water carrying capacity. Later, the model was employed to evaluate the regional water carrying capacity of each city in Guizhou province. The proposed method can provide reference and basis for the investigation on regional water carrying capacity to some extent.

In order to have the established index system accurately reflect the system states of water resources in large regions and the regional characteristics, and endow the system with strong practical operability, the following principles were followed for selecting indexes. These principles included comprehensive principle, operability, comparability and representativeness.

This research selected the evaluation indexes of regional water carrying capacity in karst area from three aspects including water supply, water demand and social economy. The indexes selected in terms of water supply system included: (1) modulus of water supply (10,000 m³/km²): it is P = 75% of the ratio of the current water supply quantity to land area (Zhang et al. 2004); (2) development level of water resources (%): P = 75% of the ratio of annual water supply quantity to total water resources; (3) per capita water resources (m³/per person): the per capita fresh water resources available in evaluation area; (4) water qualification rate (%): the percentage of the index that reaches the standard of water quality in the total water quality indexes. Indexes selected from the aspect of water demand system included (1) modulus of water demand (10,000 m³/km²): it is P = 75% of the ratio of the current water demand to land area; (2) agricultural water consumption (100 million m³): the water used for irrigation and consumed by livestock in the evaluation area (Duan et al. 2005); (3) industrial water consumption (100 million m³): water used by industrial production directly and indirectly in the evaluation area (Wang & Xia 2010); (4) domestic water consumption (100 million m³): the urban and rural domestic water consumption in the evaluation area; (5) per capita water consumption (m³/per person): the average water consumption of per person everyday in the research area; (6) the water consumption of GDP (m³/10,000 yuan): the proportion of the regional water consumption to GDP, which reflects the water efficiency of regional economy. Indexes chosen regarding social economy system included: (1) per capita GDP (yuan): the ratio of GDP to total population in the society, which is used to measure the economic development level and people's living standard; (2) natural growth rate of population (‰): the ratio of the naturally increased number in a given period (usually one year) to the average number of people in this period. According to the Guizhou Provincial Water Resources Announcement and the statistical yearbook of each autonomous prefecture and city in Guizhou province in 2013, the above indexes were selected in the research. Afterwards, the original data of detailed indexes of regional water carrying capacity in Guizhou province were sorted out, and the calculation results are shown in Table 1.

The initial data were required to be standardized to eliminate the difference and influence of different index dimensions and magnitudes. This research utilized the relative membership grade to standardize the indexes. Assume that there are m objects remained to be evaluated, and n evaluation indexes, which form the data matrix of initial indexes X = (x_ij)_m×n, then, according to the standardization formulas of each kind of indexes.

The standardized matrix R = (r_ij)_m×n can be obtained based on the formulas above.

Where, x_ij and r_ij are respectively the initial value and the standardized value of the jth index, and x_max and x_min represent the maximum and minimum values of the jth index.

Standardized processing was conducted on the initial data using formulas (1) and (2), and the obtained data are illustrated in Table 2.

Weight values were determined using the AHP, which was put forward by American operation researcher and professor Saaty in the 1980s for confirming weight value (Saaty 1977). AHP combines the qualitative and quantitative decisions to hierarchize and quantify the decision process according to the mental law. The specific solution process is shown as follows (Saaty 1980; Liu et al. 2007):

The research objects were divided into three hierarchies based on the analysis on main driving factors of regional water carrying capacity in Guizhou province. Since the evaluation of regional water carrying capacity was the ultimate goal of this research, it was applied as the target hierarchy of the model (A hierarchy). Water supply, water demand and social economy systems, as the intermediate links for solving problem, belonged to the criterion hierarchy of the model (B hierarchy). The decision hierarchy (C hierarchy) of the model was constituted by specific indexes. The required target can be obtained through the decision of C hierarchy.

According to the analysis on the main influencing factors of regional water carrying capacity in Guizhou province, the method of collecting the scores given by experts was adopted. The opinions of experts in the field, universities and scientific research units were consulted. By doing so, the main controlling factors of carrying capacity were rated according to the firsthand experience of the experts in their production practices in the field and scientific researches. The scale method of 1–9 established by T. L. Saaty was applied as the rating criterion. As to the specific procedure, the influencing factors of carrying capacity were firstly listed in a table. Then, the experts were invited to analyze and evaluate the relative importance of the main controlling factors. In this way, the quantification value of each influencing factor was obtained. Finally, according to the accumulative score of each factor, the total scores of the factors were compared, and thus the judgment set of all influential factors given by the experts was generated. Thereby, the judgment matrix of AHP evaluating the regional water carrying capacity was established (Tables 4–7). In the tables, λ_max, CI and CR are respectively the maximum eigenvalue, consistency index and mean random consistency index of the judgment matrix.

The weights of each hierarchy after single level sequencing were calculated using the judgment matrix (the columns of W in Tables 3–7).

As discovered in tables above, the λ_max, CI and CR were calculated in each matrix, and all the values of CR were less than 0.1. Therefore, the judgment matrix presented satisfied consistency, and thus can pass the consistency check.

The weight of each index C_i on the synthetical goal refers to the weight of an index C_i in the index hierarchy to the target hierarchy A through B_i hierarchy. The values in the column W^A/Ci represent the weights of each index C_i on the synthetical goal A, as illustrated in Table 7.

As a matter of fact, the established evaluation model of regional water carrying capacity in Guizhou province was a mathematical model indicating the influences of various factors. The values calculated through this model can reflect the carrying capacities of water resources in different regions. Meanwhile, this model had to be established based on the contribution mechanisms of water supply, water demand systems and social economy to the carrying capacity.

As seen in Table 8, the regional water carrying capacities in Guizhou province are arranged in a decreasing order as Qiannan, Qiandongnan, Tongren, Qianxinan, Guiyang, Bijie, Liupanshui, Zunyi, and Anshun. The reasons for this order a Qiannan, Qiandongnan and Tongren have a low development level of water resources, high per capita water resources, and a small amount of industrial water consumption. All these give rise to the great carrying capacity of water resources in these areas. Despite with medium per capita water resources, small available water supply in unit area and low per capita GDP, Qianxinan exhibits a modest water carrying capacity due to the low water demand and development degree of water resources. Though Guiyang is characterized by low per capita water resources, high development level and demand of water resources, the available water supply per unit and the per capita GDP are high with little agricultural water consumption. Therefore, the water carrying capacity in Guiyang is moderate. The relative weak water carrying capacity in Bijie and Liupanshui is attributed to their high industrial water consumption and low per capita water resources. The weak carrying capacity of water resources in Zunyi is because of the high agricultural and domestic water consumption, and small amount of per capita water resources. Owing to the high development level of water resources, little per capita water resources, poor water quality, and great GDP water consumption per unit, Anshun shows a weak water carrying capacity.

The typical karst area in China – Guizhou province was applied as the research area based on the existing studies on water resources carrying capacity. Meanwhile, after giving full considerations to water supply, water demand and social economy systems, twelve influencing indexes were selected to establish the evaluation index system of regional water carrying capacity in the karst area. Afterwards, AHP was utilized to construct the evaluation model of regional water carrying capacity, so as to evaluate the water resources carrying capacity of each city in Guizhou province. This research can provide reference for the selection of evaluation indexes in studying regional water carrying capacity, the establishment of evaluation model, and the evaluation and comparison of the water carrying capacity in larger regions.

This research was financially supported by China National Natural Science Foundation (Grant no. 41430318, 41272276, 41572222), the China National Scientific and Technical Support Program (Grant Numbers 2016YFC0801800, 2012BAB12B03), Guizhou Province Science and Technology Agency Foundation (qian ke he LH zi[2014]7617), Guizhou University Introducing Talents Research Foundation (2014-61), Guizhou Province Geological Exploration Fund (Guizhou karst groundwater system functions sustainable utilization), the Joint Open Foundation of Key Laboratory of Institute of Hydrogeology and Environmental Geology, Chinese Academy of Geological Sciences (KF201612).