Design and Implementation of a Comprehensive Evaluation Model for Shallow Groundwater Based on Matter Element Extension

The economic growth and social progress have stimulated the demand for high-quality water resources. Gu’an, a county in northern China’s Hebei Province, is a severely water-deficient area. The per-capita water resources are far below the internationally recognized standard for water shortage. The groundwater resources, all of which are freshwater, have been overexploited across the county. Due to the unreasonable exploitation and utilization of water resources, water pollution and other problems have become more and more serious. Against this backdrop, it is important to scientifically evaluate water quality, and understand the quality of water bodies in the county. The evaluation results will provide scientific basis for the protection of water environment, rationalize water exploitation and utilization, and promote the sustainable development of water resources [1-3].

Currently, water quality is mainly evaluated based on indices, matrix operation, or sample training. Among them, the matrix operation-based methods include fuzzy mathematics, grey system, and analytic hierarchy process (AHP). In water quality evaluation, the most typical sample training-based method is backpropagation neural network (BPNN). Overall, the fuzzy comprehensive evaluation (FCE) is the most widely used method for water quality evaluation. However, the FCE calculates membership based on the highest and lowest values, without considering the influence of the intermediate value. In some cases, the FCE might easily lose information, causing the evaluation results to deviate from the actual situation [4-8].

There are diverse evaluation indices for water quality. The evaluation result of a single index is not compatible with that of another index. These features conform to the basic principle of the matter element extension model. Therefore, this paper establishes a water quality evaluation model based on matter element extension, and applies the model to analyze the water quality in Gu’an county [9, 10].

3.1 Index selection

The evaluation object is the water quality of three fixed monitoring wells in Gu’an county. To make the evaluation more realistic, a total of seven indices were selected, namely, Ca²⁺, Na⁺, Cl^-, F^-, sulfate, salinity, and total hardness, according to the cumulative out-of-limit frequency of various factors in groundwater samples in Gu’an, the impacts of each pollutant on water quality, and the health damage of these pollutants [17].

3.2 Evaluation criteria

The evaluation criteria were prepared based on levels I-V in the Standard for Groundwater Quality (GB/T14848-2017), in which level V has no upper limit. Since the samples contain no factor that seriously exceeds the limit, level V was removed, and levels I-IV were adopted as the evaluation criteria (Table 1).

Table 1. The evaluation criteria (unit: mg/L)

3.3 Water quality evaluation and result analysis

According to the definitions of classic domain and node domain, classic domains R₀₁, R₀₂, R₀₃, and R₀₄ and node domain R_c can be derived from Table 1. The matter element matrices R₁, R₂, and R₃ of the evaluation samples can be obtained from the observed data.

${{\text{R}}_{01}}=\left( \begin{matrix}   \text{C}{{\text{a}}^{2+}} & \langle 0,50\rangle   \\   \text{C}{{\text{l}}^{-}} & \langle 0,50\rangle   \\   \text{N}{{\text{a}}^{+}} & \langle 0,100\rangle   \\   \text{S}0_{4}^{2-} & \langle 0,50\rangle   \\   {{\text{F}}^{-}} & \langle 0,1\rangle   \\   \text{TDS} & \langle 0,300\rangle   \\   \text{TH} & \langle 0,150\rangle   \\\end{matrix} \right)$, ${{R}_{02}}=\left( \begin{matrix}   \text{C}{{\text{a}}^{2+}} & \langle 50,100\rangle   \\   \text{C}{{\text{l}}^{-}} & \langle 50,150\rangle   \\   \text{N}{{\text{a}}^{+}} & \langle 100,150\rangle   \\   \text{S}0_{4}^{2-} & \langle 50,150\rangle   \\   {{\text{F}}^{-}} & \langle 1,1\rangle   \\   \text{TDS} & \langle 300,500\rangle   \\   \text{TH} & \langle 150,300\rangle   \\\end{matrix} \right)$,

${{R}_{03}}=\left( \begin{matrix}   \text{C}{{\text{a}}^{2+}} & \langle 100,150\rangle   \\   \text{C}{{\text{l}}^{-}} & \langle 150,250\rangle   \\   \text{N}{{\text{a}}^{+}} & \langle 150,200\rangle   \\   \text{S}0_{4}^{2-} & \langle 150,250\rangle   \\   {{\text{F}}^{-}} & \langle 1,1\rangle   \\   \text{TDS} & \langle 500,1000\rangle   \\   \text{TH} & \langle 300,450\rangle   \\\end{matrix} \right)$, ${{R}_{04}}=\left( \begin{matrix}   \text{C}{{\text{a}}^{2+}} & \langle 150,200\rangle   \\   \text{C}{{\text{l}}^{-}} & \langle 250,350\rangle   \\   \text{N}{{\text{a}}^{+}} & \langle 200,100\rangle   \\   \text{S}0_{4}^{2-} & \langle 250,350\rangle   \\   {{\text{F}}^{-}} & \langle 1,2\rangle   \\   \text{TDS} & \langle 1000,2000\rangle   \\   \text{TH} & \langle 450,650\rangle   \\\end{matrix} \right)$,

$Rc=\left( \begin{matrix}   \text{I-IV C}{{\text{a}}^{2+}} & \langle 50,100\rangle   \\   \text{      C}{{\text{l}}^{-}} & \langle 50,150\rangle   \\   \text{      N}{{\text{a}}^{+}} & \langle 100,150\rangle   \\   \text{      S}0_{4}^{2-} & \langle 250,350\rangle   \\   \text{     }{{\text{F}}^{-}} & \langle 1,1\rangle   \\   \text{   TDS} & \langle 300,500\rangle   \\   \text{  TH} & \langle 150,300\rangle   \\\end{matrix} \right)$, ${{R}_{1}}=\left( \begin{matrix}   \text{C}{{\text{a}}^{2+}} & 56.1  \\   \text{C}{{\text{l}}^{-}} & 43.9  \\   \text{N}{{\text{a}}^{+}} & 58  \\   \text{S}0_{4}^{2-} & 37.4  \\   {{\text{F}}^{-}} & 0.45  \\   \text{TDS} & 446  \\   \text{TH} & 271  \\\end{matrix} \right)$.

The above matter element matrices, node domain, and classic domains were substituted into formulas (1)-(3) to find the correlations of each evaluation index with the levels of water quality (Table 2). The weight coefficient of each index was computed by formula (5) (Table 3). Then, the correlations and weight coefficients were substituted into formula (4) to obtain the comprehensive correlation of each sample with each level.

Table 2. The correlations of indices in well 1#

Table 3. The weight coefficient of each index in well 1#

Through the above steps, the comprehensive correlations for all the three wells were calculated by matter element extension method. The results of the three wells were ranked in descending order to find the one with the best water quality (Table 4).

As shown in Table 4, the water qualities of all three wells belong to level I, indicating that the groundwater is of good quality, and fit for domestic, industrial, and agricultural uses. Substituting the above results into formulas (6) and (7), the extension index J of each well can be obtained to reflect the trend of water quality (Table 5).

Table 4. The evaluated level of each well

Table 5. The extension index J of each well

As shown in Table 5, although the water qualities of all three wells belong to level I, the water qualities are poised to degrade to level II. Hence, the groundwater in the study area is deteriorating. More attention should be paid to curve the deterioration.

(1) This paper proposes a comprehensive water quality evaluation model based on matter element extension. With simple concepts, the proposed model can make objective evaluations through simple operations. The model indices, namely, comprehensive correlation and extension index, reflect the absoluteness and relativity of the evaluated level, and help to quantify the trend of water quality in the evaluation samples [20].

(2) The proposed model was applied to evaluate the shallow groundwater samples from three wells in Gu’an county, using seven evaluation indices. The evaluation results were highly similar to those obtained by the comprehensive evaluation method. This means the proposed model is reliable enough for comprehensive evaluation of water quality.

(3) Through the evaluations by our method and normative method, the shallow groundwater in the study area has a good quality, and applies to drinking and irrigation purposes. The low natural background value indicates the limited influence of human activities. Therefore, the groundwater quality in the study area should be further protected in future. The groundwater resources must be developed and utilized rationally. Efforts should be made to minimize or eliminate groundwater pollution.