Entropy weight method coupled with an improved DRASTIC model to evaluate the special vulnerability of groundwater in Songnen Plain, Northeastern China

The Songnen Plain in northeast China is the only remaining black soil agricultural area in the world and is an important food base for China. The groundwater resources in this area are abundant, but human activities have caused them polluted. This paper established a groundwater vulnerability assessment to characterize the in ﬂ uence of human activities which used an entropy weight method. The index was tested using the nitrate pollution distribution in the groundwater to verify the effectiveness of this method. The results showed that areas with high speci ﬁ c vulnerability were distributed in the northern and eastern parts of the Songnen Plain and were consistent with areas that showed serious nitrate pollution of the groundwater. The correlation coef ﬁ cient between these areas was 0.2536, which greatly improved the vulnerability assessment without superimposing human activities in the model. The results clearly showed that human activities increased groundwater vulnerability on the Songnen Plain. The evaluation method provided a reference for similar evaluations and a basis for the protection and management of groundwater resources in this region. method improved evaluate special vulnerability

Groundwater management encompasses a broad range of activities including prevention of groundwater contamination. Vulnerability and pollution risk assessments to identify risk zones are the very first important steps to generate useful information for devising strategies aimed at groundwater protection to contamination. Delineating vulnerable zones helps water resource managers to divert groundwater development activities to other safer areas and, hence, can minimize cost of water treatment (Shrestha et al. ). This article carried on the groundwater vulnerability research, which is of great importance to the allocation and protection of groundwater resources (Foster et  The Songnen Plain hosts both large-scale commercial grain and oil production. The region of the Second Songhua River has 210 million hectares of arable land, with an annual grain output of 16.7 billion kg, accounting for 61% of Jilin Province. Groundwater is an important source of water for crop growth in this region. However, recent survey data showed that the shallow groundwater of the Songnen Plain had been variably contaminated by nitrate (Zhu et al. ; Bian et al. ). Therefore, there is an urgent need to carry out an evaluation of the groundwater vulnerability to nitrate on the Songnen Plain, in order to guide protection and management of the regional groundwater resources. In the past, vulnerability assessments were mostly focused on the water-resource scale or the basin scale. To evaluate a large-scale area, such as the Songnen Plain, it requires not only the correct evaluation parameters but also an improved model, in which the weight of each evaluation index is determined for this area. In order to evaluate the vulnerability of groundwater scientifically and reasonably, improve the reliability of the evaluation results, and provide guidance for the manage- Samples were collected in strict accordance with the technical specifications for water sample collection. The site location was fixed by a GPS three-parameter calibration, water level measurement error was less than 1 cm, and the well water was sampled using pre-treated sample bottle.
Reagents, such as volatile organics, were neutralized with two drops of concentrated hydrochloric acid. The collected samples were stored at 4 C and transferred to laboratory storage within 5 days.
Two sets of parallel samples were collected for quality control. In order to identify the groundwater quality and analyze the hydrochemical characteristics of the study area, analytical testing of 31 inorganic components (Na þ , K þ , Ca 2þ , TFe, Mn, Al, NH 4 þ , PO 4 3À , H 2 SiO 3 , Cr 6þ , Br, NO 2 À , As, Hg, Se, Cl À , SO 4 2À , F À , NO 3 À , I À , HCO 3 À , AFS-9120, China), plasma mass spectrometry (ICP-MS; Thermo Fisher X Series, America), volumetric (VOL), and gravimetric methods (GR). To ensure the accuracy and reliability of all analytical methods, each sample was analyzed 12 times, yielding a relative standard deviation (RSD%) of 15%. The self-test rate and mutual inspection rate were both 100%, giving a total of 1,409 sets of valid data for modeling.

METHODS
The main evaluation methods used in this paper were a modified DRASTIC model and an entropy weight method.
The DRASTIC model is widely used to evaluate ground- The DRASTIC formula is formulated as follows: where D i represents the score of the DRASTIC index; W j represents the weight of factor j; and R j represents the score of factor j.
x m1 x m2 . . . x mn 2 6 6 6 4 3 7 7 7 5 where x ij presents the performance value of the ith alternative on the jth criterion.
Normalization of this matrix gives Equation (3): where r ij is the data for the jth evaluation object of the indicator and r ij ∈ [0,1].
Among these indicators, when bigger is better, this yields but when smaller is better, this yields . . , m and j ¼ 1, 2, . . . , n):

(5)
Step 2: calculation of entropy where f ij ¼ r ij P m i¼1 r ij and 0 < e j < 1: If f ij is all the same value, then the entropy value of each criterion is the maximum value (e j ¼ 1). If f ij is all 0, then f ij ln f ij is also 0 in value.
Step 3: calculation of the weight of entropy The weight of the entropy of the ith indicator can be formulated as follows: where the weight has a value 0 w i l.

RESULTS AND DISCUSSION
Based on the survey results and the hydrogeological characteristics of the study area, this paper obtained six representative indicators of the DRASTIC model. The data for D were from actual measurements of the groundwater level at the sampling points. R was derived from meteorological data released by the government department. S was derived from actual survey data. T was determined from the official digital elevation model, having 30 m × 30 m accuracy. I and C were derived from geological survey results.
This article did not use the index A because attributes of A were closely related to I and C, furthermore, if the index A is used for evaluation, it will reduce the impact of the other indicators, making it difficult to accurately assess the vulnerability of the regional groundwater. According to the characteristics of each index, each attribute of each index has a score. Generally, the attribute of the index is more likely to cause groundwater pollution, and it will get a higher score. Limited by the availability of survey data, some indicators in this assessment could only use interpolation method with available data to obtain the situation without survey data area, which might bring certain uncertainty to the assessment results. The spatial distribution of each indicator was plotted using the spatial analysis module in Arc GIS 10.3 software (Esri, Redlands, CA, USA). These results are shown in Figure 3.
According to the characteristics of each index and the information it contained, the weights of each index were calculated using the entropy weight method. The weight calculation results are shown in Table 1. According to the scores and weights of each indicator, this new 'DRSTIC' model was used to calculate the inherent vulnerability of the regional groundwater (Figure 4).
To assess whether human activities have an impact on the regional groundwater quality, this paper conducted a hydrogeological analysis of the shallow groundwater aquifer, the distributions of characteristic pollutants related to human activities, and hydrochemical characteristics.
The Songnen Plain evolved from Mesozoic and Cenozoic subsidence basins, in which continental clastic sediments were deposited to a thickness of more than 8,000 m. Thus, the Songnen Plain is a large-scale groundwater aquifer   D, depth of the water table; R, net   recharge; S, soil media; T, topography; I, impact of the vadose zone media; and C, conductivity of the aquifer hydraulic) Runoff, circulation, and the regional aquifer characteristics are all conducive to self-cleaning of the groundwater system, maintaining good water quality under natural conditions. However, according to our test results, the shallow groundwater in the study area is locally contaminated by nitrate. The proportion of groundwater samples whose nitrate concentration was more than 0.5 mg/L (China groundwater quality standard class III) was 77.4%. The average concentration of nitrate was 67.2 mg/L, and the highest concentration is 1,000.0 mg/L. The distribution of nitrate in the shallow groundwater of the study area is shown in classification is based on the concentrations of six major ions (Na þ , Ca 2þ , Mg 2þ , HCO 3 À , SO 4 2À , Cl À , K þ combined with Na þ ) and groundwater salinity.    This paper outlines a new way to evaluate the vulnerability of groundwater and validates this method using a case study. Our validation shows the applicability of the evaluation method to groundwater protection and management. Although groundwater vulnerability assessment is difficult to achieve the refined assessment of each zone, in the area of regional groundwater resource management, groundwater vulnerability assessment undoubtedly provides a reliable reference in the macro aspect, which can relatively accurately measure the degree of regional groundwater vulnerability to pollution.

Indicators
Our assessment of groundwater vulnerability at such a large regional scale was limited by data availability. In the future or similar studies, more data should be obtained to improve the accuracy and reliability of the assessment.