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Groundwater vulnerability assessment is an important method for groundwater pollution risk assessment. However, vulnerability assessment results rarely consider groundwater pollution concentration. Few quantitative studies consider groundwater pollutant concentration in different hydrogeological conditions. HYDRUS-1D software can simulate different concentrations of pollutants reaching the shallow aquifer under some vadose zone conditions. However, HYDRUS-1D simulation parameter settings are complicated; thus, it is difficult to simulate groundwater pollution intensity (GPI) on the site with limited information. In this study, the issue of site data constraints for model predictions is solved. Ammonia–nitrogen is selected as an indicator, and a method for quantitative groundwater pollution assessment based on grey relational analysis (GRA) is proposed. According to two factors (inherent, extrinsic) of groundwater vulnerability assessment, and on the basis of the information from 18 contaminated sites, primary GPI control factors, including emission concentration, hydraulic conductivity, soil density and diffusion coefficient, are filtered using GRA. These four factors are utilized as variables to establish a multiple linear regression (MLR) equation, which is used to predict the GPI of polluted sites. Compared with a HYDRUS-1D simulation, the proposed GPI prediction method can effectively predict GPI with simpler input conditions. The established MLR equation satisfies a significance test and small error analysis. Comparative results between simulation values and regression values on the established case show that the regression values are closer to the measured value. Hence, the MLR equation is practical and can be applied for sensible groundwater source management and land use planning.