A New Analytic Model to Identify Lead Pollution Sources in Soil Based on Lead Fingerprint

Gobeil's model is one of the most widely used models to identify lead (Pb) pollution sources in the environment. It is based on a set of equations involving Pb isotope fractions. Although a well-established numerical method, Gobeil's model is often unable to provide an accurate estimation of each pollution sources' contribution. This paper comprehensively examines the drawbacks of Gobeil's model based on a numerical analysis and proposes a revised numerical method that provides a more accurate estimation of Pb pollution sources. Briefly, the mathematical inaccuracy of Gobeil's model mainly lies in the misinterpretation of "lead fingerprint ratio balance." To address this problem, the new analytic model relies on the mass balance of total lead in the contaminated sites, and uses a set of linear equations to obtain the contribution of each pollution source based on the lead fingerprint. A subsequent case study from an industrial park in Guanzhong area of Shaanxi Province in China shows that we can calculate the lead contribution rates accurately with the new model.