Improved grey water footprint model based on uncertainty analysis

In the practical water resources management, the allowable thresholds of pollutants are not unique. However, the conventional grey water footprint (GWF) model cannot deal with this uncertainty in the controlling threshold. To solve this problem, an improved GWF model and pollution risk evaluation method is designed according to the uncertainty analysis theory and maximum entropy principle. In this model, GWF is defined as the mathematical expectation of virtual water to dilute the pollution load within the allowable threshold, and the pollution risk is deduced by the stochastic probability by which GWF exceeds the local water resources. And then, the improved GWF model is applied in the pollution evaluation of Jiangxi Province, China. The results show that: (1) From 2013 to 2017, the annual GWF values of Jiangxi Province were 136.36 billion m3, 143.78 billion m3, 143.77 billion m3, 169.37 billion m3 and 103.36 billion m3, respectively. And their pollution risk values and grades were 0.30 (moderate), 0.27 (moderate), 0.19 (low), 0.22 (moderate), and 0.16 (low), respectively. In 2015, the determinant of the GWF was TP, and TN in other years. (2) The improved GWF model has an evaluation result which is basically consistent with WQQR, and it is an effective water resource evaluation method to deal with the uncertainty in controlling thresholds. (3) Compared with the conventional GWF model, the improved GWF model has better capacities in identifying pollution grades and recognizing pollution risks.