| Summary: | The conventional grey water footprint (GWF) cannot deal with the uncertainties induced by the background information. To solve this problem, this study develops a stochastic GWF model based on probability theory and the maximum entropy principle. The stochastic GWF model further introduces the expectation calculation and water pollution risk (WPR) identification into assessment, which are used to comprehensively evaluate the GWF and quantify the potential water shortage risk induced by pollution, respectively. To verify its effectiveness, the stochastic GWF is applied to the evaluation of chemical oxygen demand (COD) in Ningxia province, China. Results show the following: (i) compared with the conventional GWF, the stochastic GWF significant is in advantage in terms of grade identification, pollution ranking, and risk recognizing. (ii) From 2011 to 2017, the GWF expectations of COD in Ningxia provinces are 7.52, 7.32, 7.15, 6.92, 3.95, and 3.36 billion m3, and the WPRs are 0.51, 0.10, 0.13, 0.06, 0.00, and 0.00, respectively. (iii) The WPRs are determined not only by the pollution load but also by climate change and the hydrological rhythm. (iv) Only using the mathematical expectation of the background parameter for evaluation may ignore the environmental risk in the water area with high background values, making the evaluation over-optimistic. © 2021
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