Evaluating drivers and flow patterns of inter-provincial grain virtual water trade in China

China's food security is facing serious threats because the virtual water triggered by grain trade flows from the water-scarce north region to the water-rich south region in recent years. Thus, quantitatively evaluating grain virtual water flow is increasingly important. We established a multi-objective linear optimization model based on analyzing drivers of grain trade by the entropy method, and the two drivers of transport cost and grain consumption structure between provinces were analyzed. The results show that the virtual water flow of inter-provincial grain trade of China was 98.38 Gm³ in 2015, accounting for 15% of the total water consumption of grain production. The impact weights of grain transportation cost and difference of grain consumption structure between provinces on virtual water flow were 0.665 and 0.335, respectively. Although the production and consumption of grain in northern region were almost the same, the virtual water imbedded in grain trade still flowed from the north to the south under the influence of grain imports from abroad and grain consumption structure. Compared to previous methods, the model added the principle of the entropy method into linear programming analysis. This innovative model not only quantitatively evaluated the driving forces of grain trade through the weight coefficient, but also established a universal model of quantifying grain virtual water flow. Moreover, we reduced data assumptions, such as not considering actual grain imports and transport modes of grain, which improves the credibility of quantitative results. The model quantified virtual water from the perspective of driving impacts and precluded the limitations of trade data. The model can be used in other countries and regions, where trade data is difficult to obtain, to calculate trade patterns. The results are useful for decision makers to implement virtual water strategies, mitigate national water scarcity, and facilitate sustainable development of grain production.