Variation patterns of grey water footprint and its influencing factors in Shandong’s coastal cities

To investigate the spatiotemporal variation and driving mechanism of the grey water footprint (Q) in coastal areas of Shandong province from 2002 to 2021, this paper selects seven coastal cities as the study area to calculate and analyze its temporal trends and spatial patterns. The random forest model is adopted to identify the key influencing factors through relative importance analysis and partial dependence analysis. Furthermore, the structural equation model is used to quantitatively analyze the direct and indirect pathways among factors. The results indicate that the regional grey water footprint decreased at an average annual rate of 3.4%, following a three-stage pattern: an initial increase, subsequent stabilization, and a final decrease． Q_agr accounts for the largest proportion on average, making it the primary source of the total Q. In terms of spatial distribution, both the total Q and Q_agr present a pattern of higher values in the central region and lower values in the surrounding areas. Meanwhile, the distribution of Q_dom and Q_ind is highly correlated with population size and industrial structure, respectively. Fertilizer application rate per unit cultivated land (U_n−irr), aquaculture yield per unit area (Y_agr), pollutant emission per standard livestock equivalent (U_pol−liv), and industrial wastewater discharge intensity (U_ind) are the core factors for the regional Q. The partial dependence relationship reveals the marginal effect of each factor on the Q. The structural equation model further confirms that agricultural non-point source pollution is the main driving factor for the increase in Q．Agricultural pollution control and industrial pollution treatment are the primary approaches for the reduction in Q．