Water–carbon–economy multivariate spatial–temporal collaborative relationships and nonlinear projections in urban agglomerations

Abstract

A complex dynamic coupling process exists among water resource consumption, carbon emissions, and economic growth; however, their intricate collaborative mechanisms remain unclear. This study proposes a new barycenter formula-based multivariate spatial–temporal collaborative relationship model for identifying the complex relationships and interactions among the water footprint (WF), carbon footprint (CF), and gross domestic product (GDP) in the three largest urban agglomerations in the Yangtze River Economic Belt (YREB) of China. A nonlinear grey Bernoulli model is then advanced for illustrating the future evolution in WF–CF–GDP and their multivariate collaborative relationship. Results reveal that WF and CF of all urban agglomerations increase continuously, with annual growth rates of 0.59% and 5.63%, respectively. WF, CF, and GDP are significantly positively correlated, and they exhibit similar spatial clustering characteristics and centroid migration directions along the main course of the Yangtze River. Moreover, their multivariate temporal collaborative relationship (0.79) significantly surpasses their spatial (0.63), while the spatial–temporal (0.77) is intermediate. WF has the greatest impact on the binary spatial–temporal collaborative relationship between CF and GDP. In contrast, GDP has the least impact on the relationship between CF and WF. The projected WF, CF, and GDP indicate that the YREB will face more severe water and carbon pressures as its economy grows. Their multivariate spatial–temporal collaborative relationships are projected to decrease by 10.26% in 2050. These findings contribute to promoting collaborative and sustainable development of inter-regional socio-economic and ecological environment.