Research on the geometric weighting-coupling degree method for the urban ecological environment vulnerability index

Constructing a scientifically effective Urban Ecological Environment Vulnerability Index provides a solid foundation for accurately describing the evolution of urban ecological environment vulnerability and making precise predictions about its vulnerability risks. The existing composite index methods emphasize the strength of the relationships among influencing factors but overlook the synergistic relationships and interactions between dimensions. Given this, this article constructed a system of factors influencing the vulnerability of the urban ecological environment based on the theoretical models of ecological sensitivity, ecological resilience, and ecological pressure (SRP). We used a geometric weighting method to describe the strong and weak relationships of the influencing factors and introduced a coupling model from physics to portray the coordination relationship between dimensions. Finally, we proposed a method for constructing the urban ecological environment vulnerability index based on the geometric weighting-coupling degree method. We used data from 35 cities in China as a baseline to validate the stability and reliability of the proposed method. The results indicated that compared with other major index synthesis methods, the trend evolution of the peaks and troughs average values of the indices synthesized by the proposed index synthesis method is smoother, which is more consistent with the trend evolution of urban ecological environment vulnerability. The evolution of the synthesized index trend is more consistent with the stage of urban governance ecological environment vulnerability. This validated the better stability and reliability of the proposed composite index method. The geometric weighted-coupling degree index synthesis method constructed provides urban ecological environment researchers with a method to depict the trend evolution of urban ecological environment vulnerability. It may be used as a baseline and methodological reference for urban ecological environment managers to scientifically govern the urban ecological environment.