A new water security resilience indicator based on ternary connection number projection method: A case study of Beijing-Tianjin-Hebei region

• A new water security resilience indicator (WSRI) based on ternary connection number projection. • Revealing WSR from a multi process perspective of resistance, recoverability and adaptability. • The water security situation in Beijing-Tianjin-Hebei region is severe, with a low WSRI. • WSR regulation directions for Beijing,Tianjin and Hebei are recoverability, resistance and adaptability. To address the issue in existing water security resilience (WSR) evaluations where the calculation of the resilience indicator fails to fully account for the nonlinear coupling relationship in the resilience process, a connection number sequence is introduced. A projection formula for the connection number sequence is proposed. By leveraging the concept of the three-dimensional model of spatial vectors, a new WSR indicator (WSRI)based on the projection of ternary connection numbers is further put forward. Considering the impacts of resistance, recoverability and adaptability on WSR process, an evaluation indexes system is established by selecting 27 indexes such as population density, sewage treatment rate, and water resource load index, and the WSRI of the Beijing-Tianjin-Hebei (BTH) region is evaluated. The results show that from 2014 to 2023, the overall WSRI values in the BTH region are relatively low, and the water security situation remains severe. However, there is an overall trend of improvement year by year. Currently, the regulation of WSR in Beijing should lean towards recoverability, that in Tianjin should focus on resistance, and Hebei needs to further enhance its adaptability. The new resilience indicator constructed based on ternary connection number projection breaks through the inherent dependence of traditional evaluation methods on linear relationships. By means of multi-dimensional coupling analysis, it enhances the accuracy of characterizing resilience processes, thereby providing a new tool for resilience assessment of nonlinear systems.