Identifying Alternative Regimes with Uncertainty in the Performance of a Flood Defense Infrastructure

Urban flood defense facilities are facing pressure from climate change, infrastructure aging, and the increasing frequency and intensity of extreme rainfall events. Although resilience has been extensively addressed in urban flood management research, most prior studies depend on static indicators or index-based evaluations at city or regional scales, providing limited understanding of the dynamic responses of individual facilities to disturbances. This study presents a mathematical framework for assessing facility-level resilience in urban flood defense systems and for identifying critical thresholds that drive transitions between functional regimes. The proposed framework shows a composite sigmoid function to capture the nonlinear evolution of facility performance during disturbance and recovery phases. Four resilience dimensions, which are Robustness, Redundancy, Rapidity, and Resourcefulness, are explicitly linked to the parameters of the performance function, representing initial structural performance, availability of functional alternatives, recovery rate, and the resource system over time. To address uncertainty arising from incomplete or partially missing resilience indicators, the framework incorporates a probabilistic treatment of survey-based inputs. Missing or uncertain resilience attributes are modeled using probability distributions, allowing resilience dimensions to be represented as stochastic variables rather than fixed values. A systematic parametric analysis is performed by varying each resilience dimension across feasible ranges, while repeated Monte Carlo simulations are conducted to propagate indicator-level uncertainty into the dynamic performance trajectories. This enables the derivation of empirical cumulative distribution functions and density-based representations of resilience outcomes. The simulation results demonstrate pronounced threshold effects and the presence of alternative performance regimes. When resilience dimensions drop below critical levels, facilities fail to regain their original performance and instead converge toward degraded operational states with distinct probability distributions. Moreover, under scenarios of repeated disturbances, insufficient recovery intervals can trigger irreversible regime shifts, with uncertainty in recovery timing further amplifying the likelihood of such transitions, underscoring the critical role of recovery timing in environments exposed to recurrent extreme rainfall. By directly linking resilience attributes with dynamic performance modeling, and by explicitly accounting for uncertainty associated with incomplete resilience information, this framework enhances understanding of multistability and tipping points in engineered flood defense infrastructure.

Acknowledgement This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Ministry of Science and Technology (RS-2024-00356786) and Korea Environmental Industry & Technology Institute grant funded by the Ministry of Environment (RS-2023-00218973).