Phase transitions in retrofitting urban drainage systems: a computational framework for adaptation-sustainability trade-offs

Climate change is compelling nations to invest heavily in retrofitting urban drainage systems (UDSs). However, limited information can lead to inefficient resource allocation, exacerbating the redundancy-efficiency dilemma. Traditional decision-making methods, such as multi-objective optimization, fail to capture the nonlinear evolution of adaptation, as they are constrained by static scenarios and lack the flexibility to accommodate multiple adaptation pathways. This study aims to establish a global perspective on the dynamic and nonlinear relationship between adaptation and sustainability by developing a hybrid, physics-based and data-driven computational framework. The Global Minimum Adaptation Cost Trajectory (GMACT) distinctly reveals adaptation transition patterns, demonstrated through a case study on Low Impact Development (LID) in Sponge City. Early-stage LID interventions improved adaptability by 24 % with a 10 % increase in life-cycle cost (LCC), while late-stage measures showed diminishing returns, requiring a 90 % LCC rise for just a 2 % gain. The analysis uncovered a bifurcation pattern, where Pareto-optimal solutions disperse above GMACT below a cost turning point, allowing multiple viable adaptation pathways. Beyond this point, solutions converge toward GMACT, suggesting that achieving high adaptability necessitates alignment with this trajectory. Findings reinforce GMACT as a strategic reference for adaptation planning, providing UDSs policymakers with a robust decision-support tool for guiding cost-effective and sustainable UDS upgrades under deep uncertainty.