## 3 Results and Discussion
### Evaluating Operational Resilience: A Comparative Discourse  
This study utilized Critical Component Analysis (CCA) to evaluate the average Oper-R under hypothetical failure scenarios of key infrastructure components throughout their service life. Centralized networks exhibited an 8% higher Oper-R when the optimization process prioritized minimizing LCC (Table 2). However, a contrasting perspective is offered by [PERSON] et al. [24], whose global resilience analysis suggested that decentralized strategies require fewer resources while achieving superior Oper-R. This discrepancy may arise from global resilience analysis accounting for the aggregate effects of network failures. While holistic, the computational complexity of this approach limits the number of random failure scenarios analyzed at each level to several hundred, potentially reducing the comprehensiveness of its findings [15].  
Decentralized schemes have been favored in other studies, likely due to the interdependence of critical components in decentralized networks, such as outlets and downstream pipelines, which may not be easily separable or discernible. This interdependence can lead to their omission from assessments, thereby biasing results against decentralized  
Figure 7: Spatial allocation of green infrastructure (GI) in optimized GGI designs across sub-catchments for selected configurations (**(a)** Optimal GGI design A (DDL = 60%), (**(b)** Optimal GGI design B (DDL = 60%), (c) Optimal GGI design C (DDL = 80%), **(d)** Optimal GGI design D (DDL = 100%).  
schemes. Similarly, CCA-based analyses may fail to capture the adaptability advantages inherent in decentralized layouts [20]. As a result, conclusions may disproportionately favor centralized schemes due to their higher retention capacity and more comprehensive GREI and GI integration [45]. However, this does not imply that centralized systems consistently outperform in terms of Oper-R. For designs with LCC below USD 77.4M, the highest Oper-R is observed at a moderate \(DDL\) of 60% (Figure 6c).  
While global resilience analysis is claimed to provide a more comprehensive and realistic perspective, its integration into optimization processes poses significant challenges due to the unpredictability of GREI failure distributions (e.g., location and frequency). Within this study's CCA framework, Oper-R assessments were limited to simulations of three typical years, underscoring a practical limitation. [PERSON] et al. [44] introduced a structural resilience index to identify critical components and assess system Oper-R, offering computational feasibility and efficiency compared to global resilience analysis or CCA. However, this index assumes uniform sub-catchment areas per outlet, which may limit its applicability in densely urbanized areas with complex land use and limited open spaces.  
Failures in critical components of both GREI and GGI systems can lead to catastrophic flooding in densely populated areas [51; 52]. Enhancing reliability and resilience requires prioritizing severe threats and their potential impacts over the service life of the infrastructure, even if the perceived threats are of low probability [53]. In this study, an exponential distribution function was employed to estimate GREI failure probabilities. However, real-world scenarios are inherently more complex. Long-term monitoring data could enable the development of more robust statistical models, such as Weibull distributions [54], or serve as the basis for machine learning models to predict network failures [55]. Similarly, empirical data could support the development of long-term efficiency distribution functions for GI, enabling more comprehensive multi-dimensional assessments and validation in future studies [56].