## 2 Methodology
### Flood Intensity Level and Fragility Curve  
To quantify community-level resilience, the measurement of community-level functionality should be defined first. Conceptually, the community-level resilience should be measured by the probability of its \"undesired outcome\", which refers to the occurrence of an adverse impact on a community's ability to keep its original-level function [29]. It is also important to consider that community-level resilience is always influenced by many factors related to human activities, and the risk occurs when people, communities, or infrastructures can be negatively impacted by a natural hazard. Among these human activities, population dislocation has often been used as a metric for overall community resilience [30; 31; 32]. Considerable population dislocation is an undesired outcome resulting from a flooding event and will be used herein as the community resilience metric, as this is a good index reflecting the potential occupation of a community. Figure 2: Community level resilience quantification process. It should be noted that for all building archetypes, flood depth is measured from First-Floor Elevation (FFE). However, for these with crawl space foundations, it is measured from ground elevation, and the FFE is assumed to be at 1.0 m from the ground elevation; this also means that DS0 only exists in these buildings with crawl space foundations. The level of damage caused by a flooding hazard is influenced by several parameters, including the flooding depth, duration, velocity, the rate of rise in water levels, impulse (a product of water level and velocity), warning time, and frequency of occurrence. Among these factors, flooding depth is considered the most critical parameter, as it effectively determines the flood hazard's risk indices [33]. Consequently, flooding depth is used as the primary measure of flood hazard intensity in this study. Damage states (DSs) probabilities are used to describe the conditions of buildings under flooding hazards, categorized into five levels: insignificant damage (DS0), slight damage (DS1), moderate damage (DS2), extensive damage (DS3), and complete damage (DS4). This is outlined in Table 2 and based on prior studies [6]. Within the same community, buildings may experience different damage states due to variations in structural characteristics and environmental factors. Following the assumptions in [16], buildings in DS3 or DS4 are deemed unsafe for occupation unless they undergo repairs or replacement. These damage states and their corresponding probabilities provide a critical foundation for assessing building vulnerability and resilience, enabling a comprehensive analysis of flood impacts [6; 17; 34]. As for the flooding intensity measure, a single-variable approach based on the flooding depth is used to measure the flooding hazard damage. Reference [6] articulated a component-based numerical fragility and loss approach. Then, a Monte Carlo Simulation (MCS) is applied to propagate uncertainties in the resistance statistics of each component (e.g., cabinets or drywall) and for the whole-building fragility to flooding depth. The MCS was implemented using MATLAB R2024a, a computational platform chosen for its robust statistical and probabilistic modeling capabilities. Specifically, the analysis involved generating 10,000 random samples of flood depth and component resistance parameters, based on lognormal distributions with median (\(\lambda\)) and standard deviation (\(\xi\)) values derived from [6]. These samples were used to compute the exceedance probabilities of the damage states (DS0-DS4) for each building archetype, producing the fragility curves.