# Socioeconomic Impact on Urban Resilience against Flood Damage
## 2 Methodology
### Evaluation of Resilience
#### 2.1.2 Evaluation of Each Attribute  
Resilience is generally composed of four attributes, a concept utilized by various researchers [14; 22; 23]. Among these, the definition of resilience proposed by [PERSON] et al. [21] is particularly suitable for comparing resilience and socioeconomic impacts, as it allows for evaluation across different flood stages. Therefore, this study adopts [PERSON] et al. 's [21] definitions of the four attributes, which are as follows. Robustness refers to the \"Ability to withstand disaster damage\", while resourcefulness means the \"Ability to access urban recovery resources\". Redundancy means the \"Ability to substitute when urban systems are not functioning\". Lastly, rapidity refers to the \"Ability for rapid urban recovery\". Through the four attributes of resilience, \"Urban Resilience' was determined. The following describes the evaluation methods used in this study for each of the four attributes to determine 'Urban Resilience'. * Robustness  
Among the attributes of resilience, robustness allows for the assessment of the structural damage to urban facilities. Robustness is evaluated based on the flood damage to buildings and roads at different inundation depths, and is expressed as follows:  
\[SI_{t}^{ci}=\left(SI_{b}{}^{ci}+SI_{t}{}^{ci}\right)/2 \tag{1}\]  
\[SI_{b}{}^{ci}=\frac{\sum D_{max}^{id_{b}}-\sum D_{t}^{id_{b}}}{\sum D_{max}^{id _{b}}} \tag{2}\]  
\[D^{id_{b}}=D^{id_{b}}(h)\times\mathcal{C}^{id_{b}} \tag{3}\]  
Figure 2: Results of text frequency analysis of resilience definition [21]. The word “ability” was the most prominently used, indicating that most researchers define resilience in terms of ability. \[SI_{rt}^{ci}=\frac{\sum D_{max}^{id_{r}}-\sum D_{t}^{id_{r}}}{\sum D_{max}^{id_{r}}} \tag{4}\]  
\[D^{id_{r}}=D^{id_{r}}(h)\times A^{id_{r}} \tag{5}\]  
where \(SI\) is systemic impact, \(ci\) is city, \(t\) is time, \(SI_{b}\) is system impact of building, \(h\) is inundation depth (m), \(SI_{r}\) is system impact of road, \(D(h)\) is depth-damage function of each \(h\), \(D_{max}\) is max damage, \(C^{idb}\) is cost of building (USD), and \(A\) is area of road (m\({}^{2}\)). * Resourcefulness  
Resourcefulness enables the assessment of the capability to mobilize the resources needed for recovery when a city incurs damage. The city's resourcefulness is evaluated based on the expected damage from a flood and is expressed as follows:  
\[DP_{t}^{ci}=\frac{RF_{t}^{ci}}{RF^{co}} \tag{6}\]  
\[\frac{RF_{t}^{ci}}{RF^{co}}=\frac{\sum_{ci}D_{max}^{id_{b}}}{\sum_{co}D_{max}^{ id_{b}}} \tag{7}\]  
where \(DP\) is disaster preparedness, \(RF^{co}\) is reserve fund of county level, \(RF^{ci}\) is reserve fund of city level, \(\sum_{ci}D_{max}^{id_{b}}\) is maximum damage cost of city level and \(\sum_{co}D_{max}^{id_{b}}\) is maximum damage cost of county level. * Redundancy  
Redundancy is used to assess a city's evacuation capabilities. It assesses the number of alternative routes available for evacuation from flooded to unflooded roads at specific points in time during a flood, using network analysis in Python 3.8, and is expressed as follows:  
\[SR_{t}^{ci}=\frac{\sum AR_{t}^{n,n_{0}}}{\sum AR_{max}^{n,n_{0}}} \tag{8}\]  
where \(SR\) is system redundancy, \(\sum AR_{max}^{n,n_{0}}\) is max route numbers from flooded (\(n\)) to unflooded roads (\(n_{0}\)) and \(\sum AR_{t}^{n,n_{0}}\) is route numbers from flooded to unflooded roads at specific time \(t\). * Rapidity  
Rapidity evaluates the city's ability for recovery and rescue operations. Rapidity is evaluated by the number of routes that allow access within 10 min from main facilities (po-ice stations, fire stations, hospitals) to flooded locations.