# Study on the Effectiveness of Multi-Dimensional Approaches to Urban Flood Risk Assessment
## 3 Result
### Relationship Between Flood Depth and FRIB  
By utilizing risk levels rather than solely relying on flood depth as a response criterion, more efficient disaster management strategies can be developed. In this study, the FRIB was derived using the urban flood map from the Ministry of the Interior and Safety's Safety Map, and its relationship to flood depth was illustrated (Figure 5). Although FRIB has continuous values, for the practicality of disaster management and intuitive understanding, this study classified it into four discrete risk levels--'very low', 'low', 'high', and'very high'--using the Jenks Natural Breaks Classification explained in Section 2.5. The frequency of different flood depths for each risk level was then visualized through histograms and pie charts (Figure 6).  
Figure 5: Graph of the relationship between flood depth and FRIB.  
In order to examine how flood depths are distributed across different FRIB (Flood Risk Index) levels, this study employed two quantitative metrics--entropy and variance--to measure the uniformity and dispersion of the data, respectively. Entropy \(H(P)\) is defined for a given probability distribution \(P=\{p_{1},p_{2},\ldots,p_{n}\}\) by Equation (5).  
Figure 6: Distribution of FRIB levels, categorized as very low, low, high, and very high.  
\[H(P)=-\sum_{i=1}^{n}p_{i}\text{log}_{2}(p_{i}) \tag{5}\]  
where \(p_{i}\) is the proportion of data points falling into category \(i\). High entropy values indicate a more even spread of data across multiple categories, whereas low values suggest that the data is heavily concentrated in one or a few categories.  
Variance, on the other hand, measures how far individual observations deviate from the mean, reflecting how widely the data is dispersed around its central tendency. It is calculated as Equation (6).  
\[Variance=\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\mu)^{2} \tag{6}\]  
where \(x_{i}\) is an individual data point, \(\mu\) is the mean of all data points, and \(n\) is the total number of observations. High variance corresponds to a broad spread of values, while low variance indicates that the data is clustered tightly around the mean.  
Table 4 summarizes how the distribution of flood depths differs among four FRIB levels--very low, low, high, and very high--by presenting the computed entropy and variance values. The results reveal that at lower FRIB levels (very low and low), an overwhelming majority of data points lie in the shallow flood depth range (<0.5 m), leading to low entropy (indicating an uneven distribution) and relatively high variance (reflecting that the small amount of deeper data points is far from the mean). As the FRIB level increases, entropy rises and variance declines, indicating a more balanced distribution of flood depths across multiple categories. In the very high FRIB level, the highest entropy (2.419) and lowest variance (98) signify that the data is nearly uniform, with no single category dominating the distribution.  
These findings demonstrate that deeper flood depths alone do not fully determine a region's risk level. Instead, a broad spectrum of flood depths--from shallow to deep--contributes to overall flood risk, underscoring the need for inclusive response strategies and infrastructure enhancements. By employing metrics such as entropy and variance, policymakers and urban planners can better understand how different flood depths collectively shape the risk profile at each FRIB level. In turn, this holistic perspective encourages more robust urban flood management strategies that go beyond simply targeting the maximum flood depth.