2.3.1. Topographical Factors

Referring to Djamres et al. (2021) [14], the topographical factors of each mesh in the target city were quantified. The topographical factors used were "Elevation", "Slope", "Depth of concave", "Capacity of concave", "Catchment area", "Slope of upstream", "Slope of downstream", "Difference of slope", "Flow length of upstream", "Flow length of downstream", and "Difference of flow length". The method used to create each topographical factor is shown in Table 3. In this study, the 5 m mesh digital elevation model (DEM) provided by the Geospatial Information Authority of Japan (2013) [20] was used as the elevation data. This digital elevation model is produced based on Lidar data.

#### 2.3.2. Visualisation of the Topographical Characteristics of Urban Pluvial Flooding

Based on Djamres et al. (2021) [14], it was attempted to identify areas with similar topographical characteristics to those of frequent urban pluvial flooding areas as areas that are strongly influenced by topographical factors of urban pluvial flooding, based on the results of the PCA. First, from the principal component loadings evaluated in the PCA, each principal component score for the whole area mesh of each city was calculated using the following formula:

$$P\_{n(i,j)} = \sum\_{m=1}^{12} \left( a\_{m(i,j)} \cdot l\_m \right) \tag{1}$$

where *Pn*(*i*,*j*) is the principal component score of number *n* at *mesh* **(***i***,***j***)**; *am*(*i*,*j*) is the standardised value of factor *m* at *mesh* **(***i***,***j***)**; and *lm* is the factor loading of factor *m*. To assess similarity rates of topographical characteristics in frequent urban pluvial flooding areas and other areas in the city, we computed the deviation value of the averaged principal component score of urban pluvial flooding areas and scores of every mesh in the targeted areas using the following formula:

$$H\_{(i,j)} = \sum\_{n=1}^{4} \left( \left| P\_{n(i,j)} - \overline{P'\_n} \right| \cdot w\_n \right) \tag{2}$$

where *H*(*i*,*j*) is the indicator of how similar topographical characteristics with frequent urban pluvial flooding areas at *mesh* **(***x***,***y***)**; *Pn*(*i*,*j*) is the principal component score of number *n* at *mesh* **(***i***,***j***)**; *P <sup>n</sup>* is the mean principal component score of number *n* in the frequent urban pluvial flooding area; *wn* is the contribution rate of the principal component of number *n*. In other words, the smaller *H*(*i*,*j*) is, the more the location has similar topographical characteristics to the frequent urban pluvial flooding area, and the greater the influence of topographical factors on urban pluvial flooding.



#### **3. Results**

#### *3.1. Identification of Frequent Urban Pluvial Flooding Areas*

There are two points to consider in identifying frequent urban pluvial flooding areas: the frequency and extent of urban pluvial flooding. First, the frequency of urban pluvial flooding was examined. The relationship between the total years of urban pluvial flooding and the number of urban pluvial flooding areas in the raster data for each mesh size is shown in Table 4. The maximum total years of urban pluvial flooding in Osaka City and Nagoya City was 5–7 years. It is natural that when the criterion for the total years of urban pluvial flooding is small, areas that are not suitable for frequent urban pluvial flooding areas are selected. However, when the criterion is too large, the number of identified urban pluvial flooding areas becomes small, and it is not possible to obtain sufficient areas for analysis. In this study, urban pluvial flooding areas were identified as areas where urban pluvial flooding occurred more than four years (more than once every five years) in the 20 years from 1993 to 2012, considering more than half of the maximum total number of years in Osaka and Nagoya Cities.


**Table 4.** (**a**) The relationship between the total years of urban pluvial flooding and the number of urban pluvial flooding areas in the raster data for each mesh size in Osaka City. (**b**) The relationship between the total years of urban pluvial flooding and the number of urban pluvial flooding areas in the raster data for each mesh size in Nagoya City.

Next, the mesh size of frequent urban pluvial flooding areas was examined. In Table 4b, the number of frequent urban pluvial flooding areas in Nagoya City decreased as the mesh size increased in terms of the reference total years (more than four years) of frequent urban pluvial flooding. This could be since large urban pluvial flooding areas that were duplicated and over-accounted for in smaller meshes were accounted for as a single area when the mesh size increased. Furthermore, this was also considered to be since some urban pluvial flooding areas that were closely located were accounted as one area with increasing the mesh size. On the other hand, in Osaka City, the number of identified frequent urban pluvial flooding areas increased when the mesh size was larger than 30 m and was almost the same when the mesh size was larger than 100 m (Table 4a). This suggested that the urban pluvial flooding areas in Osaka City were smaller and less closely located than in Nagoya City and that a mesh size of 100 m or larger would enable the frequent urban pluvial flooding areas to be identified.

Since the objective of this study is to elucidate the specific distribution of frequent urban pluvial flooding areas and their topographical characteristics, the smaller the mesh size to be identified, the better. It is considered that the applicable mesh size to be identified was about 30 m mesh because the flooding area record has been allowed not to record cases where the flooded area was less than 1000 m2, and the number of flooded houses was less than 10 [17], as mentioned above. However, the urban pluvial flooding area record has been produced manually, and some errors may be included between the actual urban pluvial flooding area and its record. For example, a discrepancy of about 1 m to 50 m between them was recognised in the field survey, and if the mesh size was too small, the frequent urban pluvial flooding area could not be identified properly because flooded areas that occurred at the same location might be accounted for separately. Therefore, the mesh size was set to 100 m × 100 m in this study.

The frequent urban pluvial flooding areas in Osaka and Nagoya Cities identified according to the above-mentioned identifications are shown in Figure 3. In total, 70 frequent urban pluvial flooding areas were identified in Osaka City and 108 in Nagoya City. The proportion of frequent urban pluvial flooding areas in the area of each city was 0.34% in Osaka City and 0.33% in Nagoya City.

**Figure 3.** The distribution of frequent urban pluvial flooding areas (red circle) in (**a**) Osaka City and (**b**) Nagoya City.

#### *3.2. Topographical Characteristics of Frequent Urban Pluvial Flooding Areas* Principle Component Analysis (PCA) of Topographical Characteristics

The PCA of frequent urban pluvial flooding areas on topographical characteristics was performed using the topographical factors quantified in the previous chapter. Detailed results are shown in Table 5. The principal components with eigenvalues exceeding 1 were up to the fourth principal component (PCs) in both cities, with cumulative contribution rates of 85.7% for Osaka City and 88.6% for Nagoya City. This indicated that the topographical factors used in this study were appropriate for describing frequent urban pluvial flooding areas.

In Osaka City, the first principal component (PC1) accounted for 34.3% of the total variance. The factors that correlated the most with the PC1 were "Slope upstream" (0.404) and the difference of slope (0.390) in positive values. One can infer that frequent urban pluvial flooding areas had an upstream slope that was higher than the downstream slope. Principal component 2 (PC2) was negatively correlated with "Slope of downstream" and "Difference of flow length" and positively correlated with "Flow length of downstream". Therefore, PC2 was considered to be the component that aggregates the downstream situation, and one can conclude that frequent urban pluvial flooding areas had a downstream slope gentler than upstream, downstream flow length longer than upstream, and the location at a low elevation. In contrast, the third component (PC3) showed strong positive correlations with "Flow length of upstream" and "Catchment area". Therefore, PC3 was considered to be the component that aggregates the upstream situation. Principal component 4 (PC4) had negative correlations with "Depth of concave" and "Capacity of concave" and a positive correlation with "Slope of downstream". Therefore, PC4 was considered to be the component that aggregates the concave situation.

**Table 5.** (**a**) The PCA result for Osaka City. The shaded values are the factors that correlated the most in each PC. "-" indicates that no topographical factors in the principal components satisfied the 95% confidence interval. (**b**) The PCA result for Nagoya City. The shaded values are the factors that correlated the most in each PC.


In Nagoya City, PC1 had negative correlations for all factors except "Depth of concave" and "Capacity of concave", showing the opposite trend to that of Osaka City. PC2 was negatively correlated with three factors: "Flow length of upstream", "Catchment area", and "Difference of flow length". Therefore, PC2 was considered to be the component that aggregates the upstream situation and the factors related to the flow channel. PC3 had a strong positive correlation with "Flow length of downstream" and negative correlations with "Slope of downstream" and "Difference of flow length". Therefore, PC3 was considered to be the component that aggregates the downstream situation. PC4 had negative correlations with "Depth of concave" and "Capacity of concave", as did Osaka City. The results of the PCA for Osaka and Nagoya Cities showed that the topographical characteristics of the frequent urban pluvial flooding areas in both cities were different, with particularly conflicting trends in PC1.

The distribution of *H*(*i*,*j*) and the urban pluvial flooding areas of each city is shown in Figure 4. Many urban pluvial flooding areas were located in areas with small *H*(*i*,*j*), which has similar topographical characteristics to the frequent urban pluvial flooding areas. On the other hand, especially in Osaka City, the urban pluvial flooding areas were also distributed in areas with relatively large *H*(*i*,*j*), which do not have similar topographical characteristics to the frequent urban pluvial flooding areas. This suggested that factors

other than topographical characteristics that caused urban pluvial flooding were largely responsible for such areas in many parts of Osaka City and some parts of Nagoya City.

**Figure 4.** The distribution of *H*(*i*,*j*) and the urban pluvial flooding areas (light blue dot) in (**a**) Osaka City and (**b**) Nagoya City.

In addition, the average *H*(*i*,*j*) in the inundated areas by urban pluvial flooding from 1993 to 2012 (areas shown in the light blue dot in Figure 4) was calculated to be 3.26 in Osaka City and 2.81 in Nagoya City. This suggested that the distribution of urban pluvial flooding areas in Nagoya was better described by topographical characteristics than in Osaka City. Furthermore, the average *H*(*i*,*j*) for the whole area of each city, which was 2.64 in Osaka City and 3.18 in Nagoya City, was smaller in Osaka City than the average *H*(*i*,*j*) for the inundated area. This indicated that the urban pluvial flooding in Osaka City could not be described solely by topographical characteristics.

#### *3.3. Other Characteristics of Frequent Urban Pluvial Flooding Areas*

#### 3.3.1. Impact of Structures in Frequent Urban Pluvial Flooding Areas

Referring to Djamres et al. (2021) [14], the location of "dominant structures" was examined as another characteristic of these areas. Here, "dominant structures" are roads that divide sewers, railway lines (excluding subways and elevated lines), embankments, and structures with a site of more than 100 m per side. In addition, a road dividing a sewer is not a road with a sewer pipe buried directly under the centre of the road but a road with a sewer pipe buried under each side of the road. These are roads with a median strip or large road widths, such as dual carriageways in one direction, which were included in the analysis in this section because they influenced the flow of water.

Frequent urban pluvial flooding areas were classified according to the relationship between the location of "dominant structures" and the direction of inclination to "dominant structures". A conceptual diagram of the classification conditions and the proportions of the classified frequent urban pluvial flooding areas are shown in Figure 5 and Table 6. Figure 5a,d,g,h (the red line enclosure in Figure 5) show areas where "dominant structures" were located in the direction of inclination (direction of inundated water flow). In Osaka City, there were 90% of the total frequent urban pluvial flooding areas in which one or more "dominant structures" existed within 8 mesh around the area. Of the frequent urban pluvial flooding areas with "dominant structures" within 8 mesh of the perimeter, 74% of the areas had "dominant structures" in the direction of inundated water flow (Figure 5a,d,g,h).

**Figure 5.** A conceptual diagram of the classification conditions of the classified frequent urban pluvial flooding areas. (**a**–**h**) are areas where "dominant structures" were located within 8 mesh around the urban pluvial flooding area, while (**i**,**j**) are areas where "dominant structures" were not located within 8 mesh around the urban pluvial flooding area. (**h**) is the area where "dominant structures" were located in three directions around the frequent urban pluvial flooding area, and "dominant structures" were located in the front of the slope direction. The red line enclosure are areas where "dominant structures" was located in the direction of inclination (direction of inundated water flow).


**Table 6.** The proportions of the classified frequent urban pluvial flooding areas in Figure 5. The grey values are areas where "dominant structures" were located in the direction of inundated water flow.

In Nagoya City, there were 67% of the all-frequent urban pluvial flooding areas in which one or more "dominant structures" existed within 8 mesh around the area. Of the frequent urban pluvial flooding areas where "dominant structures" existed within 8 mesh of the perimeter, 28% of the areas had "dominant structures" in the direction of inundated water flow (Figure 5a,d,g,h).

A comparison of the results for Osaka and Nagoya Cities showed that the proportion of frequent urban pluvial flooding areas with "dominant structures" in Nagoya City was smaller than that in Osaka City, and in particular, the proportion of frequent urban pluvial flooding areas with "dominant structures" in the direction of the inundated water was much smaller. Therefore, the distribution of elevation and slope in frequent urban pluvial flooding areas in Osaka and Nagoya Cities was calculated based on the assumption that the topographical differences in frequent urban pluvial flooding areas might influence the characteristics of frequent urban pluvial flooding areas in both cities. The average elevation of the frequent urban pluvial flooding areas was 3.30 m in Osaka City and 3.61 m in Nagoya City, respectively. Although the elevation was higher in Nagoya City, there was no significant difference. On the other hand, the average slopes of all frequent

urban pluvial flooding areas in Osaka City and Nagoya City were 2.20% and 0.33%, respectively, indicating that the slopes of the frequent urban pluvial flooding areas in Nagoya City were much smaller than those in Osaka City. The frequency distribution of slopes at the frequent urban pluvial flooding areas in Osaka and Nagoya Cities is shown in Figure 6. Most of the frequent urban pluvial flooding areas in Nagoya City were located on almost no gradient with a slope of less than 1 degree. It was inferred that in such areas, regardless of the location of "dominant structures", the mere presence of "dominant structures" around it would dam up the inundated water and cause urban pluvial flooding. In addition, this was considered to be one of the reasons why "Slope" and "Slope of upstream" were not correlated as PCs in the PCA as the topographical characteristics of the frequent urban pluvial flooding area in Nagoya City described in the previous section.

3.3.2. Impact of Drainage System Improvements in Frequent Urban Pluvial Flooding Areas

To examine the impact of the improvement of drainage systems as another characteristic of frequent urban pluvial flooding areas, the occurrence trends of urban pluvial flooding in the urban pluvial flooding areas of Osaka and Nagoya Cities were investigated. The difference in urban pluvial floodings between the first 10 years (1993–2002) and the second 10 years (2003–2012) of the 20 years (1993–2012) is shown in Figure 7. Of the areas classified as green (1993–2002), 64 (91%) were in Osaka City compared with 8 (7%) in Nagoya City. On the other hand, red areas (2003–2012) were only 1 (1%) in Osaka City compared with 56 (52%) in Nagoya City. In addition, blue areas (1993–2012) were also only 5 (7%) in Osaka City compared with 44 (41%) in Nagoya City.

**Figure 6.** The frequency distribution of slopes at the frequent urban pluvial flooding areas in Osaka and Nagoya Cities.

**Figure 7.** The difference in urban pluvial floodings between the first 10 years (1993–2002) and the second 10 years (2003–2012) of the 20 years (1993–2012) in (**a**) Osaka City and (**b**) Nagoya City. The differences of 2 or more are shown in red, −1 to 1 in blue, and −2 or less in green. Red indicates areas where urban pluvial flooding occurred more frequently in the second 10 years, blue indicates areas where urban pluvial flooding occurred continuously throughout the 20 years, and green indicates areas where urban pluvial flooding occurred more frequently in the first 10 years.

Regarding the improvement of drainage systems, in Osaka City, the Naniwa Underground Discharge Channel (total length of 12.2 km), a large-scale drainage system to drain rainwater from the south-eastern area of Osaka City into the Sumiyoshi River, began to be constructed in 1984 and was completed in 2000, following the large-scale urban pluvial flooding caused by Typhoon No. 19 in September 1979 and Typhoon No. 10 in August 1982. As a result of such progress made in countermeasures against urban flooding, it can be inferred that urban pluvial flooding ceased to occur in frequent urban pluvial flooding areas during 2003–2012. On the other hand, Nagoya City, which is on a smaller urban scale than Osaka City, has been implementing emergency drainage system improvements in response to the large-scale urban pluvial flooding caused by the torrential rains of September 2002 and September 2006. However, it was found that most of the frequent urban pluvial flooding areas during 2003–2012 were located in areas where the improvement had not yet been completed (Figure 8). These results indicated that anthropogenic factors such as "dominant structures" and drainage system improvements influence the occurrence of urban pluvial flooding as characteristics other than topographical characteristics.

**Figure 8.** Urban flood management plan in Nagoya City (Progress as at the end of 2015) [21].

#### **4. Discussion and Summary**

This study clarified the distribution of frequent urban pluvial flooding areas in Osaka and Nagoya Cities by using urban pluvial flooding area records. The identified frequent urban pluvial flooding areas were 70 in Osaka City and 108 in Nagoya City, and their proportion to the area of each city was 0.34% in Osaka City and 0.33% in Nagoya City. Analyses of their characteristics revealed the following:


In general, urbanisation increases the accumulation of assets in topographically floodprone areas, and the risk of urban pluvial flooding increases. On the other hand, urban pluvial flood risk has been reduced through the improvement of drainage systems in such areas; however, urban pluvial flooding has also been observed in topographically less-floodprone areas due to changes in land use and land cover. In other words, as urbanisation progresses, the main cause of urban pluvial flooding is likely to shift from topographical factors to anthropogenic factors. The results of this study quantitatively showed this paradigm shift of urban pluvial flooding factors by the statistical analysis of newly defined urban pluvial flooding frequency areas. This is demonstrated as one of the methods for a major advance in urban flood modelling science proposed by Mignot and Dewals [9]. Furthermore, this study showed that it is difficult to describe past urban pluvial flooding

areas in Osaka and Nagoya Cities solely based on topographical characteristics. This was consistent with the findings of the numerical experiment [22] and statistical analyses [14] and showed that in some cases that artificial structures formed areas vulnerable to urban pluvial flooding even outside topographically flood-prone areas.

In addition, it is particularly difficult to collect flow velocity and depth observations during urban floods, as they are usually of short duration. The recent proliferation of mobile phones and online video-sharing platforms gives access to countless amateur videos [23–25], which are being used in most geophysical sciences, but difficulties with retrieving the location and time of the scenes impair the use of these data for detailed model validation [9]. The urban pluvial flooding area record used in this study and the newly defined frequent urban pluvial flooding area could be important sources for this validation.

On the other hand, although this study succeeded in quantitatively assessing the differences in the impact of topographical characteristics on the formation of frequent urban pluvial flooding areas due to urban scale by comparative analyses in Osaka and Nagoya Cities, this study only compared two cities, and the relationship between urban scale and frequent urban pluvial flooding areas has not been quantitively clarified. Further quantitative comparison with the characteristics of frequent urban pluvial flooding areas in other cities of different urban scales would help to understand the characteristics of urban pluvial flooding and their transition from topographical factors to anthropogenic factors, which is associated with urbanisation. Furthermore, socio-hydrology [26,27], which deals with the interaction between water systems and human activities, has been recently applied worldwide for flooding and water resources management [28]. Further quantitative comparative analysis of the characteristics of frequent urban pluvial flooding areas among different urban scale cities would provide a quantitative understanding of the system dynamics of urban pluvial flooding interacting with urbanisation, namely human activities.

**Author Contributions:** Conceptualization, D.K.; methodology, D.K. and K.N.; formal analysis and investigation, D.K., K.N., R.I., Y.O. and R.T.; writing—original draft preparation, D.K. and K.N.; writing—review and editing, D.K. and S.K.; visualization, D.K. and K.N.; supervision, D.K. and S.K.; funding acquisition, D.K. and S.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partly funded by the Nomura Foundation for Membrane Structure Technology and the Obayashi Foundation, and the APC was funded by the Masaki Sawamoto Research Publication Grant.

**Institutional Review Board Statement:** No applicable.

**Informed Consent Statement:** No applicable.

**Data Availability Statement:** No applicable.

**Acknowledgments:** This research was supported by CSIS Joint Research No. 1123, University of Tokyo. The urban pluvial flooding area record was provided by the River Planning Division, Water Management and Land Conservation Bureau, Ministry of Land, Infrastructure and Transport. The authors would like to express their gratitude.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

