# Evaluating Flood Exposure for Properties in Urban Areas Using a Multivariate Modelling Technique

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## Abstract

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## 1. Introduction

- Develop a multivariate model to identify and rank significant variables contributing to the exposure to urban flooding;
- To develop a model to quantify areas prone to urban flooding.

## 2. Materials/Access to Data

#### 2.1. Case Area

^{2}, with a relatively long coastline to the Oslo fjord. According to Norwegian standards, it is densely populated.

#### 2.2. Insurance Data

- Installation: A description of where the malfunction that has led to the damage is located, e.g., water pipes indoor, outdoor, sewer mains;
- Source: A description of the underlying reason for the damage, e.g., precipitation, water supply;
- Cause: Describes the actual cause for the damage, e.g., stop in sewers, aging, frost, malfunction.

- Address (property where the damage occurred);
- Compensation sum;
- Classification into codes for Installation, Source, and Cause.

#### 2.3. Geocoding

^{tm}(programming language), these units were geocoded. Once the records in a table are geocoded, they add value to the analysis as it is a very effective method for the generation of environmental variables describing the local morphology surrounding the buildings.

#### 2.4. Terrain Parameters

- Distance (elevation z, distance to coast). This group includes the altitude above mean sea level (z) and distance to the coast measured from each building’s central points (BCP);
- Slope (the slope gradient) includes the slope value from the cells. The variable sl_r100 gives the mean slope within a 100-meter radius for an area elevated higher than the BCP. The other slope values are derived from the cells at the three different resolutions mentioned above;
- Area (permeable, impermeable, and sum) was derived from the BCP and arranged in the contributing area into permeable and impermeable surface areas, all within a 100 m radius from the BCP. The upstream sealed area shown in Table 1 was calculated in two ways (abbreviations are explained in Table 1): One includes roads elevated higher than the BCP (a_Up_ro) and another includes all upstream built-up areas (a_US_im) according to [20]. When calculating an upstream area, all cells elevated higher than the BCP were included. This is a limitation, as not all those cells will drain through the BCP. A more accurate way to calculate the upstream drain area might be an opportunity for improvement in further studies. These variables were calculated in a similar way, and we considered that this simplification would not led to statistical bias;
- Curvature profile (plan and profile). Terrain curvature is expressed as the plan or profile curvature, measured along the steepest descent and the contour, respectively. The curvature number is also known as the second derivate value of the input surface by cells, based on the algorithm described by Zevenbergen and Thorne [21].

#### 2.5. Sewer Data

#### 2.6. Sampling

^{®}10.3 software (ESRI, Redlands, CA, USA).

## 3. Method

^{®}version 10.3 (CAMO Software AS, Oslo, Norway) was used for this analysis [27].

_{i}=1. An often used approach for assigning the membership of a class is the “winner-takes-all-strategy” and the majority vote [30]. This means that the highest score calculated from the model obtains the class-assignment. Transferred to this study, ŷi, Flooded > ŷi, Random should be interpreted as flooded (F) and vice versa.

## 4. Results

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author contributions

- Geir Torgersen: conception and design of the work, analysis, interpretation and drafting;
- Jan Ketil Rød: design of the work, analysis and interpretation;
- Knut Kvaal: design of the work, analysis and interpretation;
- Jarle T. Bjerkholt: conception and design of the work, analysis and interpretation;
- Oddvar G. Lindholm: conception and design of the work, analysis and interpretation.

## Conflicts of interest

## References

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Group | No | Abbrev. | Parameter | Flooded (F) Addresses | Random (R) Addresses | BCP = Building Central Point Comments | ||
---|---|---|---|---|---|---|---|---|

Aver | (SD) | Aver | (SD) | |||||

Distance | 1 | d_C | Distance to coast | 627 | (415) | 639 | (471) | Distance from BCP to coast (m) |

Distance | 2 | d_z1 | elevation_1m area | 14.95 | (11) | 22.61 | (14) | Elevation extracted from 1 m resolution DEM at location of BCP |

Distance | 3 | d_z10 | elevation_10m area | 15.34 | (11) | 22.60 | (14) | As above, 10 m resolution |

Distance | 4 | d_z50 | elevation_50m area | 15.80 | (11) | 22.57 | (14) | As above, 50 m resolution |

Slope | 5 | sl_1 | slope_1m | 2.6 | (3,1) | 5.1 | (4,6) | Mean slope extracted from 1 m resolution DEM at location of BCP |

Slope | 6 | sl_10 | slope_10m | 2.2 | (2,2) | 5.3 | (4,2) | As above, 10 m resolution |

Slope | 7 | sl_50 | slope_50m | 2.3 | (2,1) | 3.9 | (2,9) | As above, 50 m resolution |

Slope | 8 | sl_r100 | Slope_r100 | 5.9 | (3,8) | 7.7 | (3,9) | Mean slope extracted from 100 m radius at location of BCP |

Slope | 9 | sl_1_ip | slope_1m interpolated | 2.6 | (3,1) | 5.1 | (4,6) | Mean slope extracted from 1 m resolution DEM at location of BCP and its 8 first neighbors |

Slope | 10 | sl_10_ip | slope_10m interpolated | 2.2 | (2,3) | 5.5 | (4,2) | As above, 10 m resolution |

Slope | 11 | sl_50_ip | slope_50m interpolated | 2.4 | (2,0) | 3.9 | (2,6) | As above, 50 m resolution |

Area | 12 | a_Up | UpSlope area | 18,047 | (4934) | 13,171 | (5381) | Area at higher ground than BCP within 100 m radius |

Area | 13 | a_Up_ro | UpSlope impervious area | 1761 | (941) | 999 | (840) | Roads(impervious) at higher ground than BCP within 100 m radius |

Area | 14 | a_RUp_ro | Rate UpSlope impervious area | 0.10 | 0.05 | 0.07 | 0,05 | Ratio No. 13/No. 12 |

Area | 15 | a_DS | Cells downstream | 13,382 | (4957) | 18,183 | (5407) | Area at lower ground than BCP within 100 m radius |

Area | 16 | a_US | Cells upstream | 17,986 | (4957) | 13,186 | (5407) | Area at higher ground than BCP within 100 m radius |

Area | 17 | a_US_im | Cells impervious | 15,880 | (5168) | 11,167 | (5528) | Area of imperm surfaces at higher ground than BCP within 100 m radius |

Area | 18 | a_US_pe | Cells pervious | 2106 | (3158) | 1966 | (3761) | Area of perm. surfaces at higher ground than BCP within 100 m radius |

Area | 19 | a_RUS_im | Rate Cells impervious | 0.89 | (0,2) | 0.86 | 0,24 | Ratio No. 17/ No. 16 |

Curvature | 20 | c_pr1 | curvature profile 1 m | 0.16 | (1,7) | −0.17 | (3,0) | Profile curvature extracted from 1 m resolution DEM at location of BCP |

Curvature | 21 | c_pr10 | curvature profile 10 m | 0.07 | (0,3) | 0.04 | (0,6) | As above, 10 m resolution |

Curvature | 22 | c_pr50 | curvature profile 50 m | 0.07 | (0,1) | −0.01 | (0,1) | As above, 50 m resolution |

Curvature | 23 | c_pr1_ip | curvature profile 1 m interpolated | 0.14 | (1,2) | −0.13 | (2,1) | Weighted mean profile curvature extracted from 1 m resolution DEM based on four closest pixels to location of BCP |

Curvature | 24 | c_pr10_ip | curvature profile 10 m interpolated | 0.08 | (0,2) | 0.03 | (0,6) | As above, 10 m resolution |

Curvature | 25 | c_pr50_ip | curvature profile 50 m interpolated | 0.06 | (0,1) | 0.00 | (0,1) | As above, 50 m resolution |

Curvature | 26 | c_pl1 | curvature plan 1 m | 0.18 | (1,9) | 0.02 | (1,8) | Plan curvature extracted from 1 m resolution DEM at location of BCP |

Curvature | 27 | c_pl10 | curvature plan 10 m | −0.02 | (0,2) | 0.06 | (0,3) | As above, 10 m resolution |

Curvature | 28 | c_pl50 | curvature plan 50 m | −0.02 | (0,1) | 0.03 | (0,1) | As above, 50 m resolution |

Curvature | 29 | c_pl1_ip | curvature plan 1 m interpolated | 0.14 | (1,4) | 0.05 | (1,5) | Weighted mean plan curvature extracted from 1 m resolution DEM based on four closest pixels to location of BCP |

Curvature | 30 | c_pl10_ip | curvature plan 10 m interpolated | −0.02 | (0,1) | 0.06 | (0,3) | As above, 10 m resolution |

Curvature | 31 | c_pl50_ip | curvature plan 50 m interpolated | −0.02 | (0,0) | 0.02 | (0,1) | As above, 50 m resolution |

Sewer | 32 | se_C | Combined sewer mains (rate) | 66% | 46% | Rate combined system (category var) | ||

Sewer | 33 | se_S | Separate sewer mains (rate) | 34% | 54% | Rate separate system (category var) | ||

Sewer | 34 | se_D | Diameter pipe(mm) | 369 | (225) | 269 | (134) | Diameter of nearest sewer pipe |

Sewer | 35 | se_Y | Year of constructed pipe | 1972 | (26,2) | 1974 | (23,0) | Year of construction for the nearest sewer mains |

Sewer | 36 | se_HorD | Horizontal dist to sewer | 20.9 | (9,9) | 29.2 | (23,3) | Horizontal distance from BCP to the nearest sewer |

Sewer | 37 | se_V>2 | Vertical dist to sewer >2 m | 0% | 16% | Vertical distance from BCP to sewer mains >2 m (category variable) | ||

Sewer | 38 | se_V<2 | Vertical dist to sewer <2 m | 100% | 84% | Vertical distance from BCP to sewer mains<2 m (category variable) |

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## Share and Cite

**MDPI and ACS Style**

Torgersen, G.; Rød, J.K.; Kvaal, K.; Bjerkholt, J.T.; Lindholm, O.G. Evaluating Flood Exposure for Properties in Urban Areas Using a Multivariate Modelling Technique. *Water* **2017**, *9*, 318.
https://doi.org/10.3390/w9050318

**AMA Style**

Torgersen G, Rød JK, Kvaal K, Bjerkholt JT, Lindholm OG. Evaluating Flood Exposure for Properties in Urban Areas Using a Multivariate Modelling Technique. *Water*. 2017; 9(5):318.
https://doi.org/10.3390/w9050318

**Chicago/Turabian Style**

Torgersen, Geir, Jan Ketil Rød, Knut Kvaal, Jarle T. Bjerkholt, and Oddvar G. Lindholm. 2017. "Evaluating Flood Exposure for Properties in Urban Areas Using a Multivariate Modelling Technique" *Water* 9, no. 5: 318.
https://doi.org/10.3390/w9050318