# Identification of Rainfall Thresholds Likely to Trigger Flood Damages across a Mediterranean Region, Based on Insurance Data and Rainfall Observations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}and includes 284 sub-areas following the postal code (PC) segmentation. The PCs have a mean area of 11 km2 (ranging from 0.05 to 348 km

^{2}) and a mean population of 12,100 inhabitants (ranging from 990 to 59,000 inhabitants). Population data were derived from the Hellenic Statistical Authority and refer to the latest population-housing Census of 2011 [37].

#### 2.2. Data Spatial Analysis and Sources

#### 2.3. Rainfall Events

#### 2.4. Statistical Methods

#### 2.4.1. Analysis for the AMA as a Whole

#### 2.4.2. Analysis at the Municipality Level

## 3. Results

#### 3.1. Overview of the Study Area

#### 3.2. Optimal R24 Thresholds per Municipality

^{2}= 0.13, F(1, 56) = 8.55, p = 0.005). Specifically, the sample size was found to have a statistically significant and negative effect (coefficient = −0.21, p = 0.005) on the R24 p-value, which indicates that a small statistical sample may be responsible for the statistical insignificance of the logistic models of some of the examined municipalities.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the meteorological stations in the Athens Metropolitan Area (AMA), highlighting the postal code (PC) boundaries.

**Figure 2.**(

**a**) Frequency distribution (histogram) of R24, at the PC spatial analysis. (

**b**) Distribution (boxplot) of R24 over the binary damage occurrence variable, DO.

**Figure 3.**(

**a**) Fitted values of DO predicted probability as a function of R24 controlled for the population. (

**b**) ROC curve, highlighting the TPR/FPR coordinates related to the AMA optimal R24 threshold given that the difference between TPR and FPR is maximized.

**Figure 4.**Relationship (scatter plot and fit line) between statistical sample size and R24 p-value of the logistic regression models examining the effect of R24 on DO per municipality.

**Figure 5.**Optimal R24 thresholds (mm) above which flood damage is likely to occur, level of flood damage risk (3-color palette), and level of confidence in R24’s discriminating performance, at the municipality level.

**Table 1.**Results for the logistic regression analysis of the probability of damage occurrence (DO) across the PCs of the AMA depending on R24 and controlled for the population.

Variable | b | SE | p Value | 95% Conf. Interval | |
---|---|---|---|---|---|

R24 ^{1} | 3.03 | 0.18 | 0.000 | 2.68 | 3.39 |

Population ^{1} | 1.51 | 0.11 | 0.000 | 1.29 | 1.72 |

Intercept | −12.87 | 0.54 | 0.000 | −13.93 | −11.80 |

N = 8726 | |||||

LR chi^{2}(5) = 498.85 | |||||

Prob > chi^{2} = 0.000 | |||||

Pseudo R^{2} = 0.08 |

^{1}Variables were log-transformed.

ROC–AUC Metrics | ||
---|---|---|

Cross-validated (cv) mean AUC | 0.64 | |

cvSD AUC | 0.02 | |

Bootstrap bias corrected 95% CI | 0.62 | 0.66 |

k-folds | 8 |

**Table 3.**Descriptive statistics (mean, standard deviation (SD), min, max) for PCs, R24–DO pairs, and damage occurrences at the municipality level (Ν = 59).

Mean | SD | Min | Max | |
---|---|---|---|---|

R24–DO pairs ^{1} | 147.9 | 474.1 | 7 | 3695 |

Damage occurrences (i.e., DO = 1) | 17.5 | 34.7 | 0 | 266 |

% damage | 16.7 | 8.7 | 0 | 43 |

PCs | 4.8 | 11.6 | 1 | 90 |

^{1}Rainfall events with R24 above 20 mm.

**Table 4.**Statistics (mean, standard deviation (SD), min, max) of R24–DO pairs, logistic regression results, and ROC–AUC results for the municipalities and the merged ones with significant model performance (Ν = 28).

Mean | SD | Min | Max | |
---|---|---|---|---|

R24–DO pairs | 275 | 673 | 46 | 3695 |

Damage occurrences (i.e., DO = 1) | 31 | 48 | 7 | 266 |

Logistic regression results | ||||

R24 coefficient | 4.16 | 1.69 | 2.01 | 10.21 |

R24 p-value | 0.02 | 0.02 | 0.00 | 0.05 |

ROC–AUC results ^{1} | ||||

AUC (0 to 1) | 0.68 | 0.07 | 0.60 | 0.85 |

AUC SE | 0.07 | 0.03 | 0.02 | 0.13 |

LCI | 0.54 | 0.09 | 0.38 | 0.75 |

HCI | 0.82 | 0.08 | 0.68 | 1.00 |

R24 opt. (mm) ^{2} | 40.4 | 10.6 | 30.4 | 78.0 |

TPR (hit rate, %) | 68.7 | 15.7 | 50.0 | 100.0 |

FPR (false alarm rate, %) | 32.5 | 14.4 | 3.0 | 59.0 |

Correctly classified (%) | 67.9 | 11.4 | 51.0 | 92.0 |

^{1}AUC SE: standard error of AUC; LCI/HCI: low/high confidence interval.

^{2}R24 opt.: optimal R24 threshold for which the difference between TPR and FPR is maximized, given a TPR equal to or higher than 50%.

**Table 5.**Specifications for the classification of flood damage risk and confidence in discriminating performance of the estimated R24 thresholds.

Flood Damage Risk Classification | Confidence Classification | |||
---|---|---|---|---|

Class | R24 opt. (mm) | Corresponding Percentile | AUC (%) | Corresponding Percentile |

1—low | >56 | 90th | 60–70 | Minimum–68th |

2—moderate | 42–56 | 75th–90th | 70–80 | 68th–93th |

3—high | 30–42 | Minimum–75th | >80 | >93th |

**Table 6.**Selected R24 thresholds for damage occurring in the municipality of Athens for different trade-offs among TPR and FPR.

R24 (mm) | TPR (Hit Rate) % | FPR (False Alarm Rate) % | Correctly Classified % |
---|---|---|---|

35.0 | 60.2 | 40.3 | 59.7 |

41.8 ^{1} | 50.4 | 25.7 | 72.6 |

50.4 | 40.2 | 16.5 | 80.4 |

^{1}Optimal R24 threshold for which the difference between TPR and FPR is maximized.

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## Share and Cite

**MDPI and ACS Style**

Papagiannaki, K.; Kotroni, V.; Lagouvardos, K.; Bezes, A.; Vafeiadis, V.; Messini, I.; Kroustallis, E.; Totos, I.
Identification of Rainfall Thresholds Likely to Trigger Flood Damages across a Mediterranean Region, Based on Insurance Data and Rainfall Observations. *Water* **2022**, *14*, 994.
https://doi.org/10.3390/w14060994

**AMA Style**

Papagiannaki K, Kotroni V, Lagouvardos K, Bezes A, Vafeiadis V, Messini I, Kroustallis E, Totos I.
Identification of Rainfall Thresholds Likely to Trigger Flood Damages across a Mediterranean Region, Based on Insurance Data and Rainfall Observations. *Water*. 2022; 14(6):994.
https://doi.org/10.3390/w14060994

**Chicago/Turabian Style**

Papagiannaki, Katerina, Vassiliki Kotroni, Kostas Lagouvardos, Antonis Bezes, Vasileios Vafeiadis, Ioanna Messini, Efstathios Kroustallis, and Ioannis Totos.
2022. "Identification of Rainfall Thresholds Likely to Trigger Flood Damages across a Mediterranean Region, Based on Insurance Data and Rainfall Observations" *Water* 14, no. 6: 994.
https://doi.org/10.3390/w14060994