# Flood Risk Modeling under Uncertainties: The Case Study of Croatia

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study Description

#### 2.2. Flood Frequency Analysis

## 3. Results

#### 3.1. Flood Damage Estimates for Risk Characterization

#### 3.2. Flood Risk Indicators

#### 3.3. Annual Damage Distribution

#### 3.4. Uncertainty in the Damage Function

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The wider area of the city of Karlovac and selected agglomeration for the flood risk assessment.

**Figure 2.**Observed annual maximum river water depth data (1985–2020) evaluated with the GEV probability distribution for the Karlovac gauging station.

**Figure 7.**Uncertainty in the shape parameter k displayed (

**a**) for the unit damage function and (

**b**) for the agglomeration damage functions.

**Figure 8.**Exceedance probability—annual damage distributions resulting from uncertainty in the shape parameter k for households and inventory.

Type of Asset | Quantity at Risk | Unit Value | Total Damage |
---|---|---|---|

Households and inventory | households footprint area 34,000 m${}^{2}$ | 507 €/m${}^{2}$ | 17.238 $\times {10}^{6}$ € |

EAD $\left[{\mathit{\mu}}_{\mathbf{AD}}\right]$ | Standard Deviation $\left[{\mathit{\sigma}}_{\mathbf{AD}}\right]$ | Skewness $\left[{\mathit{\mu}}_{3}/{\mathit{\sigma}}_{\mathbf{AD}}^{3}\right]$ | Kurtosis $\left[{\mathit{\mu}}_{4}/{\mathit{\sigma}}_{\mathbf{AD}}^{4}\right]$ |
---|---|---|---|

0.074 | 0.1 | 1.75 | 5.55 |

Flood Event (Years) | Annual Probability of Occurrence [${\mathit{p}}_{\mathit{i}}$] | Annual Relative Damage | Monetary Loss (${\mathit{L}}_{\mathit{i}}$) ${10}^{6}$ € | Expected Monetary Loss [${\mathit{p}}_{\mathit{i}}\times {\mathit{L}}_{\mathit{i}}$] | Exceedance Probability % |
---|---|---|---|---|---|

10 | 0.1 | 0.23 | 3.96 | 0.396 | 8.7 |

25 | 0.04 | 0.33 | 5.7 | 0.22 | 4 |

50 | 0.02 | 0.39 | 6.7 | 0.13 | 2.8 |

100 | 0.01 | 0.43 | 7.4 | 0.074 | 2 |

500 | 0.002 | 0.49 | 8.4 | 0.017 | 1.4 |

1000 | 0.001 | 0.51 | 7.24 | 0.00724 | 0.97 |

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**MDPI and ACS Style**

Kekez, T.; Andricevic, R.; Knezic, S.
Flood Risk Modeling under Uncertainties: The Case Study of Croatia. *Water* **2022**, *14*, 1585.
https://doi.org/10.3390/w14101585

**AMA Style**

Kekez T, Andricevic R, Knezic S.
Flood Risk Modeling under Uncertainties: The Case Study of Croatia. *Water*. 2022; 14(10):1585.
https://doi.org/10.3390/w14101585

**Chicago/Turabian Style**

Kekez, Toni, Roko Andricevic, and Snjezana Knezic.
2022. "Flood Risk Modeling under Uncertainties: The Case Study of Croatia" *Water* 14, no. 10: 1585.
https://doi.org/10.3390/w14101585