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

^{*}

## 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

- Leopold, L.B.; Langbein, L.B. The Concept of Entropy in Landscape Evolution. Geology
**1962**, 500, A1–A20. [Google Scholar] [CrossRef] - Wagenaar, D.J.; Dahm, R.J.; Diermanse, F.L.M.; Dias, W.P.S.; Dissanayake, D.M.S.S.; Vajja, H.P.; Gehrels, J.C.; Bouwer, L.M. Evaluating adaptation measures for reducing flood risk: A case study in the city of Colombo, Sri Lanka. Int. J. Disaster Risk Reduct.
**2019**, 37, 101162. [Google Scholar] [CrossRef] - European Commission. Directive 2007/60/EC on the Assessment and Management of Flood Risks; European Palament: Brussels, Belgium, 2007; Available online: https://eur-lex.europa.eu/eli/dir/2007/60/oj (accessed on 15 January 2022).
- Boso, F.; de Barros, F.P.J.; Fiori, A.; Bellin, A. Performance analysis of statistical spatial measures for contaminant plume characterization toward risk-based decision making. Water Resour. Res.
**2013**, 49, 3119–3132. [Google Scholar] [CrossRef] - De Barros, F.P.J.; Bellin, A.; Cvetkovic, V.; Dagan, G.; Fiori, A. Aquifer heterogeneity controls on adverse human health effects and the concept of the hazard attenuation factor. Water Resour. Res.
**2016**, 52, 5911–5922. [Google Scholar] [CrossRef] [Green Version] - Enzenhoefer, R.; Nowak, W.; Helmig, R. Probabilistic exposure risk assessment with advective–dispersive well vulnerability criteria. Adv. Water Resour.
**2012**, 36, 121–132. [Google Scholar] [CrossRef] - Tartakovsky, D.M.; Dentz, M.; Lichtner, P. Probability density functions for advective-reactive transport with uncertain reaction rates. Water Resour. Res.
**2009**, 45, W07414. [Google Scholar] [CrossRef] - Andričević, R.; Galešić, M. Contaminant dilution measure for the solute transport in an estuary. Adv. Water Resour.
**2018**, 117, 65–74. [Google Scholar] [CrossRef] - Andričević, R.; Srzić, V.; Gotovac, H. Risk characterization for toxic chemicals transported in aquifers. Adv. Water Resour.
**2012**, 36, 86–97. [Google Scholar] [CrossRef] - Di Dato, M.; Galešić, M.; Šimundić, P.; Andričević, R. A novel screening tool for the health risk in recreational waters near estuary: The Carrying Capacity indicator. Sci. Total Environ.
**2019**, 694, 133584. [Google Scholar] [CrossRef] - Merz, B.; Kreibich, H.; Schwarze, R.; Thieken, A. Review article assessment of economic flood damage. Nat. Hazards Earth Syst. Sci.
**2010**, 10, 1697–1724. [Google Scholar] [CrossRef] - Wagenaar, D.; de Jong, J.; Bouwer, L.M. Multi-variable flood damage modeling with limited data using supervised learning approaches. Nat. Hazards Earth Syst. Sci.
**2017**, 17, 1683–1696. [Google Scholar] [CrossRef] [Green Version] - Wagenaar, D.; Lüdtke, S.; Schröter, K.; Bouwer, L.M.; Kreibich, H. Regional and temporal transferability of multivariable flood damage models. Water Resour. Res.
**2018**, 54, 3688–3703. [Google Scholar] [CrossRef] [Green Version] - Jonkman, S.N.; Vrijling, J.K.; Vrouwenvelder, A.C.W.M. Methods for the estimation of loss of life due to floods: A literature review and a proposal for a new method. Nat. Hazards
**2008**, 46, 353–389. [Google Scholar] [CrossRef] [Green Version] - Olsen, A.; Zhou, Q.; Linde, J.; Arnbjerg-Nielsen, K. Comparing Methods of Calculating Expected Annual Damage in Urban Pluvial Flood Risk Assessments. Water
**2015**, 7, 255–270. [Google Scholar] [CrossRef] [Green Version] - Ward, P.J.; van Pelt, S.; de Keizer, O.; Aerts, J.C.J.H.; Beersma, J.; van den Hurk, B.; te Linde, A. Including climate change projections in probabilistic flood risk assessment. J. Flood Risk Manag.
**2014**, 7, 141–151. [Google Scholar] [CrossRef] - Dottori, F.; Figueiredo, R.; Martina, M.L.V.; Molinari, D.; Scorzini, A.R. INSYDE: A synthetic, probabilistic flood damage model based on explicit cost analysis. Nat. Hazards Earth Syst. Sci.
**2016**, 16, 2577–2591. [Google Scholar] [CrossRef] [Green Version] - Foudi, S.; Osés-Eraso, N.; Tamayo, I. Integrated spatial flood risk assessment: The case of Zaragoza. Land Use Policy
**2015**, 42, 278–292. [Google Scholar] [CrossRef] - Wing, O.E.J.; Pinter, N.; Bates, P.D.; Kousky, C. New insights into US flood vulnerability revealed from flood insurance big data. Nat. Commun.
**2020**, 11, 1444. [Google Scholar] [CrossRef] [Green Version] - Prahl, B.F.; Rybski, D.; Boettle, M.; Kropp, J.P. Damage functions for climate-related hazards: Unification and uncertainty analysis. Nat. Hazards Earth Syst. Sci.
**2016**, 16, 1189–1203. [Google Scholar] [CrossRef] [Green Version] - Boettle, M.; Rybski, D.; Kropp, J.P. How changing sea level extremes and protection measures alter coastal flood damages. Water Resour. Res.
**2013**, 49, 1199–1210. [Google Scholar] [CrossRef] - Merz, B.; Hall, J.; Disse, M.; Schumann, A. Fluvial flood risk management in a changing world. Nat. Hazards Earth Syst. Sci.
**2010**, 10, 509–527. [Google Scholar] [CrossRef] [Green Version] - Boettle, M.; Kropp, J.P.; Reiber, L.; Roithmeier, O.; Rybski, D.; Walther, C. About the influence of elevation model quality and small-scale damage functions on flood damage estimation. Nat. Hazards Earth Syst. Sci.
**2011**, 11, 3327–3334. [Google Scholar] [CrossRef] - Morita, M.; Tung, Y.-K. Uncertainty quantification of flood damage estimation for urban drainage risk management. Water Sci. Technol.
**2019**, 80, 478–486. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hall, J.; Solomatine, D. A framework for uncertainty analysis in flood risk management decisions. Int. J. River Basin Manag.
**2008**, 2, 85–98. [Google Scholar] [CrossRef] [Green Version] - De Moel, H.; Aerts, J.C.C.H. Effect of uncertainty in land use, damage models and inundation depth on flood damage estimates. Nat. Hazards
**2011**, 58, 407–425. [Google Scholar] [CrossRef] [Green Version] - Azarnivand, A.; Malekian, A. Analysis of flood risk management strategies based on a group decision making process via Interval-valued intuitionistic fuzzy numbers. Water Resour. Manag.
**2016**, 30, 1903–1921. [Google Scholar] [CrossRef] - Rojas, R.; Feyen, L.; Watkiss, P. Climate change and river loods in the European Union: Socio-economic consequences and the costs and benefits of adaptation. Glob. Environ. Chang.
**2013**, 23, 1737–1751. [Google Scholar] [CrossRef] - Ward, P.J.; de Moel, H.; Aerts, J.C.J.H. How are flood risk estimates affected by the choice of return-periods? Nat. Hazards Earth Syst. Sci.
**2011**, 11, 3181–3195. [Google Scholar] [CrossRef] [Green Version] - Merz, B.; Elmer, F.; Thieken, A.H. Significance of high probability/low damage versus low probability/high damage flood events. Nat. Hazards Earth Syst. Sci.
**2009**, 9, 1033–1046. [Google Scholar] [CrossRef] - Croatian Meteorological and Hydrological Service. Climate Monitoring. 2019. Available online: https://meteo.hr/ (accessed on 25 October 2020).
- Jurković, R.S. Water balance components during recent floods in Croatia. Croat. Meteorol. J.
**2016**, 51, 61–70. [Google Scholar] - Huizinga, J.; de Moel, H.; Szewczyk, W. Global Flood Depth-Damage Functions. Methodology and the Database with Guidelines; EUR 28552 EN; Publications Office of the European Union: Luxembourg, 2017. [Google Scholar]
- Zhou, Q.; Mikkelsen, P.S.; Halsnæs, K.; Arnbjerg-Nielsen, K. Framework for economic pluvial flood risk assessment considering climate change effects and adaptation benefits. J. Hydrol.
**2012**, 414, 539–549. [Google Scholar] [CrossRef] - Kekez, T.; Knezić, S.; Andričević, R. Incorporating Uncertainty of the System Behavior in Flood Risk Assessment—Sava River Case Study. Water
**2020**, 12, 2676. [Google Scholar] [CrossRef] - Athanasios Papoulis, S. Probability, Random Variables, and Stochastic Processes, 2nd ed.; McGrow-Hill: New York, NY, USA, 1984. [Google Scholar]
- Humphreys, N. Exceedance probability in catastrophic modeling. Casualty Actuar. Soc. E-Forum
**2021**, 1–61. [Google Scholar] - Hammond, M.J.; Chen, A.S.; Djordjević, S.; Butler, D.; Mark, O. Urban flood impact assessment: A state-of-the-art review. Urban Water J.
**2015**, 12, 14–29. [Google Scholar] [CrossRef] [Green Version]

**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 $\left(\right)open="["\; close="]">{\mathit{\mu}}_{\mathbf{AD}}$ | Standard Deviation $\left(\right)open="["\; close="]">{\mathit{\sigma}}_{\mathbf{AD}}$ | Skewness $\left(\right)open="["\; close="]">{\mathit{\mu}}_{3}/{\mathit{\sigma}}_{\mathbf{AD}}^{3}$ | Kurtosis $\left(\right)open="["\; close="]">{\mathit{\mu}}_{4}/{\mathit{\sigma}}_{\mathbf{AD}}^{4}$ |
---|---|---|---|

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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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