# Systemic Flood Risk Management: The Challenge of Accounting for Hydraulic Interactions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study

## 3. Simulation Model

#### 3.1. Policies (L)

#### 3.2. Model Uncertainties (X)

#### 3.3. Model Outcomes (M)

_{min}being the lowest water level causing flood damage; u represents the effect of the chosen policy on the loss estimates; p(H) is the exceedance probability of a given water level H; T is the planning period (i.e., 200 years), r the discount rate (3.5 percent per year).

## 4. Method

- Striving for overall risk reduction and neglecting hydraulic interactions,
- ibid, but accounting for hydraulic interactions, and
- also accounting for risk distribution.

#### 4.1. Policy Problem Formulations

#### 4.2. Generating Alternatives

#### 4.3. Evaluate Alternatives Under Uncertainty

#### 4.4. Evaluating Robustness Under Different Attitudes Towards Risk

## 5. Results

#### 5.1. Generating Alternatives

#### 5.2. Evaluating Robustness Under Different Attitudes Towards Risk

## 6. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Di Baldassarre, G.; Castellarin, A.; Brath, A. Analysis of the effects of levee heightening on flood propagation : Example of the River Po, Italy. Hydrol. Sci. J.
**2009**, 54, 1007–1017. [Google Scholar] [CrossRef] - Van Mierlo, M.C.L.; Vrouwenvelder, A.; Calle, E.O.F.; Vrijling, J.K.; Jonkman, S.N.; de Bruijn, K.M.; Weerts, A.H. Assessment of flood risk accounting for river system behaviour. Int. J. River Basin Manag.
**2007**, 5, 93–104. [Google Scholar] [CrossRef] - De Bruijn, K.M.; Diermanse, F.L.M.; Van Der Doef, M.; Klijn, F. Hydrodynamic system behaviour: Its analysis and implications for flood risk management. E3S Web Conf.
**2016**, 7, 11001. [Google Scholar] [CrossRef] - Vorogushyn, S.; Bates, P.D.; de Bruijn, K.; Castellarin, A.; Kreibich, H.; Priest, S.; Schröter, K.; Bagli, S.; Blöschl, G.; Domeneghetti, A. Evolutionary leap in large-scale flood risk assessment needed. Wiley Interdiscip. Rev. Water
**2017**, 5, 1–7. [Google Scholar] [CrossRef] - Directive 2007/60/EC of the European Parliament and of the council of October 23, 2007 on the assessment and management of flood risks. Off. J. Eur. Union
**2007**, L288, 27–34. - Orlandini, S.; Moretti, G.; Albertson, J.D. Evidence of an emerging levee failure mechanism causing disastrous floods in Italy. Water Resour. Res.
**2015**, 51, 7995–8011. [Google Scholar] [CrossRef] - Hansson, S.O. Philosophical problems in cost-benefit analysis. Econ. Philos.
**2007**, 23, 163–183. [Google Scholar] [CrossRef] - Kind, J.M. Economically efficient flood protection standards for the Netherlands. J. Flood Risk Manag.
**2014**, 7, 103–117. [Google Scholar] [CrossRef] - Eijgenraam, C.; Brekelmans, R.; Hertog, D.D.E.N.; Roos, K. Optimal Strategies for Flood Prevention. Manag. Sci.
**2017**, 63, 1644–1656. [Google Scholar] [CrossRef] - Brekelmans, R.; Den Hertog, D. Safe Dike Heights at Minimal Costs: The Nonhomogeneous Case. Oper. Res.
**2012**, 60, 1342–1355. [Google Scholar] [CrossRef] - Hayenhjelm, M. What Is a Fair Distribution of Risk. In Handbook of Risk Theory; Roeser, S., Hillerbrand, R., Sandin, P., Peterson, M., Eds.; Springer: Berlin, Germany, 2012. [Google Scholar] [CrossRef]
- Ciullo, A.; de Bruijn, K.M.; Kwakkel, J.H.; Klijn, F. Accounting for the uncertain effects of hydraulic interactions in optimising embankments heights: Proof of principle for the IJssel River. J. Flood Risk Manag.
**2019**. [Google Scholar] [CrossRef] - Kasprzyk, J.R.; Nataraj, S.; Reed, P.M.; Lempert, R.J. Many objective robust decision making for complex environmental systems undergoing change. Environ. Model. Softw.
**2013**, 42, 55–71. [Google Scholar] [CrossRef] - Coello Coello, C.; Lamont, G.B.; Van Veldhuizen, D.A. Evolutionary Algorithms for Solving Multiobjective Problems; Springer: Raleigh, NC, USA, 2007. [Google Scholar] [CrossRef]
- Silva, W.; Klijn, F.; Dijkman, J. Room for the Rhine Branches in the Netherlands. What the Research Has Taught Us; WL, Delft & RIZA: Arnhem, The Netherlands, 2001. [Google Scholar]
- Lammersen, R.; Kroekenstoel, D. Transboundary effects of extreme floods along the Rhine in Northrhine-Westfalia (Germany) and Gelderland (The Netherlands). In Floods, from Defence to Management; van Alphen, J., van Beek, E., Taal, M., Eds.; Taylor & Francis Group: London, UK, 2005; pp. 531–536. [Google Scholar]
- Lempert, R.J.; Popper, S.W.; Bankes, S.C. Shaping the Next One Hundred Years: New Methods for Quantitative, Long-Term Policy Analysis; MR-1626, RAND: Santa Monica, CA, USA, 2003. [Google Scholar]
- FLOODsite. Flood Risk Assessment and Flood Risk Management. An Introduction and Guidance Based on Experiences and Findings of FLOODsite (an EU-funded Integrated Project). Deltares Delft Hydraul. Available online: floodsite.net/html/partner_area/project_docs/T29_09_01_Guidance_Screen_Version_D29_1_v2_0_P02.pdf 140 (accessed on 29 November 2019).
- Van Schijndel, S.A.H. The planning kit, a decision making tool for the Rhine branches. In Proceedings of the 3rd International Symposium Flood Defence, Nijmegen, The Netherlands, 25–27 May 2005. [Google Scholar]
- De Grave, P.; Baarse, G. Kosten van Maatregelen: Informatie Ten Behoeve van Het Project Waterveiligheid 21e Eeuw (Deltares rep. 1204144-003). Available online: http://edepot.wur.nl/346748 (accessed on 29 November 2019).
- Kollat, J.B.; Reed, P.M. The value of online adaptive search: A performance comparison of NSGA-II, -NSGAII, and MOEA. In International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005). Lecture Notes in Computer Science; Coello Coello, C., Aguirre, A., Zitzler, E., Eds.; Springer: Berlin, Germany, 2005; pp. 389–398. [Google Scholar]
- Hadka, D.; Reed, P. Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework. Evol. Comput.
**2013**, 21, 231–259. [Google Scholar] [CrossRef] [PubMed] - Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C.M.; da Fonseca, V.G. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans. Evol. Comput.
**2003**, 7, 117–132. [Google Scholar] [CrossRef] - Giuliani, M.; Castelletti, A. Is robustness really robust? How different definitions of robustness impact decision-making under climate change. Clim. Chang.
**2016**, 135, 409–424. [Google Scholar] [CrossRef] - Kwakkel, J.H.; Eker, S.; Pruyt, E. How Robust is a Robust Policy? Comparing Alternative Robustness Metrics for Robust Decision-Making. In Robustness Analysis in Decision Aiding, Optimization, and Analytics; Springer: Singapore, 2016; pp. 221–237. [Google Scholar]
- McPhail, C.; Maier, H.R.; Kwakkel, J.H.; Giuliani, M.; Castelletti, A.; Westra, S. Robustness Metrics: How Are They Calculated, When Should They Be Used and Why Do They Give Different Results? Earth’s Futur.
**2018**, 6, 169–191. [Google Scholar] [CrossRef] - Wald, A. Statistical Decision Functions; Chapman & Hall: London, UK; New York, NY, USA, 1950. [Google Scholar]
- Hurwicz, L. An Optimality Criterion for Decisionmaking under Ignorance. In Uncertain. Expect. Econ. Essays Honour GLS Shackle; Augustus M. Kelley: New York, NY, USA, 1953. [Google Scholar]
- Kwakkel, J.H. The Exploratory Modeling Workbench: An open source toolkit for exploratory modeling, scenario discovery, and (multi-objective) robust decision making. Environ. Model. Softw.
**2017**, 96, 239–250. [Google Scholar] [CrossRef] - Gini, C. Measurement of Inequality nd Incomes. Econ. J.
**1921**, 31, 124–126. [Google Scholar] [CrossRef]

**Figure 1.**Transboundary case study area with the grey line representing the administrative border. Thick black lines represent dike-rings, i.e., dike-protected areas, with the code relative to each dike-ring reported within. Dots are breaching locations, with flooding at the red dots causing transboundary damage, i.e., damage in both countries. Beside the German Rhine, four branches are identified: Boven-Rijn (downstream the German Rhine, up to the bifurcation point), Waal, Pannerdensch-Kanaal (PK in the map), the Lek and the IJssel.

**Figure 3.**An example visualizing how relative risk reduction of two areas x and y following a policy A can be compared with respect to a situation of perfect equal distribution.

**Figure 4.**Results from the epsilon-NSGAII search under a reference scenario for the three problem formulations. By showing all policies from the three formulations together, a Pareto front across formulations can be identified (i.e., squares in both panels).

**Figure 5.**Spider diagram of the risk management measures of the four selected policies. Values refer to six areas: German territory and five major Dutch river branches, the Boven-Rijn, the Waal, the Pannerdensch-Kanaal, the Lek, and the IJssel. For each of these areas, dike heightening is expressed in terms of average increase in dike height, making room for the river as average water level reduction and flow diversion as change with respect to the initial diversion.

**Figure 6.**Evolution of the Pareto front across formulations for different risk attitudes (i.e., increasing risk aversion from bottom row to top row). Left: trade-offs between total costs in Germany and the Netherlands. Right: trade-off between efficiency and equity of the system.

Uncertainty | Water Level Triggering Failure | Final Breach Width | Breach Growth Rate |
---|---|---|---|

Values | Given by fragility curves at each location | Between 35 and 350 m | The final breach width can be reached in 1, 3, or 6 days |

**Table 2.**Values of uncertainties for the reference scenario under which many-objective optimization is carried out.

Water Level Triggering Failure | Final Breach Width | Breach Growth Dynamic |
---|---|---|

Water levels given by the fragility curves at a failure probability of 0.5 | The final breach width reaches a maximum width of 150 m | The final breach width is reached in 3 days |

**Table 3.**An example showing three fictitious risk reduction policies leading to uncertain residual damage (in Millions of euros) according to three different scenarios. The preferred policies according to the Minimax, Minimin, and two Hurwicz Criteria are underlined and highlighted in bold.

First Scenario | Second Scenario | Third Scenario | Minimin $(\mathbf{Hurwicz},\text{}\mathit{\lambda}=\text{}1)$ | Hurwicz $\mathit{\lambda}$ = 0.8 | Hurwicz $\mathit{\lambda}$ = 0.2 | Minimax ($\mathbf{Hurwicz},\text{}\mathit{\lambda}$ = 0) | |
---|---|---|---|---|---|---|---|

Policy 1 | 3 | 5 | 3 | 3 | 3.4 | 4.6 | 5 |

Policy 2 | 9 | 2 | 6 | 2 | 3.4 | 7.6 | 9 |

Policy 3 | 7 | 1 | 11 | 1 | 3 | 9 | 11 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ciullo, A.; De Bruijn, K.M.; Kwakkel, J.H.; Klijn, F. Systemic Flood Risk Management: The Challenge of Accounting for Hydraulic Interactions. *Water* **2019**, *11*, 2530.
https://doi.org/10.3390/w11122530

**AMA Style**

Ciullo A, De Bruijn KM, Kwakkel JH, Klijn F. Systemic Flood Risk Management: The Challenge of Accounting for Hydraulic Interactions. *Water*. 2019; 11(12):2530.
https://doi.org/10.3390/w11122530

**Chicago/Turabian Style**

Ciullo, Alessio, Karin M. De Bruijn, Jan H. Kwakkel, and Frans Klijn. 2019. "Systemic Flood Risk Management: The Challenge of Accounting for Hydraulic Interactions" *Water* 11, no. 12: 2530.
https://doi.org/10.3390/w11122530