Robustness of economically efficient flood protection standards

A combination of Monte Carlo and cost-benefit analysis

for more information

Deltares, Department of Strategic Studies and Innovation Management

= St* / Vt = St* / Vt = St* / Vt

Introduction

Flooding is a serious threat for The Netherlands. Dikes and dunes have to provide minimum levels of protection specified by law. Today’s flood protection standards are 50 years old and will soon be updated. This is one of the objectives of the project ‘Flood protection for the 21st Century’ (Waterveiligheid 21e eeuw, WV21), carried out by the Dutch Government.

As part of WV21 a social cost-benefit analysis (SCBA) was performed to calculate economically efficient flood protection standards. The results of the SCBA will support the political decision makers who are responsible for the update of the protection standards.

OptimaliseRing

In the SCBA a dynamic optimization model, OptimaliseRing, has been used. The model determines the optimal investment strategy for dike reinforcements. In the optimal strategy, the sum of discounted investment cost and residual flood damages over a long time horizon is minimized, taking into account economic growth and climate change. In a second step, economically efficient flood protection standards for each dike ring area are derived from the optimal investment strategy. The SCBA concludes that for dike ring areas along the rivers Rhine and Meuse, existing protection standards are low compared to economically efficient levels. On the other hand, for the northern and south-western part of the Netherlands existing standards are rather high, see figures 1 and 2.

Direct approach

It turns out that the economically efficient flood protection standards determined by OptimaliseRing can be closely approximated by a simple shortcut formula depending only on the ratio of flood damage to the cost of increasing protection (see Eijgenraam, 2006).

The economically efficient flood protection standard at time t

(Popt_t) is by definition equal to the optimal level of flood risk (S_t*)

divided by the damage in case of flooding in year t (V_t):

The optimal level of flood risk can be approximated by the following

shortcut formula:

where:

= discount rate

= Investment cost for a reduction of the flood probabability by a factor 10.

Figure 1: Existing legal flood protection standards per

dike ring area

Figure 2: Economically efficient flood protection standards

(result from the SCBA)

100 1000 10000 100000 1000000 65-1: Arcen 68-1: Venlo-Velden Noord 86-1: Maasband 87-1: Meers 40-2: Heerenwaarden-Maas 9-1: Vollenhove 13-b-1: Marken

36-1: Land van Heusden/de Maaskant

36-a-1: Keent 37-1: Nederhemert 38-1: Bommelerwaard-W aal 38-2: Bommelerwaard-Maas 39-1: Alem

41-1: Land van Maas en

W

aal-W

aal

41-2: Land van Maas en

W aal-Maas 42-1: Ooij en Millingen 43-1: Betuwe, T ieler- en Culemborgerwaarden 44-1: Kromme Rijn-Rijn

44-2: Kromme Rijn-Meren 45-1: Gelderse

Vallei-Rijn 45-2: Gelderse Vallei-Meren 46-1: Eempolder 47-1: Arnhemse- en Velpsebroek 48-1: Rijn en IJssel-Boven 48-2: Rijn en IJssel-Beneden

49-1: IJsselland 50-1: Zutphen 51-1: Gorssel

52-1: Oost Veluwe 53-1: Salland 1-1: Schiermonnikoog 2-1: Ameland 3-1: Terschelling 4-1: Vlieland 10-1: Mastenbroek 11-1: IJsseldelta 15-1: Lopiker- en Krimpenerwaard 16-1: Alblasserwaard en de Vijfheerenlanden 21-1: Hoekse W aard

22-1: Eiland van Dordrecht

24-1: Land van Altena 34-1: W est-Brabant 34-a-1: Geertruidenberg 35-1: Donge 40-1: Heerenwaarden-W aal 5-1: Texel

6-1: Friesland-Groningen-Lauwersmeer 6-2: Friesland-Groningen-Groningen _{6-3: Friesland-Groningen-NoordFriesland} 6-4: Friesland-Groningen-IJsselmeer

7-1: Noordoostpolder 8-1: Flevoland-Noordoost 8-2: Flevoland-Zuid W est 12-1: Wieringen 17-1: IJsselmonde 20-1: Voorne-Putten-W est 20-2: Voorne-Putten-Midden 20-3: Voorne-Putten-Oost 25-1: Goeree-Overflakkee-Noordzee _{25-2: Goeree-Overflakkee-Haringvliet} 26-1: Schouwen Duiveland-W est 26-2: Schouwen Duiveland-Oost 27-1: Tholen en St. Philipsland 28-1: Noord-Beveland 29-1:

W alcheren-W est 29-2: W alcheren-Oost 30-1: Zuid-Beveland-W est 31-2: Zuid-Beveland-Oost 32-1: Zeeuwsch Vlaanderen-W est 32-2: Zeeuwsch Vlaanderen-Oost 13-1: Noord-Holland-Noord 13-2: Noord-Holland-W estfriesland 13-4: Noord-Holland-W aterland 14-1: Zuid-Holland-Kust 14-2: Zuid-Holland-Nwe W aterweg-W est 14-3: Zuid-Holland-Nwe W aterweg-Oost 18-1: Pernis 19-1: Rozenburg

optimal return period (year)

Figure 3: 80% confidence intervals for the economically efficient flood protection standards, following the results from the Monte Carlo analysis. Circle: mean value;

solid horizontal lines: existing flood protection standard.

= St* / Vt

Monte Carlo analysis

Approach

The calculation of economically efficient flood protection standards in the SCBA (see figure 2) is based on many uncertain variables related to costs and (avoided) flood damage. This raises the question of how robust these standards are. Confidence intervals can be determined using a Monte Carlo analysis. The full optimization model is unsuitable for this analysis since its computation time is too long. Therefore the ‘direct approach’ has been used. The Monte Carlo analysis has been performed using equations [1] and [2], augmented by uncertainty factors. For those factors probability distributions were estimated by experts.

Adding the uncertainty factors equation [1] becomes:

= St* / Vt

and equation [2]:

= St* / Vt

F1 Discount rate Triangle % per year 5.50 4.00 7.00

F2a Investment cost Triangle

F2b Dependency on upstream measures Uniform

F3a Effect a dike increase on flood probability: statistical errors Triangle factor 1.00 0.80 1.20

F3b Effect a dike increase on flood probability: method and assumptions Triangle

F4a Direct damages, given inundation Triangle factor 1.00 0.80 1.10

F4b Inundation pattern PERT factor 1.00 0.40 3.00

F5 Factor on direct damage (to include indirect damages etc.) Triangle factor 1.25 1.60 1.95

F6 Percentage of population evacuated Discrete

F7 Population affected PERT factor 1.00 0.40 3.00

F8 Mortality functions PERT factor 1.00 0.00 3.00

F9 Value of a Statistical Life Triangle million euro 6.70 1.40 11.30

F10 Value of Evacuation Triangle thousand euro 12.00 3.00 24.00

F11 Economic growth 2011 - 2050 Lognormal factor 2.08 0.19

Correlation: F2b and F3b (positive) F4b and F7 (full) F7 and F6 (negative) F7 and F8 (positive) F6 and F8 (negative)

specified per dike ring area specified per dike ring area specified per dike ring area

specified for different areas

min max standard

deviation

Uncertain parameter Type of distribution Unit most

likely 0.71 -0.43 -0.21 -0.20 0.18 0.17 0.13 -0.10 0.10 0.10 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 F4b - Inundation pattern F2a Investment cost F6 - Percentage of population evacuated F1- Discount rate F8 - Mortality function F11 - Economic growth F5 - Factor on direct damage F3a - Effect of dike increase, statistcal errors F4a - Direct damages, given inundation F9 - VOSL

Coefficient Value

Figure 4: Coefficient values for dike ring area 8-1 Table 1: Variables in the Monte Carlo analysis and their distribution

[1]

[2]

[3]

[4]

Results

Figure 3 shows the 80% confidence intervals for the

economically efficient flood protection standards. Intervals are large, on average a factor 5 between the minimum and maximum economically efficient protection standards.

Figure 4 shows as an example the contribution of the 10

most important variables to the total uncertainty for dike ring area 8-1. Here, the contribution of the uncertainty of the extent of the inundated areas is the largest, followed by the uncertainty of cost estimates.

Cost-benefit analysis

Monte Carlo analysis has been used to test the robustness of economically efficient flood protection standards calculated by a SCBA. The confidence intervals are relatively large, mainly due to uncertainties related to flood damage. Nonetheless, the relative order of efficient protection standards of dike ring areas is robust. The large uncertainties should be recognized while drawing policy conclusions from the SCBA.

Conclusions

Jarl Kind1, Johan Gauderis2 and Rianne van Duinen1 1 Deltares, Netherlands

2 RebelGroup Advisory Belgium nv

Jarl Kind1, Johan Gauderis2 and Rianne van Duinen1 1 Deltares, Netherlands

2 RebelGroup Advisory Belgium nv

References: Kind, J., 2011. Maatschappelijke kosten-batenanalyse Waterveiligheid 21e eeuw. Deltares, Delft Gauderis, J., J. Kind en R. van Duinen. Maatschappelijke kosten-batenanalyse Waterveiligheid 21e eeuw. Bijlage G: Monte Carlo-analyse. Deltares, Delft Eijgenraam, C.J.J., 2006. Optimal safety standards for dike-ring areas. CPB Discussion Paper 62, CPB, Den Haag

Robustness of economically efficient flood

protection standards

A combination of Monte Carlo and cost-benefit analysis

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