International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Flood risk and economically optimal safety targets for coastal flood defense systems Dupuits, E. J. C (Guy); Schweckendiek, T. (Timo) Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Flood Risk And Economically Optimal Safety Targets For CoastalFlood Defense SystemsE.J.C (Guy) DupuitsPhD Student, Dept. of Hydraulic Engineering, Delft Univ. of Technology, Delft,NetherlandsT. (Timo) SchweckendiekLecturer, Dept. of Hydraulic Engineering, Delft Univ. of Technology, Delft, NetherlandsSr. researcher/consultant, unit Geo-engineering, Deltares, Delft, NetherlandsABSTRACT: A front defense can improve the reliability of a rear defense in a coastal flood defensesystem. The influence of this interdependency on the accompanying economically optimal safety targetsof both front and rear defense is investigated. The results preliminary suggest that the optimal safety levelof a coastal flood defense system can only be improved with a combination of front and rear defense iffor a similar risk reduction, the front defense investment is cheaper than the rear defense. If a case needsa more complex risk and economic optimization model, the simplified approach is no longer applicableand a computational framework is recommended. Nevertheless, the simplified approach offers a fast, firstorder assessment of the economically optimal safety targets for coastal flood defense systems.1. INTRODUCTIONCoastal flood defense systems can consist of a com-bination of defenses, sometimes even with multi-ple lines of defense. A typical combination, oftenfound in estuaries, is that of a barrier separatinga large water body (front defense) and levees sur-rounding the large water body (rear defense). Ex-amples of this type of coastal flood defense systemcan be found in Lake IJssel and the Eastern Scheldtin the Netherlands, and in Neva Bay, close to SaintPetersburg in Russia.A common type of interdependence is that thereliability of the rear defense depends on the relia-bility of the front defense. For example, a workingfront defense can reduce surge levels at the rear de-fense, leading to an improved reliability of the reardefense. Because flood risk is tightly coupled tothe economic optimization, this leads to possiblydiffering optimal safety targets. Therefore, interde-pendence can be an important factor (a) in analyz-ing the flood risk of the protected area and (b) inestablishing optimal safety targets for newly builtflood defenses in such systems.To the best of our knowledge, a generic methodthat describes the effect of interdependencies oneconomic optimal safety targets for coastal flooddefense systems has not yet been presented. Apromising case study using detailed numeric com-putations was done in Zwaneveld and Verweij(2014a). However, Zwaneveld and Verweij (2014a)focused on results for the Lake IJssel case: it is un-clear if the methods used by Zwaneveld and Ver-weij (2014a) are generically applicable. On theother hand, simplified cases with multiple layers ofdefense are described in Vrijling (2013), but thesefocus on the ‘multi-layer safety’ concept and do notcover our definition of a coastal flood defense sys-tem.The aim of this study is to assess the influence ofinterdependencies in a coastal flood defense systemon the accompanying economically optimal safetytargets. A simplified coastal system, similar to thecharacteristic cases in Vrijling (2013), is used todescribe the characteristics of this system. Thesecharacteristics are then used to provide the contoursof the optimal solution.112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Furthermore, the Galveston Bay near Houston iscontemplated as input for an example application.The Galveston Bay area has millions of people liv-ing in the region and represents a large economicvalue. It does not yet have an integral flood defensesystem, but the feasibility of such a system is be-ing investigated because it is situated in a hurricaneprone area (e.g. see Bedient and Blackburn (2012)).Finally, the limits of the simplified approach formore complex case studies is discussed. To thatend, we contemplate a more comprehensive nu-meric probabilistic risk analysis and optimizationframework in the spirit of Courage et al. (2013);Zwaneveld and Verweij (2014a), which is able tocope with a more detailed model than the previoussimplified coastal system.2. OPTIMIZATION OF A SIMPLIFIEDCOASTAL FLOOD DEFENSE SYSTEMThe effect of reliability interdependency betweenfront and rear defense on the flood risk and eco-nomically optimal safety targets is investigated bymeans of simplified model (Figure 1).Figure 1: Simplified cross section of a front defense (B)and rear defense (A).2.1. Risk and annual costsAssuming that that the two flood defenses in Fig-ure 1 have two states each (failure or non-failure),a total of four (22) system states are possible. InVrouwenvelder (2014), a mathematical representa-tion of Figure 1 is given. The main assumptionin this representation is that flooding of the hinter-land can only occur if the rear defense fails, whichmeans that the system states where the rear defensedoes not fail can be ignored as contributions to theflood risk. This means that the annual system fail-ure probability Psys is a summation of the two re-maining system states:Psys = PA∩B+PA∩B (1)where PA∩B is the state where both the front andrear defenses fail, and the PA∩B where just the reardefense fails.1Reformulating Eq. 1 in terms of conditionalprobabilities instead of intersections results inEq. 2. This notation is favorable as all terms canbe related to physical states of the system.Psys = PBPA|B+PBPA|B , (2)The total societal cost for flood defense systemsis the summation of investment cost and the riskcost. The annual risk cost (Crisk) of the flood de-fense system in Figure 1 can be characterized bymultiplying the annual system failure probabilityPsys with system state dependent flood damagesDA∩B andDA∩B (Vrouwenvelder, 2014). Both flooddamages are assumed to be positive and larger thanzero. The investment costs are split in investmentcosts per defense (CA andCB). The annual risk costsare shown in Eq. 3, while the total costs are shownin Eq. 4. In the latter equation, the present value(PV ) of the annual risk cost Crisk is used.Crisk = PBPA|BDA∩B+PBPA|BDA∩B (3)TC =CA+CB+PV (Crisk) (4)2.2. Economic optimization characteristicsThe optimal safety level is determined by mini-mizing the total costs in Eq. 4 (analogue to e.g.van Dantzig (1956); Eijgenraam (2006); Vrijling(2013)). Effectively, the optimal point on the totalcost curve denotes that a further increase in safetylevel is more expensive than the reduction in riskcosts.2.2.1. Optimization principles and assumptionsFor this paper, the flood damage in Eq. 3 will besolely based on economic damages, excluding lossof life and accompanying concepts such as individ-ual risk and societal risk. In a complete risk eval-uation these concepts should be included, as donein for example Jongejan et al. (2013), but are con-sidered out of scope for this paper. An overview of1The used notation of annual failure probabilities was cho-sen for brevity. A more correct notation of, for example, PA∩Bwould be P(FA∩FB).212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015risk acceptance measures can be found for examplein Jonkman et al. (2003).The determination of both repeated investments(their size and the duration between investments)and the timing of the initial investment is left outin this paper. The timing of the investments couldalso be a part of the optimization process, for exam-ple see Eijgenraam (2006), but are left out by ex-cluding time dependent processes such as sea levelrise or economic growth. It is assumed that theinitial investment is done immediately at the startof the strengthening project, and only the size ofthat initial investment is determined. These as-sumptions simplify the present value calculations,as only the annual flood risk needs to be discounted.The present value of a annual flood risk PsysD witha discount rate r (positive and larger than zero) overan infinite time horizon is a geometric sequence,which converges to Psys Dr ; see also for example vanDantzig (1956).2.2.2. Investment, failure probability and damageThe investment, failure probability and damage re-lations in Eq. 3 & 4 need to be specified in order tomake a non-trivial optimization of the system de-scribed in Figure 1.First, the annual failure probabilities in Eq. 2 aresimplified from annual probability of exceedanceof safety level to annual exceedance of crest levelhi, making the simplifying assumption that over-flow/overtopping is the dominant failure mecha-nism (analogue to van Dantzig (1956); Eijgenraam(2006) and specifically Vrijling (2013)). Further-more, we assume the annual extreme water level tofollow an exponential distribution with parametersα j ≥ 0 and β j > 0:Pj = 1−F (hi) = e−hi−α jβ j , (5)where subscript i is either A or B, which is theflood defense in question. Subscript j belongs tothe physical system state: this relates to a specificannual failure probability distribution. Specifically,flood defense A can be associated with the systemstates A (rear defense with no front defense), A∩B(rear defense with failed front defense), or A∩ B(rear defense with functioning front defense). Con-trary to this, flood defense B can only be associatedwith system state B.Second, the investment relations (CA and CB) arealso chosen similarly to for example van Dantzig(1956); Vrijling (2013) and assumed to be a linearfunction dependent of the crest level:Ci =C f ,i+Cv,ihi (6)where subscript i is either A or B, which relates tothe flood defense in question. Furthermore,C f ,i andCv,i (both assumed > 0) are consecutively the fixedand variable cost necessary to strengthen flood de-fense i to height hi.By rewriting Eq. 5 in terms of hi, Eq. 5 can besubstituted in Eq. 6. However, this is only straight-forward in case the subscripts i and j match, whichis only true for flood defense B. Substituting theseinvestment costs definitions in Eq. 4, leads to thefollowing expanded total cost definition:TC =C f ,A+Cv,AhA+C f ,B+Cv,B (αB−βB ln(PB))+PV (Crisk) (7)What remains are definitions for the flood dam-ages DB∩A and DB∩A of Eq. 3. These are assumedto be constant and equal for each outcome, i.e.DB∩A =DB∩A =D. These assumptions, and includ-ing discount rate r as mentioned in Section 2.2.1,lead to an updated definition of the total risk costs:PV (Crisk) =(PBPA|B+PBPA|B)Dr(8)2.3. Interdependency front and rear defenseEq. 7 & 8 contain conditional probabilities, whichrepresent the interdependencies between the frontand rear defense. The front defense is assumed tohave a positive influence on the unconditional fail-ure probability distribution of the rear defense (PA).Conceptually, the extent of this positive influence isassumed to be a function dependent on the front de-fense reliability. Using the conditional annual fail-ure probability PA|B as an example, this can be writ-ten down asPA|B = fred (PB) ·PA , (9)312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015where the upper limit of a conditional failure prob-ability would then be its unconditional failure prob-ability ( fred (PB) = 1). In theory, the lower limit offred (PB) is zero, which also implies PA|B = 0. How-ever, that would practically lead to no water (threat)between the two defenses in Figure 1. Therefore, itis assumed that the failure probability of the rear de-fense cannot be reduced to zero; instead, the max-imum reduction is assumed to be n. An exampleof such a conceptual relation describing fred (PB)could be a polynomial such as n+(1−n)P2B . Forsmall values of PB, fred (PB) can be approximatedwith the constant lower bound reduction n.2.3.1. Risk reduction rear defense for a non-failing front defenseA conservative assumption would be to assume thatonly in the case of a non-failing front defense, theperformance of the rear defense can improve. Us-ing the assumption of a constant reduction factorn, and only applying it to the conditional failureprobability PA|B, changes Eq. 8 to Eq. 10. Eq. 10is rewritten into Eq. 11 using PB = 1−PB.PV (Crisk) = (PBPA+PBnPA)Dr(10)PV (Crisk) = (PBPA+(1−PB)nPA)Dr(11)The reduction factor n has a lower limit of zeroand an upper limit of one. For the upper limit ofone, Eq. 11 reduces to∑Crisk = PADr . Since the up-per limit of one implies no reduction even with aworking front defense, the front defense does notcontribute to flood protection and falls out of theequation. This also has implications for the opti-mization: because if the front defense has no effect,the optimization reduces to an optimization of a sin-gle layer of defense.The (theoretical) lower limit of zero indicatesthat with a working front defense, the rear defensehas a failure probability of zero. This effectively re-duces the risk equation to only contain the systemstate where both front and rear defenses fail. Thiscase was investigated in Vrijling (2013) as ‘a twolayer system’, and the optimal solution was foundto only invest in the defense that has the lowest vari-able cost.2.3.2. Risk reduction rear defense for both a fail-ing and non-failing front defenseIt is conceivable that even if a front defense fails,the remnants of the front defense might still havea positive influence. This reduction can be addedin the same way as in the previous section, and iscalled m. However, we assume that a failed frontdefense is less effective at reducing failure proba-bilities than a non-failing front defense; this impliesthat reduction m has to be greater than n. The up-per bound is of m is one, just like n. This expandsEq. 11 to:PV (Crisk) = (PBmPA+(1−PB)nPA)Dr(12)2.4. Economic optimizationThe total costs of Eq. 7 with the PV (Crisk) defini-tion of Eq. 12, has three variables that need to beoptimized: PB, PA and hA. Eq. 5 is used to substi-tute PA, which reduces the number of optimizationvariables to PB and hA. The optimum of Eq. 7 canbe found by finding the partial derivatives ∂∂hATCand ∂∂PBTC. Equating these partial derivatives tozero leads to two expressions for optimal values ̂hAand ̂PB. The formulation for ̂PB is shown in Eq. 13.∂∂PBTC = 0→ ̂PB =Cv,BβBre−̂hA−αAβA D(m−n)(13)Because the constant reductions m and n bothuse the unaltered distribution parameters of PA, op-timal height ̂hA can immediately be substituted inEq. 5, resulting in an an optimal annual system fail-ure probability ̂Psys, as shown in Eq. 14.∂∂hATC = 0→ ̂hA → ̂Psys = e−̂hA−αAβA→ ̂Psys =Cv,AβArD(̂PB (m−n)+n) (14)The optimal solution for a single layer of de-fense, as mentioned in for example Vrijling (2013),is ̂PA,single =Cv,AβArD . Eq. 14 reduces to ̂PA,single incase m = n = 1; this agrees with the earlier state-ment made in Section 2.3.1.412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Eq. 13 & 14 are dependent on each other. It ispossible to remove this dependency by substitutingEq. 13 in Eq. 14 and vice versa:̂PB =1(mn −1)(βACv,AβBCv,B −1) (15)̂Psys =(βACv,A−βBCv,B)rnD(16)2.5. Limits of the optimal safety targetsBecause of the substitutions made in Eq. 15 & 16,additional bounds are in effect. The first boundfollows directly from Eq. 15 & 16: ̂PB and ̂Psysboth need to larger than zero, which implies thatβACv,A > βBCv,B. This can be explained as requir-ing that, for a similar risk reduction, the front de-fense investment needs to be cheaper than the reardefense. Failing to fulfill this requirement indicatesthat the combination of front and rear defense is lesseffective than a single rear flood defense.A second requirement can be found in Eq. 13 bystating that ̂Psys ≤ 1. Rewriting this leads a require-ment for ̂PB: ̂PB ≥̂PA,single−nm−n . This lower limit for̂PB can be used in setting both the upper and lowerlimits of Eq. 15. The found lower limit is combinedwith an upper limit of 1, and can be rewritten intoan upper and lower limit for n:̂PA,single(1−CBβBCAβA)≤ n≤ m(1−CBβBCAβA)(17)Substituting consecutively the lower and upperbound of Eq. 17 back in Eq. 16 for n, leads tôPsys = 1 and ̂Psys = 1m ̂PA,single. The former is a triv-ial consequence of the lower limit for ̂PB, whichwas found by setting the upper limit of ̂Psys to one.The latter is again a confirmation that when ̂PB = 1,̂Psys reduces to ̂PA,single; even though m is still in theequation, in this case m is most likely equal to one.Finally, another upper limit for ̂PB originatesfrom choosing constant reduction factors, instead ofreductions dependent on the reliability of the frontdefense. As mentioned in Section 2.3, this meansthe formulations in Eq. 15 & 16 are only accuratewhen the reduction relation is approximately con-stant.2.6. Behavior of the optimal safety targetsThe optimal value ̂PB in Eq. 15 is only dependenton the fractions mn andβACv,AβBCv,B . If the value ofβACv,AβBCv,Band/or mn increases, ̂PB will become smaller and ̂Psyswill be larger.A smaller value for βACv,AβBCv,B implies a larger̂PB anda smaller ̂Psys. However, although a small value formn does imply a large value for ̂PB, it does not giveinformation regarding the response of ̂Psys: a smallvalue of mn can be obtained as long as m and n areapproximately in the same order. This means n canbe either small or large, which consecutively leadsto ̂Psys becoming either larger or smaller.3. CASE STUDY: HOUSTON, TEXASIn this section, an application is shown of the simpleapproach in Section 2. The input will be providedby work from a real, ongoing case study in Hous-ton, Texas. However, the fundamental schemati-zation in Section 2 is over-simplified for this casestudy; therefore the results found in this section arepurely for illustration purposes.3.1. Area of interestThe area of interest is the Galveston Bay area nearHouston, Texas, which consists of a large bay withbarrier islands; see also Figure 2. The GalvestonBay area has millions of people living in the regionand represents a large economic value. It does notyet have an integral flood defense system, but thefeasibility is being investigated because it is situ-ated in a hurricane prone area (e.g. see Bedient andBlackburn (2012)).In order to apply the model in Section 2, fictivedefenses are placed in line with the barrier island(front defense) and near Eagles Point in Figure 2(rear defense). This rear defense will protect aneconomic value which protects a first order approx-imation of the entire bay area economic value. Eventhough the economic value on the barrier islands issignificant, it is ignored in this application.3.2. Risk modelingOf primary interest is the response of the water lev-els inside the bay, with respect to the fictional frontdefense. For this purpose, the bay area uses the512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015conceptual hydraulic model as proposed in Stoeten(2013). This hydraulic model simulates the hurri-cane surge and wind setup inside the bay. A frontdefense can influence the surge by reducing the in-flow into the bay. In case of a failing front defense,no reduction is applied (m = 1).In addition to the surge and wind setup cal-culated by the model of Stoeten (2013), signifi-cant wave heights at key points inside the bay arecalculated according to Breugem and Holthuijsen(2007). Finally, the surge levels and wave heightsinside the bay are combined into annual water levelexceedance probabilities, assuming earthen leveeswith a 1:6 front slope for the rear defense (only ac-counting for overflow/overtopping), and calculatedby means of Monte Carlo simulations.Figure 3 shows results for Monte Carlo simula-tions with each 5 · 104 runs. In this figure are fourgraphs, and shows the outside water level and threesituations inside the bay: no barrier (PB = 1), abarrier with a height of +1.5m MSL (‘Barrier 1’,PB ≈ 0.7), and a barrier at +2.5m MSL (‘Barrier 2’,PB ≈ 0.3). Preliminary tests with higher front barri-ers indicate no further significant reduction in fail-ure probabilities. This figure also shows that thereis not a constant reduction, but some dependency onthe front defense reliability; otherwise the barrierFigure 2: Map of Galveston Bay. Image and descrip-tion taken from Stoeten (2013), who modified an imagefrom ESRI, DeLorme, NAVTEQ (2013).configurations would have overlapped each other inFigure 3.Figure 3: Extreme annual water level exceedance prob-abilities outside and inside the bay for three front de-fense configurations. The large markers indicate failureprobabilities at a water level of 4.6 meter.The reductions n for the three barrier schemati-zations can be determined by finding the relativedifference in annual failure probability with respectto the ‘No barrier’ situation. Using the failure prob-abilities around a water level of 4.6 meter (i.e. largemarkers in Figure 3), reduction n for ‘No barrier’,‘Barrier 1’ and ‘Barrier 2’ is consecutively 1, 0.2and 0.05.However, contrary to the description of the con-ceptual reduction relations in Section 2.3, differentwater levels lead to significantly different reductionfactors. This means that the reductions in this caseare also dependent on the annual failure probabili-ties inside the bay, and that the the conceptual re-duction relation in Section 2.3 does not accuratelycapture the actual reduction relation in this case.This could be improved by applying separate re-duction relations that modify the distribution pa-rameters of the unconditional probability, insteadof applying the reduction relation to the uncondi-tional probability itself. On the other hand, thiswould also imply that the probabilities would needto have the same distribution (e.g. exponential dis-tribution).3.3. Economic optimizationThe previously mentioned dependency of the re-duction on the water levels inside the bay is consid-ered out of scope for this paper, and ignored in any612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015further calculation. Furthermore, because the max-imum reduction already occurs at a relative high PB(0.3), the formulations in Eq. 13 & 14 are used witha constant reduction n = 0.05. As mentioned ear-lier, no reduction will be applied in case of a failingfront defense (m = 1).Values regarding investment costs and flooddamage are loosely based on Stoeten (2013): C f =2 billion, Cv,A = 1.2 billion, D = 160 billion andCv,B = 0.5 billion. Furthermore, the discount ratiois set to 0.04.Lastly, the exponential distribution parametersfor front and rear defense were gained by fittingexponential distributions on the ‘Outside’ and ‘Nobarrier’ curve in Figure 3; these parameters arerough estimates and estimated to be αB = 2.6m,βB = 0.51m, αA = 4.6m and βA = 1.0m.Using these values in Eq. 15 & 16 leads to theoptimal values ̂PB = 1.4 ·10−2 and ̂Psys = 4.7 ·10−3.In comparison, the optimal value for a single line ofdefense is ̂PA,single = 3.0 ·10−4.However, this does not necessarily tell which ofthe two defense strategies is the optimal choice yet,because the fixed costs and displacement parame-ters (α’s) do not influence Eq. 15 & 16, but do in-fluence the total costs (e.g. see Eq. 7). Therefore, afinal check which compares the total cost of a frontand rear defense with the total cost a single defenseneeds to be done. The total cost of a single lineof defense is C f ,A +Cv,ÂhA,single + ̂PA,single Dr , andamounts to C f ,A + 16.5 billion. The total cost ofa front and rear defense with the found optimal val-ues is C f ,A+C f ,B+15.5 billion.In conclusion, for the previously mentioned val-ues and depending on the extra fixed cost for a frontdefense, the combination of front and rear defensepreliminary appears to be cheaper and thus the op-timal choice.4. OUTLOOKThe simplified approach in the previous sectionprovides valuable insight into the mechanisms driv-ing the schematization of Figure 1 and the resultingoptimization. However, for a practical application,the simplified approach has its limits. These limitscan be found both in the implicit and explicit as-sumptions/simplifications made in Section 2:• Economic optimization assumptions regardingthe frequency and timing of investments (onlyonce and immediately), and the exclusion oftime dependent processes• Potential damage D is assumed to be constant.In some cases this might be a good model, butdepending on the geography of the hinterlandand the intensity of the flooding, a different,smaller damage might occur.• The used schematization where only the reardefense protects against potential damage D:more complex flood defense systems can exist,with each system having its own distinct flooddamage.For a single layer of defense, concepts such assea level rise, economic growth, (initial) waiting pe-riod and repeated investments have been discussedfor analytical solutions by for example Vrijling andvan Beurden (1990); Eijgenraam (2006). However,especially when all items mentioned above needto be considered, a computational framework be-comes a more attractive option.For example, in Zwaneveld and Verweij (2014a)and Zwaneveld and Verweij (2014b) such a numer-ical approach is discussed. Inspired by this work,a high level overview of the steps involved in boththe risk and economic models is shown in Figure 4.In this figure, the risk steps (schematization, phys-ical model & probabilistic estimation) are purpose-fully displayed inside the economic optimization.The economic optimization calls various sourcesand parameters which can be delivered either by theoutcome of the sequence of risk steps (i.e. failureprobabilities), or by the intermediate steps. For in-stance, the heights of the flood defense are relevantboth for physical model (determine risk), as wellas the economic optimization (investment costs). Ifthe risk model is coupled to damage models as well,risk costs can be obtained directly and can also beused in Zwaneveld and Verweij (2014b). These canbe obtained using a computational framework in thespirit of for example Courage et al. (2013).5. CONCLUSIONSThe work in this paper was done to understand char-acteristics of the economic optimization of coastalflood defenses, as shown in Figure 1. This was712th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Figure 4: Steps involved in the computational frame-work for economically optimal safety targets.done by deriving formulations based on a simpli-fied economic optimization of a simplified coastaldefense system. The formulas indicate that the opti-mal safety level of the system can only be improvedwith a combination of front and rear defense if for asimilar risk reduction, the front defense investmentis cheaper than the rear defense.The case study showed that the formulations de-scribing the optimal values can give answers withrelatively little effort. However, the application alsoshowed that the proposed conceptual reduction re-lation only partially describes the case study’s re-duction relation between front and rear defense.This and other issues regarding the model need tobe addressed in future work, for example by extend-ing the simplified model. However, for more com-plex cases (either in number of flood defenses, riskmodeling, damage modeling, or number and type ofeconomic optimization variables) a computationalframework is a better choice.Nevertheless, this study captures the interdepen-dency of a front defense being capable of improvingthe reliability of the rear defense in a set of trans-parent economic optimization formulations. Thesecan be used as a first order estimate in finding out ifwhat the optimal safety targets of a coastal flood de-fense system are, and whether or not such a systemcould be the economic optimal choice.6. ACKNOWLEDGEMENTSThe authors would like to thank Kasper Stoeten forhis support in sharing and discussing the probabilis-tic hurricane surge model, and Prof. Matthijs Kokfor his guidance and insightful discussions. We arealso grateful for the financial support of the DutchTechnology Foundation STW, which is part of theNetherlands Organization for Scientific Research,and which is partly funded by the Ministry of Eco-nomic Affairs.7. REFERENCESBedient, P. and Blackburn, J. (2012). Lessons from Hur-ricane Ike. Texas A&M University Press.Breugem, W. and Holthuijsen, L. (2007). “GeneralizedShallow Water Wave Growth from Lake George.”Journal of Waterway, Port, Coastal, and Ocean En-gineering, 133(3), 173–182.Courage, W., Vrouwenvelder, T., van Mierlo, T., andSchweckendiek, T. (2013). “System behaviour inflood risk calculations.” Georisk: Assessment andManagement of Risk for Engineered Systems andGeohazards, 7(2), 62–76.Eijgenraam, C. (2006). “Optimal safety standards fordike-ring areas.” Report No. 62, CPB, The Hague.Jongejan, R., Maaskant, B., ter Horst, W., Havinga, F.,Roode, N., and Stefess, H. (2013). “The VNK2-project: a fully probabilistic risk analysis for all majorlevee systems in the Netherlands.” Floods: From Riskto Opportunity (IAHS Publ. 357), Vol. 2005, IAHSPress, 75–85.Jonkman, S., van Gelder, P., and Vrijling, J. (2003). “Anoverview of quantitative risk measures for loss of lifeand economic damage.” Journal of Hazardous Mate-rials, 99(1), 1–30.Stoeten, K. (2013). “Hurricane Surge Risk ReductionFor Galveston Bay.” M.sc. thesis, M.sc. thesis (Octo-ber).van Dantzig, D. (1956). “Economic Decision Problemsfor Flood Prevention.” Econometrica, 24(3), 276–287.Vrijling, J. (2013). “Multi layer safety.” Safety, Reliabil-ity and Risk Analysis, CRC Press, 37–43.Vrijling, J. and van Beurden, I. (1990). “Sealevel rise:a probabilistic design problem.” Coastal EngineeringProceedings, 1160–1171.Vrouwenvelder, A. (2014). “Normstelling b-keringen.Private communication, TNO note.Zwaneveld, P. and Verweij, G. (2014a). “Economischoptimale waterveiligheid in het IJsselmeergebied.”Report No. 10, CPB, The Hague.Zwaneveld, P. J. and Verweij, G. (2014b). “Safe DikeHeights at Minimal Costs.” Report no., CPB, TheHague.8

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