Economic optimisation of flood risk management projects

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Economic optimisation of flood risk

management projects

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof.ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op donderdag 3 september 2015 om 12:30 uur

door

Vaia TSIMOPOULOU

Civiel Ingenieur, Aristoteles Universiteit van Thessaloniki, Griekenland Master of Science Waterboukunde, Technische Universiteit Delft

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This dissertation has been approved by the promotor: Prof.drs.ir. J.K. Vrijling

copromotor: ir. H.J. Verhagen

Composition of the doctoral committee: Rector Magnificus

Prof.drs.ir. J.K. Vrijling, promotor Civil Engineering & Geosciences, TU Delft ir. H.J. Verhagen, copromotor Civil Engineering & Geosciences, TU Delft Independent members:

Prof.dr.ir. P.H.A.J.M. van Gelder Technology, Policy & Management, TU Delft Prof.dr.ir. S.N. Jonkman Civil Engineering & Geosciences, TU Delft Prof. A. Kortenhaus University of Ghent, Belgium

Dr.ir H.G. Voortman ARCADIS Nederland BV Dr. T. Yasuda University of Kyoto, Japan

Substantial support was also offered by Prof. M. Kok

Published by Delft Academic Press ISBN: 97890-6562-3805

vanatsimop@gmail.com

This dissertation was financially supported by:

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Summary

The Netherlands has developed a flood risk management policy based on an economic rationale. After the flood disaster of 1953, when a large area of the south-western part of the country was flooded and more than 1800 people lost their lives, the so-called Delta Committee was installed, whose main purpose was to coordinate actions towards a drastic reduction of flood risk. A key element of the Delta Committee’s recommendations, which formed the foundation of the current flood risk management policy in the Netherlands, was the determination of protection standards for all major levee systems in the country, determined as overtopping probabilities of flood defences, and derived by means of cost-benefit analysis. This facilitated the realization of significant investments of capital in flood protection. In the 1990s the use of cost-benefit analysis became mandatory for the evaluation of all public investments in the Netherlands. This means that the rationale adopted in the 50s is not likely to be substantially changed in the coming decades.

Despite the significant steps that were taken by implementing the recommendations of the Delta Committee, there is still space for improvements in the Dutch flood risk management policy. First of all, the heterogeneity of failure properties along the dyke-rings and of consequence patterns in the protected areas could be more comprehensively considered. Secondly, within the framework of an adaptable policy, there are issues that still need to be thoroughly studied, like the effect that budget constraints may have on the economic efficiency of protection standards. Thirdly, in light of increasing concerns for the potential consequences of flooding in the Netherlands, new protection standards could be determined taking into account investments in multi-layer safety. That is investments not only in flood prevention measures, but also in measures for the mitigation of losses due to flooding. Fourthly, explicit restrictions for the acceptable risk of loss of life could be provided on the basis of social and not only economic criteria, which is currently the case. Acknowledging the need for improvements, the Dutch Government has already ordered an update of the national flood risk management policy.

The main objective of this dissertation is to investigate how the four aforementioned points could be addressed and accommodated in the Dutch flood risk management policy, while respecting the preservation of cost-benefit analysis as a vehicle for supporting decisions upon investments in flood protection. In particular, methods are

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developed for the identification of decisions that are economically optimal, hence in line with a cost-benefit rationale, when the conditions entailed in the aforementioned points are present. A second objective is to investigate the conditions under which investments in multi-layer safety are more economically appealing than investments in flood prevention only. These objectives are met in chapters 2-9. The content of each chapter is described below.

Chapter 2 provides background information on the methods that are used worldwide for the formulation of public safety regulations, the pros and cons of cost-benefit analysis, and the features of economic decision problems in flood risk management. In the end an inventory of economic decision problems that are relevant in flood risk management is presented. In that inventory the problems that are compatible with the economic rationale of cost-benefit analysis are indicated. Based on this analysis the economic decision problems that are further investigated in this dissertation are clarified. Such a clarification increases understanding of the overall function of the methods presented in latter chapters, while it is important for avoiding methodological inconsistencies in the use of cost-benefit analysis.

Chapter 3 focuses on the economic optimisation of flood prevention systems. Using analytical approaches, economically optimal design specifications are derived for this type of systems. The analysis starts with a very simple system, i.e. a homogeneous dyke-section with one failure mechanism. Then more complex features are gradually added, i.e. multiple failure mechanisms, multiple homogeneous dyke-segments, and consequences that vary depending on the dyke-segment that fails. This is done by following a systems approach, where failure mechanisms and homogeneous dyke-segments are treated as components of a series system. In every stage of the analysis optimisation formulae are derived, which show that the optimal designs are always proportional to the marginal costs of flood-control measures and inversely proportional to the protected economic values. In the cases of multiple failure mechanisms and multiple homogeneous sections the derived formulae constitute upper and lower bounds of the optimal failure probabilities, which show that the stronger the dependence among different failures, the lower the economically optimal failure probabilities. Regarding the optimal flooding probability in the system, the results indicate that the dependence of failures may not influence its value significantly. To that end, further research is recommended.

Chapter 4 focuses on the economic optimisation of multi-layer safety systems. In this chapter a line of thought similar to that of chapter 3 is followed. In particular, using analytical approaches, economically optimal design specifications are derived for multi-layer safety systems with two and three safety multi-layers. For the sake of simplicity, only one measure is considered per safety layer. The analysis starts with an introduction of the possible schematizations of multi-layer safety. Then the analytical optimisation of systems with two and three layers is presented, and formulae are derived for the optimal failure probability per safety layer. Just like in chapter 3, the derived formulae reveal that the optimal failure probabilities of safety layers are proportional to their marginal costs and inversely proportional to the economic values that they protect. Apart from this, it is clarified when it is more likely for a system with multiple safety layers to be more economically attractive than a prevention system. This proves to be the case primarily when the marginal cost of layer 1 gets much higher than that of higher safety layers, and secondarily when the economic value protected by multiple layers increases The analytical outcomes are validated through numerical tests in a variety of cases, where the possibility to invest in three safety layers is considered. Despite validation of the analytical results, the numerical tests indicate additional

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conditions that affect the likelihood of optimality of multi-layer safety, namely the increase of mortality rate in case of flooding and the occurrence of extreme loads that resemble typhoons and tsunamis.

Chapter 5 investigates how budget constraints and high safety requirements for human life can influence the optimal design of both prevention and multi-layer safety systems. The analysis refers to the same system layout as the one known from chapter 4, while a similar line of thought is followed. That is that the optimal designs are derived first with the use of analytical approaches, and the results are then validated through numerical tests. The analysis starts with the analytical optimisation under budget constraints. It continues with the optimisation of the same system given a safety constraint that corresponds to a lower risk to human life than that in the economically optimal solution. Then a number of numerical tests are performed, showcasing the sensitivity of the optimisation results to different budget and safety constraints. Regarding budget constraints, the analysis proves that the lower the available budget the more likely it is for multi-layer safety to be more economically attractive than prevention, while this likelihood may be increased in tsunami- and typhoon-prone areas. Regarding safety constraints, the analysis indicates that the higher the safety requirement for human life, the more likely it is for multi-layer safety to be preferred over prevention. In the end, the influence of constraints on the cost-effectiveness of investment strategies is investigated, which shows that safety layer 3 (i.e. emergency management) is more cost-effective when there are budget constraints than when there are safety constraints. Chapter 6 presents an analysis that indicates how uncertainty in the estimated costs of flood control measures can influence the result of an economic optimisation. This uncertainty is introduced in the form of random variables in the total cost function. Subsequently a Monte Carlo simulation is performed, indicating how robust an investment strategy is, i.e. how likely it is for a strategy chosen as optimal when uncertainties were not considered, to be overtaken by another strategy after uncertainties are introduced. The analysis is performed for three cases of systems, where multi-layer safety with layers 1 and 3 proved to be optimal in chapter 5. The results of the analysis indicate that uncertainty is one of the parameters that can prevent the optimality of multi-layer safety.

In Chapter 7 the theory of chapter 3 is used for the determination of economically optimal protection standards in the Netherlands. In particular, it is presented how to incorporate information about the Dutch dyke-rings provided by the national flood risk analysis project VNK2, in the analytical optimisation approach of chapter 3. The suggested procedure shows that the consideration of simultaneous failures in different parts of a dyke-ring in the Netherlands has minor influence on the optimisation results. In Chapter 8 a descriptive analysis is presented on the response of the multi-layer safety systems of Tohoku in Japan during the Great Eastern Japan Earthquake and Tsunami on March 11, 2011. This analysis shows in a practical manner why the failure probability of flood defences, i.e. layer 1 measures, needs to be lower than that of measures of higher safety layers, validating the boundary conditions used in the optimisations of chapter 4.

In Chapter 9, the theory of chapter 4 is used for the determination of an economically optimal multi-layer safety design for Rikuzentakata, a town in Tohoku that was entirely destroyed in 2011. This confirms the applicability of the optimisation model presented in chapter 4. In Chapter 10 conclusions are summarized.

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Samenvatting

Translation by Mariette van Tilburg

Nederland heeft een overstromingsrisicobeleid ontwikkeld op basis van een economische grondslag. Na de rampzalige overstromingen van 1953, toen een groot deel van het Zuidwestelijke deel van het land werd overstroomd en meer dan 1800 mensen hun leven verloren, werd de zogenaamde Delta Commissie in het leven geroepen, met als belangrijkste doel om het overstromingsrisico te verminderen. Het kernelement van de aanbevelingen van de Delta Commissie, die de basis vormden voor het huidige overstromingsrisico beleid in Nederland, was de vaststelling van normen voor de bescherming voor alle grote waterwerken in het land, bepaald door de waarschijnlijkheid van overstroming en afgeleid door middel van een kosten-batenanalyse. Dit maakt de realisatie van aanzienlijke investeringen van kapitaal in bescherming tegen overstromingen mogelijk. In de jaren negentig werd in Nederland het gebruik van kosten-batenanalyse verplicht voor de evaluatie van alle publieke investeringen. Dit betekent dat de grondgedachte uit de jaren vijftig in de komende decennia niet wezenlijk zal veranderen.

Ondanks de belangrijke maatregelen die werden genomen door de uitvoering van de aanbevelingen van de Delta-Commissie, is er ruimte voor verbetering in het Nederlandse overstromingsrisico beleid. Ten eerste, de heterogeniteit van de eigenschappen van fouten, en de patronen in de beschermde gebieden die daar het gevolg van zijn, zouden uitvoeriger in beschouwing moeten worden genomen. Ten tweede, binnen het kader van een flexibel beleid, zijn er problemen die om diepgaander studie vragen, zoals het effect dat budgettaire beperkingen kan hebben op de economische efficiëntie van beschermingsnormen. Ten derde, in het licht van toenemende bezorgdheid over potentiele gevolgen van overstromingen in Nederland, zou een nieuwe standaard van beschermingsmaatregelen met betrekking tot meerlaagse veiligheid in acht moeten worden genomen. Ten vierde, expliciete beperkingen over het aanvaardbaar risico van verlies van menselijk leven zouden moeten worden geformuleerd op basis van sociale criteria, niet slechts op economische, zoals momenteel het geval is. In het erkennen van de noodzaak voor verbetering heeft de Nederlandse regering een update vereist van het huidige nationale risico en overstromingsbeleid.

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De belangrijkste doelstelling van dit proefschrift is te onderzoeken hoe de vier bovengenoemde punten kunnen worden aangepakt en ondergebracht in het Nederlandse overstromingsrisico beleid, met inachtneming van het behoud van een kosten-batenanalyse als middel in besluitvorming op investeringen in de bescherming tegen overstroming. In het bijzonder worden methoden ontwikkeld voor de identificatie van economisch optimale besluitvorming, in lijn met een kosten-batenanalyse, waarin de voorwaarden van bovengenoemde punten aanwezig zijn. Een tweede doel is te onderzoeken onder welke voorwaarden investeringen in een meerlaagse veiligheid economisch aantrekkelijker zijn dan investeringen in preventie van slechts overstromingen. In de hoofdstukken 2-9 worden deze doelstellingen bereikt. De inhoud van elk hoofdstuk wordt hieronder beschreven.

In hoofdstuk 2 wordt achtergrondinformatie gegeven over de methoden die wereldwijd gebruikt worden voor de formulering van de verordeningen van openbare veiligheid, over de voor- en nadelen van kosten-batenanalyse, en over de kenmerken van besluitvorming op het gebied van economische problemen in overstromingsrisico-management. Een inventarisatie van de economische besluitvormingsproblemen die relevant zijn voor overstromingsrisico-management wordt gepresenteerd. In deze inventarisatie worden de problemen aangegeven die verenigbaar zijn met de economische grondslag van een kosten-batenanalyse. Op basis van deze analyse wordt de economische besluitvormingsproblematiek verduidelijkt en een inzicht verkregen in de functie van de methoden, welke van belang is voor het vermijden van methodologische inconsistenties in het gebruik van de kosten-batenanalyse.

Hoofdstuk 3 richt zich op de economische optimalisatie van de systemen voor de preventie van overstroming. Met behulp van analytische benaderingen, zijn economisch optimale ontwerpspecificaties afgeleid voor dit type systemen. De analyse begint met een zeer eenvoudig systeem, zoals een homogene sectie van een dijk met slechts één faal-mechanisme. Vervolgens worden geleidelijk aan meer complexe functies toegevoegd, o.a. meerdere faal-mechanismen, meerdere homogene secties van een dijk, en gevolgen die variëren afhankelijk van het segment van de dijk dat faalt. Dit wordt gedaan volgens een systeembenadering, waarin de faal- mechanismen en de homogene secties van een dijk worden behandeld als onderdelen van een reeks van systemen. In ieder stadium van de analyse worden optimaliseringsformules afgeleid, die aantonen dat optimaal ontwerp altijd proportioneel is tot de marginale kosten van overstromingsmaatregelen en tegenovergesteld proportioneel tot de beschermde economische waarden. In de gevallen van meerdere faalmechanisme en meerdere homogene secties, vormen de afgeleide formules een boven en beneden grens van de optimale stochastische mislukking, hetgeen aantoont dat, hoe sterker de afhankelijkheid is van de diverse mislukkingen, hoe lager de waarschijnlijkheid van economisch optimale mislukking. Met betrekking tot de optimale overstromingswaarschijnlijkheid binnen het systeem, tonen de resultaten dat afhankelijkheid van mislukking niet van noemenswaardige invloed is op de waarde. In dit opzicht wordt diepgaander onderzoek aangeraden.

Hoofdstuk 4 richt zich op de economische optimalisatie van meerlaagse veiligheidssystemen. In dit hoofdstuk wordt een zelfde gedachte gevolgd als in hoofdstuk 3. Met behulp van analytische benaderingen worden economisch optimale ontwerp-specificaties afgeleid voor meerlaagse veiligheidssystemen, met twee en drie lagen van de veiligheid. Omwille van de eenvoud, wordt slechts een maatregel per laag van de veiligheid overwogen. De analyse begint met een inleiding van de mogelijke schematisering van meerlaagse veiligheid. Vervolgens wordt de analytische optimalisatie van systemen met twee en drie lagen gepresenteerd, en de voorwaarden voor de selectie van de optimale combinatie van veiligheidslagen worden aangegeven.

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Evenals in hoofdstuk 3, geven de afgeleide formules aan dat de waarschijnlijkheid van optimale mislukking van veiligheidslagen proportioneel is tot hun marginale kosten en tegenovergesteld tot de economische waarden die zij beschermen. Los van dit wordt ook aangetoond dat een meerlaags veiligheidssysteem economisch aantrekkelijker is dan een systeem van preventie. Dit is ten eerste het geval indien de marginale kosten van laag 1 veel hoger worden dan de kosten van hogere veiligheidslagen, en ten tweede wanneer de economische waarde toeneemt die door de meerdere lagen beschermd wordt. De analytische resultaten worden gevalideerd door numerieke proeven in een aantal uiteenlopende gevallen, waarbij de mogelijkheid wordt overwogen om in drie lagen van de veiligheid te investeren. Ondanks validatie van de analytische resultaten, tonen de numerieke proeven dat bijkomstige voorwaarden, die de mate van optimalisatie van een meerlaagse veiligheid beïnvloeden, namelijk toename van mortaliteit in geval van overstroming, en gebeurtenissen zoals extreme weersomstandigheden, zoals tyfoons en tsunamis.

Hoofdstuk 5 onderzoekt hoe budget beperkingen en hoge veiligheidseisen voor menselijk leven het optimale ontwerp, van zowel preventie als meerlaagse veiligheidssystemen, kunnen beïnvloeden. De analyse heeft betrekking op de zelfde opbouw van het systeem als reeds bekend van hoofdstuk 4, terwijl ook dezelfde lijn van denken wordt gevolgd. Hetgeen betekent dat, de optimale ontwerpen eerst zijn afgeleid met behulp van analytische benaderingen, en de resultaten vervolgens worden gevalideerd door numerieke proeven. De analyse begint met de analytische optimalisatie onder budgettaire beperkingen. Het vervolgt met het optimaliseren van hetzelfde systeem, met een beperking van de veiligheid die overeen komt met een lager risico voor het menselijk leven dan die in de economisch optimale oplossing. Vervolgens worden een aantal numerieke proeven uitgevoerd, die de gevoeligheid aantonen van de optimalisatie resultaten ten opzichte van verschillende budgettaire en veiligheidsbeperkingen. Met betrekking tot budgettaire beperkingen, bewijst de analyse dat hoe lager het beschikbare budget is, hoe economisch aantrekkelijker meerlaagse veiligheid is dan preventie, en in streken met tyfoons en tsunamis, deze kans zelfs toeneemt. Met betrekking tot veiligheidsbeperkingen, geeft de analyse aan dat hoe hoger de veiligheidseisen zijn voor menselijk leven, hoe groter de waarschijnlijkheid dat een meerlaags veiligheidssysteem de voorkeur krijgt boven preventie. Tenslotte, wordt de invloed van de beperkingen op de kosteneffectiviteit van beleggingsstrategieën onderzocht, welke laat zien dat veiligheidslaag 3 (i.e. crisis management) meer rendabel is wanner er budgettaire beperkingen zijn dan wanneer er veiligheidsbeperkingen zijn. Hoofdstuk 6 presenteert een analyse die aangeeft hoe onzekerheid in de geschatte kosten van overstromingscontrolemaatregelen het resultaat kan beïnvloeden van een economische optimalisatie. Deze onzekerheid wordt ingevoerd in de vorm van stochastische variabelen in de functie van de totale kosten. Vervolgens wordt een Monte Carlo simulatie uitgevoerd, die aangeeft hoe robuust een beleggingsstrategie is, dat wil zeggen, hoe waarschijnlijk het is dat, een als optimaal gekozen strategie zonder in achtneming van onzekerheden wordt achterhaald door een andere strategie, na het invoeren van onzekerheden. De analyse is uitgevoerd voor drie gevallen van systemen, waar meerlaagse veiligheid met lagen 1 en 3 in hoofdstuk 5 optimaal bleken te zijn. De resultaten van de analyse geven aan dat onzekerheid een van de parameters is die een optimale meerlaagse veiligheid kan voorkomen.

In hoofdstuk 7 wordt de theorie uit hoofdstuk 3 gebruikt voor de bepaling van economisch optimale normen voor bescherming in Nederland. Met name aandacht voor het opnemen van informatie over de Nederlandse dijkring, volgens het nationale

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optimaliseringsbenadering uit hoofdstuk 3. De gesuggereerde procedure toont aan dat in achtneming van gelijktijdige mislukkingen in verschillende delen van een dijkring in Nederland, weinig effect heeft op optimaliseringsresultaten.

In hoofdstuk 8 wordt een beschrijvende analyse gepresenteerd van de reactie op de meerlaagse veiligheidssystemen van Tohoku, in Japan, tijdens de “ Great Eastern Japan Earthquake and Tsunami” op 11 maart 2011. Deze analyse toont aan waarom de waarschijnlijkheid van mislukking van maatregelen tegen overstroming, i.e. laag 1, lager moet zijn dan de maatregelen in hogere veiligheidslagen, en hiermee de grenscondities valideren, zoals aangetoond door de optimaliseringen in hoofdstuk 4. In hoofdstuk 9 wordt de theorie uit hoofdstuk 4 gebruikt voor de bepaling van een economisch optimaal meerlaags veiligheidsontwerp voor Rikuzentakata, een stad in Tohoku die volledig werd verwoest in 2011. Dit bevestigt de toepasbaarheid van het optimaliseringsmodel dat in hoofdstuk 4 gepresenteerd is. In hoofdstuk 10 worden de conclusies samengevat.

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Chapter 1

Introduction

1.1 An introduction to the Dutch flood risk management policy

The fact that more than 50% of the Netherlands is exposed to the risk of large-scale flooding makes flood risk management prerequisite for any type of land-based economic and social development. Even before the Middle Ages the Dutch would locate essential economic activities on artificial mounds to reduce the risk of flooding. The need to expand those activities in space made it necessary to coordinate the efforts of individuals for flood protection, contemplating collective flood risk management solutions. This led to the emergence of the dyke-ring system, which was established over time as the core type of flood protection in the Netherlands. The first river dykes together with the naturally formed dunes along the coast had a significant contribution in the reduction of flood risk, which gradually increased confidence for investments in the area. In the 13th century water boards were established with the purpose of coordinating maintenance of the dykes at a local level. The Netherlands as a nation or country did not exist at that time, which makes water boards the oldest democratic organizations in the Dutch territory (Jongejan 2008). The number of water boards kept growing, which, together with the growing role of flood defences in keeping areas of increasing economic value safe, created the need to have activities coordinated by a central authority. The need to coordinate management of river training works along the branches of the Rhine, led to the centralization of most water management activities in the 19th century, and their coordination by Rijkswaterstaat, an agency that still exists and currently belongs to the Ministry of Infrastructure and Environment (Van de Ven 2004).

After the flood disaster of 1953, a breakthrough in the Dutch flood risk management took place. At that time a large area of the south-western part of the country was flooded, causing more than 1800 fatalities, and economic damage in the order of 10% of the gross domestic product (Gerritsen 2005). In the aftermath of that devastating event, the so-called Delta Committee was founded, whose main purpose was to coordinate actions towards a drastic reduction of flood risk. A key element of the Delta Committee’s

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recommendations that formed the foundation of the current flood risk management policy in the Netherlands was the determination of protection standards for all major levee systems based on the prospects of economic development and population growth (Van Dantzig & Kriens, 1960). Those protection standards were defined in terms of overflowing probabilities of the flood defences, and were derived by means of cost-benefit analysis. In that analysis as optimal degree of safety the one minimizing the total cost in the system during its lifetime was considered. This consisted of the cost of investment in the improvement of the flood defences and the expected losses after this improvement (Van Dantzig, 1956), including loss of human lives in monetary terms. The protection standards per dyke-ring were legally mandated with the Delta Law of 1996 (figure 1.1). In that act, safety standards were given per dyke-ring, i.e. an area that is flooded if there is a breach in one of its dyke-stretches. Ever since, all dyke stretches in the country are tested every six years for compliance with the safety standards, and necessary improvements are undertaken, mostly financed by the central government of the Netherlands (Kind 2013).

Figure 1.1: Current flood protection standards in the Netherlands (Source: Ministry of Public Works, Water Management and Transportation of the Netherlands)

Since significant investments of capital were required for the reduction of flood risk in the Netherlands of the 60s, which included a shortening of the Dutch coastline of about 700 Km with the closure of all major estuaries, it is reasonable that the Dutch decided to commit to an economic approach. Not balancing safety against its actual cost may have proven harmful for the national welfare. After the financial failure of Betuweroute, a Dutch railway project in the 90s, the use of cost-benefit analysis became mandatory for all public investments in the Netherlands (Huizinga 2012). This effectively means that the rationale adopted in the 50s is not likely to be substantially changed in the coming decades.

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15 1.2 Research Motivation

Despite the significant steps that were taken by implementing the recommendations of the Delta Committee, there is still much space for improvement in the Dutch flood risk management policy. Weaknesses have been identified by Dutch experts in the field, and most of them are pointed out in this section. Acknowledging the need for improvements in that policy, the Dutch Government established a second Delta Committee in 2005, the role of which was a strategic planning for water safety in the Netherlands. Their conclusion was that safety could be guaranteed for the coming centuries, yet further research on the ways to derive the most efficient strategies was needed (Delta Committee 2008). The Government approved this advice in 2008 and incorporated it into the National Water Plan (Central Dutch Government 2009). With the National Water Plan, the need for a revision of the protection standards approach was announced. The identified weaknesses in the approach based on which the current protection standards were determined and the scientific and political advances that have been taking place for addressing them are the main source of inspiration and motivation for writing this dissertation. A secondary source of inspiration was the experience of the Great Eastern Japan Earthquake and Tsunami in 2011, which chronologically coincided with the commencement of this PhD research, and offered some valuable lessons for flood risk management practices (see e.g. Tsimopoulou et al. 2012). In this section the points where improvements are possible in the protection standards approach in the Netherlands, and some national initiatives for addressing them are presented.

1.2.1 Failure probabilities of the flood defences

The first point is associated with three problems in respect to the probabilities that are identified as protection standards. Firstly, the 1995 protection standards refer to overflow, i.e. the event that the water level exceeds the crest level of the dyke, causing flooding in the protected area. However this is only one out of many failure modes of a dyke (see e.g. Brandl & Szabo 2013; TAW 1990). This means that the probability of flooding in a dyke-ring area, which is the one needed for application of a cost-benefit analysis, is not equal to the overtopping probability, but to an aggregate value that will depend on the probabilities of all failure modes. Secondly, a uniform probability is assigned as a protection standard along the entire length of the ring. Yet dyke-rings can be hundreds of kilometres long, and their load and resistance properties can vary along their length, leading to a spatial variation of their failure probability. The cosequences due to different failures may also be different. This means that the economically optimal probability will probably vary too along the length, contrary to the assumption of one optimal probability per dyke-ring that was made for determination of the 1995 standards. The third problem is the fact that more than one failure can occur simultaneously at the same dyke-ring. Combined failures of dyke-segments may induce more severe consequences than those of their individual failures. It is therefore useful to incorporate different failure scenarios in the analysis. By resolving these problems, new protection standards could be derived that would be more accurate than the ones in effect.

A major step towards addressing this issue was an initiative of the Dutch Ministry of Infrastructure and Environment, the Regional Water Authorities and Provincial Authorities for a fully probabilistic risk assessment of all major levee systems in the Netherlands (Jongejan & Maaskant 2013). This analysis was commissioned in 2006 within the framework of “Flood Risk in the Netherlands 2” project (Veiligheid Nederland

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in Kaart or VNK2 in Dutch). In VNK2 a certain procedure is used for calculating the risk of flooding in any place in the Netherlands that is protected by flood defences. In that procedure all aforementioned problems associated with the definition of flooding probabilities are addressed. The results of VNK2 comprise a comprehensive piece of information on the risk of flooding in the Netherlands. Incorporating them in the procedures to derive protection standards can have a significant contribution in their cost efficiency. More information on the VNK2 project is provided in chapter 7.

1.2.2 Cost-benefit analysis

The second point has to do with inconsistencies in the followed procedures for determination of protection standards in different parts of the country. In fact, a cost-benefit analysis was only performed for dyke-ring 14. For the remaining dyke-ring areas along the coast, a comparative analysis of their potential flood damage was performed, while the costs for technical improvements of the dykes were neglected (Kind 2013). As for the dyke-rings in the river areas, costs and benefits were estimated and compared for only two possible protection standards, 1/500 and 1/1250 per year (Commissie Toetsing Uitgangspunten Rivierdijkversterking 1993). Such inconsistencies in the methodological approaches imply that the choice of protection standards in different parts of the country is based on different criteria. This can burden decision-making from the national Government, as it prevents the development of a common basis for comparison of the levels of safety in different parts of the country.

The problem of inconsistencies was partly solved through the project “Flood protection for the 21st Century” (Waterveiligheid 21e eeuw or WV21 in Dutch). This project was launched by the Dutch Government in 2009, to carry out research on the determination of new legal protection standards. Within its framework cost-benefit analyses were commissioned for all dyke-ring areas in the Netherlands. In all dyke-rings the same cost-benefit analysis method was used, preventing this way methodological inconsistency along different parts of the country. The used method is an extended version of the previous one, which allows determining not only the economically optimal amount to invest in dyke improvements, but also the optimal time intervals between consecutive investments. The basic principles of this approach can be found in relevant literature (e.g. Vrijling & Van Beurden 1990; Voortman & Vrijling 2003; Eijgenraam 2005). In the performed analyses new insights about the current flood risk levels from VNK2 project were taken into account, yet detailed VNK2 results for all dyke-rings were not fully available at that time, which means that the results of the analysis will have to be updated with the full results of VNK2. The protection standards suggested in WV21 are presented in the following figure.

1.2.3 Incorporation of a future vision

The third point is that the approach based on which the current protection standards were determined was not engineered with the ability to adapt to dynamic external conditions. The standards in effect were derived taking into account prospects for climate change and economic growth that deviate from the developments that took place in reality. Recent studies have shown that these standards do not properly reflect the economic values that are protected (Ten Brinke & Bannink 2004). Besides, during the 35 years that passed from the first Delta Committee’s recommendations till the safety

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standards came in effect (1960-1995), a growing awareness of environmental issues took place, such as the impact that large-scale interventions have on the environment. This led to a virtual favouring of solutions that are seen as more environmentally friendly than the dykes and flexible enough to accommodate future unknown conditions (see e.g. Smits et al. 2006).

In order to have this problem addressed, in 2010 the Delta Program was initiated. This is a national project in which the central government, provinces, water boards and municipalities work together, with the active participation of the public, stakeholders and knowledge institutes with the scope of coming up with solutions that will ensure flood protection and fresh water supply in the Netherlands in the long-term. Up to 2015, the Delta Program is aimed at the development of strategies and preparation of key decisions on these strategies. Later on, it will transform into the preparation, planning and execution of measures. Within the Delta Program solutions are developed based on a water system-based approach, which takes into account the linkages between water management, economic development and nature preservation. Three qualities should be maintained with all solutions: (1) solidarity between regions and generations, (2) flexibility in view of uncertain future trends in climate, societal demands and political priorities, and (3) sustainability of population, environment and profit (Van Alphen 2013). An issue that has been highlighted in reports of the Delta Program, as an interesting topic for further research is how to deal on a decision-making level with budget constraints that may occur and prevent undertaking an economically optimal project (see e.g. Zwaneveld & Verweij 2013). This issue is also discussed in this thesis (chapter 5).

Figure 1.2: Flood protection standards in the Netherlands suggested by WV21 (source: Kind 2011)

1.2.4 Preparation for disasters

The fourth point is that in the last decade an increasing aversion to the consequences of flooding could be perceived in the Dutch society. This can be explained by the recent

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experiences of large-scale disasters in different parts of the world, such as the Indian Ocean Tsunami in 2004 and Hurricane Katrina in 2005, combined with an increase of the expected losses of flooding in the Netherlands due to population and economic growth. In view of the growing concerns about the consequences of a potential disaster, the need of pursuing investments in measures for the mitigation of losses during flooding has been expressed through the National Water Plan (2009). Yet no specific guidance has been provided on how to explicitly take into account such investments in the determination of flood protection standards according to a cost-benefit framework. The combination of measures for the prevention of flooding with measures for the mitigation of losses is often referred to as “multi-layer safety” in the Netherlands (see also chapter 4).

1.2.5 Risk metrics for potential loss of life

The fifth point concerns the fact that the current flood risk management policy does not provide explicit restrictions on the acceptable risk of loss of life, which is decided on the basis of pure economic criteria. In particular an economic value is assigned to human life, which for the current protection standards was determined on the basis of estimated stock values of human capital (see e.g. Petty 1690; Folloni & Vittadini 2010). For future practices the method of valuation of statistical life (VOSL) is contemplated (Bockarjova et al. 2012). Given this value, an economically optimal protection standard is determined, which implicitly imposes a value to the probability of loss of life that needs to be accepted. Yet the Dutch Government is in favour of considering separate metrics for the risk to human life transferring the approach that is already used in the Dutch major hazards policy to the domain of flood security (Jonkman et al. 2008). In that approach, the risk to human life that corresponds to the economically optimal safety, as indicated by a cost-benefit analysis, needs to be compared to acceptable risk levels derived by means of social criteria. If those criteria are not satisfied, additional measures for the reduction of risk to human life need to be considered. The metrics for potential risk to human life are the individual and societal risk. Individual risk is the probability of death of a person that is constantly present at a given location. Societal risk refers to the probability of death of a large number of people, i.e. to the probability of a flood with severe consequences for human life. An overview of methods used for setting acceptable values in these two metrics can be found in literature (Vrijling & Van Gelder 2002; Jonkman et al. 2003).

The issue of separate risk metrics for loss of life is currently being resolved by the Dutch Government. Regarding individual risk, a threshold probability of 10-5_{per year in all}

dyke-ring areas has been legally mandated (Tweede Kamer 2013). As for societal risk a Governmental decision is expected to be made in the near future.

1.2.6 Synthesis

Cost-benefit analysis has played a central role in the development of the Dutch flood risk management policy. Given that it has become mandatory for all public investments in the Netherlands, it will probably keep playing an important role in the future too. The above-presented developments on scientific and political level have outdated the former policy framework by invalidating the conditions based on which the protection standards were determined. Modifications of the approach developed in the 50s are

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essential, in order for the above points to be explicitly accommodated in the economic optimisation context that the use of cost-benefit analysis introduces. This would create a common basis for the evaluation of all types of decisions related to flood protection, but it would also imply a level of stringency in policy-making that may not be desirable (see also chapter 2). Whether policy-makers decide to commit to an integral economic approach, where all these points are taken into account in the determination of new protection standards or not, is a matter of choice. In any case it would be useful to investigate if and how the new knowledge and preferences could be integrated in an economic optimisation context.

1.3 Objective and research questions

This dissertation focuses on the development of methods for the economic optimisation

of flood protection systems, taking into account the need to address a number of the

points highlighted in the previous section, namely:

a. A thorough knowledge of the failure properties of flood defence structures (§1.2.1),

b. The choice of pursuing investments in multi-layer safety (§1.2.4) c. The choice of considering separate risk metrics for human life (§1.2.5) d. The existence of budget constraints (§1.2.3)

The main objective is two-fold:

- To provide guidance on how to determine economically optimal failure probabilities of different flood control components that are part of the protection system,

- To indicate from a cost-benefit perspective which conditions make a multi-layer safety system layout preferable over a flood prevention system layout.

The central research question can be summarized as follows:

Taking into account the need to preserve cost-benefit analysis as a vehicle for supporting decisions upon investments in the Dutch flood risk management how could points a, b, c and d be explicitly integrated in the determination of optimal projects, and what are their implications for policy-making?

In order to keep the scope limited to points a, b, c, and d, a number of sub-questions have been formulated to serve as a roadmap for outlining the content of this dissertation. These sub-questions are listed below:

1. Which economic decision problems are relevant for flood protection, and which of them fit in the context of cost benefit analysis? (Chapter 2)

2. How can a flood prevention system be economically optimised, taking into account:

- the existence of multiple failure mechanisms (Chapter 3), - a spatial variability of its failure probability (Chapter 3), and - scenarios of simultaneous failures (Chapter 7)?

3. How can multiple layers of safety be incorporated in the economic optimisation process of flood protection systems? (Chapter 4)

4. How does the existence of budget and safety constraints influence the economic optimality of flood protection systems? (Chapter 5)

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5. Which parameters determine the economic optimality of multi-layer safety systems (Chapters 4 & 5)

6. Under which conditions is multi-layer safety to be preferred over prevention from a cost-benefit perspective? (Chapters 4, 5 & 6)

7. How can the robustness of optimal investment strategies against uncertainty be assessed? (Chapter 6)

1.4 Methodological approach

Three methodological approaches are used in this dissertation, based on which different research questions are answered. Question 1 is answered on the basis of a literature review on the use of cost-benefit analysis for the formulation of public safety regulations, and a descriptive analysis of economic decision problems in flood risk management. For answering questions 2-6, a number of analytical economic optimisation models are developed for fictitious flood protection systems. First systems for the prevention of flooding are only considered, i.e. systems that resemble the Dutch dyke-rings. Later on, multiple layers of safety are added. For answering question 7, a probabilistic analysis is performed with a Monte Carlo simulation.

Regarding the approach for questions 2-6, the use of fictitious systems allows keeping the respective analysis as simple as necessary for enabling the analytical derivation of economically optimal design specifications for the tested systems. In this manner insights into the variables and the ways that they influence optimality in a system can be acquired. After deriving some first conclusions, the complexity of the models is increased in a step-wise manner. In every step more of the aspects highlighted in points a, b, c, and d are incorporated, and results are acquired that can be compared to the results of the previous steps. This gives a comprehensive picture of the influence that every additional aspect has on the final optimisation result. A disadvantage of this approach is that due to the necessary simplifying assumptions, it prevents the derivation of generic optimisation formulae that can be applied in any system and country context. Such a generic overview is necessary for answering questions 5 and 6. This problem is tackled through the development of a numerical model in MATLAB, and the performance of a sensitivity analysis to different values of the problem variables, which broaden and partly validate the insights acquired through the analytical results. Some of the developed models are appropriately modified and their application in real flood protection systems is showcased.

It should be remarked that the entire analysis is performed given stationary conditions, i.e. a certain future. This means that potential variations of the problem variables over time is not taken into account, and the option to postpone an investment for later is omitted. This simplification allows for a consensual understanding of preliminary features of the optimisation problem, which is essential before consultation of decisions on where, when and how much to invest.

Furthermore, it should be noted that this dissertation focuses on economic viewpoints. This means that all protected values that are taken into account in the analysis, including intangible entities are expressed in monetary terms. Intangible entities can refer among others to human life, ecological and cultural value, national pride etc. In this dissertation only human life is taken into account though, which is the most common intangible entity in safety science.

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21 1.5 Report overview

The chapters of this report are organized as follows: Chapter 2 provides background information on the methods that are used worldwide for the formulation of public safety regulations, the pros and cons of cost-benefit analysis, and the features of economic decision problems in flood risk management. Chapter 3 focuses on the economic optimisation of flood prevention systems, i.e. systems protected by a water-retaining structure. Chapter 4 focuses on the economic optimisation of multi-layer safety systems. Chapter 5 investigates how budget constraints and high safety requirements for human life can influence the optimal design of both prevention and multi-layer safety systems. Chapter 6 presents a method for assessing how robust the optimisation results are with respect to uncertainty. Chapters 7, 8 and 9 link the outcome of the previous chapters with real life problems. In Chapter 7 the theory of chapter 3 is used for the determination of economically optimal protection standards in the Netherlands. In Chapter 8 a descriptive analysis is presented on the response of the multi-layer safety systems of Tohoku in Japan during the Great Eastern Japan Earthquake and Tsunami on March 11, 2011. In Chapter 9, the theory of chapter 4 is used for the determination of an economically optimal multi-layer safety design for Rikuzentakata, a town in Tohoku that was entirely destroyed in 2011. In Chapter 10 conclusions are summarized.

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Chapter 2

Public safety in a cost-benefit context

2.1 Introduction

This chapter presents the policy context within which the economic optimisation methods of the following chapters make sense. The methods developed and showcased in this thesis are meant to support decisions upon flood risk management projects. Projects are here defined as government actions, including laws and regulations that change the productive capacities of an economy or the distribution of wealth (Adler & Posner 1999). Flood risk management projects are actions for the reduction of flood risk that lead to improved conditions for social-economic development. Such actions can be either the formulation of a flood safety regulation or investments in measures for the reduction of flood risk that do not necessarily comply with a regulation. Both regulatory and non-regulatory projects are accompanied by the stakeholders’ commitment to a particular policy rationale. In the Netherlands flood risk management is practiced on the basis of an economic rationale. A flood safety regulation is in place, whose formulation rested on the principles of cost-benefit analysis. This economic rationale needs to be maintained in the future while accommodating a number of new conditions (see also chapter 1). In this chapter the economic principles of cost-benefit analysis that need to be preserved when the new conditions are accommodated are clarified. Such a clarification has been essential for specifying which decision problems are consistent with the Dutch cost-benefit approach, hence also the content of the forthcoming chapters.

This chapter is organized as follows: In section 2.2 some background information on the methods for the determination of acceptable risk levels is provided. Section 2.3 is focused on the use of cost-benefit analysis for the evaluation of projects. Section 2.4 explains why an economic optimisation is compatible with the existing flood risk management framework in the Netherlands by describing and classifying the decision problems that are relevant. Finally, in section 2.5 a decision-making guideline that is compatible with the selected rationale is presented. This guideline has been used as a roadmap for structuring the analyses of the latter chapters.

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23 2.2 Acceptable risk approaches for public safety

Modern societies are exposed to various types of hazards, which are responsible for thousands of human losses and severe economic damage every year. As the history of mankind proves, hazards cannot be eliminated. This has led many governments to deal with them as risks that can be assessed and effectively reduced. Estimating the magnitude of risk is necessary in order for informed decisions about risk reduction policies to be made. Given a considerable variety of risk features that people find meaningful, it would be impossible to define uniform and objective risk measures and values (Slovic 1999). This is illustrated by the great variety of risk metrics that are used in policy-making, ranging from individual risk to probability weighted sums of non-linearly valued consequence types (Jongejan et al. 2012). Overviews of used risk metrics and the safety domains where they mainly apply can be found in literature (see e.g. Bedford & Cooke 2001; Jonkman et al. 2003; Vrijling & Van Gelder 1997). These metrics can be utilised on the basis of different rationales, such as the precautionary principle (see e.g. Barrieu & Sinclair-Desgagné, 2006; Gollier & Treich, 2003), risk-risk comparisons (see e.g. Cassini 1998), or maximization of net economic benefits (see e.g. Arrow et al. 1996; Pearce & Nash 1983).

Literature offers a variety of approaches for the determination of acceptable risk levels in public safety projects. Fischhof et al. (1983) have classified these approaches in the following three categories;

1. Formal analysis. This category entails approaches that have their origin in

economic and management theory. The most prominent common feature of all formal analyses is that they treat the risk management process as a decision problem, whose solution should yield an explicit, pre-defined social optimisation criterion. Cost-benefit analysis (see e.g. Delta Report 1960; Arrow et al. 1996) and decision analysis (see e.g. Raiffa 1968) are typical examples of formal analyses.

2. Bootstrapping. Approaches of this category aim at assigning quantitative values

to acceptable risk, without recourse to a certain mathematical formula, but on the basis of continuation of policies that have evolved over time. A typical example of such an approach is the determination of design standards of coastal defences in Japan, where the most severe typhoon or tsunami ever recorded in the proximity of the structure indicates the required protection level (Tsimopoulou et al. 2012).

3. Professional judgment. This refers to the reliance on a technical expert’s opinion

about the acceptability of a given risk level. This approach is exercised when bootstrapping is not preferred and the performance of a formal analysis is not possible, or its result is not considered reliable enough due to lack of sufficient data. A typical case of professional judgements in flood risk management is when there is a lack of data on the frequency of occurrence of certain failure mechanisms of flood defences (see e.g. Möllmann & Vermeer, 2007).

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Table 2.1: Archetypal approaches to acceptable risk decisions (adapted from Fischhoff et al. 1983)

Approach Decision maker Decision-making _criterion Description

Formal analysis Government _optimisationSocietal

Specification of decisions most consistent with accepted view of facts and

values

Bootstrapping Government _{previous policies}Continuation of for future action based on Prescription of standards past or present policies Professional

judgment Technical experts Professional judgment

Specification of decisions based on the opinion of

qualified experts All aforementioned approaches for dealing with hazards can prove to be advantageous or less appealing within different institutional and national contexts. Furthermore, whatever the officially adopted approach, in practice it is common to have elements of more approaches mixed up. Professionals base sometimes their judgment on formal analyses’ results or on historical paradigms; data for formal analyses may be acquired through professional judgments; bootstrapping decisions may be refined taking into account results of formal analyses.

The above-presented approaches are strategy-oriented. This means that they assume a centralized and identifiable decision-making body, such as a national or local authority. In reality there are also process-oriented approaches, which embody market or procedural logic. A pure market approach would eliminate centralized decisions, allowing unrestrained market forces to drive the evolution of acceptable risk levels over time. The massive deregulation of infrastructure industries, such as the airlines industry, natural gas industry, telecommunications and electric power in the United States and other western countries signifies such a market-oriented approach to risk acceptability (see e.g. Oren 2001). A pure procedural approach would allow political, economic and intellectual pressures to shape decisions on the basis of sophisticated bargains and negotiations. Such a multi-actor approach with their multiple perspectives and interests is a good representation of the so-called incremental public policy frameworks (Lindblom 1990; Parsons 1995). It should be remarked that the adoption of process-oriented approaches does not exclude the possibility of actors basing their opinions and preferences on the results of formal analyses, bootstrapping or professional judgments, though without being bound to them. Process-oriented approaches are not investigated further in this thesis.

2.3 Cost-benefit analysis

Cost-benefit analysis is an economic calculus for the evaluation of all types of projects. When used for the regulation of risks to the public, it can be classified as a formal analysis. The method started gaining prominence after it was adopted for the evaluation of water-resource projects by the U.S. Army Corps of Engineers in 1930s (Russell & Baumann 2009). Originating in the economics of social welfare and resource allocation, cost-benefit analysis uses as a social optimisation criterion the maximization of net

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economic benefits over the totality of affected individuals, which can be calculated in the form of a net present value as follows (Pearce & Nash 1983):

(

)

=

å

τ _t- _t _t

t 0

NPV B C d

Equation Section (Next)

(2.1)

Where, NPV = net present value [mu(=monetary unit)], τ = planning period [years], Bt =

benefits in year t [mu], Ct = costs in year t [mu], and dt = discount factor calculated as

follows: t t 1 d (1 r) = + (2.2) Where, r = annual discount rate.

The maximization of equation (2.1) is a criterion virtually ignorant to equity concerns, because it does not specify how much each individual affected by the decision will actually gain. In order to accommodate the need for equitable distribution of benefits, the so-called Pareto optimality criterion was developed (Pareto 1935). According to it, a decision can be considered optimal if it improves the economic status of at least one individual without making any other worse off. As it is common for social policies to provide benefits to some people while harming others, the Pareto criterion would be violated unless a compensation scheme accompanied it, such as a tax relief to the harmed groups, or a direct payment (Mishan 1972). The difficulty of creating viable compensation schemes has led to the development of a less stringent criterion, the potential Pareto improvement, or Kaldor-Hicks criterion, which drops the compensation requirement, and accepts as mere equity consideration the potentiality of having “losers” compensated by the “gainers” (Hicks 1939). This means that a decision does not need to be accompanied by a compensation scheme in order to be considered optimal. Assuming the potentiality to have harmed groups compensated, the Kaldor-Hicks criterion legitimates the requirement expressed by equation (2.1).

The use of cost-benefit analysis for the regulation of risks to the public and the evaluation of risk reduction options has been subjected to a long lasting debate among scholars. The main point of criticism has been the ability of the method to produce morally relevant results when applied for decisions that influence public health, safety and the environment (Jongejan et al. 2012), in which case non-economic factors may affect people’s moral judgments (see e.g. Kahneman & Tversky 1979). In its pursuit of economic efficiency, cost-benefit analysis aims to include all consequences that are amenable to economic valuation and to exclude those that cannot be valuated (Parish 1976). There is some disagreement though as to which consequences are quantifiable. Many analysts assign monetary values only to commodities that have readily available market prices, like wages and investment costs. However indirect economic evaluation methods, like those using shadow prices or demand principles (see e.g. Samuelson & Nordhaus 2009), make it possible to also assign monetary values to intangible goods, such as human life, scenic beauty or national honour. Although the inclusion of intangibles gives a more comprehensive picture of the effect of decisions, there is some disagreement as to whether it is morally acceptable. Furthermore it has been argued that the inclusion of intangibles in a cost-benefit analysis obscures the purely economic facts and prevents a clear interpretation of its rationale (Mishan 1974). More points of criticism can be found in literature, originating mainly in the domains of political

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science and philosophy (see e.g. Wildavsky 1966; Sen 1970; Self 1972; Hunt & Schwartz 1972).

Despite the critiques, the method has also been attributed some important advantages over rival approaches, such as the potential to be comprehensive and logically sound (Fischhoff et al. 1983), the ability to increase regulatory transparency (Adler & Posner 1999), and the ability to organize disparate information in a consistent manner (Arrow et al. 1996). In order for these advantages to be enjoyed though, a cautious consideration of the following points is necessary (Jongejan 2008):

1. The outcomes of cost-benefit analyses rest on various value-laden choices, such as the choice of a discount rate. Stakeholders need to agree on those choices in order for the results of the analyses to be useful in decision-making. The same counts for the choice of valuation approaches for non-market goods.

2. Apart from the direct costs and benefits, it is possible that a number of new opportunities and risks accompany a decision, which could be taken into account in the balance of costs and benefits. It is sometimes necessary to make an arbitrary choice of the effects that will be excluded from the analysis.

3. Due to the case-specific choices of values, valuation methods and types of costs and benefits included in every cost-benefit analysis, it can be troublesome to compare reported financial balances. Intangibles for instance may not always be included in a financial balance. Hence decision-makers should be careful when prioritizing actions across policy domains on the basis of financial balances. The assumptions based on which the compared balances were derived need to be consistent.

2.4 Types of economic decision problems

There are different types of information that decision-makers might be interested in acquiring by calculating the costs and benefits of a project. The option that maximizes equation (2.1) is the solution to one out of three types of economic decision problems that may be relevant in a management cycle. The three types of decision problems can be described as follows (Pearce & Nash 1983):

1. Accept-reject. This refers to the case that decision-makers need to decide whether

a given project is to be accepted or not. From an economic perspective, a project is justifiable, hence acceptable, when its net present value is positive.

2. Optimisation. This decision problem type is relevant for a given project, when the

amount to invest in its specific features needs to be decided. In flood risk management this would be the case if a decision-making agency had already decided to undertake a specific set of flood-control measures, but had to decide yet on how much to invest in each of them. From a cost-benefit perspective, the combination of investments that maximizes the net present value of the project is to be preferred.

3. Ranking. Once acceptable projects have been identified, a comparison among

them will indicate which one is to be undertaken. Following a cost-benefit rationale, all projects under consideration would need to be optimised first. The optimised project with the highest net present value would be preferred. There are cases though that a different criterion is more suitable for decision-making, the benefit-cost ratio, i.e. the ratio of benefits over the costs of a project. This can happen when the available budget is limited, and needs to be spent in the project

Economic optimisation of flood risk management projects