IN THE NETHERLANDS
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 woensdag 21 oktober 2015 om 10:00 uur
door
Karolina Agnieszka WOJCIECHOWSKA
ingenieur in de toegepaste wiskunde, geboren te Zielona Góra, Polen.
Samenstelling Promotiecommissie:
Rector Magnificus voorzitter
Prof. drs. ir. J.K. Vrijling Technische Universiteit Delft, promotor Prof. dr. ir. M. Kok Technische Universiteit Delft, promotor
Onafhankelijke leden:
Prof. dr. ir. S.N. Jonkman Technische Universiteit Delft Prof. dr. ir. P.H.A.J.M. van Gelder Technische Universiteit Delft
Prof. dr hab. inż. E. Nachlik Cracow University of Technology (Poland) Dr. ir. A.K. Koelewijn Deltares
Dr. J.W. de Vries Koninklijk Nederlands Meteorologisch Instituut
Dit proefschrift is mede tot stand gekomen dankzij een financi¨ele bijdrage van HKV lijn in water, Flood Control 2015 en Technische Universiteit Delft.
Copyright c 2015 by K.A. Wojciechowska. Printed by Delft Academic Press.
Summary v
Samenvatting ix
1 Introduction 1
1.1 Decision making under uncertainty . . . 1
1.2 Normative decision theory . . . 4
1.3 Operational flood risk management and decision models . . . 6
1.4 Objectives and scope of the study . . . 8
1.5 Overview . . . 8
1.6 Key definitions and assumptions . . . 11
2 Derivation of dike failure probabilities in the Netherlands 15 2.1 Introduction . . . 15
2.2 Dike failure mechanisms and dike failure probabilities . . . 16
2.3 Fragility curves of dikes . . . 22
2.4 Conclusions and remarks . . . 30
3 Near-future probability forecasts for water levels and river discharges in the Netherlands 31 3.1 Introduction . . . 31
3.2 Probability forecasts for the river Rhine . . . 34
3.3 Probability forecasts for sea levels along the Dutch coast . . . 35
3.4 Probability forecasts for water levels in the deltas of the Vecht and IJssel 38 3.5 Conclusions and remarks . . . 40
4 Economic appraisal of a dike sensor system 43 4.1 Introduction . . . 43
4.2 Application area of electronic dike sensors . . . 45
4.3 Comprehensive economic appraisal of a dike sensor system . . . 50
4.4 Cost-benefit analysis in ”Flood risk in the 21st century” . . . 51
4.5 Modelling influence of dike sensor information on the annual flooding probability . . . 53
4.5.1 Case 1: learning from measurements and dike reinforcement . . 54
4.5.2 Case 2: anomaly detection and emergency flood measures . . . 57
4.6 Detailed economic appraisal of a dike sensor system . . . 60
4.6.1 Learning from measurements and dike reinforcement . . . 60
4.6.2 Anomaly detection and emergency flood measures . . . 61
4.7 Application examples . . . 61
4.7.1 Example: learning from measurements and dike reinforcement . 61 4.7.2 Example: anomaly detection and emergency flood measures . . 64
4.8 Conclusions and remarks . . . 67
5 Operational dike failure probabilities 69 5.1 Introduction . . . 69
5.2 Application of fragility curves . . . 70
5.3 Hydra-VIJ . . . 73
5.3.1 General description . . . 73
5.3.2 Probabilistic formulation of the model . . . 74
5.4 Practical framework for derivation of operational dike failure probabilities 75 5.5 Calculation examples . . . 78
5.5.1 Application of the framework . . . 78
5.5.2 Analysis of the framework . . . 81
5.6 Need for verification and integral approach . . . 84
5.7 Conclusions and remarks . . . 85
6 First insight into the probabilistic evacuation decision rule in the Netherlands 87 6.1 Introduction . . . 87
6.2 Preventive evacuation and related effects . . . 88
6.2.1 Preventive evacuation . . . 88
6.2.2 Costs and benefits of preventive evacuation . . . 90
6.3 Estimation of flood damage and loss of life in the Netherlands . . . 91
6.4 Probabilistic evacuation decision rule . . . 93
6.5 Probabilistic evacuation decision rule for main dike-ring areas in the Netherlands . . . 95
6.5.1 Flood consequences in ”Flood risk in the 21stcentury” . . . . 95
6.5.2 Assumptions . . . 96
6.5.3 Results - the threshold flooding probabilities . . . 97
6.6 Conclusions and remarks . . . 100
7 Modification of the probabilistic evacuation decision rule 103 7.1 Introduction . . . 103
7.2 Monetary valuation of a human life . . . 104
7.3 Reputation damage as a decision criterion . . . 105
7.4 The Promethee . . . 106
7.5 The modified probabilistic evacuation decision rule . . . 108
7.5.1 Definition and application . . . 108
7.5.2 Sensitivity analysis . . . 110
7.6 Remarks on using multi-criteria decision making methods . . . 112
7.7 Conclusions and remarks . . . 114
8 Dynamic decision making in operational flood risk management 115 8.1 Introduction . . . 115 8.2 Decision model I . . . 116 8.2.1 Theoretical description . . . 116 8.2.2 Application example . . . 119 8.3 Decision model II . . . 123 8.3.1 Theoretical description . . . 123 8.3.2 Application example . . . 126
8.4 Preventive evacuation of dike-ring area 48 . . . 128
8.4.1 Decision problem and main assumptions . . . 128
8.4.2 Derivation of the transition probabilities . . . 129
8.4.3 Derivation of the conditional flooding probabilities . . . 135
8.4.4 Results - optimal decisions . . . 136
8.5 Conclusions and remarks . . . 138
9 Conclusions and recommendations 141 9.1 Conclusions . . . 141
9.2 Recommendations . . . 143
Appendices 145 A Dike schematisation - uplift and piping failure mechanisms 145 B Observations of Vecht discharge at Dalfsen and level of Lake IJssel 147 C Observations of Rhine discharge at Lobith 149 D Derivation of fragility curves with Hydra-VIJ and PC-Ring 151 D.1 Hydra-VIJ . . . 151
D.2 PC-Ring . . . 151
E Verification of probability forecasts 153
F Gumbel and Gaussian copula functions 157
G Basis data for application of the framework 159
H Algorithm for application of the framework 161
I Optimisation algorithm for ”learning from measurements and dike
reinforcement” 163
J Basis data for derivation of the threshold flooding probabilities 165
K Threshold flooding probabilities 169
L Discreet decision models I and II 171
M Decision model I: false and missed alarm rates 173
Bibliography 175
Acknowledgments 185
Curriculum Vitae 187
List of publications 189
Operational flood risk management refers to activities that aim to manage (reduce) the probability and/or negative consequences of flooding just prior to the expected flood event. An inherent feature of operational flood risk management is that outcomes of decisions taken are uncertain. Execution of these decisions requires time, therefore the flood is an uncertain event in this context. The main goal of this study was to investigate and develop approaches to modelling dike failure probability and decision making in operational flood risk management in the Netherlands. The study was divided into two parts. In the first part, the concept of (operational) dike failure probability was introduced including (i) investigation of its main input-component and (ii) methods for derivation of this probability. In the second part, models for risk-based decisions in operational flood risk management were proposed. The operational dike failure probability constitutes an input to these models.
Part one: operational dike failure probability
A dike fails due to the occurrence of one or more dike failure mechanisms. In par-ticular in this study, the operational dike failure probability is defined as the dike failure probability at a near-future point in time or within a near-future time window (i.e. several hours or days ahead). The operational dike failure probability is derived using information relevant for the time point/window such as actual dike informa-tion1 and probability forecasts for the natural loads2. In the probability forecasting, a probability distribution function is assigned to a variable that has to be forecasted (e.g. river discharge) - this accounts for uncertainties related to the outcomes of the forecasting process. In this study, probability forecasts for natural loads at dikes were considered as the main input of the operational dike failure probability. Three ap-proaches, applied in the Netherlands, to derive probability forecasts for water levels and river discharges were subsequently considered. It was concluded that these ap-proaches account for different uncertainty types. Furthermore, it was observed that performance of the operational dike failure probabilities depends on performance of the probability forecasts (inputs).
Two methods for derivation of the operational dike failure probability were con-sidered. The first method is based on the fragility curves. A fragility curve of a dike
1Dike information consists of the dike’s geometry, the subsoil composition and characteristics
inside and under the dike, the revetment of the dike and geohydrological information such as the phreatic surface and pore water pressures.
2Natural loads are hydraulic loads or (nature-related) load explanatory variables such as river
discharge, sea/lake level, wind speed and wind direction.
is defined as a function from a set of loads, acting on the dike, to the set of condi-tional dike failure probabilities. When a probability forecast for the conditioning load is available, then the combination of the fragility curve and the probability forecast entails the operational dike failure probability. It was concluded that the method is relatively simple however it accounts only for the near-future uncertainty related to the conditioning loads. The second method/framework for derivation of the opera-tional dike failure probabilities was proposed using the model Hydra-VIJ as basis. Hydra-VIJ can be applied to assess the safety of dikes in the deltas of the rivers Vecht and IJssel in the Netherlands. The proposed framework is suitable to derive opera-tional dike failure probabilities in a system consisting of a river and a lake [116]. In the framework, wind is considered to be a time-independent variable, yet time-dependence of wind speeds and wind directions is observed in reality [116]. The framework can be extended such that this time-dependence is taken into account.
It was concluded that the operational dike failure probabilities constitute prob-ability forecasts for dike failure events [116] and, as all forecasts, need to be verified. Due to high dike safety standards, verification of operational dike failure probabilities is not straightforward in the Netherlands.
Attention was also paid to recent developments in dike monitoring in the Nether-lands. Electronic dike sensors were considered mostly due to their possible added value in operational flood risk management. The sensors measure, real-time, variables such as pore water pressure, temperature and/or deformations inside and under dikes, and hence contribute to dike information. The application area of electronic dike sensors was clarified:
• Successful application of electronic dike sensors in flood early warning (i.e. by means of anomaly detection in dike sensor measurements) requires that the sensors and the phenomenon they observe ”provide” sufficient time for the ap-plication of an emergency flood measure (e.g. preventive evacuation).
• Dike sensors cannot be considered as an independent source of information. In-formation about the load is needed to enhance, interpret and verify inIn-formation provided by the sensors.
• To learn from pore water pressure measurements within a reasonable period of time, it is rational to place dike sensors in dikes where the frequency of the design loads is high and/or the decimate height is low.
Because electronic dike sensors constitute a relatively new approach, two models for an economic appraisal of a dike sensor system were proposed in the context of (i) learning from measurements and dike reinforcement, and (ii) anomaly detection and emergency flood measures. In the first model, information achieved with dike sensors is used to reduce uncertainty in the pore water pressure modelling. The benefit of using the dike sensor system is then equal to the flood risk reduction that arises due to the updated (better) dike reinforcement strategy. In the second model, anomaly in dike sensor measurements is used as an indication of a dike failure mechanism development. The benefit of using the dike sensor system is then equal to the flood risk reduction that is achieved with application of emergency flood measures in case of an anomaly. The drawback of both models is that many input parameters need
to be specified and that the models do not take directly into account time aspects related to dike sensors.
Part two: models for risk-based decisions
A basic/static decision problem was defined as a problem whether to apply an emer-gency flood measure, which requires (financial) expenditures, facing an uncertain flood event. Two alternatives are considered in the problem: apply the measure and do not
apply the measure. Based on the normative decision theory, the minimum expected
monetary cost criterion was primarily applied in this study to solve the problem. Furthermore, in the context of the preventive evacuation of an area endangered by flooding, elaboration on this criterion entailed a probabilistic evacuation decision rule. The rule was applied to main dike-ring areas3 in the Netherlands resulting in a set of threshold flooding probabilities. The threshold flooding probability was defined as the ratio of costs of preventive evacuation to the avoided losses (i.e. the monetary value of fatalities saved by the evacuation) [115]. If the flooding probability of a dike-ring area exceeds the corresponding threshold flooding probability, then costs of the evacuation are lower than (financial) benefits of the evacuation and the measure is optimal from the rational point of view. In the context of this study, the flooding probability of a dike-ring area is equal to the operational dike failure probability. The developed rule contributes to the (rational) decision making under uncertainty in operational flood risk management.
Furthermore, the rule was modified such that the number of flood fatalities and the reputation of the decision maker were considered as decision criteria, next to the cost of the evacuation. Consequently, (i) the monetary valuation of a human life, which is generally troublesome, was excluded from the analysis and (ii) reputation, which can influence behaviour of the decision maker, was taken into account. The modification was based on a multi-criteria decision making method. It was concluded that the probabilistic evacuation decision rule, based on the minimum expected monetary cost criterion, constitutes a special case of the modified rule. Furthermore, it was observed that the problems related to the monetary valuation of a human life are not solved with this approach, as an indirect valuation of a human life takes place then.
The basic/static decision problem, in the monetary setting, was extended to a dy-namic decision problem by including the decision wait with application of the measure. Note that most decision making problems are dynamic in nature. Based on the literat-ure study, two dynamic decision models were proposed: decision model I and decision model II. The models can be used to determine when/whether application of an emer-gency flood measure is economically worthwhile taking into account time-dependence between the weather states4 and/or the related forecasts. In decision model I, the expected flooding is at the end of the decision process and the measure, once applied, cannot be stopped. By postponing decision to apply the measure, new information (i.e. forecasts) becomes available. This information is used to update the flooding
prob-3A dike-ring is a a system of water defences (such as dikes, dunes, hydraulic structures) and
high grounds that directly protect the land behind against flooding from the sea, the large rivers (e.g. the Rhine, the Meuse, the Vecht) and the Lakes IJssel and Marker, or a combination of these threats [100]. A dike-ring area is an area that is protected by a dike-ring [100]
4The term weather is used to generally represent hydraulic loads at the dike/dike-ring (i.e. water
levels, waves) or the load explanatory variables (e.g. river discharge, lake level, wind conditions).
ability in the model. By performing a simple calculation example, literature findings were confirmed: including alternative wait leads on average to lower costs. Decision model II constitutes an extension of decision model I as it ”allows” for a repetitive application of the measure and flooding at different times. Based on a calculation ex-ample, literature findings were again confirmed: including time-dependence between the weather states in the model leads on average to lower costs. Decision model II was applied to preventive evacuation decision of dike-ring area 48 in the Netherlands. It was generally concluded that application of both models requires much work, es-pecially estimation of the conditional probability density functions is very laborious.
Operationeel overstromingsrisicobeheer refereert aan activiteiten die als doel hebben om overstromingskansen en/of negatieve gevolgen van overstroming te beheren (ver-minderen) net voor de verwachte overstromingsgebeurtenis. Een inherent kenmerk van operationeel overstromingsrisicobeheer is dat uitkomsten van besluiten onzeker zijn. Het uitvoeren van de besluiten vereist tijd, daardoor is de overstroming een onzekere gebeurtenis in deze context. Het hoofddoel van deze studie was om be-naderingen voor de modellering van dijkfaalkansen en beslissingen in operationeel overstromingsrisicobeheer in Nederland te onderzoeken en te ontwikkelen. De studie bestond uit twee delen. In het eerste deel is het concept van (operationele) dijkfaal-kansen ge¨ıntroduceerd inclusief (i) onderzoek naar de hoofdinputcomponent van deze faalkans en (ii) methoden voor het bepalen van deze faalkans. In het tweede deel zijn modellen voor risicogestuurde beslissingen in operationeel overstromingsrisicobeheer voorgesteld. De operationele dijkfaalkans is een invoer voor deze modellen.
Deel ´e´en: operationele dijkfaalkansen
Een dijk faalt als gevolg van optreden van ´e´en of meerdere faalmechanismen. In het bijzonder in deze studie is de operationele dijkfaalkans gedefinieerd als de dijkfaalkans op een tijdstip of binnen een tijdsvenster in de nabije toekomst (enkele uren of dagen vooruit). De operationele dijkfaalkans wordt afgeleid met behulp van informatie, die relevant is voor het tijdstip/tijdsvenster, zoals actuele dijkinformatie5en kansverwach-tingen voor de natuurlijke belasting6. In de kansverwachtingen is een kansverdeling toegewezen aan een variabele die wordt voorspeld (bijvoorbeeld rivierafvoer). Op deze manier worden onzekerheden gerelateerd aan verwachtingen meegenomen. In deze stu-die zijn kansverwachtingen voor natuurlijke belastingen op dijken beschouwd als de hoofdinputcomponent van de operationele dijkfaalkans. Drie benaderingen, toegepast in Nederland, voor het afleiden van de kansverwachtingen voor waterstanden en ri-vierafvoeren zijn beschouwd. Er is geconcludeerd dat deze benaderingen verschillende typen van onzekerheid meenemen. Bovendien, prestatie van operationele dijkfaalkans is afhankelijk van de prestatie van de kansverdelingen (invoer).
Twee methoden voor het afleiden van de operationele dijkfaalkans zijn beschouwd. De eerste methode is gebaseerd op de fragility curves. Een fragility curve van een dijk wordt gedefinieerd als een functie van de set van belastingen op de dijk naar de
5Dijkinformatie bestaat uit dijkgeometrie, opbouw van ondergrond binnen en onder de dijk, de
dijkbekleding en geohydrologische informatie zoals freatische lijn en waterspanningen.
6Natuurlijke belastingen zijn hydraulische belastingen of (natuur-gerelateerde)
belastingdetermi-nanten zoals rivierafvoer, zeeniveau, windsnelheid en windrichting.
set van conditionele dijkfaalkansen. Indien een kansverwachting voor de conditionele belasting beschikbaar is, dan leidt de combinatie van de fragility curve en de kansver-wachting tot de operationele dijkfaalkans. Er is geconcludeerd dat de methode relatief eenvoudig is, maar dat de methode slechts de nabije toekomst onzekerheid van de con-ditionele belasting meeneemt en dat de nabije toekomst onzekerheid met betrekking tot andere belastingen wordt verwaarloosd. De tweede methode (raamwerk) voor het afleiden van operationele dijkfaalkansen is voorgesteld en het raamwerk gebruikt het model Hydra-VIJ as basis. Hydra-VIJ kan worden toegepast om dijken in de Vecht-en IJsseldeltas in Nederland te toetsVecht-en. Het raamwerk is bedoeld om operationele dijkfaalkansen te bepalen in een system dat bestaat uit een rivier en een meer [116]. In het raamwerk wordt de wind beschouwd als een tijdsonafhankelijke variabele, ech-ter wordt tijdsafhankelijkheid van windsnelheden en windrichtingen in werkelijkheid verwacht [116]. Het raamwerk kan worden uitgebreid zodat deze tijdsafhankelijkheid inbegrepen is.
Er is geconcludeerd dat de operationele dijkfaalkansen een kansverwachting vor-men voor een dijkdoorbraakgebeurtenis [116] en, zoals alle kansverwachtingen, moeten worden geverifieerd. Vanwege hoge veiligheidsnormen van dijken is de verificatie van operationele dijkfaalkansen niet eenvoudig in Nederland.
Er is ook aandacht was besteed aan recente ontwikkelingen in de dijkmonitoring in Nederland. Elektronische dijksensoren zijn beschouwd, vooral vanwege hun mogelijke toegevoegde waarde aan operationeel overstromingsrisicobeheer. De sensoren meten, real-time, variabelen zoals waterspanning, temperatuur en/of vervormingen binnen en onder dijken. Het toepassingsgebied van elektronische dijksensoren is verduidelijkt in deze studie:
• Succesvolle toepassing van elektronische dijksensoren in flood early warning (door middel van detectie van anomalie in dijksensormetingen) vereist dat de sensoren en het verschijnsel dat ze waarnemen genoeg tijd geven voor het toe-passen van een noodmaatregel (bijvoorbeeld preventieve evacuatie).
• Dijksensoren kunnen niet worden beschouwd als een zelfstandige bron van in-formatie. Informatie over de belasting is nodig om te verbeteren, interpreteren en verifi¨eren van de gegeven informatie.
• Om te leren van waterspanningsmetingen binnen een redelijke tijdsperiode, is het rationeel om de dijksensoren te plaatsen in dijken waar de frequentie van de ontwerpbelasting hoog is en/of de decimeringshoogte laag is.
Omdat elektronische dijksensoren een relatief nieuwe benadering vormen, zijn twee modellen voor een economische evaluatie van een dijksensorsysteem voorgesteld in het kader van (i) leren van metingen en dijkversterking en (ii) anomaliedetectie en noodregelen. In het eerste model is dijksensorinformatie gebruikt om onzekerheid in waterspanning te verminderen. De baten van het gebruiken van het dijksensorsysteem zijn dan gelijk aan de risicoreductie als gevolg van een (betere) dijkversterkingsstrate-gie. In het tweede model is anomalie in dijksensorinformatie gebruikt als een indicatie van ontwikkeling van een faalmechanisme. De baten van het gebruiken van het dijk-sensorsysteem zijn dan gelijk aan de risicoreductie als gevolg van het toepassen van een noodmaatregel in het geval van anomaliedetectie. Het nadeel van beide modellen
is dat veel invoerparameters moeten worden geschat en dat de modellen geen directe rekening houden met tijdsaspecten gerelateerd aan dijksensoren.
Deel twee: modellen voor riscogebaseerde beslissingen
Een basis/statisch beslisprobleem in operationeel overstromingsrisicobeheer is gedefi-nieerd als het probleem of een noodmaatregel, dat (financi¨ele) uitgaven vereist, moet worden toegepast gegeven een onzekere overstromingsgebeurtenis. Twee alternatie-ven worden dan beschouwd, namelijk toepassing van de maatregel en geen toepassing
van de maatregel. Uitkomsten van beide alternatieven zijn onzeker. Op basis van de
normatieve besliskunde is, in de eerste instantie, het minimaal verwachte monetaire kosten criterium toegepast. Bovendien is het criterium voor de preventieve evacuatie beslissing van een gebied bedreigd door een overstroming toegepast om een probabi-listische evacuatieregel te vinden. De regel is toegepast op de belangrijkste dijkringge-bieden7 in Nederland en dat resulteerde in een set van drempeloverstromingskansen. De drempeloverstromingskans is gedefinieerd als de verhouding van de kosten van preventieve evacuatie en de vermijde schade (gelijk aan de monetaire waarde van de dodelijke slachtoffers gered door de preventieve evacuatie) [115]. Indien de kans op overstroming van een dijkringgebied de drempeloverstromingskans overschrijdt, dan zijn de evacuatiekosten lager dan de financi¨ele voordelen van de evacuatie en de maatregel is optimaal vanuit het rationele oogpunt. In het kader van deze studie is de overstromingskans van een dijkringgebied gelijk aan de operationele dijkfaalkans. De ontwikkelde regels dragen bij aan het (rationele) beslissen onder onzekerheid in operationeel overstromingsrisicobeheer.
Bovendien is de regel ook aangepast door het aantal slachtoffers en reputatie van de beslisser (als een goede overstromingsrisico manager) als beslissingscriteria te be-schouwen, naast de kosten van de evacuatie. Dit betekent dus dat (i) de monetaire waardering van een mensenleven, dat in het algemeen lastig is, is weggelaten en (ii) reputatie, dat het gedrag van de beslisser kan be¨ınvloeden, in aanmerking is genomen. De wijziging is gebaseerd op een multi-criteria beslismethode. Er is geconcludeerd dat de probabilistische evacuatieregel, op basis van het minimaal verwachte monetaire kos-ten criterium, vormt een speciaal geval van de aangepaste regel. Verder is opgemerkt dat de problemen met de monetaire waardering van een mensenleven niet worden opgelost met deze aanpak: een indirecte waardering van een mensenleven vindt dan plaats.
Het basis/statisch beslisprobleem in de monetaire setting is uitgebreid naar een dynamisch beslisprobleem door het besluit wacht met toepassing van de
noodmaatre-gel mee te nemen. Op basis van de literatuurstudie zijn twee dynamische modellen
voorgesteld: beslismodel I en beslismodel II. De modellen kunnen worden gebruikt om te bepalen wanneer/of de toepassing van een noodmaatregel tegen overstromin-gen economisch verantwoord is rekening houdend met de tijdsafhankelijkheden tussen het weer8en/of weersverwachtingen. In beslismodel I wordt de overstroming verwacht
7Een dijkring is een systeem van waterkeringen (zoals dijken, duinen, kunstwerken,
stormvloed-keringen) en hoge gronden welke beschermen het gebied erachter tegen overstroming vanuit de zee, de grote rivieren (de Rijn, de Maas, de Vecht, enz.), het IJsselmeer en het Markermeer, of een com-binatie van deze bedreigingen [100]. Een dijkringgebied is een gebied dat is beschermd door een dijkring [100].
8De term weer is gebruikt voor hydraulische belastingen op de dijk/dijkring (waterstanden,
aan het einde van het beslisproces en de noodmaatregel, eenmaal toegepast, kan niet worden gestopt. Door het uitstellen van de beslissing komt nieuwe informatie (weers-verwachtingen) beschikbaar. Deze informatie wordt gebruikt om de overstromingskans in het model te actualiseren. Door het uitvoeren van een eenvoudige berekening zijn literatuurbevindingen bevestigd: het meenemen van alternatief wacht leidt gemiddeld tot lagere verwachte kosten. Beslismodel II vormt een uitbreiding van beslismodel I, want het model laat toe voor een herhaalde toepassing van de noodmaatregel en een overstroming op verschillende tijdstippen. Op basis van een rekenvoorbeeld, zijn lite-ratuurbevindingen weer bevestigd: het meenemen van de tijdsafhankelijkheid tussen het weer in het model leidt gemiddeld tot lagere kosten. Beslismodel II is toegepast voor een preventieve evacuatiebeslissing van dijkringgebied 48 in Nederland. De con-clusie is dat het toepassen van beide modellen veel werk vereist: in het bijzonder het schatten van de voorwaardelijke kansdichtheidsfuncties, wat heel moeizaam is.
ven) of voor belastingdeterminanten (rivierafvoer, meerpeil, windcondities, enz.)
Introduction
1.1
Decision making under uncertainty
Flood risk management aims to manage the probability and/or negative consequences of flooding on people, the economy and the environment, where the flooding probabil-ity and flood consequences are combined in the flood risk1. Dikes, storm surge barriers or water storage areas are examples of structural flood risk management measures. Particularly, operational flood risk management refers to activities that aim to man-age (reduce) the probability and/or negative consequences of flooding just prior to the expected flood. These activities include flood forecasting, issuing of flood warnings, preventive evacuation, placing of sandbags etc. Operational flood risk management is linked to the third layer of the multi-layer safety approach. The approach consists of three layers: (1) prevention of flooding realised by structural measures such as dikes and storm surge barriers, (2) mitigation of losses achieved by sustainable spatial de-velopment such as water resistant building, and (3) calamity management such as preventive evacuation [108].
An inherent feature of operational flood risk management is that outcomes of decisions taken are uncertain. Execution of these decisions requires time, therefore the flood is an uncertain event in this context. It should be emphasised that flood forecasting cannot reduce this uncertainty to zero. Forecasts of water levels are usu-ally derived using mathematical models, which approximate real physical processes and use uncertain inputs, and hence the forecasts (outputs) are also the subject to uncertainty. The uncertainty is one of the factors that causes that decisions taken are not necessarily the ”best” decisions in the aftermath. In the following paragraphs two examples of decision making under uncertainty are analysed in the context of operational flood risk management.
Example: evacuation in Dutch provinces in 1995
In January 1995, heavy precipitation in Northern France, the Belgian Ardennes and in Germany led to high water levels on the Rhine and the Meuse [115]. The Rhine discharge then reached 12, 000 m3/s at location Lobith in the Netherlands and this
1Usually, the flood risk is defined as flooding probability times consequences of flooding.
was the highest observed discharge since 1926, when a record discharge of 12, 600 m3/s
was measured [115]. The Meuse discharge reached 2900 m3/s at location Borgharen in
the Netherlands, and a record discharge of 3100 m3/s was measured in 1993 [80]. The
event directly affected three Dutch provinces: Limburg, Gelderland and Overijssel, see Figure 1.1 for locations of the provinces.
Figure 1.1: The largest water systems in the Netherlands and three provinces directly affected by the high water event in January 1995.
On the 28th of January, the situation in the province of Gelderland was alarm-ing [7]. Based on information from Germany, the water boards2 expected further increase in water levels. On Sunday the 29th of January, a crisis meeting3 was or-ganised [71]. Due to a bad condition and high saturation of the dikes4, forecasted water levels and features of the region5, participants of the meeting agreed that evac-uation of citizens was unavoidable [7]. On Monday the 30th of January, the regional management team of Nijmegen6decided to evacuate inhabitants of high flood risk
mu-2Dutch authorities responsible for managing water defences, waterways, water levels, water quality
and sewage treatment in their regions.
3Participants of the meeting: inter alia, the provincial governor (in Dutch: ”Commissaris van de
Koningin”), chairmen of the regional coordination centres, representatives of the water boards.
4The water boards stated that from Tuesday the 31th of January the safety of the dikes could
not longer be guaranteed [7].
5In case of flooding, the water depth of at least 2 meters could be reached within 24 hours [7]. 6The regional management team, under the leadership of the mayor of Nijmegen, consisted of
secretary of the municipality Nijmegen, heads of public services (police, fire brigade, medical care) and mayors of other endangered municipalities.
nicipalities: West Maas en Waal, Druten, Millingen aan de Rijn, parts of Ubbergen and Nijmegen [71]. First, voluntary evacuation and organised evacuation of hospit-als and nursing homes took place. On Tuesday the 31st of January, a compulsory evacuation of the area started. Within the next days, also other endangered areas were preventively evacuated, about 250, 000 people in total. The situation stayed ser-ious during the following days. However, the breaching of dikes and life-threatening flooding did not occur - the dikes withstood the extreme load and the evacuees were allowed to return to their homes from the 4th and the 5thof February.
In this example, the decision to preventively evacuate was taken under uncertainty. The authorities made deductions about the flood based on the observed and forecasted water levels and the expected state of the dikes. The randomness of flooding (driven in this case mainly by the dike strength uncertainty) defines here the randomness of outcomes of ”evacuate” decision, which are: (1) the number of flood fatalities is reduced when flooding occurs or (2) no benefits of the measure when flooding does not occur. In both cases, the evacuation cost has to be taken into account; the cost can be considered as a known element in the decision process. On the other hand, outcomes of ”do not evacuate” decision are: (1) the number of flood fatalities is not reduced when flooding occurs or (2) no consequences when flooding does not occur. Frieser [30] analyses the high water event from 1995 and concludes that the evacuation decision was good from an economical point of view.
Example: Red River flood in 1997
The towns of Grand Forks and East Grand Forks, situated at the opposite banks of the Red River (of the North) in the United States of America, experienced a devastating flood in April 1997 that was caused by considerable snowfall in the fall and winter, and warm and cold temperatures in the spring as described by Morss and Wahl [64]. The flood damage in these two communities was considerable; evacuation prevented fatalities as water reached roofs of houses at some places.
The extreme conditions were predicted several months in advance. However, the water level (a flood wave7with a crest of 16.46 m) exceeded the dike heights that were adjusted to withstand the outlook of 14.94 m, issued by the US National Weather Service, plus a safety margin of 0.91 m. As a result, both towns were flooded. Morss and Wahl [64] indicate that incomplete information was provided then to the author-ities and that the forecast error8was not sufficiently accounted when preparing to the event: the 14.94 m outlook was a median forecast (the ”worst-case” forecast was not derived) and the 0.91 m safety margin was lower than the forecast error.
In summary, the towns were flooded in spite of preparations. This example is very specific, since a misunderstanding/miscommunication played a role in this case [64]. However, given the fact that it is impossible to perfectly forecast water levels, this example falls into the category of decision making under uncertainty. More precisely, the decision to raise the dikes was taken under uncertainty. The authorities used the outlook to make deductions about the future water level. The randomness of the future water level defines here the randomness of outcomes of ”raise the dikes to the
7Defined as the fall and rise of the water level in a lake or a river that might lead to flooding. 8The difference between the true/observed and forecasted value. The forecast error is assessed
using data (i.e. observations and corresponding forecasts).
level X” decision, which are: (1) the towns are spared if the future water level is lower than X and (2) the towns are flooded if the future water level is higher than X. In both cases, the cost of dike heightening has to be taken into account and the cost can be considered as a known element in the decision process.
1.2
Normative decision theory
To support the difficult process of decision making under uncertainty the normative decision theory can be applied. In general, the normative decision theory together with the descriptive decision theory constitute the main branches of the decision theory. The normative theory helps to model preferences of a rational individual. The theory is described by e.g. Cooke [20] and Bedford and Cooke [6] based on the work of Leonard Savage, John von Neumann and Oskar Morgenstern. The descriptive theory, on the other hand, describes how humans make decisions. Significant results in this field, specific on decision making under uncertainty, were achieved by Daniel Kahneman and Amos Tversky [44, 45].
In the normative decision theory, preferences of an individual (decision maker) over alternatives (decisions, or acts as written in [20]) with uncertain outcomes are ordered by the expected utility. The expected utility combines probability and utility function of outcomes. The uncertainty related to the outcomes is captured by the probabilities. The utility function is a real value function that describes preferences of the decision maker over outcomes. Assuming that preferences of the decision maker are rational9, it can be written that the decision maker prefers alternative a to alternative b if and only if:
EU (a) > EU (b) (1.1)
where EU (a) and EU (b) denote the expected utilities of alternatives a and b, respect-ively. For example, if alternative a results in outcome x with probability P and in outcome y with probability 1 − P then the expected utility of alternative a is written as:
EU (a) = P · U (x) + (1 − P ) · U (y) (1.2)
and U is the utility function. In applications, the rule of maximising the expected utility is usually replaced with the rule of maximising expected monetary value (or minimising expected monetary cost). The utility of an outcome is hence assumed equal to the monetary value (cost) of this outcome and the decision maker prefers outcome x to outcome y if the monetary value (cost) of outcome x is higher (lower) than the monetary value (cost) of outcome y.
At this point, it is important to observe that the normative decision theory does not protect the decision maker from ”bad luck”, it provides methods that minimise
9The following principles must be satisfied for this purpose according to the theorem of
Sav-age: weak order, principle of definition, principle of dominance, sure thing principle, principle of refinement, strengthened principle of refinement [20, 6].
the consequences of getting an unfavourable outcome using all information available at the time of the decision making [72].
Application of the expected monetary cost criterion is presented in the following example.
Example: removal of cars in Dordrecht
In the Dutch city Dordrecht, authorities order removal of cars parked on the city quay when the forecasted water level (some days ahead) exceeds the quay height [98]. The measure aims to prevent the damage to the parked vehicles. It is assumed that the average damage to one car, in case of flooding, is counted in e5000 and the cost of removing one car ise200 (based on the work of van Ruiten et al. [98]). Although the authorities act according to a clear decision rule, the underlying problem falls into the category of decision problems under uncertainty. The overflow event is uncertain and using forecasted water level reduces this uncertainty. Assuming that P stands for the probability of the water level exceeding the quay height (the probability captures the residual uncertainty) the decision problem amounts to: ”should the cars be removed from the city quay given the probability P ?”. Two alternatives are considered, namely, ”remove the cars” and ”do not remove the cars”. The outcomes of ”remove the cars” alternative are: (1) the damage is prevented when the future water level exceeds the quay height or (2) no benefits of the measure when the water level stays below the quay height. The monetary cost of both outcomes is equal to the number of cars parked on the quay (denoted here by N ) timese200. On the other hand, the outcomes of ”do not remove the cars” alternative are: (1) the cars are damaged when the water level exceeds the quay height or (2) no consequences when the water level stays below the quay height. The monetary cost of the first outcome is equal to the number of cars parked on the quay timese5000 and the monetary cost of the second outcome is equal to zero. Consequently, the expected monetary cost of ”remove the cars” alternative iseN · 200 (i.e. P · N · 200 + (1 − P ) · N · 200) and the expected monetary cost of ”do not remove the cars” alternative iseP · N · 5000 (i.e. P · N · 5000 + (1 − P ) · 0). If probability P is equal to 0.2 and the number of cars is 50, then the expected monetary costs of ”remove the cars” and ”do not remove the cars” alternatives are e10, 000 ande50, 000, respectively. Then, according to the minimum expected monetary cost criterion, it is cheaper to remove the cars from the quay. Table 1.1 presents summary of the analysis.
Overflow (P ) No overflow (1 − P ) Expected costs
Remove cars N · 200 N · 200 N · 200
Do not remove cars N · 5000 0 P · N · 5000
Table 1.1: Expected monetary costs (ine) for removal of cars in the city Dordrecht.
1.3
Operational flood risk management and decision
models
In the context of operational flood risk management various measures can be con-sidered; these measures can have an effect on:
• Loads at water defences (decrease): e.g. deliberate flooding of an upstream area, in order to reduce water levels in the downstream areas of interest;
• Strength of water defences (increase): e.g. temporary heightening of dikes with sandbags, placing of geotextiles or an emergency support berm can increase dike’s strength;
• Flood consequences (reduction): e.g. preventive evacuation, removal of cars or building of secondary dikes can reduce flood consequences in the area of interest.
The measures that specifically increase the strength of water defences during flood threats are called emergency measures for flood prevention in the study of Lendering et al. [57]. Murphy [66] presents a problem of a decision maker who, facing an un-certain weather state, considers application of a measure that reduces the eventual loss; the author refers to this measure as protective measure. In this study, measures in operational flood risk management are generally called emergency flood measures. A basic decision problem in operational flood risk management is defined as a problem whether to apply an emergency flood measure, which requires (financial) ex-penditures, facing uncertain flood event. Two alternatives are then considered, namely, ”apply the measure” and ”do not apply the measure”. Outcomes/consequences of both alternatives are uncertain.
Generally, the outcomes can be divided into tangible and intangible outcomes. The former consists of the physical damage to buildings and terrain, vehicles, economic damage due to business interruption, evacuation and clean up costs etc. The intan-gible outcomes include flood fatalities, injured, psychological trauma, inconveniences, reputation damage etc. In contrast to the intangibles, the value of tangible outcomes can be relatively easy expressed in money. Note that only monetary outcomes of de-cisions have been considered in the example about the removal of cars in Dordrecht; the outcomes could be however extended with damage to reputation of the authorities in case of failing to remove the cars on time (i.e. when flooding occurs).
In operational flood risk management, uncertainties about the outcomes can be quantified by means of the flooding probability at a near-future point in time or within a near-future time window. In this study, the flooding probability is defined as the failure probability of a dike or a system of dikes as a result of one or more dike failure mechanisms (based on the definition of Vrijling [104]). A dike fails when load at the dike (such as water levels and waves) exceeds the strength of the dike; probability distribution functions of the load and the strength are therefore required. These distributions can be estimated using historical observations entailing e.g. the annual flooding probabilities. Due to high dike safety standards, the annual flooding probabilities are usually small in the Netherlands. To give an idea: in vital parts of the country, primary water defences were designed to resists the water levels with the exceedance frequency of 1/10, 000 per year. Different flood/dike failure events
and their occurrence probabilities are averaged in the annual flooding probability. In operational flood risk management however the focus lies on the probability of a particular future flood/dike failure event, called further the operational dike failure probability. To make deductions about the probability of occurrence of such an event, actual observations and forecasts of loads at dikes and/or observations of geohydrolo-gical processes inside and under the dikes can be used. In the Netherlands, attention is paid nowadays to near-future probability forecasting of water levels and river dis-charges. In probability forecasting, uncertainties about future values of variables are quantified by means of probabilities. Furthermore, many initiatives have been recently undertaken to study electronic dike sensors, which measure, real-time, variables such as pore water pressure, temperature and/or deformations inside and under dikes. The goal of using the dike sensors is to increase knowledge about dikes, dike failure mechanisms, improve simulation models and flood early warning. However, economic appraisal of a dike sensor system is still an outstanding issue.
Having outcomes of the alternatives in the basic decision problem valuated in money and having uncertainties about the outcomes assessed by means of the prob-abilities, the expected monetary cost of each alternative can be calculated, and con-sequently the minimum expected monetary cost criterion can be applied to find the optimal decision (i.e. the alternative that minimises the expected monetary cost). The approach can support the decision maker and/or substantiate taken decisions. According to Bedford and Cooke [6], the normative decision theory helps to structure the decision problem and this is already beneficial. Furthermore, in some cases, the minimum expected monetary cost criterion can be modified into a probabilistic de-cision rule for application of an emergency flood measure. For example, the rule can read as follows: ”an area should be preventively evacuated when flooding probability of the area exceeds 0.1”. This approach to decision making in operational flood risk management is new in the Netherlands. In practice, preventive evacuation decision is mainly based on deterministic information (e.g. observations, deterministic/point forecasts of natural loads) and the corresponding uncertainties are seldom explicitly taken into account [30, 87].
The basic decision problem (i.e. apply/do not apply an emergency flood meas-ure under uncertainty), in the monetary setting, can be extended and modified in a number of ways. For example, including the alternative ”wait with application of the measure until the next time point” constitutes one of the extensions (i.e. from a static to a dynamic approach). Most decision making problems are dynamic in nature including decision problems in operational flood risk management: in awaiting for new information, application of an emergency flood measure can be delayed in time. The alternative ”wait with application of the measure” decreases the effective-ness of the measure however allows obtaining more reliable information about the upcoming event (e.g. new forecasts of water levels become available) and therefore prevents taking a wrong decision. Furthermore, a modification of the basic decision problem is to consider application of an emergency flood measure (under uncertainty) with respect to several decision criteria. For example, the alternatives can be evalu-ated with respect to the expected number of fatalities and/or reputation damage of authorities. The multi-criteria decision making methods, founded on the normative and descriptive decision theories, offer a manner to evaluate alternatives with respect to decision criteria having different units (hence not necessary expressed in money)
and/or unequal importance.
1.4
Objectives and scope of the study
The main goal of this study is to investigate and develop approaches to modelling dike failure probability and risk-based decision making in oper-ational flood risk management in the Netherlands.
Objectives of this study are summarised as follows:
1. Investigation of methods applied in the Netherlands to derive near-future prob-ability forecasts for water levels and river discharges.
2. Conceptual investigation of electronic dike sensors and development of methods for economic appraisal of a dike sensor system.
3. Investigation and development of methods for derivation of operational dike failure probabilities focusing on (hydraulic) loads at dikes.
4. Development and application of a probabilistic decision rule for preventive evac-uation of an area endangered by flooding.
5. Investigation and development of risk-based decision models for the application of an emergency flood measure that influences flood consequences.
1.5
Overview
This document begins with an introduction (Chapter 1) and it is finalised with conclu-sions and recommendations (Chapter 9). Furthermore, this document can be divided into two parts: part that describes dike failure probabilities (Chapters 3 to 5) and part that is devoted to modelling decision making in operational flood risk management (Chapters 6 to 8).
In Chapter 2, derivation of dike failure probabilities in the Netherlands is de-scribed. Dike failure mechanisms and dike failure probabilities are the subjects of Section 2.2. The fragility curves of (existing) dikes, which constitute part of a total dike failure probability, are considered in Section 2.3. The concept of dike failure probabilities comes back in the next chapters and the application of fragility curves in operational flood risk management is presented in Chapter 5 (Section 5.2).
In Chapter 3, methods for derivation of near-future probability forecasts for water levels and river discharges in the Netherlands are described; three approaches are considered (Sections 3.2 to 3.4). Near-future probability forecasts are used to derive operational dike failure probabilities in Chapter 5.
Electronic dike sensors and modelling the economic appraisal of a dike sensor system constitute the main subjects of Chapter 4. Application area of the sensors is clarified in Section 4.2. A simple economic appraisal of a dike sensor system is given in Section 4.3. The cost-benefit analysis, conducted in the project ”Flood risk in the 21st century”, is described in Section 4.4, as this approach is used as basis for a detailed economic appraisal of a dike sensor system. The detailed economic appraisal requires
definition of annual flooding probabilities with and without dike sensor information (Section 4.5). Section 4.6 presents two models for the detailed economic appraisal in the context of (1) learning from measurements and dike reinforcement and (2) anomaly detection and emergency flood measures. Exemplary application of the models is presented in Section 4.7.
Information from Chapters 2, 3 and 4 is used in Chapter 5, which describes the concept of operational dike failure probabilities. In Section 5.2, fragility curves are applied to derive a dike failure probability for the near-future. The model Hydra-VIJ is described in Section 5.3, as this model is used as a basis in the practical approach (framework) for derivation of operational dike failure probabilities (Section 5.4). The approach is applied to calculate operational dike failure probability of an existing dike in the Netherlands (Section 5.5). General remarks about operational dike failure probabilities are given in Section 5.6.
The concept of operational dike failure probabilities is used in Chapters 6, 7 and 8. Chapter 8 can be considered separately from Chapters 6 and 7.
Chapter 6 is devoted to derivation of a probabilistic decision rule for preventive evacuation of an area endangered by flooding. In Section 6.2, definition, cost and benefits of preventive evacuation are presented. In Section 6.3, estimation of flood damage and loss of life in the Netherlands is described (the model HIS-SSM). In Section 6.4, the probabilistic evacuation decision rule is proposed based on cost and benefits of preventive evacuation. The rule is applied to main dike systems in the Netherlands in Section 6.5 using information from the project ”Flood risk in the 21st century”, which was also obtained with the model HIS-SSM.
Modification of the probabilistic evacuation decision rule is presented in Chapter 7. The rule is adjusted using a multi-criteria decision making method: the Promethee. The method is applied to preventive evacuation decision taking into account decision criteria such as the number of flood fatalities (in opposite to the monetary valuation of a human live as presented in Section 7.2) and reputation (Section 7.3). The method itself is described in Section 7.4. The modified probabilistic evacuation decision rule is defined in Section 7.5, in this section the rule is also applied to main dike systems in the Netherlands and a sensitivity analysis of the results is performed. Remarks on using multi-criteria decision making methods are given in Section 7.6.
In Chapter 8, the concept of dynamic decision making in operational flood risk management is presented. Two decision models are proposed in this chapter: decision model I (Section 8.2) and decision model II (Section 8.3). Theoretical background and simple applications of these models are given. In Section 8.4, decision model II is additionally applied to a preventive evacuation decision of an area endangered by flooding in the Netherlands.
The outline of the study is also presented in Figure 1.2 together with status of the considered subjects (i.e. literature study or proposal).
1. Introduction Part 1
2. Derivation of dike failure probabilities in the Netherlands
• Dike failure mechanisms and probability of dike failure (literature study)
• Fragility curves of dikes (literature study) • Examples of fragility curves of existing
dikes
3. Near-future probability forecasts for wa-ter levels and river discharges in the Nether-lands
• Three approaches to derivation of near-future probability forecasts (literature
study)
4. Economic appraisal of a dike sensor sys-tem
• Application area of dike sensors (literature
study)
• Models for an economic appraisal of dike sensors (proposal )
• Examples of the economic appraisal
5. Operational dike failure probabilities
• Operational dike failure probabilities derived with fragility curves (literature
study)
• Framework based on Hydra-VIJ (proposal) • Application of the framework
Part 2
6. First insight into the probabilistic evacu-ation decision rule in the Netherlands
• Preventive evacuation (literature study) • Probabilistic evacuation decision rule,
monetary setting (proposal ) • Application of the decision rule
7. Modification of the probabilistic evacu-ation decision rule
• Monetary valuation of a human life, reputation (literature study)
• Modification of the probabilistic evacuation decision rule, Promethee (proposal ) • Application of the decision rule
8. Dynamic decision making in operational flood risk management
• Decision models I and II, monetary setting (proposal )
• Application of decision model II
9. Conclusions and recommendations
Figure 1.2: Outline of the study together with status of the considered subjects (i.e. literature study or proposal).
1.6
Key definitions and assumptions
Key definitions and assumptions that apply to this study are summarised as follows: • Alternative/decision - in this study, decision is assumed to be an alternative in a decision making process and also an outcome of such a process (e.g. optimal decision is an outcome).
• Annual - in this study, the term refers to the winter half of a year (months: October - March).
• Annual dike failure probability - dike failure probability per year (the winter part of a year). In the Netherlands, a dike failure probability within the summer half of a year is such low that can be disregarded.
• Climatology - refers to the study of the climate based on observations gathered over a long period of time.
• Decimate height - in this study, the difference between the design load at the dike and the load that is exceeded 10 times more frequent than the design load.
• Design load - in this study, design load in the case of overflow failure mechan-ism is equal to the design water level; design load in the case of wave overtopping failure mechanism is equal to the level on a dike that is exceeded by water level plus waves with the frequency that corresponds to the safety standard of the dike.
• Design water level - in this study, the water level at a dike, for which the exceedance frequency corresponds to the safety standard of the dike.
• Dike failure probability - failure probability of a dike as a result of one or more dike failure mechanisms (based on the definition of Vrijling [104]). It is assumed that dike failure leads to flooding. In this study, no attention is paid to the failure probability of water defences other than dikes. The mechanisms overflow, wave overtopping, uplift and piping, and macro-stability are of the primary interest.
• Dike information - in this study, dike information consists of the dike’s geo-metry, the subsoil composition and characteristics inside and under the dike, the revetment of the dike and geohydrological information such as the phreatic surface and pore water pressures [65].
• Dike-ring - in the Netherlands, a system of water defences (such as dikes, dunes, hydraulic structures) and high grounds that directly protect the land behind against flooding from the sea, the large rivers (e.g. the Rhine, the Meuse, the Vecht) and the Lakes IJssel and Marker, or a combination of these threats [100].
• Dike-ring area - in the Netherlands, an area that is protected by a dike-ring [100].
• Dike strength - in this study, dike strength is described by the dike’s geometry (e.g. dike height, inclination), the subsoil composition and characteristics inside and under the dike and the revetment of the dike (e.g. grass, stones, asphalt).
• Flood/flooding - in this study, no distinction is made between ”flood” and ”flooding” and both terms refer to ”the spilling over or failing of the normal limits for example stream, lake, sea or accumulation of water as a result of heavy precipitation through lack or beyond of the discharge capacity of drains, or snow melt, dams or dikes break affecting areas” as defined by Balica [3].
• Flooding probability (of an area) - in this study, flooding probability refers to the failure probability of a dike or a system of dikes.
• Flood wave - a fall and rise of the water level in a lake or a river that might lead to flooding.
• Forecast - a prediction about a future value of a variable.
• Forecast system - a system that usually contains a mathematical model, which is used to produce a forecast of the predictand; (1) perfect forecast system pro-duces forecasts that are always equal to the observed value of the predictand (this is a theoretical case), (2) imperfect forecast system produces forecasts that are not always equal to the observed value of the predictand, (3) unskilled fore-cast system produces forefore-casts that are not better than information obtained from the climatology (the unskilled forecast system is a special case of an im-perfect forecast system).
• Human failure/error - in this study, it is defined as a failure to gather in-formation, interpret correctly the information and/or to apply a measure that is caused by a human. In this study, no extensive attention is paid to the role of the human error in operational flood risk management.
• Hydraulic loads - water levels and (wind) waves acting on a dike.
• Lead-time - the time between the moment for which the forecast holds and the moment of the forecast issuance.
• Loads - forces acting on a dike.
• Load explanatory variables - mostly nature-related variables that influence water levels and (wind) waves acting on a dike. Examples of these variables are river discharge, sea/lake level, wind speed and wind direction.
• Long-term - the term describes objects that refer to a long period of time (years).
• Medium-range - the term describes objects that refer to the near-future up to several days ahead but later than 24 − 72 hours ahead.
• Threshold flooding probability - the lowest flooding probability, for which preventive evacuation is economically worthwhile.
• Natural loads - hydraulic loads or (nature-related) load explanatory variables such as river discharge, sea/lake level, wind speed and wind direction.
• Near-future - the term refers to a point in time or to a time period up to several days ahead.
• Operational dike failure probability - dike failure probability at a near-future point in time or within a near-near-future time window (i.e. several hours or days ahead) derived using information that refers to the particular near-future.
• Predictand - a variable that has to be forecasted.
• Probability forecast - a predictive probability distribution function of a vari-able that has to be forecasted.
• Short-term - the term describes objects that refer to the near-future up to 72 hours ahead.
• Storm surge - a rise of sea level due to strong wind that pushes seawater towards the shore (storm surge can be also observed in lakes).
• Tidal river area - this is an area in the Netherlands in the Rhine-Meuse delta, where the sea has an influence on water levels. Also called the lower river area.
• Upper river area - this is an area in the Netherlands, where the sea has no influence on water levels, the rivers Rhine/Meuse dominate in the area. Also called the non-tidal river area.
• Wind conditions - wind speed and wind direction.
Some of the presented definitions are repeated and refined in the following chapters.
Derivation of dike failure
probabilities in the
Netherlands
2.1
Introduction
(Parts of this chapter were published in [115] and [116].)
The Netherlands is currently subdivided into 101 dike-ring areas. A dike-ring is a system of water defences (such as dikes, dunes, hydraulic structures) and high grounds that directly protect the land behind against flooding from the sea, the large rivers (e.g. the Rhine, the Meuse, the Vecht) and the Lakes IJssel and Marker, or a combination of these threats [100]. The area that is protected by a dike-ring is called a dike-ring area. Water defences that belong to a dike-ring or dikes, dames and other constructions that protect dike-ring areas constitute the so-called primary water defences [100].
A cost-benefit analysis was applied in the 1960s to derive safety standards for the dike-rings (called also safety standards for dike-ring areas). The safety standard is defined as the maximum exceedance frequency of the water level that a water defence, within a dike-ring, must withstand [29]. The standards vary from 1/10, 000 to 1/1250 per year for large dike-ring areas, depending on the economic activities, number of inhabitants in the area and type of the hazard [81]. Figure 2.1 shows main dike-ring areas in the Netherlands and the corresponding safety standards.
The primary water defences are evaluated periodically for the required safety standards. This assessment is based on the hydraulic conditions (in Dutch: ”Hydraul-ische Randvoorwaarden”) [100] and the Safety Assessment Regulation (in Dutch: ”Voorschrift Toetsen op Veiligheid Primaire Waterkeringen”) [99]. The latter consists of a set of rules for testing the water defences. The hydraulic conditions consist of water levels and wave conditions that the water defences should resist corresponding to the safety standards. The hydraulic conditions are updated regularly to account for recent technical developments or changes in the water systems and are approved by the Ministry of Infrastructure and the Environment. Hydra-models constitute official
−0.5 0 0.5 1 1.5 2 2.5 3 3.5 x 105 3.5 4 4.5 5 5.5 6 x 10 x−coordinate [m] y−coordinate [m] 1/10,000 1/4,000 1/2,000 1/1250
Figure 2.1: Main dike ring-areas in the Netherlands and the corresponding safety standards.
tools for derivation of the hydraulic conditions for primary dikes [24]. Next to the hydraulic conditions, the models estimate annual1dike failure probabilities for some dike failure mechanisms. The model PC-Ring can be also applied to asses reliability of primary water defences in the Netherlands [15].
In Section 2.2, different dike failure mechanisms are considered and the dike failure probability is defined. Furthermore, similarities and differences between the Hydra-models and PC-Ring are generally addressed. In Section 2.3, attention is paid to fragility curves of a dike, which constitute sub-components of the total dike failure probability. Also, examples of fragility curves of primary dikes in the Netherlands are given in this section.
2.2
Dike failure mechanisms and dike failure
prob-abilities
According to [75], a failure of a dike is defined as not fulfilling of its main function, which is preventing the protected area from being flooded, whereas a collapse of a dike is defined as a significant deformation of the dike. Failure of a dike may trigger its collapse and otherwise. Hydraulic loads, such as water levels and waves, constitute the major threats to water defences and whether a dike can withstand these loads depends on its strength [75]. The dike strength is described by the geometry of the dike (e.g. dike height, inclination), the revetment (e.g. grass, stones, asphalt), and the subsoil composition and characteristics inside and under the dike.
1In this study, the term ”annual” refers to the winter half of a year (months: October - March).
In the Netherlands, a dike failure probability within the summer half of a year is such low that it can be disregarded.
The failure of a dike is the result of one or more dike failure mechanisms [104]. Examples of the mechanisms are overflow, wave run-up, wave overtopping, uplift and piping or macro-stability of the inner (landward) dike slope. Overflow occurs when the water level at a dike exceeds the height of the dike leading to intrusion of water into the polder and initiation of erosion of the inner dike slope and/or other dike failure mechanisms [75]. In the case of wave run-up and wave overtopping, additionally waves contribute to the failure. Progressive erosion (and other dike failure mechanisms) may lead to a dike collapse and breach. Piping occurs when the seepage flow causes backward erosion in a water-bearing sand stratum under a dike leading to formation of open pipes between the upstream and downstream sides of the dike, which undermine the dike [76]. The intensity of the seepage flow depends on, inter alia, the difference between the water level at the dike and the water level in the polder (i.e. the inner water level). Uplift is a precondition for piping when the dike is founded on a (low-permeable) blanket layer and occurs when the layer lifts up and cracks as a result of high groundwater pressures under the layer [76]. Macro-instability of the inner dike slope occurs when massive part of the slope slides caused by insufficient shear strength of the soil [75].
Physical and empirical relations are used to describe dike failure mechanisms. The model of a dike failure mechanism usually amounts to a limit state function Z =
Z(X1, X2, . . . , Xn) that combines the load and strength variables {X1, X2, . . . , Xn},
which are relevant for the mechanism. The function is constructed such that when it is less than zero, the dike failure takes place, typically:
Z = R − S (2.1)
where R stands for the strength and S stands for the load. Below several examples of the limit state functions are given.
The limit state function for the overflow failure mechanism can be expressed as the difference between the dike height and the water level at the dike:
Zoverflow= Hd− H (2.2)
where Hd [m+NAP]2is the dike height and H [m+NAP] is the water level; the dike
is assumed to fail as soon as the water level exceeds the dike height (Zoverflow< 0). The limit state function for the wave run-up failure mechanism can be written as:
Zwave run-up= Hd− (H + Z2%) (2.3)
where Z2%[m] is the wave run-up height measured vertically from the still water line and it indicates a level that is exceeded by 2% of the number of incoming waves [78]. The limit state function for the wave overtopping failure mechanism measures the difference between the critical wave overtopping discharge and the occurring wave overtopping discharge:
2NAP is a reference level in the Netherlands and stands for New Amsterdam Ordnance Datum.
