Economic optimisation of flood risk management projects

Abstract

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 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 optimization 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 optimization 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 optimization 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 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 optimization 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 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 optimization under budget constraints. It continues with the optimization 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 optimization 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 optimization. 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 optimization 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 optimization 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 optimizations 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 optimization model presented in chapter 4. In Chapter 10 conclusions are summarized.