Computing system reliability when system components are correlated presents a challenge because it usually requires solving multi-fold integrals numerically, which is generally infeasible due to the computational cost. In Dutch flood defense reliability modeling, an efficient method for computing the failure probability of a system of correlated components – referred to here as the Equivalent Planes method – was developed and has been applied in national flood risk analysis. The accuracy of the method has never been thoroughly tested, and the method is absent in the literature; this paper addresses both of these shortcomings. The method is described in detail, including an in-depth discussion about the source of error. A suite of system configurations were defined to test the error in the Equivalent Planes method, with a focus on extreme cases to capture the upper bound of the error. The 'exact' system reliability was computed analytically for the special case of equi-correlated components, and otherwise using Monte-Carlo directional sampling. We found that errors in the system failure probability estimates were low for a wide range of system configurations, and became more substantial for large systems with highly-correlated components. In the most extreme cases we tested, the error remained within three times the true failure probability. We provided an example of how one can determine if such error is tolerable in their particular application. We also show the computational advantage of using the Equivalent Planes method; large systems with small failure probabilities which take over 17 h for Monte Carlo directional sampling were computed with the Equivalent Planes in less than one second.
Abstract Generally, the methods to derive design events in a flood‐modelling framework do not take into account the full range of extreme storm events and therefore do not take into account all aleatory uncertainties originating from rainfall intensity and spatial variability. The design event method uses a single simulation in order to represent an extreme event. The study presents a probabilistic method to derive flood inundation maps in an area where rainfall is the predominant cause of flooding. The case study area is the J akarta B asin, I ndonesia. It typically experiences high‐intensity and short‐duration storms with high spatial variability. The flood hazard estimation framework is a combination of a M onte C arlo ( MC )‐based simulation and a simplified stochastic storm generator. Several thousands of generated extreme events are run in the S obek rainfall–runoff and 1 D ‐2 D model. A frequency analysis is then conducted at each location in the flood plain in order to derive flood maps. The result shows that in general, design events overestimate the flood maps in comparison with the proposed MC approach. The MC approach takes into account spatial variability of the rainfall. However, this means that there is a need to have a high number of MC ‐generated events in order to better estimate the extreme quantiles. As a consequence, the MC approach needs much more computational resources and it is time‐consuming if a full hydrodynamic model is used. Hence, a simplified flood model may be required to reduce the simulation time.
As part of the flood risk assessment in The Netherlands, extreme hydraulic boundary conditions (HBC) at coastal water defenses are calculated to assess the safety and sufficiency of the defenses.For this purpose, extreme offshore values of wave height and wave period with a frequency of occurrence of 1/10,000 years need to be estimated.The estimation is carried out using measurements at nine offshore locations in the North Sea, with a record length of 30 years.To estimate extreme wave heights and wave periods, the Generalized Pareto Distribution (GPD), which follows from extreme value theory, was fitted to peaks-over-threshold (POT) at each of the nine measurement stations.The fitted GPD parameters and consequently the extrapolated extreme values are particularly sensitive to the choice of threshold.A reproducible method was employed for threshold selection based on the anticipated behavior of the GPD shape parameter as the threshold approaches the domain of attraction.A modified regional frequency analysis (MRFA) was subsequently carried out to spatially smooth the GPD shape parameters.Final GPD fits were made using the shape-parameter output of the MRFA to produce final extrapolated extreme value estimates.The extreme values were compared with those resulting from an operationally-used distribution function in The Netherlands known as the conditional Weibull distribution.
Abstract. This paper discusses the new method developed to analyse flood risks in river deltas. Risk analysis of river deltas is complex, because both storm surges and river discharges may cause flooding and since the effect of upstream breaches on downstream water levels and flood risks must be taken into account. A Monte Carlo based flood risk analysis framework for policy making was developed, which considers both storm surges and river flood waves and includes hydrodynamic interaction effects on flood risks. It was applied to analyse societal flood fatality risks (the probability of events with more than N fatalities) in the Rhine–Meuse delta.
Recent observations and publications have presented the possibility of a high and accelerated sea-level rise (SLR) later this century due to ice sheet instability and retreat in Antarctica. Under a high warming scenario, this may result in a sea level in 2100 that is up to 2 m higher than present and 5 m in 2150. The large uncertainties in these projections significantly increase the challenge for investment planning in coastal strategies in densely populated coastal zones such as the Netherlands. In this paper, we present the results of two studies that were carried out within the framework of the Dutch Delta Programme. The first study showed that it is not only the absolute SLR that presents a challenge but also the annual rate of rise. The latter impacts the lifetime of constructions such as barriers and pumping stations. When the rate of sea-level rise increases up to several centimeters per year, the intended lifetime of a flood defense structure may be reduced from a century to several decades. This new challenge requires new technologies, experiments, strategies, and governance. The second study explored different strategies for the long term to adapt to high SLR (>1 m) and assessed the consequences thereof on adaptation and developments in the coming 2–3 decades. We believe that strategic choices have to be made regarding the permanent closure of estuaries, the pumping or periodic storage of high river discharges, agriculture in an increasingly saline coastal area, and the maintenance of the coastline by beach nourishments. These strategic choices have to be complemented by no-regret measures such as spatial reservations for future sand extraction (for beach nourishments) and future expansion of flood defenses, water discharge, and water storage. In addition, it is advised to include flexibility in the design of new infrastructure.
Abstract. Flood defences can be designed as multiple lines of defence. This paper presents an approach for finding an optimal configuration for flood defence systems, based on an economic cost-benefit analysis with an arbitrary number of interdependent lines of defence. The proposed approach is based on a graph algorithm and is, thanks to some beneficial properties of the application, able to traverse large problems. A number of case studies were carried out to compare the optimal paths found by the proposed approach with the results of competing methods, and were found to generate (near) identical results. The work presented here makes cost-benefit analyses of complex flood defence systems with interdependent multiple lines of defence both easier and applicable to a broad range of flood defence systems with multiple lines of defence.
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