Statistically simulated time series of wave parameters are required for many coastal and offshore engineering applications, often at the resolution of approximately 1 h. Various studies have relied on autoregressive moving-average (ARMA) processes to simulate synthetic series of wave parameters in a Monte Carlo sense. However, accurately representing inter-series dependencies has remained a challenge. In particular, the relationship between wave height and period statistics is complex, due to the limiting steepness condition. Here, we present a new simulation method for joint time series of significant wave height, mean zero-crossing periods and a directional regime variable. The latter distinguishes between northern and southwestern waves. The method rests on several model components which include renewal processes, Fourier series with random coefficients, ARMA processes, copulas and regime-switching. A particular feature is a data-driven estimate for a wave height-dependent limiting wave steepness condition which is used to facilitate copula-based dependence modeling. The method was developed for and applied to a data set in the Southern North Sea. For this site, the method could simulate time series with realistic annual cycles and inter-annual variability. In the time series data, the bivariate distribution of significant wave height and mean zero-crossing period was well represented. An influence of the directional regime on the bivariate distribution could also be modeled. However, the influence was not as strong in simulated data as in observed data. Finally, simulated series captured duration and inter-arrival time of storm events well. Potential applications for output of the simulation method range from the assessment of risks to the planning and budgeting of operations in coastal and offshore environments.

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Integrated risk assessment approaches to support coastal managers' decisions when designing plans are increasingly becoming an urgent need. To enable efficient coastal management, possible present and future scenarios must be included, disaster risk reduction measures integrated, and multiple hazards dealt with. In this work, the Bayesian network-based approach to coastal risk assessment was applied and tested at two Mediterranean sandy coasts (Tordera Delta in Spain and Lido degli Estensi-Spina in Italy). Process-oriented models are used to predict hazards at the receptor scale which are converted into impacts through vulnerability relations. In each site, results from 96 simulations under different scenarios are integrated by using a Bayesian-based decision network to link forcing characteristics with expected impacts through conditional probabilities. Consultations with local stakeholders and experts have shown that the tool is valuable for communicating risks and the effects of risk reduction strategies. The tool can therefore be valuable support for coastal decision-making.

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Emergency management and long-term planning in coastal areas depend on detailed assessments (meter scale) of flood and erosion risks. Typically, models of the risk chain are fragmented into smaller parts, because the physical processes involved are very complex and consequences can be diverse. We developed a Bayesian network (BN) approach to integrate the separate models. An important contribution is the learning algorithm for the BN. As input data, we used hindcast and synthetic extreme event scenarios, information on land use and vulnerability relationships (e.g., depth-damage curves). As part of the RISC-KIT (Resilience-Increasing Strategies for Coasts toolKIT) project, we successfully tested the approach and algorithm in a range of morphological settings. We also showed that it is possible to include hazards from different origins, such as marine and riverine sources. In this article, we describe the application to the town of Wells-next-the-Sea, Norfolk, UK, which is vulnerable to storm surges. For any storm input scenario, the BN estimated the percentage of affected receptors in different zones of the site by predicting their hazards and damages. As receptor types, we considered people, residential and commercial properties, and a saltmarsh ecosystem. Additionally, the BN displays the outcome of different disaster risk reduction (DRR) measures. Because the model integrates the entire risk chain with DRR measures and predicts in real-time, it is useful for decision support in risk management of coastal areas.

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This thesis investigates how selected multivariate probabilistic methods can be adapted for risk analysis and decision making in coastal and offshore environments. In particular, the thesis makes a contribution to decision support tools for risk reduction efforts in coastal environments and to statistical simulation methods for wave conditions. Generally, very few observations on negative impacts in coastal or offshore environments are available for risk analysis or decision making due to the rare nature of extreme events. However, synthetic impact data can be generated by propagating relevant hydro meteorological conditions to the environment of interest through a chain of multiple models. Especially in coastal environments, this chain often includes computationally intensive models. @en

Stochastic descriptions and simulations of oceanographic variables are essential for coastal and marine engineering applications. In the past decade, copula-based approaches have become increasingly popular for estimating the multivariate distribution of some variables at the peak of a storm along with its duration. The modeling of the storm shape, which contributes to its impact, is often simplified. This article proposes a vine-copula approach to characterize hourly significant wave heights and corresponding mean zero-crossing periods as a random process in time. The model is applied to a data set in the North Sea, and time series with the duration of an oceanographic winter are simulated. The synthetic wave scenarios emulate storms as well as daily conditions. The results are useful, for example, as input for coastal risk analyses and for planning offshore operations. Nonetheless, selecting a vine structure, finding appropriate copula families, and estimating parameters is not straightforward. The validity of the model, as well as the conclusions that can be drawn from it, are sensitive to these choices. A valuable byproduct of the proposed vine-copula approach is the bivariate distribution of significant wave heights and corresponding mean zero-crossing periods at the given location. Its dependence structure is approximated by the flexible skew-t copula family and preserves the limiting wave steepness condition. @en

Low frequency, high impact storm events can have large impacts on sandy coasts. The physical processes governing these impacts are complex because of the feedback between the hydrodynamics of surges and waves, sediment transport and morphological change. Predicting these coastal changes using a numerical model requires a large amount of computational time, which in the case of an operational prediction for the purpose of Early Warning is not available. For this reason morphodynamic predictions are not commonly included in Early Warning Systems (EWSs). However, omitting these physical processes in an EWS may lead to potential under or over estimation of the impact of a storm event. To solve this problem, a method has been developed to construct a probabilistic Bayesian Network (BN). This BN connects three elements: offshore hydraulic boundary conditions, characteristics of the coastal zone, and onshore hazards, such as erosion and overwash depths and velocities. The hydraulic boundary conditions are derived at a water depth of approximately 20 m from a statistical analysis of observed data using copulas, and site characteristics are obtained from measurements. This BN is trained using output data from many pre-computed process-based model simulations, which connect the three elements. Once trained, the response of the BN is instantaneous and can be used as a surrogate for a process-based model in an EWS in which the BN can be updated with an observation of the hydraulic boundary conditions to give a prediction for onshore hazards. The method was applied to Praia de Faro, Portugal, a low-lying urbanised barrier island, which is subject to frequent flooding. Using a copula-based statistical analysis, which preserves the natural variability of the observations, a synthetic dataset containing 100 events was created, based on 20 years of observations, but extended to return periods of significant wave height of up to 50 years. These events were transformed from offshore to onshore using a 2D XBeach (Roelvink et al., 2009) model. Three BN configurations were constructed, of which the best performing one was able to predict onshore hazards as computed by the model with an accuracy ranging from 81% to 88% and predict events with no significant onshore hazards with an accuracy ranging from 90% to 95%. Two examples are presented on the use of a BN in operational predictions or as an analysis tool. The added value of this method is that it can be applied to many coastal sites: (1) limited observations of offshore hydrodynamic parameters can be extended using the copula method which retains the original observations’ natural variability, (2) the transformation from offshore observations to onshore hazards can be computed with any preferred coastal model and (3) a BN can be adjusted to fit any relevant connections between offshore hydraulic boundary conditions and onshore hazards. Furthermore, a BN can be continuously updated with new information and expanded to include different morphological conditions or risk reduction measures. As such, it is a promising extension of existing EWSs and as a planning tool for coastal managers.

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