In this paper we propose a new particle smoother that has a computational complexity of O(N ), where N is the number of particles. This compares favourably with the O(N 2 ) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify in many existing algorithms.Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and on the analysis of an athletics data set, that our new method also substantially outperforms the simple FilterSmoother (the only other smoother with computational cost that is linear in the number of particles).

Effective management of flooding requires models that are capable of quantifying flood risk. Quantification of flood risk involves both the quantification of probabilities of flooding and the associated consequences. Modern flood risk models account for the probabilities of extreme hydraulic loading events and also include a probabilistic representation of the performance of flood defence infrastructure and its associated reliability. The spatial and temporal variability of flood events makes probabilistic representation of the hydraulic loading conditions on the flood defences complex. In the system method used widely within England and Wales, simplifying assumptions relating to the spatial dependence of flood events are made. Recent research has shown the benefits of using improved multivariate extreme value methods to define the hydraulic loading conditions for flood risk analysis models. This paper describes the development of an improved modelling system that enhances the systems‐based risk analysis model currently applied in practice, through the incorporation of a multivariate extreme value model. The improved system has been presented on a case study site in the North West of England.

It is widely recognised that coastal flood events can arise from combinations of extreme waves and sea levels. For flood risk analysis and the design of coastal structures it is therefore necessary to assess the joint probability of the occurrence of these variables. Traditional methods have involved the application of joint probability contours, defined in terms of extremes of sea conditions that can, if applied without correction factors, lead to the underestimation of flood risk and under-design of coastal structures. This paper describes the application of a robust multivariate statistical model to analyse extreme offshore waves, wind and sea levels around the coast of England. The approach described here is risk based in that it seeks to define extremes of response variables directly, rather than the joint extremes of sea conditions. The output of the statistical model comprises a Monte Carlo simulation of extreme events. These distributions of extreme events have been transformed from offshore to nearshore using a statistical emulator of a wave transformation model. The resulting nearshore extreme sea condition distributions have the potential to be applied for a range of purposes. The application is demonstrated using two structures located on the south coast of England. Notation

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The south coast of the UK is identified as a location where significant wave swell components are present within the regional wave climate. During the winters of 2006 and 2014, several sites along the south coast of the UK were subject to significant damages where flood events were recorded. These sea states were characterised by having a double-peaked wave spectra, observing a connection between wave spectrum shape and beach response. A two-dimensional (2D) physical model study was carried out to investigate the effect of gravel beach profile response under wave spectra characterised by swell-wave and wind-wave periods in various combinations. The physical model results showed the effect of bimodal wave spectrum on beach crest erosion and were compared with the parametric model Shingle and the numerical model XBeach-G. Based on this 2D physical model study, a new parametric model, Shingle-B, was derived and an online tool developed and made available on the website for the National Network of Regional Coastal Monitoring Programmes of England. This new tool has been validated at two sites in the south of England where field data of both waves and profiles were available.