Profile extrema for visualizing and quantifying uncertainties on excursion regions. Application to coastal flooding

We consider the problem of describing excursion sets of a real-valued function $f$, i.e. the set of inputs where $f$ is above a fixed threshold. Such regions are hard to visualize if the input space dimension, $d$, is higher than 2. For a given projection matrix from the input space to a lower dimensional (usually $1,2$) subspace, we introduce profile sup (inf) functions that associate to each point in the projection's image the sup (inf) of the function constrained over the pre-image of this point by the considered projection. Plots of profile extrema functions convey a simple, although intrinsically partial, visualization of the set. We consider expensive to evaluate functions where only a very limited number of evaluations, $n$, is available, e.g. $n<100d$, and we surrogate $f$ with a posterior quantity of a Gaussian process (GP) model. We first compute profile extrema functions for the posterior mean given $n$ evaluations of $f$. We quantify the uncertainty on such estimates by studying the distribution of GP profile extrema with posterior quasi-realizations obtained from an approximating process. We control such approximation with a bound inherited from the Borell-TIS inequality. The technique is applied to analytical functions ($d=2,3$) and to a $5$-dimensional coastal flooding test case for a site located on the Atlantic French coast. Here $f$ is a numerical model returning the area of flooded surface in the coastal region given some offshore conditions. Profile extrema functions allowed us to better understand which offshore conditions impact large flooding events

How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

International audienceThe knowledge of extreme coastal water levels is useful for coastal flooding studies or the design of coastal defences. While deriving such extremes with standard analyses using tide-gauge measurements, one often needs to deal with limited effective duration of observation which can result in large statistical uncertainties. This is even truer when one faces the issue of outliers, those particularly extreme values distant from the others which increase the uncertainty on the results. In this study, we investigate how historical information , even partial, of past events reported in archives can reduce statistical uncertainties and relativise such outlying observations. A Bayesian Markov chain Monte Carlo method is developed to tackle this issue. We apply this method to the site of La Rochelle (France), where the storm Xynthia in 2010 generated a water level considered so far as an outlier. Based on 30 years of tide-gauge measurements and 8 historical events, the analysis shows that (1) integrating historical information in the analysis greatly reduces statistical uncertainties on return levels (2) Xynthia's water level no longer appears as an outlier, (3) we could have reasonably predicted the annual exceedance probability of that level beforehand (predictive probability for 2010 based on data until the end of 2009 of the same order of magnitude as the standard es-timative probability using data until the end of 2010). Such results illustrate the usefulness of historical information in extreme value analyses of coastal water levels, as well as the relevance of the proposed method to integrate heterogeneous data in such analyses

Morphodynamique d'une dune sous-marine du détroit du pas de Calais

National audienceMorphodynamics of an undersea sandwave of the Dover Straits. This paper investigates the dynamics of sandwaves in relationship with tidal currents and weather conditions. The studied sandwaves are located in the Dover Straits and are covered by megaripples. These megaripples have migration speeds of 1 mh−1 and slopes of 34◦, suggesting the potential for avalanches to occur along the flanks of the sandwave. Tidal cycles without reversing currents were observed during stormy weather.Wind-induced currents lead to a unidirectionalmigration of megaripples and sandwaves.Well-defined areas without megaripples were observed and correlated with an increase in sandwave height.We propose interpretations for understanding sandwave saturation and migratio

Climate change impact on waves in the Bay of Biscay, France

International audienceThe knowledge of offshore and coastal wave climate evolution towards the end of the twenty-first century is particularly important for human activities in a region such as the Bay of Biscay and the French Atlantic coast. Using dynamical downscaling, a high spatial resolution dataset of wave conditions in the Bay of Biscay is built for three future greenhouse gases emission scenarios. Projected wave heights, periods and directions are analysed at regional scale and more thoroughly at two buoys positions, offshore and along the coast. A general decrease of wave heights is identified (up to -20 cm during summer within the Bay of Biscay), as well as a clockwise shift of summer waves and winter swell coming from direction. The relation between those changes and wind changes is investigated and highlights a complex association of processes at several spatial scales. For instance, the intensification and the north-eastward shift of strong wind core in the North Atlantic Ocean explain the clockwise shift of winter swell directions. During summer, the decrease of the westerly winds in the Bay of Biscay explains the clockwise shift and the wave height decrease of wind sea and intermediate waves. Finally, the analysis reveals that the offshore changes in the wave height and the wave period as well as the clockwise shift in the wave direction continue toward the coast. This wave height decrease result is consistent with other regional projections and would impact the coastal dynamics by reducing the longshore sediment flux

Self-organized kilometer-scale shoreline sand wave generation: sensitivity to model and physical parameters

The instability mechanisms for self-organized kilometer-scale shoreline sand waves have been extensively explored by modeling. However, while the assumed bathymetric perturbation associated with the sand wave controls the feedback between morphology and waves, its effect on the instability onset has not been explored. In addition, no systematic investigation of the effect of the physical parameters has been done yet. Using a linear stability model, we investigate the effect of wave conditions, cross-shore profile, closure depth, and two perturbation shapes (P1: cross-shore bathymetric profile shift, and P2: bed level perturbation linearly decreasing offshore). For a P1 perturbation, no instability occurs below an absolute critical angle ¿c0˜ 40-50°. For a P2 perturbation, there is no absolute critical angle: sand waves can develop also for low-angle waves. In fact, the bathymetric perturbation shape plays a key role in low-angle wave instability: such instability only develops if the curvature of the depth contours offshore the breaking zone is larger than the shoreline one. This can occur for the P2 perturbation but not for P1. The analysis of bathymetric data suggests that both curvature configurations could exist in nature. For both perturbation types, large wave angle, small wave period, and large closure depth strongly favor instability. The cross-shore profile has almost no effect with a P1 perturbation, whereas large surf zone slope and gently sloping shoreface strongly enhance instability under low-angle waves for a P2 perturbation. Finally, predictive statistical models are set up to identify sites prone to exhibit either a critical angle close to ¿c0 or low-angle wave instability.Postprint (author's final draft

funGp: An R Package for Gaussian Process Regression with Scalar and Functional Inputs

This article introduces funGp, an R package which handles regression problems involving multiple scalar and/or functional inputs, and a scalar output, through the Gaussian process model. This is particularly of interest for the design and analysis of computer experiments with expensive-to-evaluate numerical codes that take as inputs regularly sampled time series. Rather than imposing any particular parametric input-output relationship in advance (e.g., linear, polynomial), Gaussian process models extract this information directly from the data. The package offers built-in dimension reduction, which helps to simplify the representation of the functional inputs and obtain lighter models. It also implements an ant colony based optimization algorithm which supports the calibration of multiple structural characteristics of the model such as the state of each input (active or inactive) and the type of kernel function, while seeking for greater prediction power. The implemented methods are tested and applied to a real case in the domain of marine flooding

On the use of linear stability model to characterize the morphological behaviour of a double bar system. Application to Truc Vert Beach (France).

10 pages, 9 figures, 3 tableauxInternational audienceSandy barred beaches are often characterized by the presence of rhythmic patterns such as crescentic bars. In this paper, a linear stability analysis (LSA) model is used to characterize the morphological behaviour of the double bar system of Truc Vert beach. Using a limited number of combination of representative bathymetries, wave classes and water levels, the morphodynamic response of the system is analysed, focussing on the geometrical characteristics of 3D patterns generated with the model. These characteristics are described and then compared with available observations. The shapes and the wavelengths of the instabilities predicted by the model compare well with field observations. Thus, the use of linear stability model, with representative hydrodynamic conditions and bathymetries of the considered site, allows a characterization of the global morphodynamic behaviour of a double-barred system

Vagues sur la côte aquitaine : régionalisation dynamique de 1958 à 2002

National audienceUn système de modélisation de vagues, forcé uniquement par des champs de vent a été mis en place avec le code WAVEWATCH IIITM sur une période de 44 ans (1958 à 2002) en vue d'étudier l'impact de la variabilité climatique passée sur les états de mer et sur l'érosion de la côte aquitaine. Les emboîtements hauturiers forcés par les champs de vent de la réanalyse ERA-40 ont été calibrés sur la période 1998-2002 sur 8 points de mesures. Les résultats sur 44 ans ont ensuite été validés sur 11 bouée

Morphodynamic models used to study the impact of offshore aggregate extraction:A review

http://www.cerf-jcr.org/images/stories/17127-4%20idier%20web%20only.pdfInternational audienceThis review highlights three morphodynamics modelling approaches, used for offshore marine aggregate extraction impact assessment. These approaches are based upon examples of (1) full process-based models; (2) idealised processbased models; and (3) conceptual models. Illustrated also is the way in which these models, applied for extractions on flat bed or sandbanks, can complement each other, towards the estimation of Coastal State Indicators (CSIs). This review leads to the conclusion that, for an optimal environment assessment, there are two main approaches: (1) either combine and couple the models, in order to simulate the full morphodynamics of the system over a long time-scale, taking into account also short-term events, or (2) use a set of existing models, knowing precisely their applicability to the CSI's and the reliability of their predictions, rather than using only the best model, available presently

An AHP-derived method for mapping the physical vulnerability of coastal areas at regional scales

International audienceAssessing coastal vulnerability to climate change at regional scales is now mandatory in France since the adoption of recent laws to support adaptation to climate change. However, there is presently no commonly recognised method to assess accurately how sea level rise will modify coastal processes in the coming decades. Therefore, many assessments of the physical component of coastal vulnerability are presently based on a combined use of data (e.g. digital elevation models, historical shoreline and coastal geomorphology datasets), simple models and expert opinion. In this study, we assess the applicability and usefulness of a multi-criteria decision-mapping method (the analytical hierarchy process, AHP) to map physical coastal vulnerability to erosion and flooding in a structured way. We apply the method in two regions of France: the coastal zones of Languedoc-Roussillon (north-western Mediterranean, France) and the island of La Réunion (south-western Indian Ocean), notably using the regional geological maps. As expected, the results show not only the greater vulnerability of sand spits, estuaries and low-lying areas near to coastal lagoons in both regions, but also that of a thin strip of erodible cliffs exposed to waves in La Réunion. Despite gaps in knowledge and data, the method is found to provide a flexible and transportable framework to represent and aggregate existing knowledge and to support long-term coastal zone planning through the integration of such studies into existing adaptation schemes