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Metamodelling techniques (also referred to as surrogate modelling) have shown high performance to overcome the computational burden of numerical hydrodynamic models for fast prediction of key indicators of marine flooding (e.g. total flooded area). To predict flood maps (e.g. spatial distribution of maximum value of water depth during a flood event), a commonly-used approach is to rely on principal component analysis to reduce the high dimensionality of the flood map (related to the number of pixels typically of several 1000 s) by transforming the spatial output into a low number of latent variables (typically

Occurrences of tropical cyclones at a location are rare, and for many locations, only short periods of observations or hindcasts are available. Hence, estimation of return values (corresponding to a period considerably longer than that for which data are available) for cyclone-induced significant wave height (SWH) from small samples is challenging. The STM-E (space-time maximum and exposure) model was developed to provide reduced bias in estimates of return values compared to competitor approaches in such situations and realistic estimates of return value uncertainty. STM-E exploits data from a spatial neighbourhood satisfying certain conditions, rather than data from a single location, for return value estimation. This article provides critical assessment of the STM-E model for tropical cyclones in the Caribbean Sea near Guadeloupe for which a large database of synthetic cyclones is available, corresponding to more than 3000 years of observation. Results indicate that STM-E yields values for the 500-year return value of SWH and its variability, estimated from 200 years of cyclone data, consistent with direct empirical estimates obtained by sampling 500 years of data from the full synthetic cyclone database; similar results were found for estimation of the 100-year return value from samples corresponding to approximately 50 years of data. In general, STM-E also provides reduced bias and more realistic uncertainty estimates for return values relative to single-location analysis.

International audience; Expert judgment is widely used to inform forecasts (e.g. using the 5 th , 50 th and 95 th percentile of some variable of interest) for a large variety of applications related to environment systems. This task can rely on Cooke's classical model (CM) within the probabilistic framework, and consists in combining expert information after a preliminary step where experts are weighted using calibration and informativeness scores estimated using some seed questions for which the answers can be obtained. In the literature, an alternative model (PM) has been proposed using

International audience; Shoreline change is driven by various complex processes interacting at a large range of temporal and spatial scales, making shoreline reconstructions and predictions challenging and uncertain. Despite recent progress in addressing uncertainties related to the physics of sea-level rise, very little effort is made towards understanding and reducing the uncertainties related to wave-driven shoreline response. To fill this gap, 2 the uncertainties associated with the long-term modelling of shoreline change are analysed at a high-energy cross-shore transport dominated site. Using the state-of-the-art LX-Shore shoreline change model, we produce a probabilistic shoreline reconstruction, based on 3000 simulations over the past 20 years at Truc Vert beach, southwest France, whereby sea-level rise rate, depth of closure and three model free parameters are considered uncertain variables. We further address the relative impact of each source of uncertainty on the model results performing a Global Sensitivity Analysis. This analysis shows that the shoreline changes are mainly sensitive to the three parameters of the wave-driven model, but also that the sensitivity to each of these parameters is strongly modulated seasonally and interannually, in relation with wave energy variability, and depends on the time scale of interest. These results have strong implications on the model skill sensitivity to the calibration period as well as for the predictive skill of the model in a context of future climate change affecting wave climate and extremes.

International audience; Model uncertainties are generally integrated in environmental long-running numerical simulators via a categorical variable. By focusing on Gaussian process (GP) models, we show how different categorical kernel models (exchangeable, ordinal, group, etc.) can bring valuable insights into the correlation of the simulator output values computed for different levels of the categorical variable, i.e., the interlevel dependence structure. Supported by two real case applications (cyclone-induced waves and reservoir modeling), we have proposed a cross-validation approach to select the most appropriate kernel by finding a trade-off between predictability, explainability, and stability of the covariance coefficients. This approach can be used effectively to support some physical assumptions regarding the categorical variable. Through comparison to tree-based techniques, we show that GP models can be considered a satisfactory compromise when only a few model runs (∼100) are available by presenting a high predictability and a concise and graphical way to map the interlevel dependence structure.

International audience; In this communication, we aim at getting a deep insight into the role of coastal flooding drivers is of high interest for the planning of adaptation strategies for future climate conditions. Based on the methods described in Rohmer et al. (202), NHESS, we measure the contributions of the offshore forcing conditions (wave/wind characteristics, still water level and sea level rise (SLR) projected up to 2200) to the occurrence of a flooding event at Gâvres town on the French Atlantic coast in a macrotidal environment. This procedure faces, however, two major difficulties, namely (1) the high computational time costs of the hydrodynamic numerical simulations; (2) the statistical dependence between the forcing conditions. By applying a Monte-Carlo-based approach combined with multivariate extreme value analysis, our study proposes a procedure to overcome both difficulties by calculating sensitivity measures dedicated to dependent input variables (named Shapley effects) using Gaussian process (GP) metamodels. On this basis, our results show the increasing influence of SLR over time, and a small-to-moderate contribution of wave/wind characteristics, or even negligible importance in the very long term (beyond 2100). These results were discussed in relation to our modelling choices, in particular the climate change scenario, as well as the uncertainties of the estimation procedure (Monte Carlo sampling and GP error).

Sea-level projections are usually calculated from numerical simulations using complex long-term numerical models (or a chain of models) as part of multi-model ensemble studies. Because of their importance in supporting the decision-making process for coastal risk assessment and adaptation, improving the interpretability of these projections is of great interest. Specifically, it is assumed that clear and transparent explanations of projected sea-level changes can increase the trust of the end-users, and ultimately favor their engagement in coastal adaptation. To this end, we adopt the local attribution approach developed in the machine learning community, and we combine the game-theoretic approach known as ‘SHAP’ (SHapley Additive exPlanation, Lundberg & Lee, 2017) with tree-based regression models. We applied our methodology to sea-level projections for the Greenland ice sheet computed by the ISMIP6 initiative (Goelzer et al., 2020) with a particular attention paid to the validation of the procedure. This allows us to quantify the influence of particular modelling decisions and to express the influence directly in terms of sea level change contribution. For Greenland, we show that the largest predicted sea level change, 19cm in 2100, is primarily attributable to >4.5cm (i.e. nearly 25%) to the choice of the model parameter that controls the retreat of marine-terminating outlet glaciers, i.e. to the modelling of the retreat rate of tidewater glaciers; other modelling decisions (choice of global climate model, formulation of the ice sheet model ISM, model grid size, etc.) have only a low-to-moderate influence for this case (with contribution of 1-2cm). This type of diagnosis can be performed on any member of the ensemble, and we show how the aggregation of all local attribution analyses can help guide future model development as well as scientific interpretation, particularly with regard to model spatial resolution or the selection of a specific model formulation.This study was supported by the PROTECT project, which received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 869304.ReferencesGoelzer, H., et al. (2020). The future sea-level contribution of the Greenland ice sheet: a multi-model ensemble study of ISMIP6. The Cryosphere 14, 3071-3096.Lundberg, S.M., & Lee, S.I. (2017). A unified approach to interpreting model predictions. In Proceedings of the 31st international conference on neural information processing systems (pp. 4768-4777).

Getting a deep insight into the role of coastal flooding drivers is of high interest for the planning of adaptation strategies for future climate conditions. Using global sensitivity analysis, we aim to measure the contributions of the offshore forcing conditions (wave/wind characteristics, still water level and sea level rise (SLR) projected up to 2200) to the occurrence of the flooding event (defined when the inland water volume exceeds a given threshold YC) at Gâvres town on the French Atlantic coast in a macrotidal environment. This procedure faces, however, two major difficulties, namely (1) the high computational time costs of the hydrodynamic numerical simulations; (2) the statistical dependence between the forcing conditions. By applying a Monte-Carlo-based approach combined with multivariate extreme value analysis, our study proposes a procedure to overcome both difficulties through the computation of sensitivity measures dedicated to dependent input variables (named Shapley effects) with the help of Gaussian process (GP) metamodels. On this basis, our results outline the key influence of SLR over time. Its contribution rapidly increases over time until 2100 where it almost exceeds the contributions of all other uncertainties (with Shapley effect > 40 % considering the representative concentration pathway RCP4.5 scenario). After 2100, it continues to linearly increase up to > 50 %. The SLR influence depends however on our modelling assumptions. Before 2100, it is strongly influenced by the digital elevation Model (DEM); with a DEM with lower topographic elevation (before the raise of dykes in some sectors), the SLR effect is smaller by ~40 %. This influence reduction goes in parallel with an increase in the importance of wave/wind characteristics, hence indicating how the relative effect of the flooding drivers strongly change when protective measures are adopted. By 2100, the joint role of RCP and of YC impacts the SLR influence, which is reduced by 20–30 % when the mode of the SLR probability distribution is high (for RCP8.5 in particular) and when YC is low (of 50 m3). Finally, by showing that these results are robust to the main uncertainties in the estimation procedure (Monte-Carlo sampling and GP error), the combined GP-Shapley effect approach proves to be a valuable tool to explore and characterize uncertainties related to compound coastal flooding under SLR.

International audience; Given recent scientific advances, coastal flooding events can be properly modelled. Nevertheless, such models are computationally expensive (requiring many hours), which prevents their use for forecasting and warning. In addition, there is a gap between the model outputs and information actually needed by decision makers. The present work aims to develop and test a method capable of forecasting coastal flood information adapted to users’ needs. The method must be robust and fast and must integrate the complexity of coastal flood processes. The explored solution relies on metamodels, i.e., mathematical functions that precisely and efficiently (within minutes) estimate the results that would provide the numerical model. While the principle of relying on metamodel solutions is not new, the originality of the present work is to tackle and validate the entire process from the identification of user needs to the establishment and validation of the rapid forecast and early warning system (FEWS) while relying on numerical modelling, metamodelling, the development of indicators, and information technologies. The development and validation are performed at the study site of Gâvres (France). This site is subject to wave overtopping, so the numerical phase-resolving SWASH model is used to build the learning dataset required for the metamodel setup. Gaussian process- and random forest classifier-based metamodels are used and post-processed to estimate 14 indicators of interest for FEWS users. These metamodelling and post-processing schemes are implemented in an FEWS prototype, which is employed by local users and exhibits good warning skills during the validation period. Based on this experience, we provide recommendations for the improvement and/or application of this methodology and individual steps to other sites.

Non-stationary extreme value analysis is a powerful framework to address the problem of time evolution of extremes and its link to climate variability as measured by different climate indices CI (like North Atlantic Oscillation NAO index). To model extreme sea levels (ESLs), a widely-used tool is the non-stationary Generalized Extreme Value distribution (GEV) where the parameters (location, scale and shape) are allowed to vary as a function of some covariates like the month-of-year or some CIs. A commonly used assumption is that only a few CIs impact the GEV parameters by using a linear model, and most of the time by focusing on two GEV parameters (location or/and the scale parameter). In the present study, these assumptions are revisited by relying on a data-driven spline-based GEV fitting approach combined with a penalization procedure. This allows identifying the type (non- or linear) of the CI influence for any of the three GEV parameters directly from the data, and evaluating the significance of this relation, i.e. without making any a priori assumptions as it is traditionally done. This approach is applied to the monthly maxima of sea levels derived from eight of the longest (quasi century-long) tide gauge dataset (Brest, France; Cuxhaven, Germany; Gedser, Denmark; Halifax, Canada; Honolulu, US; Newlyn, UK; San Francisco, US; Stockholm, Sweden) and by accounting for four major CIs (the North Atlantic Oscillation, the Atlantic Multidecadal Oscillation, the Nino 1 + 2 and the Southern Oscillation indices). From this analysis, we show that: (1) the links between CIs and different parameters of a GEV distribution fitted to ESL data are most of the time linear, but some of them present significant non-linear shapes; (2) multiple CIs should be considered to predict ESLs, and (3) the CI influence of the GEV distribution is not limited to the location parameter. These results are useful to understand current modes of variability of ESLs, and ultimately to improve coastal resilience through more precise extreme water level assessments.

Decision-making in the area of coastal adaptation is facing major challenges due to ambiguity (i.e., deep uncertainty) pertaining to the selection of a probability model for sea level rise (SLR) projections. Possibility distributions are mathematical tools that address this type of uncertainty since they bound all the plausible probability models that are consistent with the available data. In the present study, SLR uncertainties are represented by a possibility distribution constrained by likely ranges provided in the IPCC Fifth Assessment Report and by a review of high-end scenarios. On this basis, we propose a framework combining probabilities and possibilities to evaluate how SLR uncertainties accumulate with other sources of uncertainties, such as future greenhouse gas emissions, upper bounds of future sea level changes, the regional variability of sea level changes, the vertical ground motion, and the contributions of extremes and wave effects. We apply the framework to evaluate the probability of coastal flooding by the year 2100 at a local, low-lying coastal French urban area on the Mediterranean coast. We show that when adaptation is limited to maintaining current defenses, the level of ambiguity is too large to precisely assign a probability model to future flooding. Raising the coastal walls by 85 cm creates a safety margin that may not be considered sufficient by local stakeholders. A sensitivity analysis highlights the key role of deep uncertainties pertaining to global SLR and of the statistical uncertainty related to extremes. The ranking of uncertainties strongly depends on the decision-maker’s attitude to risk (e.g., neutral, averse), which highlights the need for research combining advanced mathematical theories of uncertainties with decision analytics and social science.

Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three main issues. First, due to computational time, standard SA techniques cannot be directly applied on the simulator. Second, the output is infinite dimensional, or at least high dimensional if the output is discretized. Third, the spatial output is non-stationary and exhibits strong local variations. We show that all these issues can be addressed all together by using functional PCA (FPCA). We first specify a functional basis, such as wavelets or B-splines, designed to handle local variations. Secondly, we select the most influential basis terms, either with an energy criterion after basis orthonormalization, or directly on the original basis with a penalized regression approach. Then FPCA further reduces dimension by doing PCA on the most influential basis coefficients, with an ad-hoc metric. Finally, fast-to-evaluate metamodels are built on the few selected principal components. They provide a proxy on which SA can be done. As a by-product, we obtain analytical formulas for variance-based sensitivity indices, generalizing known formula assuming orthonormality of basis functions., Comment: 26 pages, 12 figures, 1 algoritm

Global mean sea level rise and its acceleration are projected to aggravate coastal erosion over the 21st century, which constitutes a major challenge for coastal adaptation. Projections of shoreline retreat are highly uncertain, however, namely due to deeply uncertain mean sea level projections and the absence of consensus on a coastal impact model. An improved understanding and a better quantification of these sources of deep uncertainty are hence required to improve coastal risk management and inform adaptation decisions. In this work we present and apply a new extraprobabilistic framework to develop shoreline change projections of sandy coasts that allows consideration of intrinsic (or aleatory) and knowledge-based (or epistemic) uncertainties exhaustively and transparently. This framework builds upon an empirical shoreline change model to which we ascribe possibility functions to represent deeply uncertain variables. The model is applied to two local sites in Aquitaine (France) and Castellón (Spain). First, we validate the framework against historical shoreline observations and then develop shoreline change projections that account for possible (although unlikely) low-end and high-end mean sea level scenarios. Our high-end projections show for instance that shoreline retreats of up to 200m in Aquitaine and 130m in Castellón are plausible by 2100, while low-end projections revealed that 58 and 37m modest shoreline retreats, respectively, are also plausible. Such extended intervals of possible future shoreline changes reflect an ambiguity in the probabilistic description of shoreline change projections, which could be substantially reduced by better constraining sea level rise (SLR) projections and improving coastal impact models. We found for instance that if mean sea level by 2100 does not exceed 1m, the ambiguity can be reduced by more than 50%. This could be achieved through an ambitious climate mitigation policy and improved knowledge on ice sheets. This research has been supported by the BRGM, IHCantabria and the ERA4CS-ECLISEA project (grant no. 690462).

Ensemble-based simulations of future shoreline evolution to 2100, including sea-level rise driven erosion, are performed and analysed  Future shoreline projections uncertainties are initially controlled by modelling assumptions and after 2060 by sea-level rise uncertainties  The choice of wave-driven equilibrium modelling approach and incident wave chronology are critical to future shoreline projections 1 Abstract Most sandy coasts worldwide are under chronic erosion, which increasingly put at risk coastal communities. Sandy shorelines are highly dynamic and respond to a myriad of processes interacting at different spatial and temporal scales, making shoreline predictions challenging, especially on long time scales (i.e. decades and centuries). Shoreline modelling inherits uncertainties from the primary driver boundary conditions (e.g. sea-level rise and wave forcing) as well as uncertainties related to model assumptions and/or misspecifications of the physics. This study presents an analysis of the uncertainties associated with future shoreline evolution at the high-energy, cross-shore transport dominated, sandy beach of Truc Vert (France) over the 21 st century. We explicitly resolve wave-driven shoreline change using two different equilibrium modelling approaches to provide new insight into the contributions of sea-level rise, and free model parameters uncertainties on future shoreline change in the frame of climate change. Based on a Global Sensitivity Analysis, shoreline response during the first half of the century is found to be mainly sensitive to the equilibrium model parameters, with the influence of sea-level rise emerging in the second half of the century (~2050 or later), in both Representative Concentration Pathways 4.5 and 8.5 scenarios. The results reveal that the seasonal and interannual variability of the predicted shoreline position is sensitive to the choice of the wave-driven equilibrium based model. Finally, we discuss the importance of the chronology of wave events in future shoreline change, calling for more continuous wave projection time series to further address uncertainties in future wave conditions.

Increasing our capacity to predict extreme storm surges is one of the key issues in terms of coastal flood risk prevention and adaptation. Dynamically forecasting storm surges is computationally expensive. Here, we focus on an alternative data-driven approach and set up a weather-type statistical downscaling for daily maximum storm surge (SS) prediction, using atmospheric hindcasts (CFSR and CFSv2) and 15 years of tidal gauge station measurements. We focus on predicting the storm surge at La Rochelle&ndash, La Pallice tidal gauge station. First, based on a sensitivity analysis to the various parameters of the weather-type approach, we find that the model configuration providing the best performance in SS prediction relies on a fully supervised classification using minimum daily sea level pressure (SLP) and maximum SLP gradient, with 1&deg, resolution in the northeast Atlantic domain as the predictor. Second, we compare the resulting optimal model with the inverse barometer approach and other statistical models (multi-linear regression, semi-supervised and unsupervised weather-types based approaches). The optimal configuration provides more accurate predictions for extreme storm surges, but also the capacity to identify unusual atmospheric storm patterns that can lead to extreme storm surges, as the Xynthia storm for instance (a decrease in the maximum absolute error of 50%).

Coastal floods are driven by many hydro-meteorological forcing factors, among which are mean sea levels, tides, atmospheric storm surges, and waves. Depending on these conditions, wave overtopping may occur and, in some cases, lead to a significant flood. In the present study, we investigate the effect of the stochastic character of waves on the flood itself using a phase-resolving wave model (SWASH). We focus on the macro-tidal site of G&acirc, vres (France), consider two past flood events (both resulting from wave overtopping), and investigate how the effect of randomness of waves on the flood is changing with the forcing conditions and the time span (minutes to hours). We clearly show that the effect of waves&rsquo, stochasticity on the flood itself is far from being negligible and, especially on a short time scale (~15 min), generates an uncertainty comparable to that induced by the sea-level rise scenarios, as long as the still water level remains smaller than the critical level above which overflow occurs. This implies that lower confidence should be assigned to flood projection on sites where wave overtopping is the main process leading to flood.

A key point of landslide hazard assessment is the estimation of their runout. Empirical relations linking angle of reach to volume can be used relatively easily, but they are generally associated with large uncertainties as they do not consider the topographic specificity of a given study site. On the contrary, numerical simulations provide more detailed results on the deposits morphology, but their rheological parameters can be difficult to constrain. Simulating all possible values can be time consuming and incompatible with operational requirements of rapid estimations. We propose and compare three operational methods to derive scaling power laws relating the landslide travel distance to the destabilized volume. The first one relies only on empirical relations, the second one on numerical simulations with back-analysis, and the third one combines both approaches. Their efficiency is tested on three case studies: the Samperre cliff collapses in Martinique, Lesser Antilles (0.5 to 4&times, 106 m3), the Frank Slide rock avalanche (36&times, 106 m3) and the Samperre cliff collapses in Martinique, Lesser Antilles (0.5 to 4&times, 106 m3) the Fei Tsui debris slide in Hong Kong (0.014&times, 106 m3). Purely numerical estimations yield the smallest uncertainty, but the uncertainty on rheological parameters is difficult to quantify. Combining numerical and empirical approaches allows to reduce the uncertainty of estimation by up to 50%, in comparison to purely empirical estimations. However, it may also induces a bias in the estimation, though observations always lie in the 95% prediction intervals. We also show that empirical estimations fail to model properly the dependence between volume and travel distance, particularly for small landslides (&lt, 20,000 &lt, 0.02&times, 106 m3).

International audience; Surrogate models are often used to replace costly-to-evaluate complex coastal codes to achieve substantial computational savings. In many of those models, the hydrometeorological forcing conditions (inputs) or flood events (outputs) are conveniently parameterized by scalar representations, neglecting that the inputs are actually time series and that floods propagate spatially inland. Both facts are crucial in flood prediction for complex coastal systems. Our aim is to establish a surrogate model that accounts for time-varying inputs and provides information on spatially varying inland flooding. We introduce a multioutput Gaussian process model based on a separable kernel that correlates both functional inputs and spatial locations. Efficient implementations consider tensor-structured computations or sparse-variational approximations. In several experiments, we demonstrate the versatility of the model for both learning maps and inferring unobserved maps, numerically showing the convergence of predictions as the number of learning maps increases. We assess our framework in a coastal flood prediction application. Predictions are obtained with small error values within computation time highly compatible with short-term forecast requirements (on the order of minutes compared to the days required by hydrodynamic simulators). We conclude that our framework is a promising approach for forecast and early-warning systems.

International audience; As low-lying coastal areas can be impacted by flooding caused by dynamic components that are dependent on each other (wind, waves, water levels—tide, atmospheric surge, currents), the analysis of the return period of a single component is not representative of the return period of the total water level at the coast. It is important to assess a joint return period of all the components. Based on a semiparametric multivariate extreme value analysis, we determined the joint probabilities that significant wave heights (Hs), wind intensity at 10 m above the ground (U), and still water level (SWL) exceeded jointly imposed thresholds all along the Corsica Island coasts (Mediterranean Sea). We also considered the covariate peak direction (Dp), the peak period (Tp), and the wind direction (Du). Here, we focus on providing extreme scenarios to populate coastal hydrodynamic models, SWAN and SWASH-2DH, in order to compute the 100-year total water level (100y-TWL) all along the coasts. We show how the proposed multivariate extreme value analysis can help to more accurately define low-lying zones potentially exposed to coastal flooding, especially in Corsica where a unique value of 2 m was taken into account in previous studies. The computed 100y-TWL values are between 1 m along the eastern coasts and a maximum of 1.8 m on the western coast. The calculated values are also below the 2.4 m threshold recommended when considering the sea level rise (SLR). This highlights the added value of performing a full integration of extreme offshore conditions, together with their dependence on hydrodynamic simulations for screening out the coastal areas potentially exposed to flooding.

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.

Muller, H.; van Rooijen, A.; Idier, D.; Pedreros, R., and Rohmer, J., 2017. Assessing storm impact on a French coastal dune system using morphodynamic modeling. Natural coastal dune systems provide protection against flooding from the ocean for many coastal communities around the world. An in-depth knowledge of their erosion mechanisms under oceanic stress can help to identify potential weak spots along the coastline and eventually prevent damage to the hinterland. The objective of this study was to assess the effects of hydro-morphodynamic phenomena on the coastal dune morphology during storm events and to evaluate their level of protection. This paper focuses on the physical processes that cause erosion and breaching of sandy dune systems, which are typically a function of the coastal morphology in combination with the hydraulic loading. An XBeach model was set up for the coast of Les Boucholeurs (France), which suffered from severe erosion, dune breaching (at six locations), and inundation of ...

The characterisation of past coastal flood events is crucial for risk prevention. However, it is limited by the partial nature of historical information on flood events and the lack or limited quality of past hydro-meteorological data. In addition, coastal flood processes are complex, driven by many hydro-meteorological processes, making mechanisms and probability analysis challenging. Here, we tackle these issues by joining historical, statistical and modelling approaches. We focus on a macrotidal site (Gâvres, France) subject to overtopping and investigate the 1900–2010 period. We build a continuous hydro-meteorological database and a damage event database using archives, newspapers, maps and aerial photographs. Using together these historical information, hindcasts and hydrodynamic models, we identify nine flood events, among which five are significant flood events (four with high confidence: 1924, 1978, 2001, 2008; one with a lower confidence: 1904). These flood events are driven by the combination of sea-level rise, tide, atmospheric surge, offshore wave conditions and local wind. We further analyse the critical conditions leading to flood, including the effect of coastal defences, showing, for instance, that the present coastal defences would not have allowed to face the hydro-meteorological conditions of 09/02/1924, whose bi-variate return periods of exceedance $$T_\mathrm{R}$$ (still water level relative to the mean sea level and significant wave height) are larger than 1000 year. In the coming decades, $$T_\mathrm{R}$$ is expected to significantly decrease with sea-level rise, reaching values smaller than 1 year, for eight of the nine historical events, for a sea-level rise of 0.63 m, which is equal to the median sea-level rise projected by the 5th Assessment Report of the IPCC in this region for RCP8.5 in 2100.

Rohmer, J.; Louisor, J.; Le Cozannet, G.; Naveau, P.; Thao, S., and Bertin, X., 2020. Attribution of extreme wave height records along the North Atlantic coasts using hindcast data: Feasibility and limitations. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1268-1272. Coconut Creek (Florida), ISSN 0749-0208.Extreme Event Attribution (EEA) aims at answering questions about how much climate change influenced the probability or intensity of a specific type of extreme meteo-oceanic event. Here, we focus on wave record breaking i.e. the occurrence of an extreme significant wave height (hs) value that exceeds all past observations. The objective is to evaluate the probability changes related to climate change by estimating the fraction of attributable risk far=1–p0/p1, where p0 and p1 are probabilities of the wave record event in two different worlds: a counterfactual world without anthropogenic forcings i.e. a “world that might have been”, and the factual world, i.e. “world that is.” To define these different worlds, we rely on a wave hindcast database, which provides very long time series (1900-2008) of hs over the whole North Atlantic Ocean Basin (NAOB). We assume that the counterfactual world corresponds to the series of annual hs maxima over the period 1900-1930, and that the factual world corresponds to the annual hs maxima over the period 1978-2008. The extreme event attribution approach dedicated to record breakings was applied over NAOB, and we show large far values (>0.5) along the northern Canadian, Scottish and southwestern Norwegian coasts (over the latitudes 50°-65°N). These results are, however, carefully discussed with respect to different uncertainty sources, namely the validity of the assumptions underlying the EEA, the statistical uncertainties, the use of hindcast data instead of global climate model's results, and the limitations in the hindcast database setup.

Idier, D.; Aurouet, A.; Bachoc, F.; Baills, A.; Betancourt, J.; Durand, J.; Mouche, R.; Rohmer, J.; Gamboa, F.; Klein T.; Lambert, J.; Le Cozannet, G.; Le Roy, S.; Louisor, J.; Pedreros, R., and Veron, A.L., 2020. Toward a user-based, robust and fast running method for coastal flooding forecast, early warning, and risk prevention. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1111–1116. Coconut Creek (Florida), ISSN 0749-0208.Scientific progresses now allow properly modelling coastal flooding events. Such models are nevertheless very expensive in terms of computation time (>hours) which prevents any use for forecast and warning or even for estimating the coastal flood hazard return period together with uncertainties. In addition, there is a gap between model outputs and information actually needed by the decision makers. Within the RISCOPE project, we aim at developing a user-based method contributing to forecast, early-warning and prevention of coastal flooding risks. The method should be robust, fast and integrate the complexity of coastal flood processes. To build such coastal flooding models, the solution explored relies on meta-models, i.e. mathematical functions which estimate, with good precision and at a negligible computational cost (

International audience; Discrete Bayesian Belief Network (BBN) has become a popular method for the analysis of complex systems in various domains of application. One of its pillar is the specification of the parameters of the probabilistic dependence model (i.e. the cause-effect relation) represented via a Conditional Probability Table (CPT). Depending on the available data (observations, prior knowledge, expert-based information, etc.), CPTs can be populated in different manners, i.e. different assumptions can be made and different methods are available, which might lead to uncertain BBN-based results. Through an extensive review study of the past ten years, we aim at addressing three questions related to the CPT uncertainties. First, we show how to constrain these uncertainties either using elicitation of expert inputs, or using a combination of scarce data and expert-derived information. Second, we show how to integrate these uncertainties in the BBN-based analysis through propagation procedures either using probabilities or imprecise probabilities within the setting of credal or evidential networks. Finally, we show how to test the robustness of the BBN-based results to these uncertainties via sensitivity analysis specifically dedicated to BBNs. A special care was paid to describe the best practices for the implementation of the reviewed methods and the remaining gaps.

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) methods. However, strictly interpolating the observations may entail expensive computations due to highly restrictive sample spaces. Furthermore, having (constrained) GP emulators when data are actually noisy is also of interest for real-world implementations. Hence, we introduce a noise term for the relaxation of the interpolation conditions, and we develop the corresponding approximation of GP emulators under linear inequality constraints. We show with various toy examples that the performance of MC and MCMC samplers improves when considering noisy observations. Finally, on 2D and 5D coastal flooding applications, we show that more flexible and realistic GP implementations can be obtained by considering noise effects and by enforcing the (linear) inequality constraints.

a également fait l'objet d'une communication orale au EVAN 2019; International audience; Fragility curves (FCs) are key tools for seismic probabilistic safety assessments that are performed at the level of the nuclear power plant (NPP). These statistical methods relate the probabilistic seismic hazard loading at the given site to the required performance of the NPP safety functions. In the present study, we investigate how the tools of non-stationary extreme value analysis can be used to model in a flexible manner the tail behaviour of the engineering demand parameter as a function of the considered intensity measure. We focus the analysis on the dynamic response of an anchored steam line and of a supporting structure under seismic solicitations. The failure criterion is linked to the exceedance of the maximum equivalent stress at a given location of the steam line. A series of three-component ground-motion records (∼300) were applied at the base of the model to perform non-linear time history analyses. The set of numerical results was then used to derive a FC, which relates the failure probability to the variation in peak ground acceleration (PGA). The probabilistic model of the FC is selected via information criteria completed by diagnostics on the residuals, which support the choice of the generalised extreme value (GEV) distribution (instead of the widely used log-normal model). The GEV distribution is here non-stationary, and the relationships of the GEV parameters (location, scale and shape) are established with respect to PGA using smooth non-linear models. The procedure is data-driven, which avoids the introduction of any a priori assumption on the shape or form of these relationships. To account for the uncertainties in the mechanical and geometrical parameters of the structures (elastic stiffness, damping, pipeline thicknesses, etc.), the FC is further constructed by integrating these uncertain parameters. A penalisation procedure is proposed to set to zero the variables of little influence in the smooth non-linear models. This enables us to outline which of these parametric uncertainties have negligible influence on the failure probability as well as the nature of the influence (linear, non-linear, decreasing, increasing, etc.) with respect to each of the GEV parameters.

International audience; Ensuring the validity and credibility of Bayesian Belief Network (BBN) as a modelling tool for expert systems requires appropriate methods for sensitivity analysis (SA), in order to test the robustness of the BBN diagnostic and prognostic with respect to the parameterisation of the conditional probability model (CPM). Yet, the most widely used techniques (based on sensitivity functions for discrete BBNs) only provide a local insight on the CPM influence, i.e. by varying only one CPM parameter at a time (or a few of them) while keeping the other ones unchanged. To overcome this limitation, the present study proposes an approach for global SA relying on Beta Regression using gradient boosting (potentially combined with stability selection analysis): it presents the benefit of keeping the presentation intuitive through a graph-based approach, while being applicable to a large number of CPM parameters. The implementation of this approach is investigated for three cases, which cover a large spectrum of situations: (1) a small discrete BBN, used to capture medical knowledge, demonstrates the proposed approach; (2) a linear Gaussian BBN, used to assess the damage of reinforced concrete structures, exemplifies a case where the number of parameters is too large to be easily processed and interpreted (>40 parameters); (3) a discrete BBN, used for reliability analysis of nuclear power plant, exemplifies a case where analytical solutions for sensitivity can hardly be derived. Finally, provided that the validity of the BBR model is carefully checked, we show that the proposed approach can provide richer information than traditional SA methods at different levels: (i) it selects the most influential parameters; (ii) it provides the functional relation between the CPM parameter and the result of the probabilistic query; and (iii) it identifies how the CPM parameters can lead to situations of high probability, while quantifying the confidence in the occurrence of these situations.

Sandy shorelines are constantly evolving, threatening frequently human assets such as buildings or transport infrastructure. In these environments, sea-level rise will exacerbate coastal erosion to an amount which remains uncertain. Sandy shoreline change projections inherit the uncertainties of future mean sea-level changes, of vertical ground motions, and of other natural and anthropogenic processes affecting shoreline change variability and trends. Furthermore, the erosive impact of sea-level rise itself can be quantified using two fundamentally different models. Here, we show that this latter source of uncertainty, which has been little quantified so far, can account for 20 to 40% of the variance of shoreline projections by 2100 and beyond. This is demonstrated for four contrasting sandy beaches that are relatively unaffected by human interventions in southwestern France, where a variance-based global sensitivity analysis of shoreline projection uncertainties can be performed owing to previous observations of beach profile and shoreline changes. This means that sustained coastal observations and efforts to develop sea-level rise impact models are needed to understand and eventually reduce uncertainties of shoreline change projections, in order to ultimately support coastal land-use planning and adaptation.

The dependence between extreme storm surges and wind waves is assessed statistically along the global coasts using the outputs of two numerical models consistently forced with the same atmospheric fields. We show that 55% of the world coastlines face compound storm surge wave extremes. Hence, for a given level of probability, neglecting these dependencies leads to underestimating extreme coastal water levels. Dependencies are dominant in midlatitudes and are likely underestimated in the tropics due to limited representation of tropical cyclones. Furthermore, we show that in half of the areas with dependence, the estimated probability of occurrence of coastal extreme water levels increases significantly when it is accounted for. Translated in terms of return periods, this means that along 30% of global coastlines, extreme water levels expected at most once in a century without considering dependence between storm surges and waves become a 1 in 50-year event., This study was supported by the ERA4CS INSeaPTION project (grants 690462 and PCIN‐2017‐038).

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International audience; Geological planar facets (stratification, fault, joint…) are key features to unravel the tectonic history of rock outcrop or appreciate the stability of a hazardous rock cliff. Measuring their spatial attitude (dip and strike) is generally performed by hand with a compass/clinometer, which is time consuming, requires some degree of censoring (i.e. refusing to measure some features judged unimportant at the time), is not always possible for fractures higher up on the outcrop and is somewhat hazardous. 3D virtual geological outcrop hold the potential to alleviate these issues. Efficiently segmenting massive 3D point clouds into individual planar facets, inside a convenient software environment was lacking. FACETS is a dedicated plugin within CloudCompare v2.6.2 (http://cloudcompare.org/) implemented to perform planar facet extraction, calculate their dip and dip direction (i.e. azimuth of steepest decent) and report the extracted data in interactive stereograms. Two algorithms perform the segmentation: Kd-Tree and Fast Marching. Both divide the point cloud into sub-cells, then compute elementary planar objects and aggregate them progressively according to a planeity threshold into polygons. The boundaries of the polygons are adjusted around segmented points with a tension parameter, and the facet polygons can be exported as 3D polygon shapefiles towards third party GIS software or simply as ASCII comma separated files. One of the great features of FACETS is the capability to explore planar objects but also 3D points with normals with the stereogram tool. Poles can be readily displayed, queried and manually segmented interactively. The plugin blends seamlessly into CloudCompare to leverage all its other 3D point cloud manipulation features. A demonstration of the tool is presented to illustrate these different features. While designed for geological applications, FACETS could be more widely applied to any planar objects. For further details: http://www.cloudcompare.org/doc/wiki/index.php?title=Facets_%28plugin%29

International audience; This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.

In the area of sea-level rise, recent research has focused on assessing either likely or high end future sea levels, but less attention has been given to &ldquo, low-end&rdquo, sea-level projections, exploring best-case potential sea-level changes and providing the basis for estimating minimum adaptation needs. Here, we provide global and regional probabilistic sea-level projections using conservative projections of glaciers and ice-sheets melting and a selection of models from the Coupled Model Intercomparison Project phase 5 (CMIP5) delivering moderate thermal expansion. Our low-end sea-level projections are higher than previously estimated because they rely on modeling outcomes only, and do not add any expert judgement, aiming essentially at delivering more realistic upper tails. While there are good reasons to believe that our projections are excessively optimistic, they can be used as low-end sea-level projections in order to inform users with low aversion to uncertainty. Our low-end sea-level projection exceeds 0.5 m along most inhabited coasts by 2100 for business as usual greenhouse gas emissions (RCP8.5), which is relevant for adaptation practitioners as long as efficient climate change mitigation policies are not implemented. This means that without efficient climate mitigation, an acceleration of sea-level rise can hardly be avoided during the 21st century.

International audience; In nuclear applications, fragility curves are an essential element of the seismic probabilistic safety assessment that is performed at the level of the power plant. These statistical tools establish the link between the probabilistic seismic hazard loading at the site and the required performance of the plant's safety functions. In this context, the fragility model formalized by Kennedy & Ravindra (1984) proposes to account for the aleatory randomness and the epistemic uncertainty generated by various sources of variability, such as the representation of the seismic input or the assumptions in the structural model and in the loading patterns. Therefore, this study investigates the relative contributions of such variables to the dispersion of the resulting fragility functions, while ensuring the separation between aleatory and epistemic uncertainty sources, as advocated by the standards in effect in the nuclear industry. To this end, a coupled model of a supporting structure and an anchored steam line is considered and computed with the finite-element CAST3M software (Rahni et al., 2017). The failure criterion is related to the exceedance of a given effort value at a point of the steam line corresponding to a vertical stop. A coupled of hundreds of three-component ground-motion records are applied at the base of the model, in order to perform non-linear time-history analyses. The record selection follows the conditional spectrum method (Lin et al., 2013), in order to scale the records while ensuring the hazard consistency, through the identification of reference earthquake scenarios for each predefined hazard level. As a result, dozens of ground-motion parameters are tested as potential intensity measures (IMs), with respect to state-of-the-art indicators measuring efficiency or sufficiency. Some couples of ground-motion parameters are assembled as vector-valued IMs, in order to generate so-called fragility surfaces: these multi-variate functions may then be reinterpreted as single-IM fragility curves, where the conditional distribution of the secondary IM with respect to the main one generates additional confidence intervals for the fragility curve. It is thus shown that the aleatory randomness due to record-to-record variability may be partially transferred to an epistemic uncertainty contribution. This variability is then put in perspective with other sources of uncertainty due to modelling assumptions, such as the variability in the mechanical parameters of the model or the angle of loading of the seismic input.

International audience; Changes in mean sea level (MSL) are a major, but not the unique, cause of changes in high-percentile sea levels (HSL), e.g. the annual 99.9th quantile of sea level (among other factors, climate variability may also have huge influence). To unravel the respective influence of each contributor, we propose to use structural time series models considering six major climate indices (CI) (Artic Oscillation, North Atlantic Oscillation, Atlantic Multidecadal Oscillation, Southern Oscillation Index, Nino 1 + 2 and Nino 3.4) as well as a reconstruction of MSL. The method is applied to eight century-long tide gauges across the world (Brest (France), Newlyn (UK), Cuxhaven (Germany), Stockholm (Sweden), Gedser (Danemark), Halifax (Canada), San Francisco (US), and Honolulu (US)). The treatment within a Bayesian setting enables to derive an importance indicator, which measures how often the considered driver is included in the model. The application to the eight tide gauges outlines that MSL signal is a strong driver (except for Gedser), but is not unique. In particular, the influence of Artic Oscillation index at Cuxhaven, Stockholm and Halifax, and of Nino Sea Surface Temperature index 1 + 2 at San Francisco appear to be very strong as well. Asimilar analysis was conducted by restricting the time period of interest to the 1st part of the 20th century. Over this period, we show that the MSL dominance is lower, whereas an ensemble of CI contribute to a large part to HSL time evolution as well. The proposed setting is flexible and could be applied to incorporate any alternative predictive time series such as river discharge, tidal constituents or vertical ground motions where relevant.

Identifying the offshore forcing and breaching conditions that lead to marine inundation is of high importance for risk management. This task cannot be conducted by using a numerical hydrodynamic model due to its high computation time cost (of several minutes or even hours). In the present study, we show how the random forest (RF) classification technique can approximate the numerical model to explore these critical conditions. We focus on the Boucholeurs site, which is located on the French Atlantic coast and exposed to overflow processes. An iterative strategy is developed for selecting the numerical simulations (a total of 200) to train the RF model. The sensitivity to the input parameters is studied using permutation-based importance measures and extended versions of the partial dependence plots. The results highlight the key interplay among the high-tide level, the surge peak and the phase difference, and the complex role of the breaching location.

Idier, D.; Falqués, A.; Garcin, M., and Rohmer, J., 2018. How observed kilometric sandy shoreline undulations depend on wave climate. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 191–195. Coconut Creek (Florida), ISSN 0749-0208. Coastlines sometimes exhibit km-scale undulations, also called shoreline sandwaves. This work focuses on self-organized undulations and investigates how frequent they are, on which parameters they depend and whether existing theories of morphodynamic instabilities can explain them. We perform a wavelet analysis on shoreline data from areas appearing free of human or geological constraints and representing totally 1268 km around the world. It is found that 61% of cases exhibit undulations with wavelengths in the range 1–10 km. The wave parameter that correlates the best with their existence is the incidence angle with respect to shore normal and, to a lesser extent, the closure depth. The shoreline undulation probability increases with the angle, from 50% for low angles to almost 100% for large angles, suggesting that the High-Angle Wave Instability mechanism (HAWI) would be their primary cause, but that Low-Angle Wave Instability (LAWI) may also play a role. These results are consistent with recent theoretical investigations.

International audience; In the domain of reservoir engineering, fault stability assessment is traditionally performed by assimilating fault systems to surfaces. However, faults are complex and heterogeneous geological systems, whose compartmentalized architecture generally corresponds to an inner core surrounded by outer, often fractured, damage zones (DZ). To date, few studies have assessed the potential role of the DZ characteristics (anisotropy, complex spatial distribution, etc.) on the shear behavior of the whole system, the main challenge being the proper (numerical) integration of fracture networks in reservoir simulators. The present study was motivated by the stochastically generated fracture networks representative of DZ investigated on outcrops (Cirques de Navacelles, South of France). We propose here a methodology relying on homogenization techniques for deriving the spatial distribution of effective anisotropic hydro-poro-elastic DZ properties from these stochastic fracture networks. Using them as inputs of 2D finite-element coupled hydro-mechanical models of a reservoir-scale fault zone, the key role of the spatially-varying DZ stiffness and Biot's coefficients are highlighted: neglecting them might lead to a high over-estimation of the maximum sustainable injection pressure (by nearly 50% in the considered cases).