F Richards

X Xie

A Paiement

E Sola

P.-A Duc

MULTI-SCALE GRIDDED GABOR ATTENTION FOR CIRRUS SEGMENTATION

Keywords: Attention, multi-scale, orientation, segmentation, astronomy

In this paper, we address the challenge of segmenting global contaminants in large images. The precise delineation of such structures requires ample global context alongside understanding of textural patterns. CNNs specialise in the latter, though their ability to generate global features is limited. Attention measures long range dependencies in images, capturing global context, though at a large computational cost. We propose a gridded attention mechanism to address this limitation, greatly increasing efficiency by processing multiscale features into smaller tiles. We also enhance the attention mechanism for increased sensitivity to texture orientation, by measuring correlations across features dependent on different orientations, in addition to channel and positional attention. We present results on a new dataset of astronomical images, where the task is segmenting large contaminating dust clouds.

INTRODUCTION

Global context is vital in vision: scenes are understood through key descriptive regions, such as grass or sky, as well as through objects. This is especially relevant when processing contaminants covering large regions, such as clouds in remote sensing [START_REF] Guo | CDnetV2: CNN-based cloud detection for remote sensing imagery with cloudsnow coexistence[END_REF] and solar imaging, [START_REF] Feng | SolarNet: A sky image-based deep convolutional neural network for intra-hour solar forecasting[END_REF], or dust clouds in deep sky imaging [START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF]. Multi-scale (MS) CNNs were proposed to increase global context, e.g. [START_REF] Zhao | Pyramid scene parsing network[END_REF], though context in convolutions remains limited to the final convolutional layers, and achieving larger receptive fields requires downscaling.

Attention proposes to model long range dependencies between feature positions and channels [START_REF] Vaswani | Attention is all you need[END_REF][START_REF] Fu | Dual attention network for scene segmentation[END_REF]. While attention has been effective in capturing global context, it has a huge computational footprint. Positional attention has squared complexity in relation to image size, which is barely manageable on popular datasets with modern GPUs. This cost of attention can be reduced by downscaling features. Sacrificing texture for gained context is not a worthwhile compromise for some vision tasks, as severe downscaling significantly erodes local textures often to the detriment of model performance. Orientational information is also a valuable discriminator in identifying classes of objects. Textures are intrinsically composed of orientation dependent patterns, and thus understanding of orientations has been shown to increase performance on a variety of segmentation tasks e.g. [START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF].

In this paper, we investigate segmentation of cirrus contamination: dust clouds in the foreground of astronomical images. Cirrus pollution can be difficult to spot, ranging from a slight change in background intensity to total occlusion of galaxies, as shown in Fig. 1. This makes cirrus localisation challenging, leading to frequent disagreements in expert annotations. Background intensity levels vary even in clean regions of images, thus it is necessary to consider the entire image (>5000 px 2 ) to maximise global contextual information. Local textural patterns are also necessary discriminating properties of cirrus, which presents as a wispy texture often with filamentary structures sharing a common orientation.

We propose a gridded MS architecture (Section 2.2) that addresses the attention's high compute. Furthermore, it introduces an MS aspect with no added cost, while MS tends to be computationally expensive. We divide features of different scales into tiles of smaller constant size. Positional and channel attention is computed on these tiles to assess both local and global context in an efficient manner, before reassembling tiles into a final attention map. A closely related work is [START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF] where attention is also applied to each scale of MS features, but using whole feature maps in each attention module, resulting in very high computing costs. Additionally, we present a novel attention operator using orientation (Section 2.3), for improved sensitivity to textures. We utilise Gabor modulated convolutions [START_REF] Luan | Gabor convolutional networks[END_REF][START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF] to generate features dependent on different angles. Attention is then computed across these angles, measuring correlations between orientation dependent features. Finally, we propose a loss function to train on annotations that lack a consensus (Section 2.4), that are a particularity of fuzzy and partially transparent contaminants.

METHODOLOGY

We present enhancements of attention modules for computationally efficient segmentation of large contaminants. These enhancements are compatible with various attention modules (and backbones), and we demonstrate them on [START_REF] Fu | Dual attention network for scene segmentation[END_REF].

Background on Multi-scale Attention

Accurate identification of contaminants requires comparison to surrounding regions. Attention [START_REF] Vaswani | Attention is all you need[END_REF] has been proposed to analyse contextual relations in images through computing feature correlations. Correlations are scaled based on the strength of given features, prioritising correlations that have a larger effect on model classification. This process can be performed along any internal organisation (axis) of a feature map, allowing different contextual dependencies to be measured. Thus, attention can be computed with respect to position (correlations between regions) and/or with respect to channels (correlations between learned features) [START_REF] Fu | Dual attention network for scene segmentation[END_REF]. We utilise multiple attention operators at different spatial scales to enhance local and global contextual understanding.

An approach for generating MS features is to pool initial features into different sizes and pass them through parallel convolutional layers e.g. [START_REF] Zhao | Pyramid scene parsing network[END_REF]. Feature pyramid approaches [START_REF] Lin | Feature pyramid networks for object detection[END_REF] offer compute savings of constant factor by combining intermediate features at different scales generated by various convolutional layers. They have been used in attention works [START_REF]Psanet: Point-wise spatial attention network for scene parsing[END_REF][START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF], with attention applied to each scale apart. Tao et al. [START_REF] Tao | Hierarchical multi-scale attention for semantic segmentation[END_REF] generate features for each image scale separately, and observed a performance gain which outweighed computational cost, therefore we use a similar approach although our proposed attentions are compatible with MS features of [START_REF]Psanet: Point-wise spatial attention network for scene parsing[END_REF][START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF].

Multi-scale Gridded Attention

We propose a cost effective method for computing attention over multiple scales. Attention is costly, generally with squared complexity with respect to image size. While this effect can be managed through downscaling and cropping, the former compromises key local texture and the latter compromises key global context. It is therefore desirable to minimise the use of both while introducing a multi-scale analysis.

We illustrate gridded attention in Fig. 2. Our gridded attention module receives input MS feature maps, which we generate as in [START_REF] Tao | Hierarchical multi-scale attention for semantic segmentation[END_REF]. Each feature map is concatenated with a fused version of feature maps at all scales, similarly to [START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF], with the difference that the fused map is produced with same size as the largest feature map (before appropriate rescaling). We divide the feature maps into tiles of consistent smaller size but with multiple underlying spatial scales. Our architecture consists of multiple branches, each handling a spatial scale and comprising of a separate attention module, similar to the multi-branch architecture of [START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF]. In the example of Fig. 2, attention is computed on 21 tiles with size N 4 2 , decreasing memory usage by 21 256 . Due to the massive saving on computational resources, the model can inspect both local texture and global context even on large images (e.g. >5000px 2 in our case).

We use spatial scales with a common factor so that rescaling operations can be composed by chaining smaller rescalings. After computing attention on smaller scales, tiles are upscaled to realign resolutions. During upscaling, one upscaling convolutional block is used per scale transition, tying weights across scale branches, increasing parallelisation and inducing overlap between different scales. This is a key difference with other gridded attention methods [START_REF] Jiang | Transgan: Two pure transformers can make one strong gan, and that can scale up[END_REF] where lack of tile overlap can cause boundary artefacts.

Gabor Attention

We propose a novel attention operator for studying orientational context. Gabor modulated convolutions have been shown to increase performance on oriented textures and rotated samples e.g. [START_REF] Luan | Gabor convolutional networks[END_REF][START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF]. Such layers multiply convolutional weights by Gabor filters with different rotation parameters to generate orientation dependent features.

As illustrated in Fig. 3, we compute Gabor attention by placing independent Gabor modulations before each reshaping operation and calculate correlations across the axis representing orientations. This Gabor attention operator may be used in combination with channel and positional operators, creating an attention module with three separate attentions each measuring different dependencies among features. The three attention maps are combined with element-wise summation. We refer to this new attention module, combining positional, channel and Gabor attention, as tri-attention. By measuring correlations across the additional Gabor axis, we are able to study relationships among orientation rich features.

Super-Majority Loss function

We propose a super-majority loss (SML) function to train on probabilistic annotations. In this study, targets are generated by four (expert and non-expert) annotators [START_REF] Sola | Characterization of low surface brightness structures in annotated deep images[END_REF]. We create probabilistic targets using a weighted average, where expert annotators are weighted higher. We choose not to use approaches that propose probabilistic networks, such as [START_REF] Hu | Supervised uncertainty quantification for segmentation with multiple annotations[END_REF][START_REF] Walmsley | Galaxy Zoo: probabilistic morphology through Bayesian CNNs and active learning[END_REF], due to our comparatively small number of expert annotators.

Inspired by works on edge detection with CNNs [START_REF] Liu | Richer convolutional features for edge detection[END_REF][START_REF] Xie | Holistically-nested edge detection[END_REF], we separate consensus values into quartiles and conditionally adjust the loss function per quartile. By coarsely dividing probabilities into ranges of confidence, we mitigate against any uncertainty associated with our probabilistic consensuses. We also use focal loss [START_REF] Lin | Focal Loss for Dense Object Detection[END_REF] L f to encourage the model to focus on difficult examples rather than easy negatives or 'clean' pixels which dominate the class balance. Target pixels y with uncertain labels (0.25 < y < 0.5) are ignored, whereas supermajority consensuses (y ≥ 0.75) are prioritised by multiplying with a boosting coefficient β = 1.25. For output x:

L SML =          β • L f (x, y) if y ≥ 0.75. L f (x, y) if 0.5 ≤ y < 0.75. 0 if 0.25 < y < 0.5. L f (x, y)
otherwise.

(1)

Final Segmentation Model

We use the proposed MS gridded and Gabor attention mechanisms in combination, by using the Gabor tri-attention module in the MS gridded framework. We implement an MS attention with three spatial scales. The original feature maps and resulting attention maps are then passed through a fully connected layer to generate segmentation predictions.

As in [START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF], we generate six segmentation predictions. During training, we consider each segmentation separately and compute six loss terms for all predictions before summing them. The backbone is then explicitly forced to preserve spatial locations of features, relieving the attention module of any realigning effort. For inference, we take the average of the three segmentation computed from the attention maps.

RESULTS

Data

We produced a dataset of 186 images from the MATLAS survey [START_REF] Duc | MATLAS: a deep exploration of the surroundings of massive early-type galaxies[END_REF] (avg. image size 7000 px 2 ). 25% of images have cirrus contamination, and in contaminated images, 60% of pixels contain cirrus. We use 70% of samples for training, 15% for validation and testing. We also run experiments on the subset of contaminated images, and on an additional dataset of 300 synthesised cirrus images (size 512 px 2 ) generated similarly to [START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF] with some added simulated imaging artefacts for greater realism. In these two additional datasets, class imbalance is eased, allowing the model to focus further on discriminative cirrus features and thus more clearly revealing findings during ablation studies. We augment images with geometric transformations: flips, rotations and translations, and apply element-wise Gaussian noise with zero mean and variance of 0.1. We also pretrain on synthetised cirrus images.

Comparative Analyses on Proposed Techniques

We verify the effectiveness of the proposed methods individually. For control model, we use non-gridded MS dual attention similar to [START_REF] Sinha | Multi-scale self-guided attention for medical image segmentation[END_REF] in our MS architecture, though with a simple backbone with four convolutional layers. All networks are trained for 200 epochs with the Adam optimiser [START_REF] Diederik | Adam: A method for stochastic optimization[END_REF] with learning rate 10 -3 and L2 weight regularisation 10 -7 . Learning rate is decreased every epoch by a factor of 0.98. We score models using the intersection over union (IoU) averaged over five splits, and also report standard error across splits. We fix batch size and overall parameter size across modifications to be roughly equal and downscale images to the maximum size our GPUs could accommodate for each network.

We perform an ablation study on proposed attention techniques, shown in Table 1. The effectiveness of the proposed loss is first compared against a focal loss with rounded probabilistic labels 1. On our dataset of real images containing probabilistic annotations, ignoring pixels with uncertain annotation and prioritising very certain pixels is helpful, with the proposed super-majority loss increasing performance. On the synthetic the probabilities of simulated labels do not correlate well with actual prediction difficulty, and the

All images

Cirrus only Synth. Control 0.469(0.005) 0.814(0.013) 0.831(0.001) SML 0.483(0.006) 0.822(0.013) 0.830(0.001) SML+Gabor 0.497(0.007) 0.861(0.015) 0.867(0.002) SML+Grid 0.542(0.003) 0.886(0.016) 0.844(0.003) All 0.548(0.003) 0.892(0.013) 0.871(0.002) U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] 0.381(0.128) 0.685(0.096) 0.794(0.001) LGCN [START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF] 0.414(0.049) 0.741(0.033) 0.891(0.001) proposed loss was not able to provide an improvement. We see that the control MS attention model offers a sizeable benefit on real data, indicating that dual attention is well suited to large contaminant segmentation. The proposed MS gridded attention significantly compounds this positive effect, showing that the ability to study long range dependencies across multiple scales is beneficial. The proposed tri-attention increases accuracy on all cirrus segmentation scenarios, indicating that sensitivity to texture orientation is helpful in localising the fuzzy and textured contaminants. The two attention techniques benefit from being combined, with further improved results. On real images, when compared against a popular U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] baseline and the state-of-the-art cirrus segmentation method LGCN [START_REF] Richards | Learnable Gabor modulated complex-valued networks for orientation robustness[END_REF], it outperforms both by a large margin. On synthetic images, LGCN outperforms attention models due to no long range correlations existing within the small images.

Proposed Cirrus Segmentation

We construct a final model from the best performing components of the previous section and analyse the predictions. We significantly increase the parameter size of our segmentation model and swap the simple backbone network out for a ResNet-50 [START_REF] He | Deep residual learning for image recognition[END_REF] network. To account for this larger network, we increase training epochs to 400. We also increase the size of both the training and testing sets by dividing the validation samples between them. Cirrus dust is faint in comparison to bright stars. To compensate for this we add an initial layer to the network implementing arcsinh scaling, popular in astronomical image processing: X s = arcsinh (aX + b), where a, b are learned. We also use ensemble predictions, where 5 models are trained, and predictions from each model are averaged over to give the final segmentation. Inference takes an average time of ∼ 0.4s per sample on a single GTX 1080 Ti, which could be significantly reduced with optimisation efforts such as model compilation, pruning or half precision weights.

In Table 2 we report both IoU and Dice scores, with Dice being more biased to precision. We observe that there is a very large performance increase from models in the compar-ative analysis, owing to the larger parameter space, additional training samples and longer training period. We see that a single model is outperformed by the model ensemble by a significant margin. Aggregating predictions also appears to handle the class imbalance issue better than the single model, when comparing the predicted distributions of cloud coverage across images against target groundtruth distribution, with Kullback-Leibler divergences being respectively 0.40 and 0.07 for the single and ensemble models. Prediction aggregation appears to also increase the gap between IoU and Dice scores, indicating that precision is increased through averaging over predictions. This may be due to the aggregation smoothing over-eager positive predictions from single models within the ensemble. Fig. 1 shows some examples of predictions by the best performing ensemble model.

Cloud segmentation in natural images

We evaluate the proposed methodology on cloud segmentation in natural images from the Singapore Whole sky IMaging SEGmentation database [START_REF] Dev | Color-Based Segmentation of Sky/Cloud Images From Ground-Based Cameras[END_REF] (SWIMSEG). This task is highly relevant to the proposed methodology: both local and global features are key to good performance on this dataset, as difficult positive regions of light cloud can only be correctly identified based on subtle textural patterns and comparison with surrounding regions. SWIMSEG contains 1013 600px 2 images of sky patches and corresponding cloud segmentations. Training, validation and testing sets each contain 861, 101 and 51 samples, respectively. The model and training setup used is identical to those of Section 3.3. Results are detailed in Table 3, where we report the segmentation IoU and Dice score on the testing set as in [START_REF] Dev | Color-Based Segmentation of Sky/Cloud Images From Ground-Based Cameras[END_REF][START_REF] Song | An Efficient Solution for Semantic Segmentation of Three Groundbased Cloud Datasets[END_REF][START_REF] Dev | CloudSegNet: A deep network for nychthemeron cloud image segmentation[END_REF]. The tri-attention model achieves respective IoU and Dice scores of 0.90 and 0.95, representing a significant improvement over state of the art.

CONCLUSION

We presented a computationally efficient multi-scale attention architecture that is sensitive to texture orientation for segmentation of global contaminants in large images. Efficiency is achieved through a gridded architecture, and orientation sensitivity is provided by a new Gabor attention operator. To address the challenge of uncertain groundtruth labelling, we proposed a simple consensus loss. These contributions are combined into a new state-of-the-art model for the segmentation of cirrus contaminants from astronomical images. Reliable performance was achieved with only a small training dataset of images. Our model can process an entire image in one pass with minimal downscaling, meaning that the proposed method can be easily integrated into data processing pipelines for imaging instruments to obtain contamination masks. In future work it would be interesting, using the methodologies presented in this work, to craft a deep generative model capable of removing global contaminants.

Fig. 1 :

 1 Fig. 1: Cirrus dust of various strengths (top), with uncertain annotations (middle) and predictions (bottom).

Fig. 2 :Fig. 3 :

 23 Fig. 2: Proposed MS gridded attention.

Table 1 :

 1 Segmentation IoU in format mean(std).

		Single Ensemble
	IoU	0.745	0.790
	Dice 0.766	0.814

Table 2 :

 2 Proposed cirrus segmentation results

		Ours Dev et al. [2] Dev et al. [3] Song et al. [20]
	IoU	0.90	0.69	0.80	0.86
	Dice 0.95	0.82	0.89	0.92

Table 3 :

 3 Segmentation scores on the SWIMSEG sky/cloud segmentation dataset.


Serge S Suanez
email: serge.suanez@univ-brest.fr

Pierre Stéphan

Ronan Autret

Julien Houron

France Floc'h

Laurence David

Jérôme Ammann

Mickaël Accensi

André Gaël

Damien Le Guyader

Suanez Serge

Stéphan Pierre

Autret Ronan

Houron Julien

Floc'h France

David Laurence

Ammann Jérôme

Accensi Mickael

André Gael

Le Guyader Damien

Cancouët Romain

Catastrophic overwash and rapid retreat of a gravel barrier spit during storm events (Sillon de

come   L'archive ouverte pluridisciplinaire

Introduction

Gravel-dominated barrier spits presenting a single-crested ridge are highly sensitive to landward migration due to cross-shore dynamics associated with rollover processes. This barrier retreat is the main morphological response to relative sea-level rise (SLR) operating over different timescales from microscale to megascale. Orford et al. (1995a) defined appropriate timescales for the analysis of the rate of sea-level rise in the study of gravel-barrier retreat; they extend from microscale (<10 0 yr), to mesoscale (10 0 to10 2 yr), to macroscale (10 2 to 10 3 yr), and finally to megascale (>10 3 yr). In addition, subdivisions for mesoscale specification span across inter-annual (1 to 5 yr), to sub-decadal (5 to 10 yr), culminating in decadal (10 1 to 10 2 yr) timescales. Orford and Carter (1995) distinguished (i) microscale (<10 0 yr), controlling the rise of water level due to storm events associated with barrier crest overtopping and overwashing that lead, respectively, to reduced and accelerated barrier retreat, and (ii) macroscale (10 2 yr), governing secular sea-level rise that influences the rhythm of coastal retreat by controlling the rate at which the coastal erosion front passes across the terrestrial basement. As indicated by Orford et al. (1995a[START_REF] Orford | Control domains and morphological phases in gravel-dominated coastal barriers of Nova Scotia[END_REF], the mesoscale (10 0 to 10 2 yr) rather than the macroscale (>10 2 yr) SLR rate is the critical control on barrier retreat, as mesoscale sea-level variation in combination with storm surge potential is able to rapidly raise water levels to the elevation threshold sufficient for barrier overwash and hence drive barrier retreat due to rollover.

Significant rollover processes occur during extreme events when wave runup overtop, overwash, or strongly inundate the crest of the barrier over a very short time-period (i.e., microscale <10 0 yr) [START_REF] Matias | Overwash threshold for gravel barriers[END_REF][START_REF] Masselink | Response of wave-dominated and mixed-energy barriers to storms[END_REF][START_REF] Brown | Modelling gravel barrier response to storms and sudden relative sea-level change using XBeach-G[END_REF][START_REF] Phillips | Modeling impact of intertidal foreshore evolution on gravel barrier erosion and wave runup with XBeach-X[END_REF][START_REF] Pollard | Impact of management regime and regime change on gravel barrier response to a major storm surge[END_REF]. The most effective storm-impact scaling model describing the response of the barriers to storms was proposed by [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF]. It is based on the elevation difference between the peak overflow elevation (Oe) and the height of the barrier crest (Bh), which is known as "freeboard" [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF][START_REF] Orford | Extreme events and the morphodynamics of gravel-dominated coastal barriers: strengthening uncertain ground[END_REF] (Figure 1). Oe corresponds to the extreme water level (EWL), also corresponding to the maximum runup elevation Rhigh. Therefore, this parameter is calculated as follow:

Oe=EWL=Rhigh = tide + surge + runup (η + R) [1]
where runup is the sum of wave setup (η) and swash elevation (R).

Depending on the water flow across the barrier (Od,q), where d is the water depth, and q the volumetric discharge, morphological responses of the barriers to storm impact are ranged into four distinct regimes: swash overtopping, discrete overwash, sluicing overwash, and catastrophic overwash/breaching [START_REF] Orford | Extreme events and the morphodynamics of gravel-dominated coastal barriers: strengthening uncertain ground[END_REF] (Figure 1). Swash overtopping occurs when the peak overflow elevation reaches the top of the barrier without crest overwashing (i.e., positive to neutral freeboard), inducing an accretion of the crest due to the infiltration of the uprush reaching the crest without efficient backwash. Then, as the swash runup elevation increases, overwashing processes become more destructive. The discrete "overwash" induces a slight erosion of the crest when wave runup passes over it. The "sluicing overwash" process completely removes the top-barrier due to an energetic and unidirectional flow that is largely unaffected by percolation. In some cases, the lowering of the crest due to erosion is related to deposition of small-scale back-barrier washover fans. The last regime,"catastrophic overwash", occurs during intense storms generating extreme sea-level increases. Overflow induces a strong erosion of the complete barrier in the form of a breach or throat, and washover fans and splays are deposited on the back-barrier. This latter extreme storm-impact regime leads to intense landward barrier retreat and/or barrier breaching which generally corresponds to the final "catastrophic step" of significant long-term rollover processes [START_REF] Carter | The morphodynamics of coarse clastic beaches and barriers: a short and long-term perspective[END_REF][START_REF] Orford | Control domains and morphological phases in gravel-dominated coastal barriers of Nova Scotia[END_REF][START_REF] Orford | Organisational controls, typologies and time scales of paraglacial gravel-dominated coastal systems[END_REF]. The use of this model is therefore strongly dependant on the evaluation of the swash runup elevation for estimation of the peak overflow elevation (Oe), which also corresponds to extreme water level (EWL). This component is the key parameter controlling the occurrence of gravel barrier overwashing [START_REF] Matias | Overwash threshold for gravel barriers[END_REF][START_REF] Masselink | Response of wave-dominated and mixed-energy barriers to storms[END_REF]. In contrast to sandy beaches (e.g., [START_REF] Stockdon | Empirical parameterization of setup, swash, and runup[END_REF], only a few recent studies of wave runup estimation based on field-runup have been carried out on steep gravel beaches or barriers [START_REF] Powell | Predicting short term profile response for shingle beaches[END_REF][START_REF] Polidoro | Improved maximum run-up formula for mixed beaches based on field data[END_REF][START_REF] Poate | A new parameterisation for runup on gravel beaches[END_REF][START_REF] Didier | Wave runup parameterization for sandy, gravel and platform beaches in a fetchlimited, large estuarine system[END_REF].

According to the Davis (1972) classification, gravel barriers are often divided into two types, drift-aligned and swash-aligned. This distinction is based on the plan view geometry of the barrier and its morphodynamic relationship to longshore sediment scarcity for a swashaligned barrier, and significant surplus of longshore sediment transport for a drift-aligned barrier. Many studies based on eastern Canadian and northwest European data have established the nature of the swash-aligned gravel barrier response to SLR at the mesoscale [START_REF] Orford | Gravel barrier migration and sea level rise: some observations from Story Head, Nova Scotia, Canada[END_REF][START_REF] Forbes | Gravel-barrier migration and overstepping[END_REF][START_REF] Carter | The morphodynamics of coarse clastic beaches and barriers: a short and long-term perspective[END_REF]Orford et al. 1995b[START_REF] Orford | Control domains and morphological phases in gravel-dominated coastal barriers of Nova Scotia[END_REF]. In this paper we examine the cross-shore morphological dynamics of the gravel spit of the Sillon de Talbert a swash-aligned barrier [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF] that has been evolving to a drift-aligned barrier during the last few decades (Suanez et al., 2018a). This study is based on a high frequency beach profile survey which has been ongoing since September 2012. It consists of weekly to monthly topo-morphological measurements along two transects situated on the most retreating zones of the spit. This survey is also based on hydrodynamic in situ measurements (waves and water levels) using pressure sensors and WW3 wave modelling. The morphological changes of the spit related to cross-shore dynamics are addressed using the storm-impact model of [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF]. The calculation of the runup (R) -as a main component of the height of the extreme water level (EWL)-was based on the calibration of the existing empirical formula of [START_REF] Hunt | Design of seawalls and breakwaters[END_REF], modified by [START_REF] Battjes | Surf similarity[END_REF]. The parametrisation of this equation was based on the field measurements of the wrack lines related to the highest high-tide runup elevation and the analysis of morphosedimentary and hydrodynamic conditions, following the methods of [START_REF] Cariolet | Runup estimations on macrotidal sandy beach[END_REF] and [START_REF] Suanez | Observations and predictions of wave runup, extreme water levels, and medium-term dune erosion during storm conditions[END_REF].

Study site

The gravel barrier spit of the Sillon de Talbert is located on the northern Brittany coast (France) in the department of Côtes d'Armor (Figure 2). The morphological setting of this gravel barrier spit has been detailed by [START_REF] Stéphan | Franchissement et recul des cordons de galets par rollover. Impact de la tempête du 10 mars 2008 dans l'évolution récente du Sillon de Talbert (Côtes d'Armor, Bretagne)[END_REF], 2012, 2018), and Suanez et al. (2018a). The gravel barrier spit of the Sillon de Talbert is driven by both longshore and crossshore dynamics. However, since sediment transfers due to cross-shore dynamic are dominant comparing to longshore sediment transferts (430,000 m 3 vs 52,000 m 3 between 2002 and 2019) [START_REF] Suanez | Medium-Term Longshore and Cross-shore Dynamics of a Gravel Spit Driving by Storm Events (Sillon de Talbert, Brittany, France)[END_REF], the Sillon de Talbert is considered as a single-ridge swash-aligned barrier that stretches over 3.5 km long. It is composed of a mixture of sand and gravel sediment with an estimated volume of 1.23 10 6 m 3 . On the distal part of the spit, the sandy fraction decreases, while the gravel sediment significantly increases. The beach face is characterized by a slope break point about 1 m above the mean water level, delimiting the spit accumulation from the large flat rocky platform (0.01%). The upper part of the beach face shows steeper slopes of between 5% and 15%. According to the morphological and sedimentary features, [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF] have subdivided the barrier into four distinct morphosedimentary units, from Unit 1, corresponding to the proximal sandy dune section, to Unit 4, forming the distal section (Figure 3a). These two sections are the most stable in terms of shoreline dynamics. This is due to (i) the coastal defence structures (i.e., rip-rap and groin) remaining on Unit 1 preventing erosion processes, and (ii) the longshore sediment transport that supplies the distal part of the spit (i.e., Unit 4) inducing significant accretion and enlargement of this section. These two sections -Units 1 and 4-are characterized by crest heights reaching 8.5 m to 9.5 m above sea level (a.s.l.), respectively. Conversely, both Units 2 and 3, corresponding to the proximal gravel section and the median section, respectively, have displayed the most retreat in the last 80 years [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF]Suanez et al., 2018a). The crest height is about 7 m a.s.l. for Unit 2, and 7.5 m a.s.l. for Unit 3. This coastal area is located in a macrotidal to megatidal environment with a maximum tidal range of 10.95 m (SHOM, 2016). The most frequent swells come from the WNW with a resultant vector of around 302° (Figure 2d). Consequently, the waves break with a slight angle according to the coastline's orientation ( 54°). This non-parallel swash alignment ( >0) generates a longshore drift oriented to the NE. Modal heights (Hm0) of deep sea waves are between 1 and 1.5 m and modal periods (Tpic) are between 9 and 10 seconds. During storms, wave heights can reach 9 m with periods of 20 seconds.

Based on the analysis of ancient maps [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF], the long-term morphological evolution of the Sillon de Talbert indicates that up to the end of the 17 th century it was connected to the islets of the Olone archipelago located in the NE. The detachment of the barrier occurred in the early 18 th century and gave rise to a 3.2 km long gravel spit (Stephan et al., 2012). This is probably due to the severe storm event of November 26, 1703, which was one of the most extreme events recorded along the south England and northwest French coasts over the past few centuries [START_REF] Lamb | Historic storms of the North Sea, British Isles and Northwest Europe[END_REF]. The transformation from anchored barrier to barrier spit triggered an alongshore drift sediment transport that was associated to (i) a slight longshore cannibalization process, which increased throughout the 19 th and 20 th centuries due to sediment depletion, and (ii) a "cross-shore" landward displacement by rollover facilitated by the disconnection. Using the back-barrier edge (see Figure 1b) [START_REF] Pinot | Fixer le plan ou gérer le profil : l'exemple du Sillon du Talbert[END_REF]Pinot ( ) estimated long-term (1775Pinot ( -1966) ) rate of spit retreat at -0.5 m.yr -1 . [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF] have shown same estimation of average landward migration rate up to -1.1 m.yr -1 between 1930 and 2010, and they highlight the inefficiency of the longshore 1,400 m long riprap, installed from the mid-70's to the beginning of the 80's, in preventing the retreat of the barrier spit (Figure 3d). More recently, [START_REF] Stéphan | Monitoring the medium-term retreat of a gravel spit barrier and management strategies, Sillon de Talbert (North Brittany, France)[END_REF] and Suanez et al. (2018a) demonstrated that this rate has increased for the last fifteen years (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017), reaching -2 m.yr -1 , with a maximum spit migration up to -150 m on the median section, and -160 m on the gravel proximal section (Figure 3a), where a breach opened in March 2018 (Figure 3e). Suanez et al. (2018a) indicated that storm events combined with high spring tide levels control more than 95% of this retreat due to catastrophic overwash/inundation processes (Figure 3b and3c). This was the case during the Johanna storm of March 10, 2008 when the maximum spit retreat reached -22 m [START_REF] Stéphan | Franchissement et recul des cordons de galets par rollover. Impact de la tempête du 10 mars 2008 dans l'évolution récente du Sillon de Talbert (Côtes d'Armor, Bretagne)[END_REF]. It was also the case during the stormy winter of 2013-2014 when the maximum spit retreat reached -30 m [START_REF] Blaise | Bilan des tempêtes de l'hiver 2013-2014 sur la dynamique de recul du trait de côte en Bretagne[END_REF]. Figure 3b illustrates the overwashing of the section (i.e., Unit 1) where the crest height is one of the highest (i.e., 8.5 m to 9 m a.s.l.).

Data and methods

Beach profile measurements

The monitoring of topo-morphological changes is based on two beach profile measurements carried out between September 2012 and December 2019 along two transects situated on both spit sections where retreat rates are the most significant (Figure 4). These sections correspond to Unit 2 (proximal gravel section) and Unit 3 (median section) (see Figure 3a). This survey was performed at a weekly to monthly frequency using a Leica tacheometer TCR303 and DGPS Topcon HiperV (Suanez et al., 2018b). A total of 116 and 119 profiles were measured on transects A and B, respectively. Each measurement was calibrated using the geodesic marker from the French datum and the geodesic network provided by the IGN (Institut Géographique National). The position of the control points was measured to estimate the margin of error reaching ± 5 to 7 cm in x, y, and ± 2 cm in z. Beach profile measurements were used to monitor the morphological changes of the spit, such as (i) the crest lowering/elevation (Δhcrest) and the crest horizontal displacement (Δxcrest), (ii) the spit back-barrier landward retreat (Δrspit), and (iii) the seaward beach face slope (tan ) corresponding to the swash zone. It was calculated on the section of the beach profile defined by the crest of the barrier as the upper bound, and the base of the barrier front (break point between the platform and the seaward beach face) as the lower bound. In addition, quantification of the changes in sediment budget was measured for the three sections of the profile, i.e., the beach face, the crest, and the backbarrier, in order to analyze the sediment transport due to overtopping, discrete and sluicing overwashing processes, respectively. The distinction between these three sections is based on the consideration of morphological breaks in the slope.

In July 2014, a granulometric and sedimentological analysis was performed along both profiles A and B [START_REF] Fichaut | Caractérisation de la sédimentologie du Sillon du Talbert (Commune de Pleubian -Juillet 2014)[END_REF]. This work was based on sediment samples taken at the surface and at depth when the characteristics of the latter were different from those at the surface, especially in terms of the share of sandy sediments compared to coarse sediments (gravels and pebbles).

The sandy fraction is always significant along profile A, except on the back-barrier where it is absent on the surface. It represents between 30% and 60% of the sedimentary material (Figure 4e). The sandy material is largely dominant at the top of the beach face where it is frequently removed by the wind and feeds the embryo dunes located at the top of the barrier. These results are in agreement with earlier work by [START_REF] Morel | De la géomorphologie à la gestion des cordons de galets littoraux du bassin de la Manche et de ses abords : études de cas (Bretagne, Haute-Normandie, Picardie, Sud Angleterre) et réflexions générales[END_REF], and confirmed by [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF] to justify the morphosedimentary compartmentalization of the barrier. The authors indicated that this section (i.e., proximal section as Unit 2, see Figure 3a) is characterized by a heterogeneous mixture of poorly sorted sand and pebbles representing less than 40% of the material. In contrast, profile B shows a completely different sediment grain size distribution. The coarse fraction (gravels and pebbles) represents the majority of the surficial sediment along this profile. The sandy fraction, a much lower proportion (about 10%), is encountered only at depth of about 0.15 m, essentially on the sea-face beach (Figure 4f). This grain size distribution gives this section of the barrier a greater permeability because the interstitial voids are not filled with fine sediments. These sedimentological characteristics were also described by [START_REF] Morel | De la géomorphologie à la gestion des cordons de galets littoraux du bassin de la Manche et de ses abords : études de cas (Bretagne, Haute-Normandie, Picardie, Sud Angleterre) et réflexions générales[END_REF] and [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF], indicating that the median section of the barrier (Unit 3, see Figure 3a) was primarily coarse sediment (>70%).

Hydrodynamic analysis: data acquisition and methods

Offshore wave modeling

Offshore wave data between 01/09/2012 and 31/12/2019 were obtained from the HOMERE hindcast data set [START_REF] Boudière | A suitable metocean hindcast database for the design of Marine energy converters[END_REF]. This hindcast uses the WAVEWATCH III V4.18 spectral model [START_REF] Tolman | User Manual and System Documentation of WAVEWATCH III ® version 4.18[END_REF][START_REF] Roland | On the developments of spectral wave models: numerics and parameterizations for the coastal ocean[END_REF] and the NORGAS-UG configuration. This configuration was implemented with unstructured and higher resolution grids on the coastal zone, thus enabling the reproduction of the wave climate in the shallow zone. It was forced by the wind fields from the CFSR reanalysis with a resolution ranging from 0.25° to 0.5° [START_REF] Saha | The NCEP Climate Forecast System Reanalysis[END_REF] and by the surface currents generated from an atlas of harmonic tidal constituents obtained from outputs of the MARS circulation model [START_REF] Lazure | An external-internal mode coupling for a 3D hydrodynamical model for applications at regional scale (MARS)[END_REF]. The present dataset corresponds to coordinates 3.047°W, 48.927°N, at a depth of about -50 m, node #65681 (Figure 2b).

Wave parameters such as direction (D), wave height (Hm0), and period (Tm0,-1) were extracted for the analysis of offshore wave conditions. To produce a clearly identifiable significant extreme storm event threshold, the 0.01% exceedance (99.9 th percentile) wave height is calculated [START_REF] Grieco | A climatology of extreme wave height events impacting eastern Lake Ontario shorelines[END_REF]. A threshold of about 5 m (5.07 m precisely) was obtained using the 7-year data set. The wave energy flux, F, of these major events was calculated using (see [START_REF] Barnard | Extreme oceanographic forcing and coastal response due to the 2015-2016 El Niño[END_REF]:

𝐹 = 𝜌𝑔 2 𝐻 𝑚0 2 𝑇 𝑚0,-1 64𝜋 [2]
where F is expressed per unit crest length of the wave (in J.m -2 ), ρ = 1,025 kg.m -3 is the density of seawater, g = 9.81 m.s -2 is the acceleration due to gravity, Hm0 is the significant wave height, and Tm0,-1 is the wave period.

Hydrodynamic records in the shallow zone

The survey was also based on hydrodynamic records (wave and water level) in the shallow zone using an OSSI-010-003C pressure sensor (Ocean Sensor Systems Inc. ® , accuracy ± 1.5 cm specification). These records started in September 2012 and are ongoing (Suanez et al., 2018c). The pressure sensor was deployed in the tidal zone along profile B, at -0.461 m a.s.l., which approximately corresponds to the mean sea water level (Figure 4a and4b). Therefore, the sensor was out of the water twice a day during low tide. A recording frequency of 5 Hz was chosen to reproduce the wave spectrum as accurately as possible.

The OSSI pressure sensor data were corrected i) from the atmospheric mean sea level pressure recorded at the Ploumanac'h Météo France record station (Figure 2a), and ii) the non-hydrostatic pressure following the linear wave theory [START_REF] Homma | Response characteristics of underwater wave gauge[END_REF][START_REF] Bishop | Measuring waves with pressure transducers[END_REF]. The mean surface elevation (h) was extracted using a moving mean over 10 minutes of signal. In order to retrieve the wave spectrum and wave averaged parameters, Fourier transforms of the detrended water level were used. The Fast Fourier Transform method was applied over 1,024 data points (at 5 Hz) for incident gravity wave bands (between 0.04 and 0.4 Hz). Since the signal is not perfectly periodic, leakage issues could induce artifacts in the resulting spectrum. To avoid this, a Hamming window was applied to the signal, leading to zero values at the edges. An average was carried out over several contiguous spectra with 50% overlap. The average was performed over 15 minutes for the incident band [START_REF] Pierson | The power spectrum analysis of ocean-wave records[END_REF]. The mean spectral wave parameters, i.e., signicant wave height Hm0 and the equivalent spectral mean period Tm0,-1, were then computed (IAHR, 1989). Following the same method as above, extreme wave height (Hm0) events based on 99.9 th percentile (up to 1.8 m) were inventoried.

For both the offshore and shallow wave data set, wave parameters such as wave height (Hm0) and mean period (Tm0,-1) recorded at both daily high tide levels were selected for the specific hydrodynamic analysis related to morphological changes. The comparison between the WW3 offshore wave modelling and the OSSI shallow wave records was conducted using linear regression. It shows a good fit with R 2 of 78%, with highest Hm0-OSSI reaching about 2 m vs 5 m to 6 m for offshore wave heights (Hm0-WW3) (Figure 5a). This reflects relevant wave energy dissipation across the large and flat nearshore rocky platform facing the gravel barrier spit.

Tide gauge records from the SHOM

Since there is no tide gauge station on the Sillon de Talbert, data from both daily predicted high tide levels were obtained by modeling at the Les Héaux-de-Bréhat lighthouse site (Figure 2b). These data were computed and provided by the French hydrographic body called SHOM (Service Hydrographique et Océanographique de la Marine). However, the closest referenced tide gauge station managed by SHOM corresponds to the station of Roscoff located at about 70 km west of the Sillon de Talbert (Figure 2a). The data recorded at this station were used to calculate surge level at the same time of both daily high tide levels mentioned previously. Then, the surge level at Roscoff was added to the predicted tide level obtained at the Les Héaux-de-Bréhat site in order to acquire the maximum water level for both daily high tide levels. This approach was the most accurate method for estimating the observed tide level on the Sillon de Talbert, considering there is no tide gauge station in this zone.

The correlation between the SHOM observed tide level and the OSSI water level for both daily high tides was conducted, showing a very good fit (R 2 : 97%) (Figure 5b). Therefore, data obtained by the OSSI wave gauge sensor were used to fill the gaps when the SHOM observed tide data were missing, and vice versa.

Maximum swash elevation field measurement

The maximum swash elevation (as a maximum wave runup) was based on the wrack deposit measurement, assuming that this limit corresponded to the highest level reached by wave runup during the previous high tide preceding the measurement [START_REF] Cariolet | Runup estimations on macrotidal sandy beach[END_REF][START_REF] Suanez | Observations and predictions of wave runup, extreme water levels, and medium-term dune erosion during storm conditions[END_REF]. Most of the time, the wrack deposit accumulated during the previoust high tide is clearly identifiable because it is wet, and/or its physiognomic aspect is not deteriorated. This indicator was used to quantify in-situ environmental conditions and dimensional swash parameters for the best calibration of the runup formula [START_REF] Plant | How well can wave runup be predicted? Comment on Laudier et al[END_REF]. Then, this runup component was applied to determine the hydrodynamic conditions (i.e., extreme water level) related the storm-impact scaling model of [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF] describing the response of the spit barriers to storms as one of four types: overtopping, discrete overwash, sluicing overwash, and catastrophic overwash.

Depending on the meteorological conditions prevailing before the measurement, the limit of the position of the wrack line was either very easy to identify, (Figure 6a and6b), or completely impossible to identify (Figure 6c). In the later case, while the beach profile was measured, the position of the wrack limit was not. When it was not possible to precisely determine this limit, this uncertainty was recorded during the field measurement process in such a way as to use this information during data processing (Figure 7). When the wrack line overtopped the crest -towards back-barrier-due to overwash processes (Figure 6d), the height of the top of the crest was selected as the maximum swash runup elevation. In this case this information was also used during data processing (Figure 7). As such, it is possible to notice that the number of overwash events was at least twice as great for profile A than for profile B. This is explained by the fact that the height of the spit is lower in that sector of profile A than that of profile B.

The wave characteristics (Hm0 and Tm0,-1) associated with these highest levels were calculated on a 2-hour time step around the time of high tide level (1 hour before, and 1 hour after).

When it was not possible to determine and measure precisely the wrack line as the swash limit (i.e., Figure 6c), the uncertainty component was taken into account during data processing by removing the data which were considered outliers. As shown in Figure 8, there is a very good correlation between the observed tide and the height of the swash limit. It should be noted that some data which were qualified as unreliable in the field were retained because they appeared to be consistent. Points below the 1:1 line indicate a negative runup value. These values can be interpreted as the margin of error inherent to the method ( 0.2 m). In this case, the wrack line has moved down the profile with the backwash flow, especially at the top of the barrier where the slope is particularly steep. The amplitude of the swash limit reach 2.5 m to 6.4 m for profile A, against 2.1 m to 7.2 m for profile B. The amplitude of the maximum swash elevation (ΔRmax = swash limitobserved tide) is between 1.6 m and 2.2 m for profiles A and B, respectively (Figure 7). Finally, the data indicated that the process of crest overtopping due to sluicing overwash or catastrophic overwash was twice as frequent on profile A (6 events) than profile B (3 events).

Results

Morphological beach profile changes

The results show very similar evolution along both profiles A and B, characterized by alternating erosive and recovery phases (Figure 9): (i) a first phase, from September 18, 2012 to December 18, 2013, indicates no significant changes. The variation of the height of the crest (Δhcrest) never exceeded ± 20 cm, and its position (see Δxcrest) remained very stable, particularly for profile B (Figure 9g). In detail, both envelopes of profiles showed the migration of berms along the seaward beach face characterized by a slope (tanβ) of about 0.10 and 0.16 for profiles A and B, respectively (Figure 9d and9h).

(ii) a second phase, from the beginning of January 2014 to March 5, 2014, was characterized by significant changes related to severe erosion. During this period, the crest of the barrier spit lowered by -0.45 m and -1.35 m along profiles A and B, respectively (Figure 9b and 9f), and retreated by about -12 m to -14 m (Figure 9c and9g). Both envelopes of profiles A and B show an intense erosion of the seaward beach face, and similarly a significant accretion on the back-barrier. These morphological changes took place in three stages; at the beginning of January (see profile 07/01/2014), February (see profile 13/02/2014), and March (see profile 05/03/2014) (Figure 9a and9e). This evolution illustrated the process of rollover due to catastrophic inundation and erosion leading to a great landward displacement of the barrier spit. Similarly, the slope (tanβ) of the beach face decreased from 0.10 to 0.07 for profile A, and from 0.16 to 0.11 for profile B (Figure 9d and9h). (iii) from April 2014 to December 2017, a third phase was mainly characterized by the elevation of the crest of the barrier spit reaching about +0.44 m at profile A, and +1.1 m at profile B (Figure 9b and9f). This process of recovery led to the top barrier regaining its prestorm altitude for both profiles. However, this recovery phase was interrupted by a brief but significant episode of crest lowering on February 12, 2016. The profiles show that the rise of the crest was related to erosion of the beach face (Figure 9a and9e). Therefore, the part of the sediment eroded to the beach face contributed to the elevation of the crest, inducing an increase of the slope (tanβ) of the seaward beach from 0.07 to 0.095 for profile A, and from 0.11 to 0.12 for profile B. In terms of barrier spit migration, a significant landward displacement of the crest of about 7 m was experienced principally on profile B as shown by the February 12, 2016 measurement (Figure 9g). Similarly, a net back-barrier landward migration of 8.5 m and 6 m occurred for profiles A and B, respectively (Figure 9a and9e). (iv) between December 4, 2017 and January 5, 2018, a major episode of crest lowering and retreat was experienced on both profiles A and B. Crest lowering reached -0.42 m and -1.28 m on profiles A and B, respectively (Figure 9b and 9f), while the retreat of the crest was about -6.25 m and -8 m, respectively (Figure 9c and9g). This fourth phase was strongly erosive, and once again, the majority of the sediment eroded from the top of the spit was transferred and deposited to the back-barrier, inducing a global landward barrier spit migration of about -5 m to -6 m for both profiles (Figure 9a and9e). This erosive event was also related to a decrease of the beach face slope on both profiles (Figure 9d and9h). (v) a fifth and final phase began after January 5, 2018, until the end of December 2019. It is characterized by the crest elevation reaching +0.32 m and +1.25 m on profiles A and B, respectively (Figure 9b and 9f), while the position of the crest experienced significant progradation of +2 m and +7 m on profiles A and B, respectively (Figure 9c and9g). Similarly, the slope of the seaward beach face increased from 0.088 to 0.093 and from 0.093 to 0.132 for profiles A and B, respectively (Figure 9d and9h).

Regarding all the parameters over the entire survey period between September 2012 and December 2019, the crest migration on profile A (i.e., proximal gravel section) and profile B (i.e., median section) indicated that the crest (Δxcrest) of the Sillon de Talbert has retreated by about -22 m to -30 m, respectively, while the back-barrier spit retreat (Δrspit) reached about -23 m to -30 m. This landward displacement due to rollover processes represents a migration rate of about -3 to -4 m.y -1 over the last 7 years. The variation of crest height (Δhcrest) for profile A reached about 0.5 m with a minimum of 6 m and a maximum of 6.5 m. For profile B, it was about 1.9 m with a minimum of 5.7 m and a maximum of 7.6 m. For both profiles, it takes about 12 to 14 months to completely restore the crest height after a major lowering due to crest overwash processes. Such was the case after the stormy winter of 2013-14, the Imogen storm of February 8, 2016, and the Eleanor storm of January 3-4, 2018.

Hydrodynamic forcing and overwashing processes

Offshore waves display seasonal variations of significant wave height. There was a maximum Hm0 of 5 m, exceeding the 99.9 th percentile, during the winter periods, which corresponds to the major storm events that occurred during the survey period (Figure 10a), i.e., February 28, 2014 (6.23 m) during the Andrea storm, February 8, 2016 (6.81 m) during the Imogen storm, January 3, 2018 (6.07 m) during the Eleanor storm, and December 9, 2019 (6.10 m) during the Atiyah storm. Taking into account a significant wave height of >5 m, sixteen extreme events were inventoried from December 2012 to December 2019 (Table 1). The early spring period was also affected by extreme significant wave heights, as was the case during the Doris storm on March 9, 2016 (5.44 m).

Regarding the wave energy flux, a threshold up to 1.5 x 10 6 J/m² was defined taking into account a wave height of Hm0 >5 m (99.9 th percentile), associated with a period of 11.5 s, to describe the strongest events. Six storm events were inventoried, including Ruth on February 8-9, 2014, Andréa on February 28, 2014, the storm of February 24, 2015, Imogen on February 8, 2016, Eleanor on January 3, 2018, and Atiyah on December 9, 2019 (Table 1). Storm Imogen was the most significant event with more than 3.34 x 10 6 J.m -2 of energy (Figure 10b).

The major storm events inventoried using shallow wave height records are quite different from the ones related to offshore wave heights (Table 2). These events are well identified regarding shallow wave height (i.e., Cristine, 2015-02-24, Eleanor, and 2019-12-13, storm events). Two more storm events were detected, i.e., the low pressure system "Nadja" (2014-02-01), and Egon (2017-01-12/13). The absence of the Imogen storm is due to the fact that the OSSI pressure sensor did not record any data during this period (Figure 10c). Significant major morphogenetic events combining highest storm waves and extreme water levels were statistically identified using a 3% exceedance threshold for observed tide and significant wave height (Figure 10d). Following this approach, seven significant morphogenetic events leading to a catastrophic overwash were detected. The major one exceeding 1% exceedance occurred January 3, 2018; it was related to storm Eleanor (Table 3).

Wave runup parameterisation

The wave runup parametrization is based on the simple equation from [START_REF] Hunt | Design of seawalls and breakwaters[END_REF] describing the linear relationship between the normalized wave runup and the beach slope divided by the offshore wave steepness, named by [START_REF] Battjes | Surf similarity[END_REF], the surf similarity parameter Iribarren number (ξ0). This relationship can be written as follow:

𝑅 𝐻 0 = 𝐶𝜉 0 [3]
where C is a nondimensional constant, and ξ0 is the Iribarren number given by:

𝜉 0 = 𝑡𝑎𝑛𝛽 √𝐻 0 /𝐿 0 [4]
where tanβ is the beach slope, H0 corresponds to offshore wave height (equivalent to Hm0 for WW3-wave in deep water), and L0 is the deep water wavelength using linear wave theory:

𝐿 0 = 𝑔𝑇 𝑚0,-1 2 2𝜋 = 1,561𝑇 2 [5]
where g is the acceleration due to gravity; Tm0,-1 is the mean period; 2π/T is the radian frequency.

The dependence of wave runup on offshore and shallow wave parameters was assessed through a correlation analysis. Several parameters such as Hm0 and Tm0,-1 for WW3 offshore deep water wave height, and the ratio of wave height to wave steepness Hm0/(Hm0/L0) 0.5 = (Hm0L0) 0.5 were tested. As indicated by [START_REF] Poate | A new parameterisation for runup on gravel beaches[END_REF] and [START_REF] Dodet | Wave runup over steep rocky cliffs[END_REF], the importance of wave periods is better investigated using mean periods (i.e., Tm0,-1), instead of peak period parameter (Tp).

For Hm0 the square correlation (R 2 ) ranged respectively between 0.35 (profile A) and 0.41 (profile B) (Figure 11a). Considering the wave period (Tm0,-1) for the wavelength (L0) calculation, [START_REF] Hunt | Design of seawalls and breakwaters[END_REF] indicates that both wave height and wave period are significant factors in determining the runup, and their combination in a Hunt-like parameter (Hm0L0) 0.5 gives better fits. The square correlation increases to 0.49 and 0.50 (Figure 11b). Finally, the morphological component was considered by introducing the beach slope tanβ in the wave runup dependence on slope analysis. The correlation between Rmax and tanβ (Hm0L0) 0.5 once again increases to 0.54 and 0.55 (Figure 11c).

Based on this analysis, a parameterisation for the prediction of maximum runup (Rmax) on the Sillon de Talbert was produced. The resulting optimised runup formula based on the offshore wave data set (WW3 wave parameters) is given by: Rmax = 0.58Hm0ξ0 (for Profile A)

[6] Rmax = 0.52Hm0ξ0 (for Profile B) [7] giving:

Rmax = 0.5Hm0ξ0 (for both profiles) [8]

Application of Orford and Carter's storm impact scale model

As indicated in the introduction, the storm impact scale model of [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF] is based on the elevation difference between the extreme water level (EWL) -as the peak overflow elevation (Oe)-, and the height of the barrier crest (Bh). In this study, the EWL was calculated using equation [1], where the wave runup component was estimated using equations [6] and [7].

The height of the EWL was then subtracted from the height of the crest of the barrier (Bh) along both profiles in order to identify periods when the barrier was overtopped or discretely or severely overwashed (Figure 12). The flow depth (Od,q) overtopping the crest barrier (see [START_REF] Orford | Extreme events and the morphodynamics of gravel-dominated coastal barriers: strengthening uncertain ground[END_REF] was empirically thresholded by taking into account the morphological response of the barrier measured in the field to define three regimes corresponding to Orford and Carter's model. It appears that the overtopping regime takes place with Od values between 0 and 25 cm, the discrete overwash regime with Od values from 25 to 45 cm, and the overwash regime with Od values greater than 45 cm (Figure 12b and12e). The catastrophic inundation regime was not retained because no breach openings were observed along the two measured profiles during the entire observation period. Moreover, the wave energy flux was calculated for each flow depth that overtopped/overwashed the barrier, and was plotted using proportional circles in order to identify the most morphogenic episodes (Figure 12b and12e). In a way, the wave energy flux component can replace the volume (q) of the flow depth (Od,q) and allows one to hierarchize the overtopping events according to the power of the flow. Finally, all these data were compared to the sediment budget calculated on the three sections of the barrier along the two profiles (see methodological section): the beach face, the crest, and the back of the barrier (Figure 12c and12f).

The results show a strong similarity for both profiles. Three periods characterized by significant morphogenic events are inventoried. They show flow depth (Od,q) levels of around >45 cm, inducing a sluicing overwash regime, notably (i) during the winter of 2013-2014 (January 3-4 with maximum Od,q of about 0.6 m for profile A, and 0.5 m for profile B; February 1-2 with maximum Od,q of about 0.8 m for profile A, and 0.5 for profile B; and March 3, 2014 with maximum Od,q of about 0.8 m for profile B, and 0.43 m for profile A), and (ii) during the Eleanor storm of January 3, 2018 with Od,q of about 0.7 m for profile A, and 0.43 for profile B. During the third event of February 9, 2016, corresponding to storm Imogen, the maximum Od,q reached about 0.7 m for profile B while the flow depth was much lower on profile A, reaching 0.36 m (Figure 12b and12e).

In most cases, these sluicing overwash events generated the largest sediment transfers between the beach face and back barrier (Table 4). In some cases, the volumes removed from the beach face and the back-barrier perfectly balance (e.g., 2014 February, 13 for both profiles), illustrating the rollover processes described and quantified by Suanez et al. (2018a). For cases where these volumes do not balance, notably when the volumes eroded at the beach face are less or greater than those accumulated at the back-barrier, we hypothesize that longshore sediment transfers have occurred in addition to the cross-shore sediment transfers due to rollover. These longshore sediment transfers have also been described and quantified by [START_REF] Suanez | Medium-Term Longshore and Cross-shore Dynamics of a Gravel Spit Driving by Storm Events (Sillon de Talbert, Brittany, France)[END_REF].

However, the wave energy flux (i.e., F parameter) is involved in the change of the morphodynamic regime based on the flow depth (Od,q). Indeed, for some events, the morphological response of the barrier spit generated by lower overtopping levels corresponding to the discrete overwash regime (0.25<Od<0.45 m), was similar to that corresponding to a sluicing overwash regime with Od >0.45 m. For example, this is the case for the Imogen storm of February 9, 2016 at profile A (Od,q of about 0.36 m), and the Eleanor storm of January 3, 2018 at profile B (Od,q of about 0.43 m) (Table 4 and Figure 12). Therefore, the wave energy flux (i.e., F parameter) indicates that the application of the Orford and Carter's storm impact scale model might be improved by considering this component.

Discussion

Barrier migration rates

The Sillon de Talbert experienced a significant landward migration during the survey period (2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019), with maximum values reaching -23 to -30 m for profiles A and B respectively, corresponding to -3.3 to -4.3 m.y -1 . By comparison, the pluri-secular landward migration rates estimated by [START_REF] Pinot | Fixer le plan ou gérer le profil : l'exemple du Sillon du Talbert[END_REF] reached about -0.5 m.y -1 . For the last several decades , [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF] calculated a maximum retreat reaching about -1.6 m.y -1 , increasing to between -3.5 to -4 m.y -1 from 2002 to 2017 [START_REF] Stéphan | Monitoring the medium-term retreat of a gravel spit barrier and management strategies, Sillon de Talbert (North Brittany, France)[END_REF]Suanez et al., 2018a).

The acceleration of the rate of landward migration for the Sillon de Talbert spit during the past decades raises the question of the SLR implication. The long-term analysis of SLR based on a dataset recorded at Roscoff station (see Figure 2a) indicates a sea-level rise reaching of 1.8 0.26 mm.yr -1 and 1.23 0.6 mm.yr -1 over both periods 1970-2018[START_REF] Carter | The morphodynamics of coarse clastic beaches and barriers: a short and long-term perspective[END_REF]-2018[START_REF] Dodet | Characterization of sea-level variations along the metropolitan coasts of France: Waves, tides, storm surges and long-term changes[END_REF]. Therefore, there is no evidence of an increase in SLR over the last 25 years. For the Sillon de Talbert, Orford et al. (1995b) estimated the migration rate to about 0.32 m.yr 1 expected with a SLR rate of 1 mm.yr -1 . According to the SLR estimated by [START_REF] Dodet | Characterization of sea-level variations along the metropolitan coasts of France: Waves, tides, storm surges and long-term changes[END_REF], the landward migration of the Sillon de Talbert would have reached -28 m over the period of 1970-2018 to -10 m over the period of 1993-2018. These values are far below the measurement of the barrier landward retreat performed by [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF]. In addition, the analysis of extreme water level (EWL) (including predicted tide + surge + wave runup) conducted by [START_REF] Stéphan | Long-term morphodynamic evolution of the Sillon de Talbert gravel barrier (Brittany, France)[END_REF] over the period of 1979-2010, showed no evidence of an increase in significant morphogenetic events leading to barrier overwash processes. Therefore, meso to macroscale (>10 1 to 10 2 yr) SLR cannot adequately explain the increase of landward migration rates of the Sillon de Talbert barrier spit, at least since the early 2000s. According to the results obtained in this study, about 83% to 90% (respectively for profile A and B) of the global retreat of the Sillon de Talbert is related to the impact of three significant morphogenic episodes combining energetic storm waves and high spring tide levels (i.e., February 1-2 2014, the Imogen storm of February 9 2016, and the Eleanor storm of January 3-4 2018), with a frequency of occurrence of 2 to 3 years. If we extend the analysis to the early 2000s (see Suanez et al., 2018a), a few additional episodes with a frequency of occurrence of 2 to 4 years, including the storm of March 10, 2008, can also be considered. These results are in agreement with those obtained by Orford et al. (1995aOrford et al. ( , 1995b) ) and confirm the determining role of microscale (<10 0 yr) SLR. The increase in the frequency of occurrence of significant morphogenetic events (i.e. combining storm and high spring tide) could be related to a change in the regime of high winter wave heights (decile 90 th ) in the northern part of the North-East Atlantic [START_REF] Dodet | Wave climate variability in the North-East Atlantic Ocean over the last six decades[END_REF]. The long-term analysis conducted by the authors shows an increasing trend up to 1.2 m (0.02 m.yr -1 ) of winter-means (from 1 st of December to 1 st of April) Hs90 at 55°N of latitudes. Thus, increasing storm magnitude also increases the likelihood of EWL inducing barrier overwash when combined with high tide levels.

The increase of barrier landward migration over the last several decades has also been reported by [START_REF] Forbes | Gravel-barrier migration and overstepping[END_REF] on the Story Head barrier (Atlantic coast of Nova Scotia). The authors indicated a landward migration rate of about -1 m.yr -1 between 1854 to 1917, -2 m.yr - 1 between 1917 and 1954, and -6 to -8 m.yr -1 between 1954 and 1988. Regarding the same dataset, [START_REF] Orford | Gravel barrier migration and sea level rise: some observations from Story Head, Nova Scotia, Canada[END_REF] analyzed the link between the sea-level change and the retreat of the barrier by distinguishing both the landward migration of the beach face and the backbarrier. They indicated that the landward migration of the seaward barrier shoreline was linearly proportional to the mesoscale (10 0 to 10 2 yr) sea-level change, however the backbarrier migration rate is not significantly related to these rates of sea-level change. The authors interpreted this difference between seaward and back-barrier migration as the role of storm intensity (frequency and magnitude) superimposed on long-term sea-level change. Orford et al. (1995a) indicated that barrier retreat best fit with the sub-decadal (<10 1 yr) SLR rate which controls surge frequency/magnitude, recognized as the dynamic landward migration through crest overwashing processes. The authors concluded that mesoscale (10 0 -10 2 yr) rather than macroscale (>10 2 yr) SLR rate is the critical control on barrier retreat, as mesoscale SLR variations in combination with surge potential are able to raise water level to the elevation threshold sufficient for barrier overwash and hence drive barrier retreat. They specifically noted that the higher the sub-decadal sea-level rise rate, the faster the rate of retreat of the swashaligned gravel barrier (Orford et al., 1995b).

However, the relationship between mesoscale sub-decadal SLR and barrier retreat is also a function of the barrier's inertia as defined by the barrier's cross-sectional volume (Orford et al., 1995b[START_REF] Orford | Organisational controls, typologies and time scales of paraglacial gravel-dominated coastal systems[END_REF]. The authors concluded that the smaller the barrier's cross sectional area, the faster the retreat rate regardless of the decadal-mesoscale rate of SLR. The cross-sectional volumes of the profiles A and B are 287 and 348 m 3 , respectively, while the barrier retreat reaches -23 m for profile A and up to -30 m for profile B over the survey period (2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019). From these observations, we can see that Orford et al. (1995b), barrier inertia "model" does not seem to work in our case.

In addition, the evolution of these volumes for both profiles between 2002 and 2019 shows a decrease in the sediment budget for profile A (about -35 m 3 ), while profile B gained about +50 m 3 of sediment (Figure 13). This evolution supports the trend of the global sediment budget of the spit for the last 15 years [START_REF] Stéphan | Monitoring the medium-term retreat of a gravel spit barrier and management strategies, Sillon de Talbert (North Brittany, France)[END_REF]Suanez et al., 2018a). Profile A, located closest to the proximal part of the spit, loses more sediment than profile B located further NE towards the distal part. This contrast illustrates the cannibalization phenomenon from which the sediments eroded at the proximal part feed the distal part of the spit due to the sediment transfer generated by the longshore drift oriented SW-NE.

Similarly, the sediment budget calculated over the survey period (2012-2019) also indicates a difference in evolution between the two profiles. Profile B shows a significant increase of about +27 m 3 .m.l., while the gain recorded by profile A is much lower (+11 m 3 .m.l.). These data also confirm that the Orford et al. (1995b), barrier inertia "model" does not work in this case.

The sediment grain size distribution of the upper part of the barrier, including the crest, must then be taken into account to explain the differences in migration speed between the two profiles, and the fact that Orford et al. (1995b) model does not work in this case. The high proportion of sand inside the barrier body along the profile A (see above, section 3.1.) fills the interstitial voids, increasing the inertia of the barrier because the coarser sediments (i.e., gravel fraction) are trapped in the sandy matrix. The rollover process inducing the landward barrier migration is therefore diminished because the coarse sediments are less mobile. Conversely, the high proportion of coarser sediments (i.e., gravels) on the profile B favors the gradual accumulation of coarse material on the crest through overstopping resulting in steeper beachface gradients [START_REF] Masselink | The role of swash infiltration in determining the beachface gradient: a numerical study[END_REF]. The greater the volumes of sediment accumulated on the crest, the greater the landward displacement by rollover during catastrophic overwash event. Thus, in the case of the profile A, the high proportion of sandy sediments inhibits overtopping processes and reduces the potential overwashed volumes of sediments (and thus, the speed retreat of the barrier).

The remaining 10% to 17% of barrier spit retreat corresponds to processes of adjustment of the slope of the back barrier slope, notably during phases of morphogenic calm. During these phases of fair weather conditions, the crest of the barrier rises under the action of small fairweather waves, while the slope of the front beach steepens (Figure 9). At the same time, the slope of the back-barrier decreases due to equilibrium slope readjustment processes. These processes are particularly illustrative of the rollover phenomenon described by [START_REF] Orford | Extreme events and the morphodynamics of gravel-dominated coastal barriers: strengthening uncertain ground[END_REF].

Calibration of runup formula

According to [START_REF] Stockdon | Empirical parameterization of setup, swash, and runup[END_REF], who analyzed a large runup dataset acquired on several sandy beaches, the highest wave runup (R2%) is dominated by energetic incident wave for reflective conditions associated to plunging and collapsing/surging breakers as indicated by Iribarren number (ξ0>1.25). In our case, both profiles show rather intermediate to reflective morphodynamic conditions with an average Iribarren number (ξ0) between 0.83 (with max up to 2.66) and 1.28 (with max up to 4.27) for profiles A and B, respectively. The authors distinguished the R2% runup elevation between incident and infragravity frequencies and showed that the dimensional incident swash better fit with ξ0H0 = tanβ (H0L0) 1/2 for reflective conditions, while the dimensional infragravity swash better scaled with (H0L0) 1/2 . Following the same approach, we demonstrated that taking into account the beach slope through the Irribaren number (ξ0) substantially improved the mathematical model from 49-50% R 2 significance for (H0L0) 1/2 to 54-55% for tanβ (H0L0) 1/2 (Figure 11). [START_REF] Stockdon | Empirical parameterization of setup, swash, and runup[END_REF] proposed the following simplified expression for runup for reflective conditions with an rms error of 47 cm:

R2% = 0.73βf (H0L0) 1/2 [9]
where βf is beach slope.

The use of Stockdon's equation (which is one of the most widely used runup predictors at present) shows that the results obtained for the two profiles overestimate the field reality by about 0.5 m for profile A, and by more than 0.7 m for profile B (Figure 14), even though Stockdon's equation is calibrated for a runup of 2% exceedance (R2%), while our is for a maximum runup (Rmax). While for profile A, this overestimation is within the orders of magnitude of the rms reported by [START_REF] Stockdon | Empirical parameterization of setup, swash, and runup[END_REF], it is much larger for profile B.

The overestimation of the Stockdon's equation can be explained by the fact that it has been calibrated on sandy beaches, which have moderate roughness and porosity compared to gravel environments. In our case, the largest bed roughness for gravel particles induces a flow retardation, which may also be increased by higher the percolation leading to a loss of swash volume. Both processes contribute to limit the runup, explaining that the porous structures are widely used as breakwaters for coastal defence [START_REF] Twu | A highly wave dissipation offshore breakwater[END_REF][START_REF] Venkateswarlu | Numerical investigation on the wave dissipating performance due to multiple porous structures[END_REF][START_REF] Guo | Wave energy dissipation of a submerged horizontal flexible porous membrane under oblique wave interaction[END_REF]. In addition, as indicated by [START_REF] Poate | A new parameterisation for runup on gravel beaches[END_REF], while these equations fit the range of gravel beach field data, the inclusion of a dimensional constant (C) implies that the equations can only be used for conditions similar to those in the field and model data set. That makes difficult to transpose an equation calibrated on one specific site to another one.

The barrier dynamics are thus strongly affected by the gravel dynamics, including coarse particle size and strong percolation of water inside the porous media, leading to enhanced wave dissipation. Applying Xbeach-G in several environments, including our study site, [START_REF] Mccall | Modelling the morphodynamics of gravel beaches during storms with XBeach-G[END_REF] demonstrated the difficulty in reproducing the morphodynamic response of the Sillon de Talbert during the Johanna storm of March, 10 2008. The Xbeach-G simulations predicted higher wave dissipation than observed, likely caused by higher estimates of overwash. The new dataset presented here, with a precise distribution of grain size over the whole profile, could help future studies considering the influence of the granulometry distribution in Xbeach-G. Grain size plays a major role in this environment, impacting the wave dissipation, backwash and overwash gravel transport and cascading effects.

Validation of the Orford and Carter's storm impact scale model

Based on the morphological changes, especially of the crest and the back-barrier, an empirical thresholding of the overtopping levels was proposed to distinguish the different regimes of Orford and Carter's storm impact scale model [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF]. Thus, the overtopping regime was defined as between 0 and 0.25 m, the discrete overwash regime between more than 0.25 and 0.45 m, and the overwash regime greater than 0.45 m, while the catastrophic inundation regime was not retained because no breach openings were observed along the two measured profiles over the entire observation period. These levels of overtopping are particularly indicative of the major significant morphogenic events that generated a landward retreat of the barrier. In our case, it is the three events of February 1-2, 2014, February 9, 2016, and January 3, 2018. This landward migration is also very well indicated by changes in the sediment budget, particularly between the front and back beaches. In general, we can attest that Orford and Carter's model works well, and that it allows one to model the most noteworthy morphogenic episodes contributing to significant morphological changes of the barrier beach, including the landward retreat by the rollover process.

The results obtained in this study show, however, that wave energy flux is a key factor in the change of morphodynamic regime, for instance from discrete to sluicing overwash. Thus, this energetic parameter constitutes a third variable in addition to the observed tide (including the surge) and the wave runup in the quantification of the hydrodynamic forcing (Od,q) of Orford and Carter's model. Therefore, the flow depth (Od,q) component proposed by [START_REF] Orford | Extreme events and the morphodynamics of gravel-dominated coastal barriers: strengthening uncertain ground[END_REF], where d is the depth, and q the volume of the flow, could be redefined as (Od,F), considering the wave energy flux parameter (F) is first, much easier to calculate than the volume (q) of water overtopping the barrier. Secondly, considering the same extreme water level Oe for the following two cases (i) high spring tide + low surge + low wave condition (inducing a low runup), (ii) small spring tide + large surge + high wave condition (inducing a high runup), the morphological changes will be more significant in the second case because the wave energy flux is proportionally higher.

Conclusion

The high-frequency topomorphological and hydrological survey of the Sillon de Talbert underway since September 2002, has definitely enhanced the understanding of the morphodynamic functioning of this gravel spit. The main result of this survey is the calculation of the rapid landward migration rate, reaching -3.3 to -4.3 m.y -1 over the last 7 years (September 2012 to December 2019), which is of the same magnitude as the retreating rates measured over the last 20 years (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021). These values indicate an eightfold increase in the speed of the landward migration of the spit since the 18 th century, and a two-to threefold increase since the beginning of the 20 th century. This rapid retreat is not related to long-term sea level rise (i.e., macroscale of 10 2 to 10 3 yr forcing), but to the impact of short-term morphogenic events (i.e., micro to mesoscale of 10 0 to10 2 yr processes) combining storm waves and high spring tides. These short-term processes are fairly well quantified and modeled from the storm-impact scale model of [START_REF] Orford | Crestal overtop and washover sedimentation on a fringing sandy gravel barrier coast, Carnsore Point, Southeast Ireland[END_REF]. Over 83% to 90% of the barrier spit retreating occurs under the sluicing overwash regime and/or by discrete overwash when the wave energy flux is sufficient to generate catastrophic overwash conditions. The remaining

Table 4

 4

	2015-01-29 19h (5.20	low	pressure	system	*
	m)	« Mischka »
	2015-01-30 7h (5.59 m)	« Mischka » low pressure	system	*
	2016-02-08 10h (6.13 m)	Imogen			(2.11*10 6 J/m²)
	2016-03-02 14h (5.11 m)	no name			*
	2016-03-09 11h (5.07 m)	low pressure system « Doris »	*
	2016-03-09 19h (5.11 m)	low pressure system « Doris »	*
	2016-03-09 21h (5.10 m)	low pressure system « Doris »	*
	2018-01-03 9h (5.89 m) Eleanor			(1.82*10 6 J/m²)
	2018-12-09 10h (5.33 m)	no name			*
	2018-01-16 22h (6.19 m)	Fionn			(2.00*10 6 J/m²)
	2019-01-27 12h (5.00 m)	Martin			*
	2019-12-09 6h (6.21 m) Atiyah			(2.02*10 6 J/m²)
	2019-12-13 9h (5.79 m) no name			(1.56*10 6 J/m²)
			Table 1

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10% to 17% corresponds to processes of adjustment of the equilibrium slope of the back barrier, notably during phases of morphogenic calm.