Maria Gonzalez-Santamarta

Laurie Ceccato

Ana Sofia Carvalho

Jean-Christophe Rain

Rune Matthiesen

Manuel S Rodriguez
email: manuel.rodriguez@lcc-toulouse.fr

Isolation and Mass Spectrometry Identification of K48 and K63 Ubiquitin Proteome Using Chain-Specific Nanobodies

Keywords: Ubiquitin, Nanobodies, Post-translational modifications, Proteome, Isolation, Mass Spectrometry. Running head: Ubiquitin proteome isolation using nanobodies 1

come   L'archive ouverte pluridisciplinaire

Introduction

Protein ubiquitylation regulates virtually all cellular processes, underlining its importance in the cell well-being, and its implications in multiple pathologies [START_REF] Gâtel | Ubiquitin, SUMO, and Nedd8 as Therapeutic Targets in Cancer[END_REF].

Ubiquitin (Ub) attachment (AKA conjugation) occurs mainly in lysine (K) residues on the target proteins but also on any of the 8 reactive residues present on Ub itself (M1, K6, K11, K27, K29, K33, K48 or K63) [START_REF] Gonzalez-Santamarta | Ubiquitin-chain dynamics in physiology and pathology[END_REF]. For this reason, Ub imposes distinct conformations to the target protein depending on the number of moieties attached to its surface, or the type of Ub chains formed. The complexity of the Ub chains increases when other post-translational modifications (PTMs) such as phosphorylation, acetylation, SUMOylation or NEDDylation act on the same Ub reactive residues. This complex language and its regulation, known as "the Ubiquitin Code", is far from being fully understood and only some generic functions for few Ub chains have been elucidated over the years [START_REF] Dittmar | Linear Ubiquitin Chains: Cellular Functions and Strategies for Detection and Quantification[END_REF]. For example, typical Ub chains, like K48 and K11 have been associated to proteasomal degradation, while K63 is usually linked to the regulation of signal transduction and the autophagy pathway. Less abundant atypical Ub chains such as K6, K27, K29, K33, and M1 have not been fully deciphered most likely due to the difficulty to fully characterise their functions [START_REF] Dittmar | Linear Ubiquitin Chains: Cellular Functions and Strategies for Detection and Quantification[END_REF][START_REF] Swatek | Ubiquitin modifications[END_REF]. The high reversibility and heterogeneity of those Ub modifications complicate their isolation, quantitation, and characterisation of the functions they regulate. A better characterisation of the molecular mechanisms underlying Ub regulated processes is essential to understand cell physiology and pathology [START_REF] Gonzalez-Santamarta | Ubiquitin-chain dynamics in physiology and pathology[END_REF].

Multiple approaches have been used to understand Ub chain-specific functions including the use of Ub K to R mutants and tagged Ub-like molecules (UbLs).

However, the use of Ub mutants and overexpression has disadvantages, mainly because they can induce perturbations in the natural equilibrium of Ub chains and UbL molecules resulting in aberrant patterns of protein ubiquitylation complicating data interpretation (5). Furthermore, some of these techniques cannot be used to analyse samples derived from patients (6, 7). Ub-binding domains with Ub-chains preferences have been also used to explore processes regulated by protein ubiquitylation when associated to mass spectrometry (MS) [START_REF] Mattern | Using Ubiquitin Binders to Decipher the Ubiquitin Code[END_REF][START_REF] Lopitz-Otsoa | Integrative analysis of the ubiquitin proteome isolated using Tandem Ubiquitin Binding Entities (TUBEs)[END_REF]. Moreover, Ub antibodies directed against specific Ub-linkages showed some success in immunoprecipitation and immunofluorescence application. However, only few Ub-chain specific antibodies have been developed in part due to the low reactivity of this highly conserved molecule. In contrast, antibodies recognising the double glycine ("diGly") Ub signature showed good success in MS studies even if these cannot distinguish the common signature shared with NEDD8 or ISG15 [START_REF] Bezstarosti | Detection of Protein Ubiquitination Sites by Peptide Enrichment and Mass Spectrometry[END_REF][START_REF] Van Wijk | Visualizing ubiquitination in mammalian cells[END_REF]. An important aspect that has contributed to increase our understanding of functions regulated by Ub is the huge progress in MS technology, achieved by enhancing sensitivity, accuracy and duty cycle of the machines and improving in the sample preparation methods.

Camelid heavy-chain antibodies, also known as VHH (variable heavy homodimers) or nanobodies, are single domain antigen-binding fragments that have been used in research, diagnostics and therapeutics [START_REF] Chakravarty | Nanobody: the "magic bullet" for molecular imaging?[END_REF][START_REF] Meyer | Nanobody-based products as research and diagnostic tools[END_REF][START_REF] Salvador | Nanobody: outstanding features for diagnostic and therapeutic applications[END_REF]. Nanobodies have a smaller size than mammalian antibodies, a single-domain nature, and can be produced as a robust entity very efficiently and with high solubility. Due to its monomeric nature, high stability, selectivity and small size, VHH have been used as sensitive detection probes in complex samples. Even if it is not the most obvious, VHHs can be generated against small peptides, and can be used to purify ligands, for immunoprecipitation, interference with protein conformation/localisation, or regulate functions (in vivo immunomodulators) [START_REF] Meyer | Nanobody-based products as research and diagnostic tools[END_REF][START_REF] Salvador | Nanobody: outstanding features for diagnostic and therapeutic applications[END_REF].

Taking advantage of a full synthetic system that bypass immunogenicity and specificity problems, this scaffold has been used to develop chain-specific nanobodies [START_REF] Mattern | Using Ubiquitin Binders to Decipher the Ubiquitin Code[END_REF]. When isolated by phage display these polypeptides can be used as minibodies when cloned into vectors expressing the heavy chain of various species or as nanobodies when cloned in vectors with multiple tags (14).

Here we report the protocol for the purification of endogenous Ub chains using K63 and K48 nanobodies that can be used for identification of target proteins by MS. The protocol includes 4 sections, 1) The purification of Ub chain-specific nanobodies from bacteria; 2) The crosslinking of these nanobodies into a magnetic column (see Figure 1); 3) Isolation of ubiquitylated proteins from mammalian cells and 4) Sample preparation for MS analysis (see Figure 2). The purified material obtained from mammalian cells can also be used for western blot (WB) analysis or immunoprecipitations with antibodies recognising proteins of interest. In this protocol, we have used mantle cell lymphoma cells, but depending on the cell type and the application of interest, this protocol can be easily adapted.

Materials

All materials have been prepared with ultrapure water, filtered and stored at 4ºC. Fresh solutions should be used (see Note 1).

Nanobodies purification

1. Nanobodies used in this protocol are commercially available (Nanotag Biotechnologies, N1910 and N1810).

2. Nanobodies can also be produced using Escherichia coli (WK6 strain).

3. 100 mg/ml carbenicillin LB-agarose plates 12. Boiling Buffer (BB) 3X: 50 mM Tris-HCl, pH 6.8, 10% glycerol, 2% SDS, Bromophenol Blue, 5% β-mercaptoethanol.

13. Ultracentrifuge filters (15 ml), nominal molecular weight cut off 3 kDa.

14. Dialysis tubing, benzoilated.

15. Prepacked gravity-flow chromatography empty plastic columns.

16. Glycerol 100%. 17. Water bath incubator (for heat-shock at 42ºC).

18. Bacteria incubator (37ºC).

19. Bacteria incubator with shaking (20-37ºC).

20. Tip sonicator.

21. Magnetic tube holder.

22. Anti Ub antibody P4D1.

Nanobody-magnetic beads crosslinking

Here, we describe a BS3 (bis(sulfosuccinimidyl)suberate)-based crosslinking protocol that provides the best enrichment of ubiquitylated proteins with a low background (see

Note 2).

1. Ni-NTA Magnetic Agarose Beads were pre-washed twice with cold PBS and kept at 4°C until use.

2. Autoclaved sterile 1x PBS.

3. Ub chain-specific nanobodies (Nanotag). 8. Rotating wheel for microcentrifuge tubes. 9. Magnetic tube holder for microcentrifuge tubes.

Isolation of ubiquitylated proteins from mammalian cells

Methods

Purification of Ub chain-specific nanobodies

Nanobodies are produced in Escherichia coli WK6 strain using the protocol described below for production of recombinant histidinylated proteins since these small polypeptides contain an N-terminal histidine (His) tag (see Figure 1) (see Note 5).

1. Transform bacteria with a nanobody-containing plasmid by heat shock at 42ºC during 2 minutes and grow them overnight for selection in 100 mg/ml carbenicillin LB-agarose plates.

2. The day after, pre-culture clones in 50 ml of TB containing carbenicillin at the same concentration.

3. Scale the culture up to 1 L in TB (supplemented with 1% of glucose) shacking at 37°C, to reach a 0.7-0.8 confluence at an optical density (OD) of 600 nm.

4. Induce nanobody expression by the addition of 1 mM IPTG, and let bacteria grow for 16 hours at 37°C or overnight (O/N) at 28°C.

5. Collect 1 ml of culture before and after IPTG induction to control the proper nanobody induction.

6. Pellet bacteria by centrifugation at 6,693 x g for 30 minutes at 4°C.

7. Wash pellet twice with cold PBS and resuspend in 10 ml of cold sterile PBS.

8. Lyse bacteria with BLB on ice by sonication at 10 μm (at least six pulses of 30 seconds, 1 minute incubation on ice between each pulse). 9. Clarify lysate by ultracentrifugation for 1 hour at 45,000 x g at 4°C.

10. Incubate the clarified lysate with 1 ml of Ni-NTA agarose-beads, overnight, rotating at 4°C in a 50 ml tube.

11. Load agarose beads into a prepacked gravity-flow chromatography column and wash 10 times with 10 ml of NWB.

12. Elute nanobodies, 10 times with 1 ml of NEB and check the eluted protein peak by colorimetry intensity using the Bradford assay reagent.

13. Pool the most concentrated fractions and measure protein concentration by Bradford or any other method of choice.

14. Transfer the sample into benzoilated dialysis tubing and dialyse against 5 L of exchange buffer (DB) O/N at 4ºC.

15. Concentrate dialysed proteins by using ultracentrifuge filter.

16. Estimate final protein concentration, using the nanodrop or any other method of your choice. 17. Supplement with 10% glycerol to store aliquoted samples at -80°C, until use.

Nickel magnetic beads crosslinking protocol

Prepare nickel-magnetic beads for the affinity column and use a magnetic holder for microcentrifuge tubes to purify nanobody-interacting proteins (see Note 6 and Note 7).

To increase the number of washes and reduce the binding of non-specific proteins, crosslink nanobodies magnetic beads prior the isolation of ubiquitylated proteins (see

Note 8).

1. For a large-scale purification of ubiquitylated proteins, crosslink 300-500 μg of nanobodies to 300 μl of nickel-magnetic beads in 1.5 ml microcentrifuge tubes (see Note Note 9, Note 10 and Note 11).

2. Adjust the volume to the maximal tube capacity with Binding Buffer and incubate for 1-2 hours at 4°C using a rotating wheel (see Note 12).

3. After incubation, let the sample in the magnetic rack/holder for at least 5 minutes until magnetic beads are all attached to the magnet.

4. Keep the samples in the magnetic rack and remove the supernatant using aspiration or a 1 ml pipette.

5. Wash beads twice with cold sterile PBS and let beads attach to the magnet for every wash.

6. Incubate beads with 5 mM BS3 (CB) in the rotating wheel at RT for 1h.

7. Wash magnetic beads once with PBS, to remove the remaining BS3 solution.

8. Incubate beads with Blocking Buffer at RT for 15 minutes while rotating.

9. Wash beads with PBS to remove the remaining Blocking Buffer.

10. Wash once with 0.5 M K2HPO4 to remove non-specific binding to the Nickel beads.

11. Wash three times with PBS to eliminate K2HPO4 residues.

12. Wash and equilibrate crosslinked nanobody-nickel magnetic beads in Binding Buffer. Beads can be stored at 4ºC for a few hours until the lysis of eukaryote cells is performed.

Isolation of ubiquitylated proteins from mammalian cells

The following protocol is implemented using 40 million Mantle Cell Lymphoma (MCL) cells for a large-scale purification to be analysed by MS (see Note 10). To evaluate the capture efficiency and background, silver staining and WB against Ub antibodies are performed with all fractions before sending samples to MS analysis.

1. Prepare lysates using 40 x 10 6 cells (or 2 mg of total protein) per experimental point.

Pellet cells by 5 minutes centrifugation 300 x g at RT and wash twice with cold PBS.

Keep cell pellets on ice until use. 5. Incubate supernatants with the crosslinked magnetic beads for 2 hours at 4°C in a rotating wheel (see Note 14).

6. After the binding step, use a magnetic holder to separate and collect the flow-through fraction (FT). Mix 1/20 (50 μl) of FT with equal volume of BB and save to control the efficiency of the capture.

7. Remove supernatants as much as possible using a vacuum aspiration system or 1 ml pipette.

8. To eliminate unspecific proteins bound to nanobodies and with the help of the magnetic holder, wash beads 4-6 times with 1 ml of PBS-Tween 0.05% (see Note 15

and Note 16).

8. Perform a final wash with 1 ml of cold PBS to transfer the sample to a new 1.5 ml tube.

9. Dry beads using the magnetic holder and a vacuum aspiration system. 12. Use a magnetic holder to collect the captured proteins of interest and eliminate beads. Keep the captured fraction at -80ºC until MS analysis.

13. Analyse the input, flow-through and captured fractions using an SDS polyacrylamide gel electrophoresis (SDS-PAGE) and stain the gel using Coomassie blue or silver staining. All fractions can be analysed by WB against anti-Ub antibodies.

Sample preparation for Mass Spectrometry analysis

1. Load captured proteins obtained in section 3.3 (step 10) into ultracentrifuge filters with 30 kDa cut off and spin 25 minutes at 14,000 x g (see Note 19).

2. Wash proteins in the retentate with 0.2 ml of Urea Buffer, six times by spinning 25 minutes at 14,000 x g.

3.

Incubate proteins in the retentate with 0.1 ml of 0.05 M iodoacetamide for 20 minutes.

4. Spin proteins in the retentate for 35 minutes at 14,000 x g.

5.

Wash proteins in the retentate with 0.1 ml of Urea Buffer, four times by spinning 25 minutes at 14,000 x g.

6.

Wash proteins in the retentate with 0.1 ml of 0.04 M ammonium bicarbonate, pH 8.0, four times by spinning 25 minutes at 14,000 x g.

7.

Incubate proteins in the retentate with 40 μl 0.01 μg/μl of trypsin overnight at 37°C.

8. Collect digested proteins by adding 40 μl of 0.04 M ammonium bicarbonate, pH 8.0, two times by spinning 25 minutes at 14,000 x g. 9. Desalt peptides using reverse phase C18 HPLC column and then store them at -20°C, before MS analysis.

Notes

1. Solutions should not be stored for more than one week before their use.

2. Other crosslinking procedures can be tested to optimise the recovery of the captured ubiquitylated proteins, including dimethyl pimelimidate-based protocols.

3. This medium was used to grow mantle cell lymphoma cell lines (MCL) but medium can be adapted to other cell lines.

4. Alternative inhibitors such as MG132 instead of bortezomib, PR619 instead of chemical deubiquitinase inhibitors such as iodoacetamide or N-ethylmaleimide can be used to avoid losing ubiquitylated proteins during the lysis step.

5. The His tag or a Myc tag also included in the nanobody can be used to analyse the integrity and the quality of purification of these tools.

6. In order to reduce contaminants during the isolation of ubiquitylated proteins from mammalian cells, affinity chromatography is performed within a clean area using gloves during all the procedure.

7. Affinity columns can be prepared using other supports such as nickel-agarose or nickel-sepharose beads.

8. Magnetic beads also avoid the use of centrifugation steps that could precipitate unspecific high molecular weight protein complexes 9. Excess of Nickel beads should be prepared since some could be lost during the washing steps of the crosslinking protocol.

10. Different cells provide distinct total protein concentration per million of cells. For this reason, 500 μg of total protein is a better reference to set up a protocol before scaling up to 2 mg of total protein per point.

11. The number of beads and nanobodies required to capture the ubiquitylated fraction from a given sample must be optimised to avoid saturation of the beads or nanobodies.

This situation could make difficult the identification of physiological differences between samples.

12. If aggregates are observed during the nanobody/beads binding step, the concentration of detergent should be increased in the Binding Buffer.

13. Cell lysis should be done on ice to prevent enzymatic activities that could remove Ub or degrade modified proteins. The time between the lysis and the incubation with the crosslinked nanobodies should be as short as possible.

14. Binding time can be adjusted: increase it if ubiquitylated proteins are highly abundant or decrease it in the opposite situation. During the binding step, keep tubes safely close to avoid spills.

15. The use of crosslinked nanobodies allows to increase the number of washes or the use of stringent washing conditions if required. Detergent can be added to increase the stringency.

16. The different washing steps were optimised to reduce the binding of unspecific proteins compared to a negative control (magnetic beads only). 17. Do not freeze magnetic beads bound to captured ubiquitylated proteins prior the final heating step, since this could damage the magnetic properties of some beads.

18. Eluted magnetic beads can be resuspended in Boiling Buffer to test if some ubiquitylated proteins are still attached. In this case, another boiling step is required to recover those proteins.

19. If the protein sample volume exceeds 0.5 ml, perform step 1 of section 3.4 the number of times necessary to load the entire sample volume to the ultracentrifuge filter.

Acknowledgements:

14. Moutel S, Bery N, Bernard V, et al (2016) NaLi-H1: A universal synthetic library of humanized nanobodies providing highly functional antibodies and intrabodies. Elife 5: :e16228. doi.org/10.7554/eLife.16228

4 .

 4 Terrific Broth (TB): Resuspend 47.6 g of TB powder and 8 ml of glycerol in 1 L of distilled water and autoclave. TB media must be supplemented with 1% of glucose when indicated. 5. IPTG (isopropyl β-D-1-thiogalactopyranoside): 1 M IPTG. 6. Sterile cold 1x Phosphate Buffered Saline (PBS). 7. Bacteria Lysis Buffer (BLB): 10 mM imidazole, 1 mg/ml of polymyxin B, 1 mM phenylmethylsulfonyl fluoride (PMSF), 1.2 mg/ml lysozyme Cf, 2 mM dithiothreitol (DTT) in 1x PBS. 8. Ni-NTA agarose-beads: Beads must be pre-washed three times during 5 minutes with ten volumes of 1x PBS followed by centrifugation at 300 x g for 5 minutes to obtain a 50% (vbeads/vlysate) working reagent. 9. Nickel Column Washing Buffer (NWB): 50 mM Tris pH8, 500 mM NaCl, 10 mM imidazole. 10. Nickel Column Elution Buffer (NEB): 50 mM Tris pH8, 500 mM NaCl, 200 mM imidazole, 10 mM DTT. 11. Dialysis Buffer (DB): 50 mM Tris pH 8 and 500 mM NaCl.

4 .

 4 Crosslinking Buffer (CB): 5 mM BS3. Prepare 1 M aliquots and store at -20ºC. 5. Binding Buffer: 50 mM Tris-HCl pH 8.5, 150 mM NaCl, and 0.5% Igepal. pH adjusted in a chemical hood. Store solution at 4ºC. 6. Blocking Buffer: 1.5 M Tris-HCl pH 7.5. pH adjusted in a chemical hood. Store solution at 4ºC. 7. Prepare 0.5 M K2HPO4 in ultrapure water and filtrate. Store at room temperature (RT).

2 .Note 4 )

 24 Lyse cells pellets with 500 μl of CLB supplemented with protease inhibitors (see during 10 minutes. Disrupt cell pellets by gentle pipetting or intermittent soft shaking. All the procedure should be done on ice or at 4°C (see Note 13).

3 . 4 .

 34 Clarify samples by centrifuging at 48,000 x g during 20 minutes at 4°C. Save 1/20 of clarified supernatant (50 μl) to control the input fraction. Mix the input fraction with an equal volume of BB and store at -20 °C.

10 .

 10 Resuspend beads in 100 l of 1x BB and keep at RT until use. 11. Just before WB analysis, boil samples for 45 minutes at 95°C (see Note 17 and Note 18) with strong agitation.

Figure 1 .

 1 Figure 1. Purification and preparation of nanobody-affinity column. A) Production of

Figure 2 .

 2 Figure 2. Isolation of ubiquitylated proteins and sample preparation for MS analysis. A)

We thank all members of the UbiCARE lab, Clémence Coutelle-Rebut for the proofreading of this manuscript. MGS is a fellow from the UbiCODE project funded by the EU's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement (No 765445) and the Association contre le Cancer (ARC). We acknowledge the COST Action CA20113 `PROTEOCURE` supported by COST (European Cooperation in Science and Technology). MSR was also funded by CONACyT-SRE (Mexico) grant 0280365 and the REPERE and prématuration (Ubipièges) programs of Occitanie.


Paul M Bayle
email: p.m.bayle@bath.ac.uk

Chris E Blenkinsopp

Kévin Martins
email: kevin.martins@u-bordeaux.fr

George M Kaminsky
email: george.kaminsky@ecy.wa.gov

Keywords: Dynamic Cobble Berm Revetment, Lidar, Swash processes, Sediment uxes, Morphodynamics

Dynamic cobble berm revetments are a promising soft engineering technique capable of protecting sandy coastlines by armouring the sand and dissipating wave energy to protect the hinterland against wave attack. They also form composite beaches as they are essentially mimicking natural composite beach structure and behaviour. This type of coastal protections and beaches have recently been investigated, and this led to a better understanding of their overall behaviour under varying water levels and wave conditions. However, the short-term dynamics of the wash zone (where all bed changes occur) has never been studied at high-resolution, and this is needed to fully understand the underlying dynamics of such structures and relate it to observed processes at larger scale. To do so, the revetment at North Cove (WA, USA) was monitored for a nine-day period in January 2019 over a spring tidal cycle and with signicant wave heights oshore reaching 6 m. A 2-D lidar was used to survey a cross-shore prole of the revetment, and record all surface changes and interaction with swashes at high spatial (0.1 m) and temporal (swash-by-swash) resolution. The revetment was found to rapidly reshape under these energetic conditions, but reached a relatively stable state during the rising tide. The analysis of bed-level changes and net cross-shore mass uxes over the revetment showed that revetment changes are mainly driven by very small events, with some rare large bed-level changes of a magnitude comparable to the median cobble diameter. The distribution of event mass uxes nearly balanced out over the duration of a tide, meaning that positive and negative uxes tended to be symmetrical. Furthermore, measured net uxes magnitude were 18 times smaller than the absolute uxes, which demonstrated the dynamic stability of the revetment as substantial movement occur on a wave-by-wave timescale but these balance out over time. The analysis of swash revealed that the revetment section where the swash reaches a maximum depth between 0.15 -0.45 m undergoes the more extreme uxes. Swashes deeper than 0.45 m only occurred in zones inundated more than 50 % of the time, and smaller extreme uxes were measured over the revetment section where these deep swashes were recorded. Bed level change oscillations over the revetment were observed, and the cross shore limit of these was correlated with the mean wave period at the toe of the revetment. Overall, the water depth at the toe of the revetment was identied as the key parameter to describe the energy reaching the revetment. This study enables the morphodynamics

Swash-by-swash morphology change on a dynamic cobble berm revetment: high-resolution cross-shore measurements.

Introduction

Dynamic cobble berm revetments are a type of soft engineering technique intended to protect sandy coastlines against erosion and ooding ( [START_REF] Allan | The use of passive integrated transponder (pit) tags to trace cobble transport in a mixed sand-and-gravel beach on the high-energy oregon coast, usa[END_REF][START_REF] Allan | Monitoring the response and ecacy of a dynamic revetment constructed adjacent to the columbia river south jetty, Clatsop county, Oregon[END_REF][START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF].

Dynamic cobble berm revetments are a sub-category of dynamic revetments which specically aim to create an articial composite beach, which consists of a lower sandy foreshore and a backshore berm or ridge composed of gravels. The gravel ridge is a highly-dynamic feature that armours the underlying sand [START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF][START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF] and provides overtopping protection to the hinterland [START_REF] Allan | The use of passive integrated transponder (pit) tags to trace cobble transport in a mixed sand-and-gravel beach on the high-energy oregon coast, usa[END_REF][START_REF] Komar | Design with nature strategies for shore protection -the construction of a cobble berm and articial dune in an oregon state park[END_REF][START_REF] Loman | Physical model testing of an innovative cobble shore, part i: Verication of cross-shore prole deformation[END_REF][START_REF] Allan | Hateld Marine Science Center Dynamic Revetment Project[END_REF][START_REF] Allan | Dynamic revetments for coastal erosion stabilization: a feasible analysis for application on the oregon coast[END_REF][START_REF] Allan | Monitoring the response and ecacy of a dynamic revetment constructed adjacent to the columbia river south jetty, Clatsop county, Oregon[END_REF]Blenkinsopp et al., 2022a).

Composite beaches have long been recognised as an eective form of natural coastal protection (e.g., see [START_REF] Ahrens | Dynamic revetment[END_REF][START_REF] Allan | Monitoring the response and ecacy of a dynamic revetment constructed adjacent to the columbia river south jetty, Clatsop county, Oregon[END_REF], showing a great degree of stability and adaptability in response to wave attack [START_REF] Van Rijn | Modelling erosion of gravel/shingle beaches and barriers[END_REF]. Although these coastal landforms are ubiquitous in some regions of the globe [START_REF] Kirk | Mixed sand and gravel beaches: morphology, processes and sediments[END_REF], they have received much less attention than purely sand or gravel beaches. In addition, while the concept of dynamic revetments is not new (e.g., [START_REF] Van Der Meer | Dynamic stability of rock slopes and gravel beaches[END_REF][START_REF] Powell | The dynamic response of shingle beaches to random waves[END_REF][START_REF] Lorang | An articial perch-gravel beach as a shore protection structure[END_REF][START_REF] Ward | Laboratory study of a dynamic berm revetment[END_REF]Komar & Allan, 2010, and many others), examples of application in the eld are scarce and monitoring programs of existing structures are very limited [START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF]. As a consequence, there is an overall lack of understanding of dynamic cobble berm revetments and composite beaches dynamics, and their behaviour under the combined eect of varying water levels and wave conditions is not well documented.

Dynamic cobble berm revetments (and gravel ridges of composite beaches) are in some aspects similar to that of pure gravel beaches. They are both predominantly inuenced by swash processes which can generate signicant changes in both the cross-shore and longshore direction over short time scales [START_REF] Jennings | A eld based classication scheme for gravel beaches[END_REF]. They are also both highly porous, resulting in substantial inltration/exltration of water through the gravel under swash motion [START_REF] Holland | Mixed sand and gravel beaches: accurate measurement of active layer depth to develop predictive models of sediment transport[END_REF]. While many studies have contributed to a better understanding of wave-by-wave swash dynamics and gravel transport on pure gravel beaches (e.g., [START_REF] Carter | Coarse clastic barrier beaches: a discussion of the distinctive dynamic and morphosedimentary characteristics[END_REF][START_REF] Williams | Bardex (barrier dynamics experiment): Taking the beach into the laboratory[END_REF][START_REF] Poate | Uk storms 2014: Gravel beach response[END_REF][START_REF] Almeida | Observations of gravel beach dynamics during high energy wave conditions using a laser scanner[END_REF], equivalent studies on composite beaches or dynamic cobble berm revetments are rare. Yet, such short-term analyses of the swash zone are important for dynamic revetment and composite beach research because the gravel component of the beach diers from a pure gravel beach as it is founded on a relatively impermeable sand layer [START_REF] Jennings | A eld based classication scheme for gravel beaches[END_REF]. Consequently, study of the morphodynamics of dynamic cobble berm revetments at the swash-by-swash time scale is useful to better understand the global behaviour of these structures. In parallel, while longshore sediment transport plays an important role in the long-term erosion trend at the site, cross-shore sediment transport dominates at the short-term swash-by-swash time scale during high energy wave events as is typically the case for pure sand (e.g., [START_REF] Blenkinsopp | Measurements of the time-varying free-surface prole across the swash zone obtained using an industrial lidar[END_REF][START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] and gravel beaches (e.g., [START_REF] Williams | Bardex (barrier dynamics experiment): Taking the beach into the laboratory[END_REF][START_REF] Almeida | Observations of gravel beach dynamics during high energy wave conditions using a laser scanner[END_REF]. Therefore, similar crossshore high-resolution investigation of composite beach/dynamic cobble berm revetment morphodynamics is benecial for scientists and engineers.

Dynamic cobble berm revetments and composite beach ridges are by essence composed of three layers:

1) A layer of pure gravels, which generally behaves like a pure gravel beach. This layer is subjected to longand cross-shore transport, which over time, tends to generate a net landward transport of particles [START_REF] Carter | Coarse clastic barrier beaches: a discussion of the distinctive dynamic and morphosedimentary characteristics[END_REF]. Cross-shore sorting of particles in the pure gravel layer is common, with the direction of sorting dependent on the hydrodynamic capacity of the swash to bring the largest particles into motion [START_REF] Bluck | Sedimentation of beach gravels: Examples from south wales[END_REF][START_REF] Orford | Discrimination of particle zonation on a pebble beach[END_REF][START_REF] Williams | Particle size and shape in pebble-beach sedimentation[END_REF][START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF]. 2) A layer of mixed gravel and sand, composed of coarse sand and small pebbles. This layer is vertically sorted, with particle size decreasing with depth [START_REF] Pye | Advice on Sustainable Management of Coastal Shingle Resources[END_REF]. 3) A layer of pure sand. The presence of these three layers makes the hydraulic conductivity and water table of a beach with a dynamic revetment or a composite beach dierent from pure gravel beaches, and is expected to inuence the swash dynamics [START_REF] Holland | Mixed sand and gravel beaches: accurate measurement of active layer depth to develop predictive models of sediment transport[END_REF][START_REF] Blenkinsopp | Wave runup on composite beaches and dynamic cobble berm revetments[END_REF]. The swash motions at the wave-by-wave scale cause rearrangement of surface particles, which can in turn lead to temporary exposure and movement of underlying gravel and sand.

In addition, sand beneath the cobbles can be eroded by the water percolating through the permeable pure gravel layer [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF]; it can also accumulate and compact due to kinetic sieving, which results from the vibratory mechanism of the swash [START_REF] Wright | Morphodynamics of high energy beaches and surf zones[END_REF]. In tidal environments, the tide level plays a key role in the dynamics of composite beaches as hydrodynamic conditions change from dissipative at low and mid tide (shoreline on the mildly sloping sand beach face) to reective conditions around high tide, when the swashes interact with the much steeper gravel berm [START_REF] Blenkinsopp | Wave runup on composite beaches and dynamic cobble berm revetments[END_REF]. These processes were investigated through both a laboratory [START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF] and eld study [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF] and provided physical explanations of the overall dynamics and stability of dynamic revetment and composite beaches. Here we investigate cross-shore processes at the swash-by-swash scale to better understand swash zone morphodynamics of dynamic cobble berm revetments and composite beach ridges, and when possible, relate them to observed processes at larger scale.

To address the aforementioned points and better understand the dynamics of dynamic revetments and composite beaches, the present study investigates for the rst time swash processes and swash-induced sediment mass uxes on a dynamic cobble berm revetment. The analysis is performed at temporal scales ranging from seconds to the tidal timescale, so that observed changes are put in perspective with hydrodynamic forcing. The study uses high-resolution hydrodynamic and topographic measurements collected using a 2-D lidar scanner along a cross-shore transect of the dynamic cobble berm revetment in North Cove, Washington State, USA [START_REF] Kaminsky | Nature-based dynamic revetment construction at north cove, washington, usa[END_REF]. The eld experiment was performed over a nine-day period around a spring tide in January 2019, during energetic wave conditions at a location with a history of extreme erosion [START_REF] Kaminsky | Historical evolution of the columbia river littoral cell[END_REF].

The paper is structured as follows: Section 2 presents the methodology, including a description of the study area, the lidar setup, the environmental conditions during the experiment and the data processing techniques. Section 3 presents the swash analysis of cross-shore mass uxes. Section 4 discusses the results in terms of sediment transport, and compares the main ndings with a similar study on sandy beaches. Finally, Section 5 concludes and suggests potential future work.

Methodology

Study Site

The town of North Cove is situated on the U.S. Pacic northwest coast along the northern shore of the Willapa Bay entrance in Washington State (see Figure 1a). This open sandy coast faces the Pacic ocean and is therefore exposed to a severe wave climate, particularly in winter with storms producing deep-water signicant wave heights greater than 10 m at least once a year [START_REF] Allan | Extreme storms in the pacic northwest coast during the 1997-98 el niño and 1998-99 la niña[END_REF][START_REF] Ruggiero | Seasonal to interannual morphodynamics along a high-energy dissipative littoral cell[END_REF][START_REF] Michalsen | Feasibility of long-term shoreline stabilisation alternatives between North Cove and Tokeland[END_REF]. Semi-diurnal tides dominate this part of the coastline, with a tidal range ranging from 2 to 4 m [START_REF] Kaminsky | Historical evolution of the columbia river littoral cell[END_REF]. Ocean waves entering the bay drive longshore sediment transport toward the southeast, which may be enhanced by the ood tide. Wind waves from the south generated within the bay can drive nearshore sediment transport toward the northwest, aided by the ebb tide [START_REF] Lesser | An Approach to Medium-term Coastal Morphological Modelling[END_REF]. The combination of energetic hydrodynamics, storm events and northward migration of the main tidal channel within the inlet has led to chronic coastal erosion at North Cove over several decades, with an average recession estimated at 20 m/yr between 1950 and 1999 [START_REF] Kaminsky | Historical evolution of the columbia river littoral cell[END_REF].

A maximum rate of recession of 37.3 m/yr was observed between 1963 and 1974. 37.3 m/yr was observed between 1963 and 1974. At the beginning of the 21 st century, this reduced to approximately 13 m/yr.

More details on the overall sediment transport processes along the coast can be found in [START_REF] Kaminsky | Historical evolution of the columbia river littoral cell[END_REF] and [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF].

Following existing examples of dynamic revetments constructed along the west coast of the USA [START_REF] Allan | Monitoring the response and ecacy of a dynamic revetment constructed adjacent to the columbia river south jetty, Clatsop county, Oregon[END_REF][START_REF] Allan | Hateld Marine Science Center Dynamic Revetment Project[END_REF][START_REF] Allan | Dynamic revetments for coastal erosion stabilization: a feasible analysis for application on the oregon coast[END_REF], the extreme erosion at North Cove motivated the installation of a dynamic cobble berm revetment to protect the coastline from further erosion. The complete history of the site, the description of the initial placement and the detailed beach and revetment state can be found in [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF], section 2.1. Starting in February 2017, an ad-hoc revetment was built using angular and poorly sorted rock from a local quarry. The material has a diameter range varying from a few centimetres to almost one metre (D 50 = 0.15 m) and is primarily basalt with a bulk density of 1830 kg/m 3 , although other type of rock can be found. The hardness of the material means that it tends to fracture and abrade into smaller pieces, reducing the D 50 over time, and adding coarse sand to the material range. The revetment material is therefore very heterogeneous in terms of shape and size, and the angularity of the material facilitates interlocking in comparison with more rounded shingle often found on composite beaches. For the remainder of this paper, the construction material will be referenced as 'cobbles', as this characterises the predominant material size within the revetment. Cobbles were placed incrementally over time to reach a total volume of 16.23 m 3 /m around the monitoring site (Figure 1a). At the experiment location, the revetment has a cross-shore width of approximately 20 m in winter (storm season). The revetment reached its present condition (gross shape, width and elevation) rapidly after instalment (in the order of days), however it remains dynamic in essence as its shape and slope continuously change [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF]. Wave action over time has led to cross-shore sorting, with cobble size decreasing landward. Due to the presence of this revetment, the beach is considered to be an articial composite beach: cobbles composing the upper ridge are in direct interaction with waves at mid and high tide (Figure 1c); at low tide, the shoreline is typically around 120 m seaward of the cobble toe, and the sub-aerial beach is dominated by sand (Figure 1b) with a D 50 of about 0.18 mm [START_REF] Kaminsky | Historical evolution of the columbia river littoral cell[END_REF].

The revetment at North Cove was chosen as the study site for this experiment because examples of dynamic cobble berm revetments are rare and there is a thorough ongoing monitoring programme being undertaken at the site [START_REF] Weiner | North Cove Dynamic Revetment Monitoring: Winter 2018-2019[END_REF][START_REF] Kaminsky | Nature-based dynamic revetment construction at north cove, washington, usa[END_REF] which this experiment was timed to coincide with.

Field experiment

The eld experiment was performed over nine days, from 17/01/2019 to 25/01/2019, around the second spring tide of January. This monitoring period will be referred to as "spring tidal cycle" for , 2019). The analysis performed by [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF] revealed that the revetment remained a coherent structure over the spring tidal cycle, only losing an average of 0.67 m 3 /m over the study area.

This volume loss was mainly associated with sand erosion from within or beneath the cobbles since no cobbles were transported seaward of the revetment toe. Figure 4e shows an example of the pure cobble and mixed sand and cobble layer resting on pure sand. All proles and available pure cobble layer thickness recorded during the experiment are presented in Figure 8 and 9 in [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF], along with a conceptual model of layer thickness evolution. The present contribution focuses on swash-driven cross-shore uxes studied at the scale of individual swash events using high-resolution hydrodynamic and topographic data from a 2-D lidar which captured high-frequency revetment prole data along a single cross-shore transect (Figure 1a). A SICK LMS 511 lidar scanner was deployed for this experiment, and was mounted on top of a 6 mpole strongly attached to a large drift log at the top of the revetment. The pole and lidar were anchored with four guy lines making it nearly immobile even in strong winds (Figure 2a). The lidar collected free surface elevation and revetment prole measurements along a 18.7 m-long 2D cross-shore transect of the cobble revetment (Figure 2b) for approximately six hours around each high tide of the spring cycle (three hours before and after) to capture interactions between waves and cobbles. The lidar collected data at 25 Hz with an angular resolution of 0.1667 • across a 150 • eld-of-view. In the remainder of the paper, the cross-shore data are given relative to the lidar position, with the distance x increasing seaward.

Elevations z are given relative to the North American Vertical Datum 1988 (NAVD88).

The height of the lidar was chosen so that its swath covered most of the revetment section while keeping a high spatial resolution. In this conguration, the lidar is high enough for its signal not to be aected by shadowing of cobbles (only very large cobbles at the toe could sometimes create a shadow area, but this area was smaller than the grid size used -0.1 m see Section 2.4.1). The horizontal resolution of the lidar decreases with distance [START_REF] Almeida | Observations of gravel beach dynamics during high energy wave conditions using a laser scanner[END_REF], therefore the horizontal resolution at the toe of the revetment must be kept below or equal to the grid size. The conguration and height reported here provided a horizontal resolution ranging from 2 cm right below the lidar to 10 cm at the seaward edge of the revetment prole. The vertical resolution of the lidar is 1 mm, and this in constant in space over the range used in this study.

Environmental Conditions

The weather conditions during the experiment were obtained from publicly available continuously operating stations. Water levels were obtained for the Toke Point station (station 9440910; Figure 1a) Center open-source platform. Figure 3 shows the timeseries of wave and water-level data for the duration of the eld experiment: wave data were available every half hour (Figure 3a andb); and water level data every six minutes (Figure 3c). The wave conditions during the spring tidal cycle were characterised by large and long-period swell wave conditions, peaking at H s = 6 m and T p = 15 s on 19/1 at the Waverider buoy. During the experiment, although incident waves came from varying directions (west and southwest) at the Waverider buoy, the conguration of the studied site (orientation and very dissipative beach) mean the dynamic revetment is swash-aligned, generating approximately alongshore uniform longshore transport [START_REF] Kaminsky | Nature-based dynamic revetment construction at north cove, washington, usa[END_REF][START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF].

Lidar data processing

Separation of hydrodynamic and topographic measurements

The lidar dataset was rst converted from polar to cartesian coordinates, despiked and interpolated onto a 0.1 m horizontal grid (e.g., see [START_REF] Almeida | Observations of gravel beach dynamics during high energy wave conditions using a laser scanner[END_REF][START_REF] Martins | Monitoring individual wave characteristics in the inner surf with a 2-dimensional laser scanner (LiDAR)[END_REF][START_REF] Martins | High-resolution monitoring of wave transformation in the surf zone using a LiDAR scanner array[END_REF]. The output from this process is a series of timeseries of yet non separated bed and swash surface elevations at 0.1 m cross-shore intervals. At each location, the "bed" elevation (when the swash depth is zero) and "swash" elevation data were separated following [START_REF] Almeida | Observations of gravel beach dynamics during high energy wave conditions using a laser scanner[END_REF] and [START_REF] Martins | Monitoring individual wave characteristics in the inner surf with a 2-dimensional laser scanner (LiDAR)[END_REF]. This methodology, based on the technique proposed by [START_REF] Turner | sediment ux per swash: Reply to discussion by t.e. baldock 'measurement of wave-by-wave bed-levels in the swash zone[END_REF] for ultrasonic bed-level sensors, starts by computing the variance of the elevation timeseries over a moving 4 s window at each cross-shore location (i.e., at each grid point). The median of the variance over the tide is then calculated for each grid point, and used as a threshold below which points are considered as stationary (corresponding to the bed).

The threshold therefore varies with cross-shore distance from the lidar, as suggested by [START_REF] Almeida | Observations of gravel beach dynamics during high energy wave conditions using a laser scanner[END_REF], which minimises the error associated with horizontal resolution. A minimum value of 0.0002 m 2 for at least 2.4 s was set as the threshold for bed detection. Figure 4 shows an example of this separation process over a four-minute window at four cross-shore locations across the revetment. Note that the bed elevation measured with the lidar only corresponds to the cobble surface and does not capture the sandy beach seaward of the revetment toe. Figure 4e shows the prole measured after the 22/1-10h high tide, including measured of layers thickness. 'Note that the revetment is a low volume revetment which eectively consists of a few layers of pure cobbles, but it was shown to have a valid coastal protection function [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF]. Further post-processing of the separated bed/swash elevation data enables the instantaneous shoreline position, which is dened at the most landward point where the swash depth is larger than 0 m, to be tracked in both time and space enabling extraction of the runup and rundown limits [START_REF] Blenkinsopp | Wave runup on composite beaches and dynamic cobble berm revetments[END_REF].

Denition of individual swash events

The same nomenclature as in [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] is used hereafter to refer to swash terminology.

Following [START_REF] Hughes | Hydrokinematic regions within the swash zone[END_REF], individual swash events correspond to an inundation event between consecutive occurrences of a dry bed at a xed location in space. As illustrated in Figure 4, each swash event can be composed of several incident waves/bores, dened by local maxima in the swash elevation 240 timeseries. Since at high tide, the most seaward locations in the lidar transect can be continuously submerged, a maximum of 25 bores were allowed per individual swash event. This method and threshold was successfully used in [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] to identify swashes with long duration which are considered more characteristic of the inner surf zone, and this approach was found to perform well for the current analysis. Using the "bed" timeseries, the net bed-level changes caused by each swash event were computed for each cross-shore lidar measurement position using the bed elevation immediately before and after that event. The net cross-shore mass ux per swash event past any point on the revetment face is directly obtained from these bed-level changes at each discrete point on the revetment surface, and will be referred to as "event mass ux" and noted Q event for the remainder of the paper. The volume ux per metre of coastline q(x ′ ) (positive onshore) past the cross-shore location x ′ for each swash event is given by:

q(x ′ ) = ∫ x0 x ′ ∆z(x)dx (1)
given in m 3 /m, where x 0 is the lidar position (i.e., q(x 0 ) = 0, as the drift log barrier prevents any transport further this point), ∆z is the bed-level change at each lidar grid point (m) and dx is the crossshore spacing between each grid point (0.1 m). The corresponding event mass ux per metre of coastline, Q(x ′ ) (positive onshore) is then given by:

Q event (x ′ ) = ρ b q(x ′ ) (2)
given in kg/m, where ρ b is the bulk mass density (ρ b = 1830 kg/m 3 ). This method has previously been applied by [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] in a eld experiment investigating swash processes on a sandy beach.

It was also illustrated for multiple events in Turner et al. (2009).

The experimental data allow the event mass ux, which includes both sand and cobble transport (suspended sand within swashes could not be separated from cobbles) to be quantied for all individual swash events acting on the revetment. Furthermore, knowing the duration of each swash, the net crossshore mass ux per second was calculated by simply dividing the event mass ux by the duration of the swash. The obtained mass ux rate per metre of coastline, given in kg/(sm), will be referred to as the "mass ux" (as opposed to the previous "event mass ux") for the remainder of the paper, and noted as

Q s .

Results

All the recorded tide used for the analysis are shown in Table 1. The results section is separated into two subsections: the rst subsection will present an "example tide" (19/1-17h, Table 1) to (1) illustrate the analysis that was done for all tides, and (2) demonstrate consistent behaviour observed during all tides important for understanding the observed swash-induced bed level changes; the second subsection will focus on the bulk analysis of the swash and uxes of all tides combined. Note that two tides (18/1-19h and 19/1-08h) are not used for the bulk analysis because several large cobbles were manually placed and removed along the lidar measurement transect, which would lead to a bias in the analysis.

Observed cross-shore revetment dynamics

For the following analysis, the data from the overnight high tide on 19/1 are used. During this tide, the oshore wave height, wave period and mean water level reached a maximum of 4.05 m, 13.3 s and 2.48 m respectively, which rank this tide fth out of the 16 high tides recorded in terms of oshore wave power (therefore this tide is also representative of the energetic conditions over the spring tidal cycle).

This tide will be referred to as "the example tide" for the remainder of the paper.

Table 1: Mean oshore wave energy (E), mean wave energy (Etoe) and mean wave period (T m02,toe ) at the toe of the revetment during the 14 tides used in this paper. The data at the toe of the revetment were calculated at high tide when the lidar measurements at the toe of the revetment corresponded to the surf zone. Those data could not be obtained accurately for the 17/1-18h. Qnet is the net cross-shore mass ux measured over the entire tide at the maximum mean shoreline position for each high tide. Q abs is the sum of the absolute value of all uxes measured at the same position as

Qnet. The last two variables are used in Section 4.2.

Tide

(DD/M-hh) Using the "bed" timeseries (Section 2.4.1), net bed-level changes relative to the revetment face morphology at the start of the timeseries were computed every second at each cross-shore position on the 0.1 m grid. Figure 5 shows the morphological evolution of the revetment face through the example tide over the whole revetment width, where red marks erosion and blue accretion. Note that Figure 5 is used to contextualise the analysis performed, but nonetheless, the pattern of accretion in the upper swash and erosion in the lower swash is recurrent in all recorded tides (see Figure 8 and 9 in [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF].

E (kJ/m 2 ) E toe (kJ/m 2 ) T m02,toe (s)
Q net (kg/m) Q abs kg/m)
Figure 6a presents percentage occurrence distributions of bed-level changes per individual swash event at three locations across the revetment face. The majority of swashes induced a net bed-level change smaller than ±3 cm at all three locations. The same analysis was completed for all tides with similar results. The distribution in the upper part of the revetment at x = 6.4 m is wider, indicating larger bedlevel changes in the upper part of the revetment due to the presence of small cobbles (grading decreasing landward). The maximum swash-induced net bed-level change was +6 cm during the example tide, and -14 cm over all tides. Note that these changes are well outside the range displayed in Figure 6a. Notably, these large single-event bed-level changes are of the same order of magnitude as the total net morphological change at any point on the revetment. Figure 6b shows the percentage occurrence of event mass uxes, The net morphological change swash zone over the example tide is characterised by accretion of up to 21 cm. Note that the drift log barrier (Figure 1c and Figure 2a) is at x = 0.7 m.

recorded at the same three cross-shore locations as in Figure 6a. Similar distribution is obtained, and the standard deviation is smaller on the upper beach face, with the average value over all tides varying from 9.7 kg/m per swash at x = 6.4 m to 17.1 kg/m per swash at x = 14.4 m. Rare events produced large event mass uxes, with a maximum of +180 kg/m during the example tide, and -233 kg/m over all recorded tides. The results shown in Figure 6b are almost symmetrically distributed, and a similar distribution is observed for all tides, whether they experienced net erosion or accretion. This suggests that the volume changes caused by cobble transport over hundreds of swash events almost balance over longer time scales.

The resulting net bed level change or ux at a specic location can be due to either the sum of slight imbalance between positive and negative swashes or few extremes events. This will be discussed further in Section 3.2.1 and in the discussion section of this paper.

The zero-equivalent swash-induced bed-level changes represented by the central bar on Figure 6 also tends to vary across-shore. However, due to the vertical precision of the lidar (±1 mm, Section 2.2), a quantitative interpretation cannot be performed with high condence within this range and is the reason why only the analysis of the distribution over the whole range plotted in Figure 6 was discussed above.

Rates of bed volume change

The balance of onshore and oshore sediment uxes observed in Figure 6 is further illustrated in event-by-event bed level changes measured every 12 s (corresponding mean oshore peak period), and then averaged over ten-minute windows. The net volume change is a way to quantify the net change in revetment morphology between time t and t+10 min minutes. The gross volume change is used as a way to indicate the total amount of sediment transport over a ten-minute period, by summing every change occurring between all t and t+12 s periods contained in a ten-minute window.

Figure 7a shows the net and gross rate of bed volume change (in m 2 /s) over the course of the example tide. It shows that both rates increase and decrease with the water level. This can be explained by the fact that the surf zone at North Cove is highly dissipative at all tide levels when the wave height is large. Thus, the surf zone is saturated in energy and the energy reaching the revetment depends on the water level. This is illustrated in Figure 8, which shows that the wave height at the toe of the revetment is a function of the water depth at the toe, as observed by [START_REF] Blenkinsopp | Wave runup on composite beaches and dynamic cobble berm revetments[END_REF] for composite beaches and dynamic cobble berm revetments. Thus the energy available to mobilise cobbles and produce bed volume change is directly related to the water depth at the toe.

Figure 7b shows that the ratio between the gross and net rate varies between 2 and 8. Note that similar values were observed for all recorded tides, and this is close to the ratio of 10 measured in prototype scale laboratory testing by [START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF] on a dynamic cobble berm revetment composed of rounded and well-sorted cobbles with D 50 = 6.4 cm. This ratio shows that the revetment elevation is constantly changing over ten minutes, but that the nal magnitude of net change is 2 to 8 times smaller than the sum of the absolute positive and negative changes which cause it. In other words, the cobbles composing the revetment show a highly-dynamic behaviour, moving both seaward and landward throughout the tide. However, because it was shown in Figure 6 that the ux distribution at all points on the revetment was for the example tide, (a) calculated over the entire revetment prole length (18.7 m), and (c) calculated every ten minutes from the runup limit (dashed line in Figure 5) to a point four meters seaward, which represents the upper swash region. Note that two y-axes are used to present both datasets on the same gure. Bottom panels: Ratio of the gross over the net rate (dV /dV10) of bed volume change per 10 minute window for the example tide, (b) calculated over the entire revetment prole length (18.7 m), and (d) calculated every ten minutes from the runup limit to a point four meters seaward. The dashed and solid lines represent the runup limit and the mean shoreline position (measured every 10 minutes) respectively.

approximately symmetrical, the net change caused by this movement is much smaller, leading to overall stability of the revetment. Note that for most of the recorded tides, the ratio tends to be slightly smaller during the rising tide than during the falling tide.

Figure 7c examines the gross and net rate of volume change over a four-meter window bounded at the landward boundary by the averaged ten-minute runup limit (dashed black line). This method allows only the rates characterising the upper swash to be captured, as it moves up and down the revetment face over the tide. It is clear that the trend of both rates within the four-meter window is very dierent from the trend over the full revetment, and this is true for all recorded tides. The gross rate over the four-meter 335 window is almost constant over the tide, with a slight decrease during the falling tide, while the net rate is more variable. The ratio of the gross over net rate, calculated over the same four-metre window and shown in Figure 7d, shows similar values as over the whole revetment (Figure 7b), except during the falling tide when it reaches values between 15 and 20. Note that this is the case for all recorded tides.

Given that over the four-metre window, the gross rate is approximately constant and always larger than the net rate, this increasing ratio can only be due to a decrease in net rate. This is further conrmed by computing the total gross rate over the whole swash zone divided by the four-meter window gross rate, and the total net rate divided by the four-meter window net rate (i.e., values in Figure 7a divided by values in Figure 7c). The gross rate ratio varies from 1 at low tide to 9 at high tide, and it is correlated with the tidal elevation hence the amount of revetment area covered by the swash. The net rate ratio also has a value of 1 at low tide, but its maximum (12) occurs during the rst couple of hours of the falling tide. This conrms that the net changes caused by the upper part of the swash decrease during the falling tide, contributing less to the total net change.

This analysis shows that during the rising tide when the energy reaching the revetment increases (Figure 8), the revetment rapidly reshapes but then remains relatively stable under the action of the upper part of the swash as the tide recedes. This suggests that under increasing wave forcing, the revetment globally evolves to a dierent shape before reaching a relative stability, however the overall movement of cobbles (gross rate) always remains important. At the intra-tidal scale, this is consistent with the study of [START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF] who observed that the front slope of a dynamic cobble berm revetment at prototype scale can substantially reshape and change within 20 minutes or less under the action of waves, and then remain almost unchanged. At the inter-tidal scale, this is consistent with [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF] who observed that the current revetment adjust to new wave forcing over a few tides, before being relatively stable under that forcing.

Bulk analysis of swash characteristics

In this section, all periods when the swash zone coincided with the dynamic revetment (mid to high tides shown using grey shaded bands in Figure 3) are used to analyse swash-induced mass uxes and swash depth characteristics over the spring tidal cycle. The magnitude of uxes at a specic point on the beach are dependent on the position of the swash zone, and hence vary with the water level (Figure 3c and Figure 8). To remove this spatial bias from the analysis of uxes, the percentage of time that the bed is inundated (t i ) at each 0.1 m grid point is used to indicate relative position within the swash zone (e.g., [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF][START_REF] Masselink | Net sediment transport and morphological change in the swash zone of a high-energy sandy beach from swash event to tidal cycle time-scales[END_REF][START_REF] Masselink | Suspended sediment transport in the swash zone of a dissipative beach[END_REF][START_REF] Aagaard | Sediment suspension and turbulence in the swash zone of dissipative beaches[END_REF][START_REF] Masselink | Flow velocities, sediment transport and morphological change in the swash zone of two contrasting beaches[END_REF]. The percentage inundation t i was calculated over ten-minute time windows for all tides. Figure 9 shows a contour plot illustrating the percentage of bed inundation t i over the revetment for the example tide. Note that because the revetment surface is irregular due to the cobble surface, it is possible to have an inundated point landward of a dry point at the same time step. This is particularly the case at the bottom of the revetment, where large cobbles are common and can protrude through the water surface, but this does not aect the analysis.

Swash-induced event mass uxes spatial variations

To investigate the relationship between the inundation-normalised cross-shore position and the event mass uxes, every measured event mass ux was assigned to a percentage inundation class based on the value of t i at the time of occurrence, with a class size of 10 % bed inundation ranging from 0 -10 % to 90-100 %. Figure 10 shows that while the data in all classes are approximately symmetrically distributed, a distinct spatial variation in the magnitude of event mass uxes is evident. The variation evolves from a peaked distribution in the upper swash, with more than 60 % of events within the range ±4 kg/m per shows the mean and standard deviations of the mean event mass ux magnitude. Because the sign is removed when calculating the event mass ux magnitudes, all values are positive and approximately an order of magnitude larger than the mean values presented in Figure 11c. Figure 11b shows that both the mean and the standard deviation of the event mass ux magnitude increase with percentage inundation t i , which is consistent with the distributions shown in Figure 10. Figure 11c shows that swash areas with t i > 80 % have a high negative mean value, suggesting that material is transported seaward from these locations within the normalised swash zone. These high negative uxes represent cobbles which are transported from the top and middle part to the lower part of the revetment, and accumulate at the revetment toe, around x = 18 -20 m. They also represent erosion of the sand underneath the revetment, which was transported seaward of the revetment during the experiment as demonstrated by Bayle et al.

(2021).

Depth of swashes

To investigate the distribution of mass uxes further, the maximum depth of each swash event was extracted and related to the event mass ux for all cross-shore point on the revetment and all recorded events. In order to remove the eect of splashes, the depth presented is the 95 th percentile depth for each swash. Nonetheless, it will be referred to as the "maximum depth" for the rest of the paper. As a reminder, the calculation of the maximum depth of a swash is assessed independently from the duration of the swash -for instance, a maximum depth of 0.40 m can either represent a short swash reaching this depth once, or a longer swash attaining this depth several times. Figure 12 shows that the mean and standard deviation of the maximum depth of a swash tend to increase as the duration of a swash increases.

To eliminate this temporal bias from the ux analysis, event mass ux values are presented per second in this section, and will be referred to simply as "mass ux", noted Q s (see Section 2.4.3). The analysis of the bulk distribution of the maximum depth of individual swash events for all points on the revetment and for all tides revealed that 99 % of all swashes have a maximum depth smaller than 70 cm, with 50 % 415 being smaller than 15 cm. Moreover, it showed that 50 % of the depth of swashes which resulted in zero net uxes are smaller than 3 cm, and 95 % are smaller than 15 cm. For this reason, swashes smaller than 15 cm are referred to hereafter as "shallow events". as a function of the maximum depth of the associated swash event, at each point on the revetment and ranging from 0 -0.05 m to > 0.70 m. It shows that the mean mass ux magnitude increases with the maximum depth of swash, but the standard deviation of mass uxes only varies from 1.2 kg/m/s in the 0 -10 % inundation class to 2.1 kg/m/s in the 90 -100 % class. This increase in mean magnitude is very similar to that shown in Figure 11b per inundation class. By contrast, the standard deviation of the magnitude is more constant with varying depth of swash than inundation class. This suggests that while event mass uxes are of high magnitude in areas with t i > 80 %, mass uxes can be of high magnitude in areas with a maximum depth of swash of 0.20 m or larger (Figure 13b). In addition, Figure 13a shows that the mass uxes caused by swashes with a depth between 0.15 -0.45 m, referred to as "mid-depth events", are negatively skewed. They also have a relatively large negative mean mass ux (Figure 13c)

and generate large extreme mass uxes with maximum magnitude of 40 kg/m/s (not shown). By contrast, events deeper than 0.45 m, referred to as "deep events", generated smaller extreme mass uxes (maximum magnitude of 14 kg/m/s, not shown). Therefore, the part of the revetment slope inclined to undergo large extreme mass uxes is where the mid-depth events occur, so where the swash water body has a maximum depth between 0.15 -0.45 m. These extreme mass uxes likely occurred near the location of bore collapse where the energy available to initiate sediment transport is greatest. In contrast, the deep part of the swash mainly generates ows which, unlike for pure sandy beaches, do not signicantly mobilise cobbles hence generate less and smaller extreme uxes. Given this observation, plus the fact that deep events are generally long in duration (Figure 12) and that large extreme mass uxes already occur in the mid-depth part of the swash, it is normal to measure smaller extreme mass uxes in the deep part of the swash even though high magnitude event mass uxes are present in areas with t i > 80 %.

Cross-shore bed change oscillations

To further analyse the inundated sections of the revetment, an analysis of spatial and temporal variation of event mass uxes over the example tide is shown in Figure 14. Figure 14a presents a timeseries of net cross-shore mass uxes measured at a single point on the revetment (x = 12.5 m) determined every two-minute and ten-minute intervals. It shows that while the majority of single event uxes at a point on the revetment cause little or no revetment mass change (Figure 6a), large onshore and oshore mass uxes occur throughout the tide. The two lower panels in Figure 14 present contour plots of the net cross-shore mass uxes within two-minute (Figure 14b) and ten-minute (Figure 14c) intervals.

Figure 14b shows that at the two minutes sampling interval, there is evidence of oscillating periods of onshore and zero/oshore mass uxes particularly in the lower parts of the swash zone throughout the entire duration of the tide, although periods of oshore transport are more common. This is conrmed by Figure 14c which clearly shows a tendency toward erosive periods when the uxes are summed over ten minutes. Similar oscillations were observed on a sandy beach by [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] who suggested that they indicate the presence of a form of dynamic equilibrium caused by combination of negative feedback and short-term process dampening to limit the overall rate of morphological change. However, the relationship between these oscillations and external forcing is yet to be analysed. A feature of Figure 14c is that these ux oscillations tend to be weaker in the upper swash zone except during the rst 1 -2 hours of the rising tide. This supports the observation made in Section 3.1.2 that the upper part of the swash is more inclined to generate net bed changes during the rising tide, suggesting prole stability in the upper part of the swash is reached relatively quickly and subsequent variability is 460 small. The limit of these oscillations was extracted from the ten-minute period with a semi-automatised method using the net cross-shore mass ux summed over each 10 % inundation line. From the 100 % to the 0 % inundation line, the rst line characterised by a rate of change negatively larger than 80 kg/m per t i is taken as the ux oscillation limit, thus associated to an inundation percentage t i .

For each recorded tide, the value of percentage inundation at which the oscillation limit occurred is 465 presented as a function of the mean wave period (T m02 ) recorded at the toe of the revetment (Figure 15).

The plot shows a correlation between the relative position of this limit in the swash and the mean wave period, with a coecient of correlation (r 2 = 0.78). It indicates that as the period increases (decreases), Percentage inundation window t i (%)

Figure 15: Plot of the ux oscillation limit (% of inundation) against the mean wave period (Tm02) at the toe of the revetment.

Values of the Pearson r 2 correlation coecient is 0.78.

the line of delimitation moves landward (seaward) within the normalised swash. This suggests that the longer the wave period, the greater chance of larger uxes occurring closer to the runup limit. Locations landward of this limit are only composed of short swashes with a duration of less than 15 seconds (similar range for each recorded tide). Referring to Figure 12 shows that swashes shorter than 15 seconds are also relatively shallow. These shallow events have a small mean mass ux magnitude, with a negative mean mass ux (Figure 13b,c). For this reason, most of the mass uxes measured above this limit are negative (Figure 14b,c), and typically lead to minimal net change over two and ten minutes time periods because the revetment is in a relatively stable state after the initial cobble rearrangements which occurred during the rising tide. Accurate data on local water level elevation during energetic events are important to set the revetment at the right elevation (more specically, the revetment toe), and this is translated in the recently developed empirical runup equation for composite beaches by [START_REF] Blenkinsopp | Wave runup on composite beaches and dynamic cobble berm revetments[END_REF].

Discussion

The discussion is divided into two subsections: the rst discusses the results in term of sediment transport and the implication of this work in terms of dynamics revetment; the second compares the current results with those obtained for sandy beaches, focusing on a comparison with [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] who performed very similar analysis.

Sediment transport

The swash analysis of all tides recorded during the spring tidal cycle showed that onshore and oshore uxes almost balance over the tide and over the entire swash area. Net changes are the consequence of either the accumulation of a slight imbalance between positive and negative swashes or a few extremes events. In other words, except when a large cobble or group of cobbles is mobilised to cause a large net change, it is likely that most of the time mobilised cobbles simply readjust their position relative to each other, potentially achieving better interlocking. It is further noted that due to the large size of the sediment composing the revetment, the movement of a single stone can lead to substantial bed elevation change at a single point and it may be that a depression is left on the revetment surface which becomes a natural location for future deposition. This helps to explain why the revetment remains a coherent structure over time and does not undergo major changes at either the intra-and inter-tidal timescale.

The majority of net morphology change at a location occurs during the rising tide as swash rst reaches it. The majority of net change happens over timescales of tens of minutes with the cobble slope rapidly reaching a quasi-stable state as shown in [START_REF] Bayle | Performance of a dynamic cobble berm revetment for coastal protection, under increasing water level[END_REF]. This has implications for the design of dynamic cobble berm revetments since the shape and slope will rapidly change to a quasiequilibrium shape driven by the forcing conditions. Therefore, it is likely to be unnecessary to overdesign the revetment geometry, since a relatively rough placement is expected to rapidly reshape to an "deterministic" quasi-equilibrium shape and slope under swash action. However, it will be necessary to ensure that sucient cobble volume is available for this shape to be formed. To aid the specication of cobble volume, [START_REF] Blenkinsopp | Wave runup on composite beaches and dynamic cobble berm revetments[END_REF] presents measurements of quasi-stable revetment slopes in the range 1:3 to 1:8 and provide a method to estimate wave runup on dynamic revetments which can be used to determine the expected crest elevation.

Small bed changes also possibly represent changes in the sand within or underlying the revetment, as observed in [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF], through sand erosion (i.e., winnowing caused by the backwash water) and sand compaction (kinetic sieving), although the latter is generally a slower process. The water table is thought to be of importance in the underlying sand dynamics, as presented by [START_REF] Kulkarni | Morphological variations of a mixed sediment beachface (teignmouth, uk)[END_REF] for a mixed beach. However, unlike mixed beaches, composite beaches and dynamic cobble berm revetments have a natural underlying lter layer of mixed sand and gravel (Figure 4) at the "runo interface" dened in the conceptual model of [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF], which limits the underlying sand erosion. Nonetheless, during the rising tide, the water table rises but remains at the sand-cobble interface or below, and remains below the area aected directly by the upper swash. Therefore, the upper swash percolating through the cobbles reaches unsaturated sand, with empty void spaces into which water can inltrate, promoting erosion of the underlying sand as water drains back out through the revetment. The water table reaches its maximum at high tide, and remains relatively higher during the falling tide than the rising tide due to capillarity. As a consequence, during the falling tide, the upper swash percolating through cobbles reaches a saturated sand/lter layer with less free void space, resulting in less inltration and hence reduced sand mobilisation as the water ows seaward at the runo interface. The dynamics of both sediment types (sand and gravel) detailed above explains why the rising tide generates globally more net change in the upper part of the swash than the falling tide. This highlights at the swash scale the importance of the naturally formed mixed sand and cobble lter layer where the "runo interface" develops. For the poorlysorted and angular material used for the structure reported on here, this lter layer built up naturally at the study site. It is not clear whether this lter layer should be a design feature so that it is present immediately after construction, or whether to simply allow natural sorting over time. To gain clarity, the time taken for this natural sorting requires further investigation now that the process has been identied.

This sorting is also very likely related to the thickness of the cobble layer mobilised by the swash, and this also needs to be investigated.

This study also showed that while mean event mass uxes are high in the inundation zone t i > 80 %, the analysis of the maximum depth of swash recorded per inundation class (not shown) revealed that overall, deep events (> 0.45 m) only occurred in areas inundated more than 50 % of the time. By contrast, it was identied that the largest extreme mass uxes occurred where the swash reaches a maximum depth between 0.15 -0.45 m. As a consequence, extreme net changes occurring in the upper swash during the rising tide (Section 3.1.2) are likely located where the swash reaches depths between 0.15 -0.45 m.

Comparison with sandy beaches

The present results suggest strong similarities with sandy beaches in terms of sediment transport in the swash zone. It was showed that a single swash event can produce large changes of the order of magnitude of the cobble diameter D 50 = 15 cm, but that in general, these events are rare. These large events are also three to six times larger than those observed on sandy beaches [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF][START_REF] Baldock | Field observations of instantaneous cross-shore free surface proles and ow depths in the swash zone[END_REF][START_REF] Turner | sediment ux per swash: Reply to discussion by t.e. baldock 'measurement of wave-by-wave bed-levels in the swash zone[END_REF], which may be expected on a dynamic cobble berm revetment as the movement of a single cobble can signicantly change the bed elevation at a point on the surface.

The percentage of inundation distribution of swash-induced uxes (Figure 10) was very similar to that measured on sandy beaches by [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] and suggests that the inundation variability of swash-induced uxes are independent of the bed-type. Furthermore, the bed change oscillation pattern presented in Section 4.1 was also observed on a sandy beach by [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF], which conrms a degree of independence from the bed-type. In addition, the enhanced net bed level changes in the upper part of the swash during the rising tide is also observed on a sandy beach, but to a lower degree.

Event mass uxes, both for the mean and extreme events, are around 20 % smaller than those observed on sandy beaches [START_REF] Puleo | Tidal variability of swash zone sediment suspension and transport[END_REF][START_REF] Masselink | Net sediment transport and morphological change in the swash zone of a high-energy sandy beach from swash event to tidal cycle time-scales[END_REF][START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF]. The majority of event mass uxes measured on the dynamic revetment and previously observed on sandy beaches are in the ±10 kg/m range. However, overall, cobbles are less mobile but a small movement can cause a much larger change due to the size of particles. Generally, the smaller uxes per event measured on the revetment compared to sandy beaches supports the idea that the revetment is more stable and resistant to wave attack than a sandy beach.

Figure 7 also showed that the revetment is able to rapidly reshape and reach a relatively stable shape during the rising tide, resulting in a decrease in net change after the rst interactions with the upper swash. To extend this, the ratio of the net ux (Q net ) to the sum of absolute uxes (Q abs ) from all individual swashes at the maximum mean shoreline position over the course of each tide was calculated (not shown). It is observed that the net cross-shore mass ux is on average 18 times smaller than the absolute cross-shore mass ux. Using the same method, [START_REF] Blenkinsopp | Swash zone sediment uxes: Field observations[END_REF] measured net mass uxes that were on average 63 times smaller than the absolute uxes for sandy beaches. The smaller values of this ratio measured on the dynamic revetment suggest that there is relatively less sediment movement on a wave-by-wave timescale than on a sandy beach. Cobbles composing the revetment are hard to bring in motion but have the potential to cause lots of change if they are moved, while with sand initiation of motion is easier but a lot of particles have to be moved to cause signicant changes.

The relatively small variability in the revetment geometry even when subjected to large waves, high water levels and powerful swash events is useful information for coastal engineers. By giving information on how much the revetment volume and shape changes over the course of a high tide (typically by no more than ±0.2 m, Figure 5, so about one or two layer of pure cobble), the measurements presented here suggest that it is not necessary to add a very large volume of cobbles to the revetment face to cope with this variability and prevent exposure of the underlying sand surface. While the revetment in its current state provides ecient protection of the sand scarp during energetic events [START_REF] Bayle | Behaviour and performance of a dynamic cobble berm revetment during a spring tidal cycle in north cove, washington, usa[END_REF], long-term analysis of its behaviour under extreme conditions and longshore sediment transport is required to fully assess its performance and resilience.

Conclusion

The dynamic revetment at North Cove (WA, USA) was monitored over nine days in January 2019, corresponding to almost a spring tidal cycle. The swash zone was continuously monitored using a 2-D lidar, and these high-resolution measurements were for the rst time used on dynamic revetment (and composite beach) to assess the cross-shore mass uxes of material moved by individual swash events.

The analysis of bed-level changes and net cross-shore mass uxes over the revetment demonstrated that revetment changes were mainly driven by very small events (±3 cm and ±50 kg/m), with some rare large bed-level changes of a magnitude similar to the median cobble diameter (D 50 = 0.15 m).

For every tide, the distribution of event mass uxes was nearly symmetrical, with positive and negative uxes tended to balance out over a tide, meaning that the revetment was constantly changing but stable.

The revetment underwent relatively more net change during the rising than the falling tide, with the upper part of the swash causing the main net changes toward a relatively stable state. This was hypothesised to be due to the combination of groundwater inltration and water table elevation, as well as the presence of a runo interface, a feature for composite beaches and dynamic revetments. Furthermore, it was also shown that over a tide, the absolute sum of all uxes at the maximum mean water was on average 18 times larger than the magnitude of the net ux at the same point. Some very generic design guidelines are suggested for the design and instalment of dynamic cobble berm revetment.

The analysis of event mass uxes as a function of percentage inundation showed that areas with t i > 80 % are subject to large mean event mass ux. In parallel, the analysis of net cross-shore mass ux per second revealed that the revetment section where the swash reached a maximum depth between 0.15 -0.45 m undergoes the more extreme uxes. Swashes deeper than 0.45 m only occurred in zones inundated more than 50 % of the time, and smaller extreme uxes were measured over the corresponding section of the revetment.

Flux oscillations were observed as for sandy beaches, and the cross shore limit of these, detected over the ten-minute windows, was correlated with the mean wave period at the toe of the revetment. Overall, the water depth at the toe of the revetment played an important role in the amount of energy that reaches the revetment, as the surf zone is often saturated during energetic events.

Future work should focus on a way to monitor the vertical interface between sand and cobbles at a high spatial and temporal resolution. Although it was identied that both materials were mobilised by swashes, the event-by-event dynamics of this interface remains unclear, and the separation of both components remains a challenge.

the communication and public relations around the experiment. Finally, we thank William Bazeley, Neil

Price, Robert Dyer and David Surgenor from the University of Bath for their technical support during the experiment preparation.

Figure 1 :

 1 Figure 1: (a) Geographical location of the North Cove dynamic cobble berm revetment. The Grays Harbor Waverider buoy is shown as a yellow triangle, and the Toke Point tide station as a green circle, in the bottom left map. (b) Photographs of the dynamic revetment on the 24/01/2019 at low tide; (c) Photographs of the dynamic revetment on the 21/01/2019 at mid-tide (during ood). Note that the top of the revetment is delimited by an articial drift log barrier. Under very high water levels and energetic conditions, the maximum runup limit reaches this log barrier. Photos taken by Paul Bayle.

165

  the remainder of the paper. The principal motivation of the experiment was to collect comprehensive data which captured the morphological evolution of the dynamic revetment over the study area shown in Figure1ain order to analyse the behaviour and dynamics of the revetment. The overall revetment topographic evolution was surveyed with Real-Time Kinematic Global Navigation Satellite System (RTK-GNSS) and individual cobbles were tracked with Radio Frequency Identication (RFID, e.g. see Weiner 170 et al.

Figure 2 :

 2 Figure 2: (a) Photographs of the lidar deployment. The left-hand image was taken at low tide along the lidar transect looking landward. The right-hand image shows the lidar when recording during a high tide, looking alongshore. The central photograph shows a close-up of the lidar mounting system. (b) Cross-shore prole of the beach along the lidar transect measured using RTK-GNSS. Note that the minimum water level recorded by the tide gauge (Figure 1a) during the experiment was z = -1 m referenced to the North American Vertical Datum 1988 (NAVD88), and therefore is not represented on the gure. Photos taken by George Kaminsky, Heather Weiner, and Paul Bayle

  from the NOAA tides and currents open data platform. The validated version of the data is used in this study. Wave height, period, and direction were obtained from the Coastal Data Information Program (CDIP) Grays Harbor Waverider buoy (station 46211; Figure 1a) from the NOAA National Data Buoy

Figure 3 :

 3 Figure 3: Timeseries of: (a) Signicant wave height, Hs (m); (b) Peak wave period Tp (s); and (c) Mean water level (m) relativeto the NAVD88 datum. The shaded areas indicate when the Lidar was recording during mid-and high tides, which corresponds to periods when there was swash interaction with the revetment (from collision regime to overwash regime,[START_REF] Sallenger | Storm impact scale for barrier islands[END_REF]). Times are given in Pacic Time (GMT-8).

Figure 4 :

 4 Figure 4: Example of "swash" and "bed" extraction over a four-minute window, extracted at 07:48 during the 18/01/2019 high tide, at (a) x = 1 m, (b) x = 4.4 m, (c) x = 9.4 m and (d) x = 14.4 m. Blue lines represent the "swash" timeseries, red lines the "bed" timeseries and dashed black lines the continuous and "interpolated bed" timeseries. The position of each cross-shore point presented in (a-d) are shown by red bar on (e), where a cross-section of the revetment after 22/1-10h tide is shown. The dark and light shaded area represent respectively the pure cobble layer and the mixed sand and cobble layer found above pure sand.

  245 2.4.3. Net cross-shore mass ux

Figure 5 :

 5 Figure5: Change in bed-level through the swash zone during the example tide, measured using the lidar (the magnitude of x increases in the oshore direction). The dashed and solid lines represent the runup limit and the mean shoreline position respectively. The colour scheme represents net bed-level change in metres relative to the revetment face morphology at the start of the timeseries.

Figure 7 .Figure 6 :

 76 Figure 7. In this gure, the "net" and "gross" rate of bed volume change as dened in Bayle et al. (2020) is used. The "net" volume change (per metre width) per second represents the rate of volume change over ten minutes, denoted dV 10 , which is eectively the mean rate of change over ten minutes.The "gross" volume change (per metre width) per second, denoted dV , is quantied by summing the

Figure 7 :

 7 Figure 7: Top panels: Gross (lled circle) and net (empty circle) rate of bed volume change in m 2 /s, per 10 minutes windows

Figure 8 :

 8 Figure 8: Time series of the signicant wave height (black dots) and water depth (red line) at the toe of the revetment. These two variables were derived from the Lidar measurements when interaction between the revetment and wave/swash occurred (grey shaded areas).

Figure 9 :

 9 Figure 9: Contour plot showing the distribution of the percentage of time that the bed is inundated, ti as a function of time during the example tide. Percentage of bed inundation was calculated as a ten-minute average. The dashed white and thick black lines represent the runup limit and the mean shoreline position respectively.

Figure 10 :

 10 Figure10: Percentage occurrence of event mass uxes grouped in terms of percentage inundation, ti for all tides recorded by the lidar. The number of swash events n used for each histogram is included on the plot, and is relatively high due to the spatial coverage of the lidar, which gives one data point every 0.1 m.

Figure 11 :

 11 Figure 11: (a) Skewness of event mass ux distribution induced by all detected swash events; (b) mean magnitude (histogram) and standard deviation (error bar) of event mass ux; and (c) mean event mass ux, as a function of percentage inundation, ti for all tides recorded by the lidar.

Figure 12 :

 12 Figure 12: Mean and standard deviation (error bar) of the maximum depth of swash measured per 15 s window of swash duration.

Figure 13

 13 Figure 13: (a) Skewness of mass ux induced by all detected swash events; (b) mean magnitude (histogram) and standard deviation (error bar) of mass ux; and (c) Mean mass ux, as a function of the maximum depth of individual swashes. Note that the bin size increases by 0.05 m and are shown for every other tick.

Figure

  Figure13bpresents the bulk mean magnitude and standard deviation of the mass uxes (kg/m/s)

Figure 14 :

 14 Figure 14: (a) Timeseries of net cross-shore mass ux for the example tide at two and ten-minute intervals, at x = 12.5 m. Contour plots of net cross-shore mass ux during the example tide summed over (b) two-minute and (c) ten-minute time windows. Notethat 2 minutes was chosen as it represents the longest swash event recorded. The dashed thick line (violet) marks the cross-shore percentage of inundation limit of the ux oscillations (e.g., manually estimated cross-shore limit landward of which bed oscillations are minimal in (c)), at ti = 40 % for the example tide. The dashed and solid lines represent the runup limit and the mean shoreline position respectively. Note that the colour bar scale ranges between ±150 kg/m in (b) and ±200 kg/m in (c).

Acknowledgements

Funding: Paul Bayle is supported by a PhD scholarship through the EPSRC CDT in Water Informatics: Science & Engineering (WISE). Travelling and living fees associated with this experiment were

partially covered by a Santander Mobility Grant, obtained via the University of Bath.

The authors want to thank the entire Washington Department of Ecology CMAP team, for their logistical support in the eld. The authors would also like to thank the community of North Cove for their warm welcome and support throughout the experiment. Special thanks to Richard and Dianne Harris for providing a warm and dry place during the experiment, and to Connie Allen for organising