# Meteorological Conditions Influence the Migration of a Marine Dune Field in the Southern North Sea

Noémie Durand, Pablo Tassi, Olivier Blanpain, Alice Lefebvre

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Noémie Durand, Pablo Tassi, Olivier Blanpain, Alice Lefebvre. Meteorological Conditions Influence the Migration of a Marine Dune Field in the Southern North Sea. Journal of Geophysical Research: Earth Surface, 2025, 130 (1), 10.1029/2024JF007731. hal-04872799

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Distributed under a Creative Commons Attribution 4.0 International License
JGR Earth Surface

RESEARCH ARTICLE

10.1029/2024JF007731

**Special Collection:**
Marine and River Dune Dynamics

**Key Points:**

* A numerical model is developed and applied to a real site to study the propagation of marine dunes for the first time in 3D on a large scale

* Under real-life conditions wind forcing is shown to have just as great an effect on dune migration as tidal forcing

* Counter-prevailing winds can temporarily reverse the migration of large marine dunes while maintaining their asymmetry

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

N. Durand, noedurand@openbook.team

**Citation:**

Durand, N., Tassi, P., Blanpain, O., & Lefebvre, A. (2025). Meteorological conditions influence the migration of a marine dune field in the southern North Sea. *Journal of Geophysical Research: Earth Surface, 130*, e2024JF007731. https://doi.org/10.1029/2024JF007731

Received 11 MAR 2024

Accepted 26 NOV 2024

**Author Contributions:**

**Conceptualization:** Noémie Durand

**Data curation:** Noémie Durand

**Formal analysis:** Noémie Durand

**Investigation:** Noémie Durand

**Methodology:** Noémie Durand

**Project administration:** Alice Lefebvre

**Resources:** Noémie Durand

**Software:** Noémie Durand

**Supervision:** Pablo Tassi, Olivier Blanpain, Alice Lefebvre

**Visualization:** Noémie Durand

**Writing – original draft:** Noémie Durand

© 2025. The Author(s). This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Meteorological Conditions Influence the Migration of a Marine Dune Field in the Southern North Sea

Noémie Durand¹,² ID, Pablo Tassi²,³ ID, Olivier Blanpain¹, and Alice Lefebvre⁴ ID

¹France Energies Marines, Brest, France, ²LHSV, ENPC, Institut Polytechnique de Paris, EDF R&D, Chatou, France, ³EDF Recherche & Développement, Chatou, France, ⁴MARUM, University of Bremen, Bremen, Germany

**Abstract** A field of marine dunes has been studied in the Southern Bight of the North Sea. These large dunes, 1–5 m in height and several hundred meters in length, are highly mobile: migration rates of up to 30 m/year have been observed in places. The area is dominated by tides and is characterized by strong currents. Winds are predominantly from the southwest and, to a lesser extent, from the north. A large-scale 3D numerical model was used to simulate the migration of this dune field over time. It is based on the process-based opentelemac system. The model has been calibrated and validated against in situ bathymetric data and is therefore suited to our objective: to explore the contribution of weather (wind and atmospheric pressure) to the propagation of large marine dunes, in relation to that of tidal currents. To do this, a 4-month period was simulated, with and without meteorological effects being taken into account in the numerical model. The results highlight the fundamental role of wind conditions in an accurate representation of seabed changes over time. They also show how meteorological events that are different from the prevailing conditions influence the short-term evolution of the dune field.

**Plain Language Summary** Marine dunes are large sedimentary formations, typically 1–5 m high, which run transversely to the flow and are highly mobile. They are found all over the world, in a wide variety of environments, including in shallow shelf seas such as the North Sea. Their presence poses problems for marine renewable energy projects located there. It is therefore crucial to be able to simulate their evolution over time. A large-scale computer model has been developed to represent a field of marine dunes off the coast of Dunkirk, France. The model reproduces the migration observed after 4 months. It was then run with the tide alone and with the tide + meteorological effects. This allows us to determine the contribution of wind-induced currents compared with tide-induced currents to the dynamics of large marine dunes. The results show that the migration of the marine dunes is intimately related to the amplitude and direction of the residual flow, which are influenced by wind conditions. Meteorological forcing is necessary to obtain an accurate representation of seabed changes over time. Although winds that are different from the prevailing winds may temporarily reverse the general migration trend, they are too sporadic to fundamentally alter the sedimentary dynamics of the area.

1. Introduction

Large dynamic sedimentary bedforms are common on the seabed of shallow shelf seas around the world. The North Sea is one of the better studied shelf seas (Besio et al., 2004; Games & Gordon, 2014; Terwindt, 1971), but these bedforms have also been documented in the Irish Sea (Creane et al., 2022; van Landeghem et al., 2009), the Bisanseto Sea in Japan (Katoh et al., 1998), the Taiwan Strait (Zhou et al., 2020), the Banks Strait north of Australia (Auguste et al., 2021), or south of Martha's Vineyard in Massachusetts (Pessanha et al., 2023) to name but a few. They are sometimes referred to in the literature as sand waves. We call them large marine dunes according to Ashley (1990)'s classification, reproduced in Table S1 in Supporting Information S1, and in opposition to fluvial or even aeolian dunes (Courrech du Pont et al., 2024). Large marine dunes are present in areas where many European offshore wind farms (OWFs) are currently located, or are planned to be located (https://map.4coffshore.com/offshorewind/). Constantly reshaped by flow, they present a challenge for the design (Whitehouse et al., 2000), implementation (Barrie & Conway, 2014), safety and maintenance (Games & Gordon, 2014; Langhorne, 1977; Németh et al., 2003) of marine renewable energy systems. Therefore, it is essential to understand the controlling environmental parameters and to predict the large-scale evolution and migration of marine dunes.
Writing – review & editing: Pablo Tassi,
Olivier Blanpain, Alice Lefebvre

Large marine dunes develop almost exclusively on sandy seabeds (Besio et al., 2003; R. Bijker et al., 1998; Hulscher & van den Brink, 2001; Terwindt, 1971), where near-bed currents are sufficiently strong to entrain, transport and deposit sediment particles. They form and grow as a result of tidal movements (Hulscher, 1996) in conjunction with the composition and availability of sediments and local topography. They migrate as a result of tidal asymmetry and/or a residual flow (Fredsøe & Deigaard, 1992; Németh et al., 2002; van Gerwen et al., 2018).

The role of residual flows in the formation and evolution of marine dunes has been studied numerically using idealized models for the most part. Németh et al. (2002) developed the linear stability model of Hulscher (1996) to explore two mechanisms capable of generating a residual flow: wind, and pressure gradient. They found that, for an equivalent residual flow (0.1 m/s in their Figure 3), a higher migration speed was obtained from a pressure gradient than from a surface wind stress. They suggested that tidal asymmetry due to higher harmonics would also trigger dune movement, but to a lesser extent. Besio et al. (2004) superimposed a steady current on a tidal current, considering only the M2 and M4 tidal constituents. They showed that the direction of movement of the marine dunes was controlled by the relative strength of the two components of the current and by the phase difference between the tidal constituents. In this respect, it could differ from the direction of the steady current. van Gerwen et al. (2018) adopted the idealized two-dimensional, vertical (2DV) model developed by Borsje et al. (2013, 2014) to study the growth of marine dunes towards equilibrium. They found that the bedforms are shaped by residual flows and travel in their direction. Stronger residual flows resulted in higher migration speeds and lower equi-librium dune heights.

Campmans and co-authors specifically studied the influence of wind (and wave) climate(s) on the evolution of marine dunes using linear and non-linear idealized models. They identified that even a small proportion of storms in the year had a noticeable impact (Campmans, Roos, de Vriend, & Hulscher, 2018) and that the seasonal variability of the climate was reflected in the seasonal variability of dune dynamics. Migration speeds tend to be higher (and growth rates lower) during the winter months than during the rest of the year (Campmans, Roos, Schrijen, & Hulscher, 2018). With a lookup table approach, they further estimated that average wind and wave conditions accounted for 2/3 of the migration, while extreme wind and wave conditions made a modest contri-bution. More recently, Overes et al. (2024) have investigated the role of time-varying, non-tidal currents in a process-based 2DV model and concluded that these types of currents can substantially increase sediment erosion and accretion patterns, used as an indicator of dune migration. These conclusions are corroborated by field ob-servations, which indicate that the long-term migration of dunes is primarily determined by the strength of the residual flow. However, meteorological events directly affect their short-term evolution. Depending on their di-rection relative to the background currents, wind-induced currents have been shown to deflect (Krewinkel, 2017), increase, slow down (Le Bot & Trentesaux, 2004), or even reverse the effect of tidal currents on dune migration (Harris, 1989, 1991; Lanckneus & De Moor, 1991).

These numerical studies are insightful but do not represent real-life settings. In nature, marine dune fields are not always regular trains of dunes with linear crests (Figure 1). Their morphology and evolution react to spatial and temporal variations in hydrodynamic conditions. For these reasons, attempts have been made in recent years to move away from idealized geometries (e.g., sinusoidal dunes, transects) and schematized forcing (e.g., simplified tidal flow and/or representative winds). Auguste et al. (2021) explored sensitivities of very large marine dunes to environmental parameters in Banks Strait, Australia. Creane et al. (2023) studied sediment transport pathways at Arklow Bank in the Irish Sea. Both used climate reanalysis data to provide realistic wind and wave forcing. Both used a depth-averaged, horizontal (2DH) modeling approach. Krabbendam et al. (2023) and Nnafie et al. (2023) were among the first to use a three-dimensional (3D) modeling approach. They developed local-scale models (3 km × 3 km) of specific dune fields in the southern North Sea to examine their response to background topography and sediment availability. The representation of tidal forcing is still relatively simple (4 constituents) and meteorological forcing is not taken into account. Pessanha et al. (2023) used a hybrid approach, in which a depth-averaged model of a larger area provided flow conditions for a very local 3D model (estimated around 500 m × 500 m, not specified by the authors) off Martha's Vineyard in the USA. The large-area model is driven by sea levels extracted from a regional ocean tide model and by wind and wave conditions derived from in situ observational data.

The modeling of marine dunes in three dimensions is still at an early stage, all the more if the aim is to model the evolution of dunes on a large scale, with input data that accurately simulate the conditions experienced in situ. We have developed and validated a complex process-based 3D model with real(istic) input for an area offshore
<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) General location map. The footprint of the proposed offshore wind farm is marked by a dashed black line; the extent of the numerical model is marked by a dashed colored line. (b) Location of 2019–2021 bathymetric survey tiles in relation to known bathymetric features (Source of the background data: Shom 2015, https://opentopomap.org/, and European Environment Agency shoreline). (c) Close-up view on tile #1 in the navigation channel showing bed levels in November 2019 (Source of the data: FEM, 2021a). Dune profiles are extracted along section a'-a'.</figcaption></figure>

Dunkirk, in the Southern Bight of the North Sea (Figure 1), where large marine dunes are present. Recent metocean and bathymetric data are available. The observations reveal that the dunes behave differently for periods of (approximately) the same duration. Their evolution is irregular over time, which we hypothesize is due to
the influence of meteorological forcing on tidal forcing. Therefore, the model is used to explore the link between meteorological contributions and the migration of large marine dunes (for time scales of the order of months and space scales of the order of meters to kilometers).

In the next section, we present the study area in the southern North Sea and the in situ data relevant to this work. A description of the 3D morphodynamic numerical model follows. Simulations are carried out with tidal forcing only, then adding wind and atmospheric pressure contributions. The results of these simulations are presented in Section 3 and the implications discussed in Section 4. Section 5 concludes this work.

## 2. Study Area and Methods

### 2.1. Study Area and In Situ Data

Dunkirk is located on the northern coast of France, open to the Southern Bight of the North Sea (Figure 1a). The region is home to a complex network of large bedforms, ranging from flow-transverse marine dunes to flow-parallel sandbanks. The seabed there is relatively shallow: bed levels shallower than 30 m below Mean Sea Level (MSL) extend as far as ca. 20 km from the coastline. The region is characterized by a semi-diurnal, macro-tidal regime, with a spring tidal range of the order of 5.5 m (Shom, 2020), and flood currents generally stronger than ebb currents.

#### 2.1.1. Metocean Surveys

Site-specific meteorological and hydrodynamic campaigns have been conducted in recent years (2016–2022) for the Dunkirk OWF project and for research purposes. These records complement the information presented by others (e.g., Latapy, 2020; Tresca, 2013) to qualify the environmental conditions offshore Dunkirk.

Current velocities were measured in September 2016 (Nortek AWAC and AQUADOPP) (Shom, 2021a) and in May–June 2021 (Nortek Signature500, Signature1000 and Vector) (FEM, 2021b). The instruments were mounted on rigid frames and lowered on the seabed, just outside the navigation channel to the port of Dunkirk, and within the footprint of the proposed OWF (Durand et al., 2022a). The Acoustic Doppler Current Profilers (ADCP) were set up to measure the current characteristics throughout the water column, every 50 cm, 1 m or 2 m depending on depth and instrument. Near-surface currents are typically not measured, nor are near-bed currents, due to the configuration of the deployment and the blanking zone of the instrument. This was remedied by using Acoustic Doppler Velocimeters (ADV) positioned close to the seabed. Acoustic Surface Tracking data were collected during the 2021 campaign, concurrently with velocity and pressure data, to derive sea levels.

The flow is aligned with geographical features and topography, trending approximately east-northeast during the flood cycle and west-southwest during the ebb cycle. Current reversal does not occur at high or low tide but 3–3.5 hr later, around MSL. Peak flood currents are stronger than peak ebb currents in the approach channel to Dunkirk (depth-averaged speed of up to 1.2 m/s vs. 0.8 m/s), resulting in a net current toward the east there. This is in line with current knowledge, on a regional scale, in the southern North Sea. However, the predominance can be reversed locally in favor of ebb currents (Héquette et al., 2008; Vicaire, 1991). This is the case, for example, within the OWF footprint and the sandbank system. Tidal currents are modified by meteorological effects that enhance or abate (even suppress) them depending on the wind direction with respect to the current direction.

The winds offshore Dunkirk have a very distinct seasonality (Guerber et al., 2008). Long-term wind data (1997–2021) measured 10 m above the water surface with a Vaisala anemometer WAA151 and a Vaisala wind vane WAV151 were obtained from the Westhinder platform, located approximately 30 km from the coast (VLIZ, 2022). The prevailing wind direction is southwesterly, in line with the general atmospheric circulation and the Atlantic pressure fronts moving east. These winds blow parallel to the general orientation of the coastline at Dunkirk, with the flood and against the ebb. However, in spring, there is a high proportion of cold northeasterly winds, fed by high pressure over Scandinavia. These winds blow with the ebb and against the flood. Further analysis of the data shows that gales account for 9.2% of the records. These high wind events (wind speed >14 m/s, corresponding to Beaufort Scale 7 and above) come mainly from the southwest (50.8%, maximum of 30 m/s), and only marginally from the northeast (4.5%, maximum of 22 m/s).
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Dune profiles along section a'-a", in tile #1, showing the evolution observed in situ between November 2019 and July 2021. Flood currents flow from left to right.</figcaption></figure>

### 2.1.2. Bathymetric Surveys

Eight bathymetric surveys (S1 to S8) have been carried out between 2019 and 2021 using an R2 Sonic 2024 broadband multibeam echo sounder supplemented by a Trimble BD982/960 GNSS receiver module (positioning system) (FEM, 2021a). The surveys covered three predefined areas selected for the diversity of bedforms encountered: (a) in the approach channel (1000 × 500 m², extended to 1900 × 500 m² for S7 and S8), (b) immediately north of the Breedt sandbank (1000 × 500 m²), and (c) on the slopes of the Binnen Ratel sandbank (850 × 750 m²). The general location of the bathymetric tiles is shown in Figures 1a and 1b. Figure S1 in Supporting Information S1 illustrates the terminology used in this article with a schematic cross-sectional view of a marine dune.

Digital Terrain Models (DTMs) were constructed by the surveyor for each data set at a resolution of 0.5 m (margin of error for position and depth ≈0.05 m estimated using the A-priori Multibeam Uncertainty Simulation Tool). The DTMs document the evolution of the dune fields off Dunkirk over successive periods ranging from 1 month to 4.5 months. At times, the morphology of the dunes changes, resulting in an apparent migration of the crest, while at other times the body of the dunes moves as a whole. This is illustrated for tile #1 along section a'-a" in Figure 2. There, the dunes are highly mobile during the S1-S2 period (compared with S3-S4 and S6-S7 of similar duration). During this period, the dunes travel about 15 m to the east while retaining their morphology. On the contrary, the steep slopes of the dunes become gentler during periods S2-S3 and S7-S8. Overall, the dunes in tile #1 have been observed to migrate at a net speed reaching 30 m/year (Le Bot et al., 2023). By and large the patterns and rhythms of dune evolution are similar in tile #3, but the dunes are noticeably less mobile.

A total of 19 bed samples were collected in bathymetric tiles #1 and #2, and in the OWF area, with a Sipek sediment grab sampler on 23 October 2019 and again on 17 May 2020 (FEM, 2020). The samples were analyzed by sieving using opening diameters between 63 µm and 12.5 mm. This provides information on the surficial grain size distribution. There is little evidence of spatial or seasonal trends from these limited data. The majority of samples (89%) have a unimodal distribution. The sediments are reasonably well-sorted slightly gravelly and gravelly sands (USCS) with median grain sizes $d_{50}$ between 240 µm and 450 µm. These grain size parameters are in general agreement with the data compiled by the Shom in recent years (Shom, 2021b).

### 2.2. Model Set-Up and Validation

The opentelemac system (www.opentelemac.org) is applied to Dunkirk and its approaches to study the propagation of the marine dune field in response to environmental parameters. To this end, hydrodynamic and morphodynamic models of the area have been developed, independently calibrated and validated, then internally coupled.
The same computational domain and spatial discretization are used throughout. The domain covers ca. 80 km of coastline, from Calais in the west to Ostend in the east. Its offshore extent varies between ca. 15 km in the west and 75 km in the east (dashed colored line in Figure 1a). One of the strengths of the opentelemac system lies in its use of an unstructured finite element mesh. This allows a spatially variable resolution to be defined, focusing on areas of interest and relaxing the resolution away from these areas. A horizontal mesh size of ca. 10 m is used to represent the bathymetric survey tiles where our aim is to reproduce the evolution of the dune field over time. This spatial resolution was shown to adequately capture variations in the seabed at the scale of marine dunes, while limiting computational cost. Five planes were used in the vertical. Vertical resolution is described in Section 2.2.3 in relation to the choice of the sediment transport predictor. Several seabed maps have been constructed for different modeling purposes, based on the most relevant data available for each time period.

### 2.2.1. Hydrodynamics

TELEMAC-3D, the 3-dimensional (3D) hydrodynamic module of the opentelemac system, solves the Navier-Stokes equations without the hydrostatic pressure assumption (Hervouet, 2007). Bed friction is parameterized with a Nikuradse roughness. Typically, bedform roughness is added to grain roughness to implicitly account for secondary bedforms that large-scale models cannot resolve. However, in this application, secondary bedforms are not present throughout the entire computational domain. Therefore, we only considered skin roughness and adopted a value of $k_s = 2.5 \times d_{50} = 862.5$ µm (Soulsby, 1997), based on a grain size representative of the region. Horizontal and vertical turbulence scales are differentiated in TELEMAC-3D. We adopted a constant kinematic viscosity ($10^{-6}$ m²/s) in the horizontal direction, and the Tsanis mixing length model in the vertical direction (Tsanis, 1989).

Time-varying tidal sea levels are applied along the open water boundaries of the model from the FES2014 global atlas of ocean tides (Lyard et al., 2021). These astronomical levels are devoid of other influences (e.g., meteorological) and are therefore corrected for the “inverted barometer” effect caused by variations in atmospheric pressure relative to 1 atm. In addition, spatially and temporally varying wind and atmospheric pressure fields (Bouttier, 2007) are applied over the computational domain to account for this effect as well as set-up and surface currents caused by wind blowing over the water surface.

The calibration and validation of the hydrodynamics is performed in two steps. The first step demonstrates the ability of the model to simulate the astronomical tide. The second step demonstrates the ability of the model to reproduce the non-tidal effects by adding wind and atmospheric pressure contributions (Durand et al., 2022b). For each step, the model predictions are compared over a complete spring-neap tidal cycle with sea levels (calibration) and with depth-averaged currents (validation). In step 1, the model predictions are compared with synthesized data obtained by tidal harmonic analysis (Codiga, 2011) to remove the non-tidal components from the observed records. In step 2, the predictions are directly compared with the measurements. An “excellent” performance of the model as a whole was obtained according to the classification scheme proposed by Sutherland et al. (2004) (RMAE < 20%) (Durand et al., 2023b). The interested reader is referred to Appendix A and Texts S1 and S2 in Supporting Information S1 for more details on the formulation, development and validation of the hydrodynamic model.

### 2.2.2. Prevailing Sediment Transport Mechanisms

Validated numerical models are useful to overcome the spatial and temporal limitations of field observations. Durand et al. (2023b) have produced sediment mobility maps from oceanographic considerations, on the basis of a 2-year simulation with this validated hydrodynamic model and a validated wave model of the same area (Durand et al., 2022a). These maps refine our understanding of the dominant sediment transport processes in the region and justify modeling assumptions.

Bedload is identified as the prevailing mechanism of sediment transport based on an analytical indicator, the Rouse number $P = w_s/\kappa u_*$ > 2.5 throughout the computational domain ($w_s$ the sediment fall velocity, $\kappa$ the von Kármán constant, $u_*$ the friction velocity) (Fredsøe & Deigaard, 1992). This is consistent with the findings of Borsje et al. (2014) and Damen et al. (2018) on the Dutch continental shelf.

Tides are identified as the main driving force overall, and in particular for water depths >15 mMSL. This analysis uses a classification scheme (Porter-Smith et al., 2004) based on the relative ability of currents and waves,
separately, to mobilize sediment from the seabed. The role of waves is however highlighted at the top of the sandbanks, where wave orbital velocities are higher due to shallower water depths.

### 2.2.3. Sediment Transport and Bed Evolution

GAIA is the morphodynamic module of the opentelemac system (Tassi et al., 2023). A unimodal distribution with a median grain diameter of $d_{50} = 345$ µm, and $d_{90} = 1$ mm is adopted, in accordance with the uniform bed samples collected in situ in recent years. In the absence of site-specific values, we assume a sediment density of 2650 kg/m³, an angle of repose of 32°, and a porosity of 40%.

Following the results of the site analysis by Durand et al. (2023b), which indicate that sediments are predominantly mobilized by the strong tidal currents in our areas of interest (depths > 15 mMSL), we omit the contribution of the waves and GAIA is internally coupled with TELEMAC-3D alone to provide the hydrodynamic conditions that drive the sediment transport processes. The suspended load is not treated explicitly by an advection/diffusion equation for sediment concentration in the water column. Bedload fluxes are computed, which participate in the sediment continuity equation (Exner equation) to determine the evolution of seabed levels at each point in the computational domain. We do not apply a morphological acceleration factor in the simulations.

Various formulations of the sediment transport rate have been proposed for sands and the coastal environment (Bailard, 1981; E. W. Bijker, 1968; Dibajnia & Watanabe, 1996; Soulsby, 1997; Soulsby & Damgaard, 2005; van der A et al., 2013; van Rijn, 2007). Several of these predictors have been investigated in a preliminary phase, in a small flume-like representation of tile #1 (Durand et al., 2023a). These tests have shown that the Soulsby-van Rijn total load predictor (hereafter SvR97, Equation A6 in Appendix A, based on depth-averaged velocities) is as capable of reproducing the dune migration as a formalism based on shear-stresses. This may be explained by energy arguments. Dune migration is predicted very satisfactorily in tile #1 (Anomaly Correlation Coefficient (ACC) of 95%) when a scaling factor is applied. As the predictor is based on depth-averaged velocities, the number of vertical levels can be relatively small in the model to limit the computational cost. We used five irregularly spaced sigma planes, one for the seabed, one for the water surface, with intermediate planes defined at approximately 1/6th, 1/3rd and 2/3rd of the water column.

The local slope of the seabed can influence both the magnitude and the direction of bedload transport. The transport rate can be corrected accordingly. The correction proposed by Koch and Flokstra (1980) is the only parameterization in the morphodynamic module GAIA that is consistent with the use of the SvR97 predictor. It modifies directly the bedload transport rate and acts as a diffusion term in the bed evolution equation. Durand et al. (2023a, for a small flume configuration) conclude that taking into account the slope effect is detrimental to the good performance of the model: the dunes subside and decay rapidly over time. We have had the same experience in our large-scale model, and the correction for the local seabed slope is left out in our simulations.

The morphodynamic model is calibrated by comparing its predictions after 4 months with bed levels extracted from the 2nd bathymetric survey S2 along section a'-a" (see Figure 1c for location). Figure S3 in Supporting Information S1 presents the results of the calibration. The model is validated by comparing its predictions to a greater spatial extent than that of the transect: in bathymetric survey tile #1 and tile #3. Its performance is also assessed for longer time scales of the order of 1 year (up to S5). While the shape of the dunes tends to become more symmetrical over time in the model, their height and migration speed are reproduced satisfactorily. So are the patterns of evolution, including the slower dynamics observed in tile #3 compared with tile #1. The interested reader is referred to Appendix A and to Text S3 in Supporting Information S1 for more details on the formulation, development and validation of the morphodynamic model.

### 2.3. Simulated Scenarios and Analysis of Results

To determine the role of weather (wind and atmospheric pressure) in the evolution of large marine dunes, we have simulated a one-year period between the first bathymetric survey (S1, 17-Nov-19) and the fifth survey (S5, 5-Dec-20). Case I only considers tidal forcing. Weather contributions are added in the form of time- and space-varying wind and atmospheric pressure fields in Case II (validated model configuration). All other model settings are identical between Case I and Case II simulations. In this article, the analysis of the results focuses on the 4-month period between S1 and S2 (17-Mar-20), as this is one of the most active periods. We will refer to this period as "Winter 2020" in the remainder.
<table><caption>**Table 1**
*Overview of Model Simulations*</caption><thead><tr><th></th><th>Analysis period</th><th>Weather contributions</th></tr></thead><tbody><tr><td>Case I</td><td>17-Nov-19 to 17-Mar-20</td><td>No</td></tr><tr><td>Case II</td><td>17-Nov-19 to 17-Mar-20</td><td>Wind and atm. Pressure</td></tr><tr><td>Case III</td><td>25-Sep-20 6 a.m. to 28-Sep-20 9 p.m.</td><td>No</td></tr><tr><td>Case IV</td><td>25-Sep-20 6 a.m. to 28-Sep-20 9 p.m.</td><td>Wind and atm. Pressure</td></tr><tr><td>Case V</td><td>18-Sep-20 6 a.m. to 21-Sep-20 9 p.m.</td><td>Wind and atm. Pressure 7 days ahead</td></tr></tbody></table>

To explore specifically how meteorological events from a direction opposite to that of the dominant sediment transport affect dune dynamics, a sustained storm from the northwest was considered. For this, we have simulated the period between bathymetric surveys S4 (31-Aug-20) and S5 (5-Dec-20), without (Case III) and with (Case IV) wind and atmospheric pressure contributions. The analysis focuses on the period around the storm: from 25-Sep-20 6 a.m. to 28-Sep-20 9 p.m. (referred to as the “September 2020 storm” in the following). The storm coincides with a neap tide. A hypothetical case (Case V) was developed, in which the storm coincides with the previous spring tide, by shifting the wind and atmospheric pressure fields 7 days forward compared to Case IV. This simulation was run for a shorter duration, until the end of September 2020.

An overview of the model simulations is presented in Table 1.

### 2.3.1. Assessment of Residual Flow

Bedload transport is approximately proportional to the Shields parameter raised to the power of 3/2 (or the current speed cubed). Therefore, any inequality in the currents results in inequalities in bedload transport. This leads to net sediment transport in the dominant direction, provided the threshold of motion is exceeded. In shallow shelf seas, the tidal wave is distorted due to topographic effects. This process and the interaction between tidal constituents cause an asymmetry of the tidal wave. The flood tends to dominate (faster currents) and the ebb to subordinate (slower currents) (Reynaud & Dalrymple, 2012). This inequality in the ebb and flood currents can be further influenced by other currents such as wind-induced or geostrophic currents.

The peak velocity asymmetry, $V_a$, is sometimes used as a marker for tidal asymmetry (e.g., Pessanha et al., 2023). Le Bot and Trentesaux (2004) define $V_a$ as the difference between the flood velocity peaks and the ebb velocity peaks and use it, in combination with the strength of wind-driven currents, to explain the types of dune morphology in the Dover Strait. We find this parameter incomplete because it does not take into account the duration of the flood and ebb phases. Albeit faster, the flood is also shorter in duration than the ebb off Dunkirk, and this has an impact on sediment transport rates.

Instead, we use the total residual flow as a marker with which to assess the effect of meteorological conditions on dune migration and we calculate a rolling average of the current velocities over the period of the main tidal cycle (the M2 component in this application) (Davies & Robins, 2017). Three iterations of a 12-hr boxcar filter are needed since the hourly resolution of the model output does not allow the average to be calculated over an exact tidal cycle (=12 hr 25 min). Diurnal oscillations are still apparent in the analysis. Although this marker has limitations (such as not accounting for the non-linearities introduced by a threshold of motion and the power of 3), it serves as a simple indicator based solely on hydrodynamics, without any prior assumptions about the sediment transport predictor.

### 2.3.2. Assessment of Dune Migration

The evolution of the seabed over a given period is obtained from in situ observations and model predictions by subtracting the initial DTM from the final DTM, and is represented in the form of a difference map. This map identifies areas of erosion and accretion resulting from the migration of the bedforms. The larger the erosion/ accretion footprint, the further a bedform has moved from its initial position.

Although this type of analysis provides information on the direction of migration of the marine dunes, it does not quantify the distance they travel (or their migration speed). Therefore, seabed profiles are extracted along sections
a'-a" in tile #1, and along sections b'-b" and c'-c" in tile #3 (see Figure 4 for location). These latter transects are selected because they illustrate the variability of dune morphologies and sediment transport patterns on the slopes of the sandbank, toward the top (b'-b") and bottom (c'-c"), where water depths are greater. Section b'-b" is drawn more or less perpendicular to the crest of the large dunes. This was not possible for section c'-c" given the constraints (size and shape) of the bathymetric survey tile (see Figure 4).

Many authors have quantified the speed of dune migration from the ratio of crest displacement to time (including Le Bot et al., 2023, from these bathymetric survey data). However, changes in the position of the crest may result from changes in dune morphology alone, without migration of the dune as a whole. This is illustrated in Figure 2 between surveys S3 and S4 for example. In this context, it may be more appropriate to consider the mid-point of the steep face of the dune, rather than the crest, as a marker of dune migration (Dong, 2015). This is the approach we adopt here. A spline is fitted to the seabed levels predicted by the model to add the resolution lacking from the model mesh (from 10 m to 1 cm resolution). The mid-point is taken to be half-way between the highest and the next lowest seabed levels (Figure S1 in Supporting Information S1). Its horizontal displacement is divided by the model output time step to obtain an hourly migration speed expressed in m/yr. We have restricted this analysis to the second crescent-shaped dune in tile #1, where it crosses section a'-a".

# 3. Results

## 3.1. Winter 2020: Cases I and II

### 3.1.1. Evolution of the Seabed

The seabed evolution predicted in tile #1 is depicted in Figure 3: in panel (b) for Case I and in panel (c) for Case II. In these maps, shades of blue indicate a lowering of the seabed (erosion), and shades of brown indicate a rising of the seabed (accretion) at the end of the 4-month period. The same color scale is used throughout to enable direct comparisons. A 100 m resolution grid is superimposed on the difference maps to facilitate the georeferencing of seabed features and their evolution. The changes observed in situ during the same period are presented in panel (a) for reference.

The migration of the large dunes is directed to the east, in line with the orientation of the navigation channel. The most significant changes occur to the north of the channel (upper half of the survey tile). A maximum bed level variation of +2.5 m, and a minimum variation of -1.3 m, are predicted for Case I. These variations are associated with the two crescent-shaped dunes and the sinuous dune that follows them, noting that these dunes are also the highest in tile #1 (2-3 m in height). The changes are more pronounced for Case II, where a maximum bed level variation of +3.4 m is predicted for the westernmost crescent-shaped dune, and a minimum of -1.9 m for the sinuous dune. Modest changes are predicted in both cases for the smaller dunes further east, which are around 1 m high.

The seabed evolution predicted in tile #3 is depicted in panels (b) and (c) of Figure 4 for Cases I and II respectively. The seabed is markedly less mobile than in tile #1. For Case I, most of the changes are predicted to occur at the northern end of the tile, past section c'-c", where the water is deepest. The maximum bed level variation over the 4-month period is ±1.1 m. Remarkably, these dunes migrate to the southwest, as indicated by the brown shades below the blue shades in Figure 4b. This is in agreement with the direction of the local residual flow, which in this simulation is directed to the southwest at the bottom of the Binnen Ratel sandbank, turns about the -21 m MSL isocontour and is directed to the east on the slopes of the sandbank (not shown in this article). This is not in agreement with the observations (panel (a)). In the remainder of the area, at water depths of less than 21 m, changes in seabed elevation of the order of -0.2/+0.6 m are predicted at most. For Case II, the seabed is more mobile on the slopes of the Binnen Ratel sandbank (water depths shallower than ca. 16 m, top right of the figure) than further down toward the natural channel between the Binnen Ratel sandbank and the Dyck Oriental sandbank (bottom left of the figure). On the slopes, the largest predicted bed level variations after 4 months are -1.9/+2.7 m. They are of the order of -0.5/+0.7 m to the north of the bathymetric survey tile, in the channel. It is interesting to note the moderate changes in seabed elevation predicted by the model between the large dunes. These fluctuations are also observed in the bathymetric survey data (panel (a)) and are attributed to the migration of secondary bedforms at a 20-40° angle to the orientation of the large dunes, identified by dark blue lines in Figure 4c.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a) Observed bathymetric changes, calculated as the difference between final seabed levels (S2, 17-Mar-20) and initial seabed levels (S1, 17-Nov-19) in tile #1. (b) Predicted bathymetric changes for Case I. (c) Predicted bathymetric changes for Case II, for which meteorological contributions are added in the model predictions. Shades of blue indicate lowering of the seabed (erosion) and shades of brown indicate rising (accretion).</figcaption></figure>

The propagation of small dunes or ripples (0.2–0.6 m high and 5–10 m long) is apparent in the in situ observations both in tile #1 (lower diagonal in Figure 3a) and in tile #3 (between dunes in Figure 4a) whereas model predictions indicate no movement in these regions. This is because these small bedforms are not resolved in the model due to its 10 m horizontal resolution.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** (a) Observed bathymetric changes, calculated as the difference between final seabed levels (S2, 17-Mar-20) and initial seabed levels (S1, 17-Nov-19) in tile #3. (b) Predicted bathymetric changes for Case I. (c) Predicted bathymetric changes for Case II, for which meteorological contributions are added to the model predictions. The secondary bedforms are identified by dark blue lines around section b'-b''. In all figures, blue indicates lowering of the seabed (erosion) and brown indicates rising (accretion). North points to the left.</figcaption></figure>

As regards the evolution of large marine dunes, Case II predictions agree closely with in situ observations in tile #1 as in tile #3. Although there is a tendency to exaggerate the amount of erosion on the gentle side of the dunes, the order of magnitude of changes in seabed elevation is correctly predicted overall. The footprint of the changes is larger to some extent in the model than in the observations. This is attributed in part to the resolution of the model,
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Evolution of the dune profile between S1, 17-Nov-19 (initial) and S2, 17-Mar-20 (final), extracted in tile #1 along section a'-a" (a) from the survey data and Case I model predictions; (b) from the survey data and Case II model predictions; (c) observed and predicted anomaly, calculated as the difference between the final and initial dune profiles.</figcaption></figure>

but also to the modification of the morphology of the dunes over time, in particular the softening of the steep slopes already noted during the calibration phase (Text S3 in Supporting Information S1) and illustrated in Figure 5.

### 3.1.2. Dune Profiles Along Predefined Sections

If we first examine the dune profile along section a'-a" (tile #1) in Figure 5, the height of the dunes remains mostly unchanged after 4 months in the predictions (from black dashed lines to solid orange lines, in panel (a) for Case I as well as in panel (b) for Case II). The model results show that gentle slopes are conserved and steep slopes are softened. The crests stay back instead of dipping forward, resulting in a more symmetrical profile than initially. This effect on the morphology of the dunes is attributed to the predictor chosen for the sediment transport rate (Durand et al., 2023a, in a smaller configuration) and is apparent in both Case I and Case II model predictions. This is not the case in the profiles surveyed (orange dashed line in Figure 5) where the leading face retains its steep angle of inclination at the end of the 4-month period. The crests predicted for case I have become narrow and sharp (panel (a)), but not for Case II (panel (b)) or the observations (consider, in particular, the last dune of the transect, which is flat-crested).

The dunes travel variable distances for Case I, defined halfway up the steep face: approximately 6.5 m, 10.0 and 9.0 m starting from the westernmost dune (left). More consistent and longer migration distances are predicted for Case II, with the addition of the meteorological forcing (18.0 m, 20.5 and 20.0 m starting from the westernmost dune). These values are close to those derived from the survey profiles: approximately 20.0 m for the 3 dunes. This close agreement is further illustrated in Figure 5c in terms of the anomaly, or the difference between final and initial seabed elevations. It is clear from this figure that the erosion and accretion patterns are correctly predicted along section a'-a" when the meteorological forcing is included in the simulation.

The counterpart of Figure 5 for tile #1 is given in Figure 6 for tile #3, section b'-b" (panels (a) to (c)) and section c'-c" (panels (d) to (f)). The height of the dunes can be reduced in section b'-b" after 4 months, by approximately
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Evolution of the dune profile between S1, 17-Nov-19 (initial) and S2, 17-Mar-20 (final), extracted in tile #3 along section b'-b'' (a) from the survey data and Case I model predictions; (b) from the survey data and Case II model predictions; (c) observed and predicted anomaly, calculated as the difference between the final and initial dune profiles. (d), (e), (f) for section c'-c''.</figcaption></figure>
<table><caption>**Table 2**
Performance of the Model Predictions Against Observed Data (S1 to S2)</caption><thead><tr><th></th><th>Bias (m)</th><th>RMSE (m)</th><th>ACC (-)</th><th>BSS (-)</th></tr></thead><tbody><tr><td colspan="5">section a'-a"</td></tr><tr><td>Case I</td><td>0.02</td><td>0.37</td><td>0.89</td><td>0.71</td></tr><tr><td>Case II</td><td>0.01</td><td>0.23</td><td>0.95</td><td>0.89</td></tr><tr><td colspan="5">section b'-b"</td></tr><tr><td>Case I</td><td>-0.04</td><td>0.33</td><td>0.74</td><td>0.46</td></tr><tr><td>Case II</td><td>-0.01</td><td>0.34</td><td>0.84</td><td>0.41</td></tr></tbody></table>

0.25 m for the 2 westernmost dunes and Case I, 0.5 m for the westernmost dune and Case II. Sharp crests and steep slopes are retained for the most part in the model predictions, noting that, in contrast, the leading faces have become steeper in the observations.

Migration distances under 5.0 m are predicted toward the top of the Binnen Ratel sandbank for Case I over the 4-month period. Noticeably longer distances are predicted for Case II: 19.0 m, 18.5 and 22.0 m respectively along section b'-b", exceeding those observed (12.0 m, 13.5 and 14.0 m) by 5-8 m. Section c'-c" is located on the edge of the mobile bedforms and little movement is shown in the observations as well as in the model predictions. Note that the dunes travel by an estimated distance of -9.0 m,

for Case I, with tidal forcing only, in the opposite direction to that observed. This is also shown in panel (f) where the patterns of erosion and accretion are out of sync with observations. The dunes travel in the correct direction for Case II, at the rate of 2.0 m in 4 months. This value is close to that derived from the survey profiles = 2.5 m. The water depth at the base of the dunes is of the order of 20 m below MSL there (as was the case for section a'-a" where equally satisfactory agreement was obtained).

The agreement between predictions and observations is quantified with statistical metrics: bias, Root Mean Square Error (RMSE), ACC and Brier Skill Score (BSS). The result of this analysis is summarized in Table 2 for sections a'-a" and b'-b" (section c'-c" is incomplete and therefore statistics were not computed for it) and confirms that including meteorological (wind) forcing (Case II) improves the skill of the morphodynamic model.

## 3.2. September 2020 Storm: Cases III, IV, and V

Maps of seabed evolution were not produced, nor were dune profiles extracted along the predefined transects for these simulations (too short a period to show significant change). Instead, we examine residual bedload transport rates to determine the effect of the storm on dune dynamics, focusing on the navigation channel. These are calculated from the instantaneous bedload transport extracted from the model, taking vector averages over the duration of the storm. They are presented in Figure 7 for Case III (tide only, panel (a)), Case IV (tide, wind and atmospheric pressure, panel (b)) and Case V (tide, wind and atmospheric pressure brought forward 7 days, panel (c)).

A comparison of the results reveals contrasting characteristics. With tidal forcing alone, residual transport vectors are generally directed eastwards (75°N). They are relatively weak (the storm coincides with a neap cycle), with mean and maximum values of 0.0007 kg/m/s and 0.0026 kg/m/s respectively over the extent of tile #1 (minimum value close to zero). Higher values are predicted to the north of the navigation channel, where the flow is more strongly flood-dominated, than to the south where little sediment transport is expected. Residual transport vectors are an order of magnitude higher when meteorological forcing is added (Case IV), with mean, maximum, and minimum values of 0.008, 0.017, and 0.002 kg/m/s respectively. In this case, higher values are predicted to the south of the navigation channel, increasing over the dunes and directing sediment transport westwards (260°N).

Tidal currents being stronger for a spring tide than for a neap tide, a significant residual sediment transport is generated for Case V. Mean, maximum, and minimum values of 0.045, 0.097, and 0.005 kg/m/s are predicted respectively. The residual is again directed westwards to the south of the navigation channel. However, its direction reverses to the north of the channel, where the ebb currents are weaker and insufficient to sustain westward transport.

Not presented in this article, similar findings extend to tile #3. Residual transport vectors are strong and directed southwestwards at the bottom of the Binnen Ratel sandbank slope, but are weak and generally directed eastwards (70°N) in tile #3 (Case III). Residual transport vectors are stronger, particularly atop the dunes, and consistently directly southwestwards (235°N) for Case IV. They are even stronger for Case V, but turn around on the slopes of the sandbank, in shallower depths, to be directed eastwards, noting that this corresponds to the direction of the smaller secondary bedforms.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Residual sediment transport predicted by the model over the northwesterly storm that occurred between 25-Sep-20 6 a.m. and 28-Sep-20 9 p.m. (a) Case III: tidal contributions only in the 3D model. (b) Case IV: with actual wind and atmospheric pressure fields (this means that the event coincides with a neap tide). (c) Case V: for a hypothetical scenario in which the wind and atmospheric pressure fields are brought forward to coincide with a spring tide. Vectors are shown on a regular 80 m × 45 m grid for clarity; the scale is different for each panel.</figcaption></figure>

**4. Discussion**

In this work, the effect of including weather contributions (actual wind and atmospheric pressure) in morphodynamic simulations was quantified. Total sediment transport was modeled as bedload, and wave processes were not included. These simplifications are justified by a site analysis of environmental conditions in Durand et al. (2023b). The results of the simulations show that, although the tide is an important (and predictable) factor in the sediment dynamics of the region, meteorological events significantly influence these dynamics. A better prediction of marine dune migration is obtained when simulations take into account both tidal and meteorological forcings. Winds blowing in the opposite direction to the predominant sediment transport pathways are capable of reversing them. These results and their implications on large-scale marine dune dynamics are discussed in the
following sections. When time histories are presented or figures quoted, they are used to illustrate the argument, and are relevant to the navigation channel to Dunkirk, and a point located near the second crescent-shaped dune in tile #1.

## 4.1. Influence of Wind Conditions on Residual Flow

Dune migration is the result of an asymmetry in the flow (Fredsøe & Deigaard, 1992; Németh et al., 2002; van Gerwen et al., 2018). Without it, whatever its origin, marine dunes grow toward their equilibrium height (Hulscher, 1996). There can only be oscillations about a fixed position, but no (net) migration. This is the result obtained, for example, by Campmans, Roos, de Vriend, and Hulscher (2018) with simplified representations of tides and waves, based on the M2 constituent and linear wave theory. No movement was predicted as a result of the symmetrical excursions of the tides and waves.

The tide is described by 34 constituents in our model (Text S1 in Supporting Information S1). This gives a realistic representation of site conditions and, in particular, of the (spatially varying) asymmetry between the flood and the ebb phases. Focusing on the navigation channel to Dunkirk, the flood is predominant there. An eastbound net velocity of the order of 0.04 m/s is calculated when only tidal currents are considered (Cases I and III). This value is slightly low compared with the values van Gerwen et al. (2018) quote from the literature for the southern North Sea but is consistent with those used in idealized models (Besio et al., 2004; Németh et al., 2002; van Gerwen et al., 2018). However, tidal currents alone are insufficient to fully describe the migration of the marine dunes (compare panels (b) with panels (a) in Figures 3 and 4). It is therefore expected that wind events influence noticeably the total residual flow (net velocity).

As a general rule, wind-induced currents are of the order of 2% of the wind speed near the water surface (Weber, 1983). Their amplitude decreases with depth. On their own, wind-induced currents are too weak to mobilize the sediment on the seabed (consider that a gale force wind of 20 m/s generates a surface current of the order of 0.4 m/s). But superimposed on tidal currents, they can enhance, hinder (or even suppress) them depending on their direction relative to the tide, and on the state of the tide (Figures 8b, 8d, and 8e). This directly affects the balance between ebb and flood currents, and therefore the residual flow responsible for sediment transport (Harris, 1991). In the following, we consider the depth-averaged velocities predicted by the 3D model since this is the input parameter for the SvR97 sediment transport predictor.

Strong positive net velocities (in excess of 0.15 m/s) in the navigation channel are associated with periods of intense southwesterly wind. For example, values of up to 0.32 m/s are predicted on 9 February 2020 (Case II). On this occasion, the wind speed exceeds 20 m/s for more than 12 hr. Southwesterly winds are prevalent during the Winter 2020 period (S1 to S2) (20%, 35%, and 19% of records from the S, SW and W sectors, respectively). Only a small proportion comes from the North Sea (8% from the NW and 5% from the N). This is specific to winter winds. Over a year, the directional distribution is less skewed toward the S to W sectors, with a higher proportion of northerly winds (in particular in spring, 14% from the NE). As a result of the predominant southwesterly wind, an average net velocity of 0.07 m/s is calculated over the 4-month period between S1 and S2 (Case II), an increase of a factor 1.5 compared with the 0.04 m/s calculated for Case I and tidal forcing alone.

If winds broadly following the flood currents (i.e., propagating from the Channel) enhance the flood-dominated residual flow, winds opposing them (i.e., originating in the North Sea) weaken it. Negative net velocities in the navigation channel occur during periods of northwesterly or northerly winds. They are few during the Winter 2020 period and marked by dark red circles in Figure 8b. But strong winds blew from the northwest (310°N to 360°N) between 25 September 6 a.m. and 28 September 9 p.m. (September 2020 storm). Most of the time above 10 m/s, they reached 23 m/s (9 on the Beaufort scale) on 25 September at 6 p.m. This event was the strongest of the year from this direction. It was associated with an episode of low pressure in the southern North Sea and coincided with a neap tidal cycle. Flood currents were significantly reduced as a result, with peak velocities of 0.13 m/s in the morning of 27 September 2020 (compared with 0.64 m/s for Case III). The residual flow, generally oriented toward the east in the navigation channel, is reversed during this period. This is illustrated in Figures 8d and 8e, where the September 2020 storm is identified by a dark red rectangle.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Instantaneous depth-averaged velocities predicted by the 3D model in the navigation channel (a) for Case I; (b) for Case II; (c) for Case III; (d) for Case IV; and (e) for Case V. Positive values are associated with the flood cycle, trending eastwards. Negative values with the ebb cycle, trending westwards. The shading encompasses velocities below the threshold of motion: *U*<sub>cr</sub> (Equation A6). Negative net velocities, marked by dark red circles in panel (b), are directed opposite the prevailing easterly direction. When applicable, the offshore wind is represented by segments whose length and orientation are true to the wind speed and direction at 10 m above sea level.</figcaption></figure>
## 4.2. Influence of Wind Conditions on Dune Migration

The results presented in Section 3 demonstrate that wind and atmospheric pressure conditions are crucial to correctly reproduce dune migration in the model. The dynamics of the marine dunes is slower compared to observations with tidal forcing only: in tile #1 by a factor of 2–3, and in tile #3 by up to a factor of 4. Importantly, the direction of migration of the dunes can be misrepresented. This is the case, for example, in tile #3, where the dunes in section c’-c” are predicted to move in the opposite direction to that observed in situ during the Winter 2020 period. The role of meteorological events in the evolution of large marine dunes is further evidenced when we consider the September 2020 storm and the resulting reversal of predicted sediment transport direction.

Focusing on the second crescent-shaped dune in tile #1, the effects of wind and atmospheric pressure conditions are reflected in the dynamics of the dunes. Migration speed varies with time. The cyclical variations in Figure 9 (with a period of about 12 hr) correspond to tidal forcing and variations in current velocity with the state of the tide. There are periods when the dunes are immobile (zero migration). These periods are largely associated with neap tides, for which even peak tidal currents barely exceed the threshold velocity $U_{cr}$ in the SvR97 transport rate predictor (=0.41–0.43 m/s for the in situ sediments and range of water depths, Equation A6) if not combined with wind-induced currents. Increased migration toward the east (positive values) is broadly correlated to winds from the southwest (S to W sectors) (e.g., from 9–16 February 2020); increased migration toward the west (negative values) to winds from the W to NE sectors (e.g., the September 2020 storm).

The net migration speed calculated over 4 months is more than doubled (54.1 m/yr vs. 23.3 m/yr, Table 3) when both tidal and meteorological forcings are taken into account. This observation is consistent with the findings of for example, van Gerwen et al. (2018) who suggested that the migration speed of marine dunes increased with the strength of the residual flow and Overes et al. (2024) who suggested that it could be twice as fast when non-tidal influences were considered. Overes et al. (2024) also observed the temporal variability of the erosion and accretion patterns, which is introduced when non-tidal influences are considered at the boundaries of their model.

These results agree qualitatively with observational evidence that meteorological events play a part in the evolution of marine dunes. Harris (1989, 1991), for example, attributed the seasonal inversion of large dune asymmetry in Australia to seasonal changes in wind-induced currents during the monsoon season (bearing in mind that asymmetry is generally accepted as an indicator of the sediment transport in the direction of the steep dune side). Le Bot and Trentesaux (2004) correlated the types of dune morphology to the asymmetry of tidal currents (the imbalance between the ebb and flood cycles) and to the relative strength and orientation of wind-induced currents (their Figure 10). They remarked that dune migration is accelerated if wind-induced currents follow the tidal residual and that it is reduced, or even reversed, in the opposite direction. In the southern North Sea, off Great Yarmouth, Krewinkel (2017) identified annual variability in the speed and direction of observed dune migration, which he ascribed to the wind conditions. The rate of migration was higher and the direction deviated when the climate was more extreme and with a higher proportion of southerly winds.

A few authors have studied the role of wind forcing on dune migration numerically. Campmans, Roos, de Vriend, and Hulscher (2018) offered that the speed of migration decreases with increasing obliquity of the winds in relation to the tidal axis (0°, 30°, 60° and 90° tested). In their (idealized) model, winds at 90° to the main current do not result in migration. These conclusions are not in line with our findings. We have not simulated a case where net movement does not occur as a result of tide alone, as in Campmans, Roos, de Vriend, and Hulscher (2018). But the northwesterly winds considered in the September 2020 storm and present in the Winter 2020 period broadly correspond to their 90° case. These winds are not only responsible for migration, they are also responsible for reversing the direction of sediment transport. These results may not apply to all configurations. In our 3D model, the regional flow patterns are modified horizontally and vertically when a wind field is applied, over the shallow areas atop the sandbanks, which in turn alters the general circulation. The currents being constrained by the channels between the sandbanks and the proximity of the coast, their direction in deeper areas (e.g., in the navigation channel and tile #1) does not substantially change when a wind blows, but their magnitude does, with the results we have shown. In any case, we interpret that results presented by Campmans, Roos, de Vriend, and Hulscher (2018) are a direct consequence of their modeling assumptions. By design, only the projection of the wind stress on the tidal axis is considered (source term reduced to its x-component $\vec{F} = (F_x, 0)$ in the momentum equation). This component decreases the further the wind direction is from that of the tidal currents, to become exactly 0 for winds at 90°. What it does highlight, however, in agreement with other authors (e.g., van Gerwen
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Instantaneous migration speed of the mid-point of the dune steep face predicted by the sediment transport and bed evolution model in the navigation channel (a) for Case I; (b) for Case II; (c) for Case III; (d) for Case IV; and (e) for Case V. Positive values are associated with the flood cycle, trending eastwards; negative values with the ebb cycle, trending westwards. When applicable, the offshore wind is represented by segments whose length and orientation are true to the wind speed and direction at 10 m above sea level.</figcaption></figure>
<caption>**Table 3**</caption>

Migration Speeds Calculated for the Second Crescent-Shaped Dune in Tile #1

<table><thead><tr><th></th><th>Case I</th><th>Case II</th><th>Case III</th><th>Case IV</th></tr></thead><tbody><tr><td>S1-S2: 17-Nov-19 to 17-Mar-20</td><td>23.3 m/yr</td><td>54.1 m/yr</td><td>—</td><td>—</td></tr><tr><td>S4-S5: 31-Aug-20 to 5-Dec-20</td><td>—</td><td>—</td><td>25.8 m/yr</td><td>34.5 m/yr</td></tr><tr><td>Storm: 25-Sep-20 6 a.m. to 28-Sep-20 9 p.m.</td><td>—</td><td>—</td><td>0.8 cm/day</td><td>-8.4 cm/day</td></tr><tr><td>S1-S5: 17-Nov-19 to 5-Dec-20</td><td>29.5 m/yr</td><td>39.9 m/yr</td><td>—</td><td>—</td></tr></tbody></table>

et al., 2018), is that the speed of dune migration is linked to the strength of the residual flow, with stronger flow (0° case) leading to higher rates than weaker flow (60° case).

Pessanha et al. (2023) have also investigated wind contributions to marine dune dynamics, in a local 3D model this time. They indicated that the migration speed of the dunes was underestimated by more than 50% compared with bathymetric survey data collected on Wasque Shoals, in the southeastern corner of Martha's Vineyard, when tidal and wind-induced currents only were considered in their modeling. The model is based on a realistic representation of hydrometeorological forcings. Winds were blowing from the northwest during the measurement period. The fetch is quite limited from this direction due to the presence of the island, and it could well be that the wind-induced currents are not completely developed when they reach Wasque Shoals. Furthermore, unlike our study area, Wasque Shoals is a very shallow environment (less than 7 m water depth), open to the Atlantic Ocean, where wave action can be expected to play a significant role, particularly in winter. Therefore, it is not surprising that the tidal and meteorological forcings were unable to describe the migration of the Wasque Shoals dunes with sufficient accuracy, and that wave forcing was also necessary.

Albeit included in the simulations, the effects of atmospheric pressure gradients have not been discussed in this work. Németh et al. (2002) indicated that the speed of dune migration is higher when the residual flow is generated by a pressure gradient rather than a wind stress. They concluded that shear-stress drives sediment transport in linear dune dynamics and that the velocity profile across the water column is of lesser importance. This view was tested with our model in a simulation in which the input wind field was left out. Only the atmospheric pressure field was applied to simulate the September 2020 storm. The results are not presented here but do indicate little effect on the residual sediment transport. Therefore, we conclude that atmospheric pressure gradients are not a significant factor in the migration of large marine dunes under real conditions.

### 4.3. Implications for Dune Dynamics (Migration and Shape)

Campmans, Roos, Schrijen, and Hulscher (2018) have attempted to formulate the dynamics of dunes in terms of the relative influence of moderate and frequent events versus more energetic and infrequent events. The question is perhaps best put in terms of the proportion (frequency and duration) of favorable events that amplify the dynamics induced by the tide alone, versus adverse events that counteract these dynamics. On the one hand, adverse wind events that differ from the prevailing conditions temporarily affect and may reverse the general migration trend. On the other hand, events such as the September 2020 storm are, for the most part, short-lived and sporadic. They result in transient dune evolution, which may be substantial but dissipate once the driving winds die down or change direction. Predicted residual sediment transport vectors calculated over a full spring/neap tidal cycle around the September 2020 storm are directed eastwards (75°N, not presented), despite the short incursion to the west shown in Figure 7, with a maximum value of 0.027 kg/m/s over the northernmost part of the first crescent-shaped dune in tile #1, and a spatial mean value of 0.013 kg/m/s. This supports the view that if adverse wind events influence short-term sediment transport patterns, as also noted by Le Bot et al. (2000), the long-term dynamics of large marine dunes is likely governed by the consistent, prevailing conditions (e.g., Campmans, Roos, Schrijen, & Hulscher, 2018; Idier et al., 2002). This view is further corroborated by the in situ data: the in situ bathymetric data collected between 31-Aug-20 (S4) and 5-Dec-20 (S5) also show a net eastward migration over the 3-month period including the September 2020 storm.

In proportion to the time elapsed between bathymetric surveys, the net dune migration is less significant between surveys S4 and S5 (34.5 m/yr for 96 days = 43.5 m/yr for 121 days) than that observed between surveys S1 and S2 (54.1 m/yr for 121 days) (Table 3). This reduction can be attributed in part to events such as the September 2020 storm, which, by reversing the dynamics of the dune, cause their position to fluctuate, and therefore slow the net
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Evolution of the observed dune profile between S2, 17-Mar-20 and S3, 16-Apr-20, extracted in tile #1 along section a'-a''.</figcaption></figure>

migration over the period. It is perhaps above all a reflection of the seasonality of wind conditions (Campmans, Roos, Schrijen, & Hulscher, 2018). Indeed, the net migration of the second crescent-shaped dune in tile #1 is also predicted to be a factor of 1.4 faster during the winter than it is over a full year, with respective speeds of 54.1 m/yr (S1-S2) and 39.9 m/yr (S1-S5).

The asymmetry of the dune profile is generally accepted to be an indicator of the direction of its migration, from soft to steep dune sides (although its use as a predictor is disputed; Knaapen, 2005; van Landeghem et al., 2012). We consider that dune asymmetry reflects the prevailing direction of migration, not the instantaneous direction. There will be times, as this work shows, when dune migration will occur in the opposite direction to that indicated by their shape due to adverse winds. However, the volume of sediment in large marine dunes is such that complete reversal of their asymmetry is not conceivable on short time scales (Ernstsen et al., 2006) and would require sustained adverse conditions.

Complete reversal has been observed, for example, in the Torres Strait, Australia, where it is attributed to seasonal changes in the wind regime (mainly southeasterly trade winds vs. mainly northwesterly monsoon winds) (Harris, 1989, 1991). But this is unlikely to occur following short-lived wind events. The model results show a discreet westward migration of the dunes during the September 2020 storm, most apparent in its upper section. They do not indicate any significant change in morphology, noting that net migration was estimated at -8 cm/day for the second crescent-shaped dune in tile #1 (Table 3), which would be barely noticeable on the scale of a dune 3 m high and 175 m long after 3.5 days.

Winds blew from the northeast for extended periods between surveys S2, 17-Mar-20 and S3, 16-Apr-20 (40% of the records from the sector centered on 45°N, typical duration greater than 5 days). The reversal of the upper section of the dune, which responds more closely to the local flow direction, is apparent in both the observations (Figure 10) and in the model results along section a'-a''. This translates into softer leading faces, if not a complete reversal of the asymmetry of the dunes.

## 4.4. Predictive Model Capabilities

What does this mean for the prediction of the large-scale evolution and migration of marine dunes? First and foremost, if morphodynamic models are useful to overcome spatial and temporal limitations, there is no doubt that they must first be calibrated against site-specific data. There exists no universal predictor or set of parameters that can describe the complex processes and interactions between tides, winds, (waves) sediment transport and bed evolution in a coastal environment. Blind tests conducted by six research laboratories as part of the SEDMOC project (van Rijn et al., 2001) revealed a significant spread (typically of the order of 100) in predicted sediment transport rates. Krabbendam et al. (2021) reached similar conclusions, who were able to obtain good agreement on dune migration after calibration of the sediment transport predictor to site-specific data but warned against the generalization of these parameters (scale factor and slope parameter) to other areas or periods. Therefore, it seems essential to calibrate the model to improve its predictive ability when in situ data are available (Soulsby, 1997). Failing that, predictions are speculative at best (Anthony & Aagaard, 2020).

Separately, we have shown that tidal currents, which effect is predictable, are important but not sufficient to completely describe dune dynamics in our study area. The migration of the dunes responds closely to wind conditions and, as such, is subject to seasonal to decennial variability. In this context, it is clear that time scale is an essential factor. We only need to cite Lanckneus and De Moor (1991), who observed a net yearly migration
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Evolution of performance metrics along section a'-a", in tile #1, in relation to observations from S2 (17-Mar-20) to S8 (21-Jul-21).</figcaption></figure>

near zero in the northern Kwintebank, on the Belgian continental shelf, but reported that the dunes had in fact moved 28 m back and forth in that time. Extrapolating the speed of migration from short to long periods is a hazardous exercise. Langhorne (1982) reached the same conclusion from observational evidence, who indicated that the alteration of sediment transport trends as a result of meteorological influences did not allow the extrapolation of the migration speed.

Figure 11 shows the evolution of statistical metrics: bias, RMSE, ACC and BSS calculated in relation to bathymetric surveys S2 to S8 (section a'-a"). The metrics remain stable for approximately 1 year, but after that period, they start to deteriorate. While the RMSE consistently increases over time (which we attribute partly to the predicted dune profile, and partly to diffusion), the ACC reaches a new plateau and remains relatively constant between the first and second year. This analysis supports using the model as a predictive tool for time frames of 1–2 years. Caution should be exercised beyond that.

The lifespan of an OWF is now typically 30 years, with leases that can last up to 60 years (two full project life cycles). Simulations of this length are difficult to envisage at the present time with complex process-based 3D models and realistic input, which is why idealized configurations (models, geometries, or forcings) are still widely used. However, these models lack a complete representation of the physical processes, which in our opinion precludes their use. Another common approach consists in the use of a morphological acceleration factor (Lesser et al., 2004; Ranasinghe et al., 2011) for simulations spanning several decades. However, this approach is limited by the non-linearity introduced when considering meteorological events (and other non-tidal processes). A compromise seems necessary. A sensible approach would perhaps be to determine the response of the system for one representative year (including wind and atmospheric pressure contributions) and to refine this analysis with the predicted response to a matrix of specific adverse or extreme events carefully selected from the long-term site-specific metocean data. In our opinion, simulation of real-life conditions should still be favored for periods of the order of a few years.

**5. Conclusions**

A large-scale 3D numerical model is developed, based on the process-based opentelemac system, to study the migration of large marine dunes in response to tidal and meteorological influences. It is applied to a large coastal area in the Southern Bight of the North Sea. This area features a range of bedforms, including marine dunes 1–5 m high and hundreds of meter long.

The model is successfully calibrated and validated against in situ metocean and bathymetric data for a dynamic period during the winter of 2019–2020. It is capable of simulating accurately the evolution of the seabed off Dunkirk for time scales of the order of months (up to 1–2 years).

We hypothesized that marine dune migration is intimately linked to the amplitude and direction of the residual flow, which are tidally induced and influenced by weather conditions (particularly wind). The results of our model demonstrate the need to include meteorological forcing in the modeling to obtain an accurate representation of changes in the seabed over time. Failing that, dune migration speeds could be underestimated by as much as a factor of 2.
North Sea winds, which differ from prevailing conditions, influence the short-term evolution of the dune field. In this application, we show that sustained northwesterly winds can counteract the weak tidal residual trending east and cause migration toward the west, contrary to the general trend, and the shape of the dunes. These events are too sporadic to fundamentally alter the sediment dynamics of the area, but are expected to slow down net migration over long periods of time.

These results provide a better understanding of the role of weather contributions in an open marine environment. They can be transferred to similar environments: shallow shelf seas dominated by tides, relatively strong currents of the order of 0.5–1.0 m/s, moderate winds with a marked directionality, and sandy seabed with median grain size of the order of 200–500 µm. By using complex process-based 3D modeling on a large scale and with realistic forcing, this work extends previous research that relied on the analysis of observational data or idealized modeling.

The migration of marine dunes is subject to seasonal and multi-year variability in the wind regime, which raises questions about suitable time scales to monitor dune movement, and strategies for long-term forecasting. This becomes especially relevant over the lifetime of an OWF project, considering the potential impacts of climate change.

## Appendix A: Formulation of the OpenTELEMAC System

The openTELEMAC system is a state-of-the-art free surface flow suite of solvers based on the finite element method, on unstructured grids. It comprises several modules, each describing different physical processes, of which TELEMAC-3D is the three-dimensional hydrodynamic module (Hervouet, 2007), and GAIA the sediment transport and bed evolution module (Tassi et al., 2023).

TELEMAC-3D solves the 3D Reynolds-Averaged Navier-Stokes equations. We use the so-called “non-hydrostatic” form, with no assumption on the pressure. Together with the continuity Equation A1, the Navier-Stokes equations are written in Cartesian coordinates as:

$$ \vec{\nabla} \cdot \vec{U} = S_h \quad (A1) $$

$$ \partial_t \vec{U} + (\vec{U} \cdot \vec{\nabla}) \vec{U} = -\frac{1}{\rho} \vec{\nabla} p + \nu \Delta \vec{U} + \vec{g} + \vec{S} \quad (A2) $$

where $t$ denotes the time (s). $\rho$ is the density of the fluid (kg/m³); $\nu$ the kinematic viscosity (m²/s); and $\vec{g}$ the gravitational acceleration (m/s²). The $S$ terms are source and sink terms in the different equations: $S_h$ (1/s) represents a flux of water such as rain, evaporation or discharges ($S_h = 0$ for this work); $\vec{S}$ (m/s²) represents external forces (e.g., Coriolis acceleration), which are applied directly to the water body, as well as contact forces (e.g., wind or bottom friction), which are applied to its surface. The pressure $p$ (Pa) and the three velocity components $\vec{U} = (u, v, w)$ (m/s) are the unknowns in these equations, computed at each node and layer of the computational domain.

Wind forcing appears in Equation A2 through the two-dimensional condition at the surface:

$$ \nu \partial_n \vec{U}_H = \frac{\vec{\tau}_{wind}}{\rho} = \frac{\rho_{air}}{\rho} a_{wind} \|\vec{V}_{10m}\| \vec{V}_{10m} \quad (A3) $$

where $\vec{U}_H$ denotes the horizontal velocity at the surface and $\vec{\tau}_{wind}$ the wind stress, expressed in Heaps (1965) and Flather (1979) in terms of a quadratic function of the wind velocity, $\vec{V}_{10m}$, commonly defined 10 m above sea level. $a_{wind}$ is a dimensionless drag coefficient, dependent on the wind velocity, and hiding complex phenomena (e.g., sea surface roughness, wind speed, fetch). In Equation A3, $\rho_{air}$ is the air density (kg/m³).

Atmospheric pressure gradients are integrated with the source terms:

$$ \vec{S}_{atm} = -\frac{1}{\rho} \vec{\nabla} p_{atm} \quad (A4) $$
where $p_{atm}$ denotes the atmospheric pressure at sea level.

TELEMAC-3D is internally coupled with GAIA to provide the conditions that drive the sediment transport and bed evolution processes. The coupling strategy adopted in the opentelemac system is based on synchronous-decoupled techniques. TELEMAC-3D computes the hydrodynamic solution for a given (fixed) bed map. GAIA is then called to update the bed map according to the revised hydrodynamics. The revised bed map is fed back into TELEMAC-3D. This loop is repeated at each model time step.

The change in bed level is computed in GAIA by solving the sediment mass conservation equation, also known as the Exner equation. This equation expresses the fact that bed levels rise in proportion to the amount of sediment that is no longer transported, and conversely, lower in proportion to the amount of sediment that is entrained by the flow. In its simplest form (bedload transport of one class of non-cohesive sediment), this equation reads:

$$ (1 - \lambda_p) \partial_t (\rho_s z_b) + \vec{\nabla} \cdot \vec{Q}_{mb} = 0 \qquad (A5) $$

where $z_b$ denotes the bottom elevation (m) and $\lambda_p$ the bed porosity. $\vec{Q}_{mb} = (Q_{mb,x}, Q_{mb,y})$ is the bedload mass transport rate = $\rho_s \vec{Q}_b$ (kg/m/s), with $\rho_s$ the sediment density (kg/m³).

Total sediment transport can be divided into suspended sediment transport, where sediment put in suspension by the turbulence of the flowing water is transported by the ambient current, and bedload transport, where sediment is transported in almost continuous contact with the bed, by rolling, sliding or being carried by saltation. Suspended sediment transport is not explicitly considered in this work and will not be expanded upon here. Bedload transport is taken into account by computing bedload fluxes in accordance with formulations published in the literature.

We have used that proposed by Soulsby and van Rijn (Soulsby, 1997), which reads in the absence of wave processes:

$$ \vec{Q}_b = (A_{sb} + A_{ss}) \vec{U}_{2D} [\|\vec{U}_{2D}\| - U_{cr}]^{2.4} \qquad (A6) $$

where $\vec{Q}_b$ is the volumetric transport rate per unit width (m²/s). $A_{sb} = f(h^{-0.2})$ denotes the bedload coefficient ($h$ the water depth), $A_{ss} = f(d_{50}^{-0.8})$ the suspended load coefficient. These coefficients had originally been derived for rivers, both from physical and empirical considerations. They are valid for water depths between 1 and 20 m, depth-averaged velocities of between 0.5 and 5 m/s and sediment grains between 0.1 and 2 mm. $\vec{U}_{2D}$ is the depth-averaged current velocity and $\|\vec{U}_{2D}\|$ its norm; $U_{cr} = f(d_{50}, h/d_{90})$ the threshold velocity defined by van Rijn (1984).

## Data Availability Statement

The opentelemac system used in this research can be downloaded from https://opentelemac.org/. Large-scale bathymetric data from the French Naval Hydrographic and Oceanographic Service are publicly available at https://diffusion.shom.fr/donnees/bathymerie/mnt-facade-atl-homonim.html and https://diffusion.shom.fr/donnees/bathymerie/mnt-topo/mnt-cotier-pas-de-calais.html. Older hydrodynamic and sedimentary data mentioned in this article have been released and are available from Shom (2021a, 2021b). The recent metocean and bathymetric data collected specifically for this project are not currently available to the public or research community. Access can be requested from France Energies Marines (https://www.france-energies-marines.org/contact/). Derived data and analysis are available at Durand (2024).

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N.D. is supported by France Energies Marines, through the MODULLES project. MODULLES is co-funded by the French National Research Agency as part of the France 2030 Investment Plan, under reference number ANR-10-IEED-0006-34, and by France Energies Marines and its members. Computer time was provided under the EDF R&D POWERX project. The authors thank the partners of the MODULLES project for providing site-specific data and giving permission to publish this work.
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