# A coupling approach for long-term 3D morphological evolution of sandy coasts under sea-level rise

Mohammad Traboulsi, Déborah Idier, Bruno Castelle, Arthur Robinet, Vincent Marieu, Elsa Durand, R. Jak Mccarroll

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Mohammad Traboulsi, Déborah Idier, Bruno Castelle, Arthur Robinet, Vincent Marieu, et al. A coupling approach for long-term 3D morphological evolution of sandy coasts under sea-level rise. Environmental Modelling and Software, 2025, 193, pp.106624. 10.1016/j.envsoft.2025.106624. hal-05200530

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# A coupling approach for long-term 3D morphological evolution of sandy coasts under sea-level rise

Mohammad Traboulsi<sup>a,b,●,*</sup>, Déborah Idier<sup>a</sup>, Bruno Castelle<sup>b</sup>, Arthur Robinet<sup>c</sup>, Vincent Marieu<sup>b</sup>, Elsa Durand<sup>a,b,d</sup>, R. Jak McCarroll<sup>e</sup>

## ARTICLE INFO

Keywords:

Shoreline change

Nearshore morphology

Modeling

Sea level rise

Artificial structures

Sandy coasts

## ABSTRACT

This study presents a modular modeling framework for simulating medium- to long-term (decadal to centennial) coastal evolution, focusing on shoreface translation under the combined effects of sea-level rise (SLR) and waves. On these timescales, short-term storm-driven processes are treated as noise superimposed on longer-term trends. We couple the one-dimensional ShoreTrans model, which simulates SLR-driven profile adjustment, with the two-dimensional reduced-complexity model LX-Shore, which captures longshore sediment transport gradients. This coupling enables efficient simulation of three-dimensional morphological change across diverse sandy coastal settings, including environments with dunes, barriers, and hard structures. The framework is first applied to synthetic test cases to explore sensitivity to coupling strategies, then tested on a 5-km beach-dune system in southwest France fronted by a 1.2-km seawall. Results show reasonable agreement with observed shoreline evolution and demonstrate the value of the coupled approach in capturing morphodynamic feedbacks and trajectory shifts not reproduced when shoreline and shoreface processes are modeled independently.

## 1. Introduction

Coastal regions provide critical socioeconomic benefits and are home to approximately 40% of the world's population (Poumadère et al., 2015). Among these environments, sandy coastlines, which account for approximately one-third of the ice-free global shoreline (Luijendijk et al., 2018), are particularly attractive. In the context of climate change and rising sea levels, sandy coasts are expected to undergo significant long-term transformations (Ranasinghe, 2016). Even in regions where incident wave energy is projected to remain stable or decrease, such as along the Atlantic coast of Europe (Perez et al., 2015), sandy coasts remain vulnerable to significant long-term morphological change.

Incident wave energy is projected to remain stable or even decrease in certain regions, such as along the Atlantic coast of Europe (Perez et al., 2015). At the same time, shoreline fluctuations driven by cross-shore processes, ranging from storm-scale (hours) to seasonal or inter-annual timescales, are generally well captured by equilibrium-based models (e.g. Yates et al., 2009; Splinter et al., 2014; Jaramillo et al., 2021) and can be regarded as high-frequency noise superimposed on

longer-term trends (Fenster et al., 2001). Accordingly, the dominant drivers of coastal change over the coming century are expected to be sea-level rise (SLR) (Vousdoukas et al., 2017; Cooper et al., 2020) and gradients in longshore sediment transport (LST) (Ashton and Murray, 2006a). For wave-dominated coasts, capturing the coupled influence of SLR and LST is therefore critical to predicting long-term shoreline evolution.

A wide range of reduced-complexity models have been developed to simulate long-term shoreline evolution (e.g. Vitousek et al., 2017; Antolínez et al., 2019; Robinet et al., 2018; Tran and Barthélemy, 2020; Chataigner et al., 2022), particularly in response to gradients in longshore sediment transport and sea-level rise. These models are computationally efficient and well-suited for long-term projections, unlike process-based models which are limited by high computational demands and error accumulation over decadal timescales (Zhang et al., 2012; Seenath, 2022b). Despite these advantages, several practical challenges remain. Some models depend on long-term observational datasets or require inverse calibration, limiting their use in data-scarce

<footnote><sup>a</sup> BRGM, Orléans, F-45060, France</footnote>

<footnote><sup>b</sup> Univ. Bordeaux, CNRS, Bordeaux INP, EPOC, UMR 5805, Allée Geoffroy Saint-Hilaire, Pessac, 33600, France</footnote>

<footnote><sup>c</sup> BRGM, 24 Av. Léonard de Vinci, Pessac, F-33600, France</footnote>

<footnote><sup>d</sup> Waeles Marine Consultants, 53 rue du Commandant Groix, Brest, 29200, France</footnote>

<footnote><sup>e</sup> The University of Melbourne, Melbourne, Victoria, 3010, Australia</footnote>

<footnote>* Corresponding author at: BRGM, Orléans, F-45060, France.
E-mail address: m.traboulsi@brgm.fr (M. Traboulsi).</footnote>
settings (Karunarathna and Reeve, 2013; Jaramillo et al., 2024; Azo-
rakos et al., 2024). Cross-shore dynamics are often addressed using
static profiles, which can limit the model's ability to represent long-
term morphological responses such as barrier rollover or profile retreat
under sea-level rise (Cooper et al., 2020; Lakku et al., 2024; Seenath,
2023, 2022a). Moreover, models that handle more complex shoreline
geometries often rely on further simplifications (e.g., shore-parallel
contours, fixed transects, fixed closure depth), limiting their application
to real-world coastlines, especially where human interventions are, or
will be, implemented (Seenath, 2022b; Jaramillo et al., 2024; Vitousek
et al., 2017).

In response to these limitations, recent efforts have explored data-
driven strategies (e.g. Montaño et al., 2020). These include integrating
machine learning models trained on remote sensing or in-situ datasets.
These approaches offer strong potential for site-specific forecasting and
uncertainty quantification. While they often lack physical interpretabil-
ity and can be constrained by data availability, they complement
physics-based models by enabling rapid assessments and supporting
probabilistic shoreline mapping in complex settings (e.g., Karunarathna
and Reeve, 2013; Kumar et al., 2020; Gomez-de La Peña et al., 2023).
A notable example of over-simplification in many reduced-
complexity models is the continued reliance on the Bruun rule (Bruun,
1962) to estimate shoreline retreat under sea-level rise. Despite its
simplicity and minimal data requirements, which have contributed
to its widespread use (Terres De Lima et al., 2021; D'Anna et al.,
2021; Vousdoukas et al., 2020), the Bruun rule has been criticized
for its underlying assumptions. In particular, the Bruun rule over-
looks key factors such as shoreface morphology, sediment supply,
accommodation space, and anthropogenic influences (Cooper et al.,
2020). While efforts have been made to refine the Bruun rule by
incorporating additional processes (e.g., dune dynamics, probabilistic
frameworks), these adaptations still fail to capture the full complexity
of coastal morphodynamics (Rosati et al., 2013; Davidson-Arnott, 2005;
Ranasinghe et al., 2011).

The ShoreTrans model (McCarroll et al., 2021) represents a sig-
nificant advance, providing a rules-based, sediment budget approach
to simulate dynamic shoreface adjustments under SLR. Unlike previ-
ous attempts, ShoreTrans can incorporate a range of coastal features
– including dunes, barriers, seawalls, and cliffs – but is inherently
one-dimensional, operating along fixed, shore-normal transects. Cru-
cially, ShoreTrans does not resolve alongshore sediment transport in-
ternally and cannot simulate evolving shoreline orientation or planform
change. ShoreTrans has also been integrated into hybrid modeling
frameworks such as IH-LANSloc (Álvarez-Cuesta et al., 2023), which
combine shoreline evolution with shoreface profile adjustment. While
such approaches improve, among other aspects, the representation of
long-term cross-shore dynamics, they typically rely on fixed shore-
normal transects, limiting their ability to simulate evolving shoreline
planforms such as cuspatе forelands, embayed beaches, or flying spits.

To address these limitations, we developed a modular coupling
framework specifically designed for long-term morphological evolu-
tion (called LX-ST). LX-ST integrates the grid-based shoreline model
LX-Shore (Robinet et al., 2018), which handles alongshore sediment
transport and planform evolution, with the ShoreTrans model, which
simulates cross-shore profile response to sea-level rise and sediment
imbalances. LX-ST enables transects to evolve dynamically in both
space and orientation, capturing two-way feedback between shoreline
position and profile adjustment. This coupling does not aim to replace
hybrid approaches such as IH-LANSloc, which are better-suited for
storm-scale or short-term applications. Rather, LX-ST is designed for
decadal to centennial applications, where wave-driven cross-shore fluc-
tuations are assumed to act as stochastic variability superimposed on
long-term trends. The framework supports a broader range of morpho-
logical behaviors – including dune rollover, shoreline reorientation, and
the interaction with hard structures – without requiring site-specific
reconfiguration.

This interactive coupling aims to enable the simulation of medium-
to long-term coastal evolution in settings where neither model alone
can fully represent the governing processes. The shoreline compo-
nent supports complex morphologies, including non-erodible elements,
headlands, spits, and embayments, while the shoreface component
replaces static-profile assumptions with a dynamic, volume-conserving
method capable of simulating diverse barrier responses — such as
rollover, encroachment, and localized erosion in front of hard defenses.
By allowing transects to remain orthogonal to the evolving shoreline,
LX-ST captures the critical feedback between shoreline curvature, long-
shore sediment transport gradients, and long-term cross-shore profile
evolution induced by sea-level rise. This approach enables a more
consistent two-dimensional representation of long-term coastal change
under sea-level rise.

The paper is organized as follows. Section 2 describes the coupling
architecture and overall methodology. Section 3 applies the approach
to three synthetic test cases, followed by a real-world application in
Section 4, which presents long-term shoreline change projections for
a 5-km beach-dune system near Lacanau, southwest France. Section 5
discusses model limitations and outlines future research directions.
Finally, Section 6 summarizes the key findings.

**2. Method**

**2.1. ShoreTrans**

ShoreTrans is a shoreface translation and sediment budgeting model
recognized for its simplicity and rules-based structure (McCarroll et al.,
2021). Unlike traditional models (e.g. Bruun, 1962), which typically
assume a consistent profile shape and focus solely on the translation of
the shoreline, ShoreTrans estimates changes in the real profile shape.
This capability enables accurate and realistic modeling of coastal dy-
namics. The model accounts for various factors, including armoring,
hard rock cliffs, outcropping rocks, dune accretion, sediment fluxes
(both longshore and cross-shore), and sediment sources and sinks. It
effectively incorporates the effects of sea-level rise (SLR) and sediment
supply, making it adaptable to diverse coastal environments including
sandy, gravelly, rocky, and engineered coasts. ShoreTrans is suitable
for modeling coastal changes over temporal scales ranging from 10 to
100 years.

ShoreTrans requires a 2D cross-shore profile. The model translates
the active profile vertically and landward until the net sediment volume
change equals zero. The active profile is the segment that responds to
immediate changes caused by incident wave action, adapting at a pace
that typically exceeds the rate of translation induced by SLR. Depending
on the profile's shape, its upper boundary is defined as the dune toe or
the barrier crest, while the lower boundary is considered the depth of
closure *DoC*. The upper boundary also serves as the translation point —
the reference location around which the active profile shifts in response
to sea-level rise and sediment dynamics.

Once the basic translation parameters are established, ShoreTrans
uses an algorithmic approach to optimize translation, ensuring volume
conservation. This is achieved by minimizing the error in volume
change ($\Delta V_{error}$) using a fixed cross-shore resolution (1 m).
The ShoreTrans model identifies four distinct barrier response types
(Fig. 1), each characterized by specific dynamics and responses to SLR
and other environmental changes. Translation points are typically lo-
cated at either the dune toe or crest, depending on the barrier response
type described below. These types are as follows:

1. *Barrier Rollover*: The entire back-barrier and active profile are
raised and shifted onshore. This response typically occurs in
low-elevation barriers with a gentle hinterland gradient, where
sediment is transported onshore, often through overwash pro-
cesses.

This interactive coupling aims to enable the simulation of medium-
to long-term coastal evolution in settings where neither model alone
can fully represent the governing processes. The shoreline compo-
nent supports complex morphologies, including non-erodible elements,
headlands, spits, and embayments, while the shoreface component
replaces static-profile assumptions with a dynamic, volume-conserving
method capable of simulating diverse barrier responses — such as
rollover, encroachment, and localized erosion in front of hard defenses.
By allowing transects to remain orthogonal to the evolving shoreline,
LX-ST captures the critical feedback between shoreline curvature, long-
shore sediment transport gradients, and long-term cross-shore profile
evolution induced by sea-level rise. This approach enables a more
consistent two-dimensional representation of long-term coastal change
under sea-level rise.

The paper is organized as follows. Section 2 describes the coupling
architecture and overall methodology. Section 3 applies the approach
to three synthetic test cases, followed by a real-world application in
Section 4, which presents long-term shoreline change projections for
a 5-km beach-dune system near Lacanau, southwest France. Section 5
discusses model limitations and outlines future research directions.
Finally, Section 6 summarizes the key findings.

2. Method

2.1. ShoreTrans

ShoreTrans is a shoreface translation and sediment budgeting model
recognized for its simplicity and rules-based structure (McCarroll et al.,
2021). Unlike traditional models (e.g. Bruun, 1962), which typically
assume a consistent profile shape and focus solely on the translation of
the shoreline, ShoreTrans estimates changes in the real profile shape.
This capability enables accurate and realistic modeling of coastal dy-
namics. The model accounts for various factors, including armoring,
hard rock cliffs, outcropping rocks, dune accretion, sediment fluxes
(both longshore and cross-shore), and sediment sources and sinks. It
effectively incorporates the effects of sea-level rise (SLR) and sediment
supply, making it adaptable to diverse coastal environments including
sandy, gravelly, rocky, and engineered coasts. ShoreTrans is suitable
for modeling coastal changes over temporal scales ranging from 10 to
100 years.

ShoreTrans requires a 2D cross-shore profile. The model translates
the active profile vertically and landward until the net sediment volume
change equals zero. The active profile is the segment that responds to
immediate changes caused by incident wave action, adapting at a pace
that typically exceeds the rate of translation induced by SLR. Depending
on the profile's shape, its upper boundary is defined as the dune toe or
the barrier crest, while the lower boundary is considered the depth of
closure *DoC*. The upper boundary also serves as the translation point —
the reference location around which the active profile shifts in response
to sea-level rise and sediment dynamics.

Once the basic translation parameters are established, ShoreTrans
uses an algorithmic approach to optimize translation, ensuring volume
conservation. This is achieved by minimizing the error in volume
change ($\Delta V_{error}$) using a fixed cross-shore resolution (1 m).

The ShoreTrans model identifies four distinct barrier response types (Fig. 1), each characterized by specific dynamics and responses to SLR and other environmental changes. Translation points are typically located at either the dune toe or crest, depending on the barrier response type described below. These types are as follows:

1. *Barrier Rollover*: The entire back-barrier and active profile are raised and shifted onshore. This response typically occurs in low-elevation barriers with a gentle hinterland gradient, where sediment is transported onshore, often through overwash processes.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Schematics of the ShoreTrans barrier response types with and without a seawall. Accretion (red), erosion (blue), initial/final mean sea levels (blue), and the seawall (dashed black) are indicated.</figcaption></figure>

2. **Barrier Rollover (Keep up with SLR):** The barrier crest is raised by the amount of sea level rise and translated onshore. A landward slope extends from the crest at an angle (Φ) until it intersects the initial profile. This response is seen in barriers where dunes or barrier crests dynamically respond to rising sea levels.

3. **Barrier Rollover (Maintain Initial Height):** Similar to the previous type, but after translation, the barrier crest is capped at its initial level. This type of response occurs when the barrier or dune can roll over but is constrained in its vertical growth, possibly due to limitations in sediment supply or other geomorphological controls.

4. **Encroachment Barrier:** Here, the active profile is translated, but no increase in bed level is allowed onshore. This type of response is more common on bay barriers and mainland beaches characterized by steep topography.

In addition to these modes, the 'wall effect' is an important phenomenon to consider when a seawall is present. While not classified as a distinct mode, the wall effect describes how the presence of a seawall alters sediment dynamics (Fig. 1e), concentrating erosion directly in front of the structure. This occurs because the erosion that would typically occur landward of the seawall is redistributed offshore, producing a triangular erosion wedge, with its deepest point at the wall base. The extent of this wedge is often assumed to be one-third of the cross-shore width of the active profile.

Since LX-Shore is written in Fortran, the original ShoreTrans code (written in Matlab) has been rewritten in Fortran. Additionally, developments have been made to reduce computation time and allow the spatial resolution to be specified as a user-defined parameter.

## 2.2. LX-Shore

LX-Shore is a reduced-complexity shoreline model designed to simulate shoreline change along wave-dominated sandy coasts on large spatial, O(100-100000 m), and temporal, O(1-100 y), scales (Robinet et al., 2018). It is based on the concept of a grid-based one-line model approach (Fig. 2) first introduced in the CEM model by Ashton et al. (2001), Ashton and Murray (2006a,b).

A key strength of LX-Shore is its ability to model diverse shoreline morphologies, including sand spits, embayed beaches, salients, and non-erodable elements such as headlands and coastal defenses. This versatility is achieved by modeling changes in sediment volume contained within each grid cell instead of modeling explicitly cross-shore changes of the nodes composing the shoreline (Ashton et al., 2001; Ashton and Murray, 2006a,b). The sediment content of each cell is expressed as a fraction, determined by the ratio of the current sediment volume to the cell's maximum capacity, accounting for its size and any non-erodable regions. This sediment fraction ranges from 0 (water) to 1 (land). By applying simple interface reconstruction methods, complex shoreline geometries can be derived from any configuration of sediment fraction grid.

LX-Shore computes changes in sediment fraction driven by longshore and cross-shore transports (Fig. 2) (Robinet et al., 2018, 2020a). Longshore sediment transport is computed using either the CERC formula (USACE, 1984) or the formula of Kamphuis (1991). LX-Shore accounts for sediment bypassing around hard structures that obstruct longshore sediment transport (Durand et al., 2024). The short- to
<figure><img src="image_4.png" /><figcaption>Fig. 2. Overview of LX-Shore: (a) Architecture and functionalities (b) Main processes (from Robinet et al., 2020c). Dark gray and yellow areas within the grid cells represent non-erodible and erodible regions, respectively.</figcaption></figure>

medium-term cross-shore sediment transport is resolved using an adaptation of the equilibrium model ShoreFor (Davidson et al., 2013; Splinter et al., 2014), which is here switched off given the timescales addressed in this contribution. Wave conditions at breaking can be estimated either with the direct empirical formula of Larson et al. (2010) or the SWAN spectral wave model (Booij et al., 1999). The latter is particularly valuable for complex bathymetric settings, where wave refraction and energy focusing significantly influence breaking wave conditions and, consequently, shoreline evolution (Robinet et al., 2020b).

LX-Shore has been applied successfully to both synthetic scenarios (e.g., groynes, breakwaters, cuspates, flying sandspits) and real-world sites such as Truc Vert (France), Narrabeen (Australia), and Tairua (New Zealand) (Robinet et al., 2018, 2020a,b; Montaño et al., 2020).

By default, LX-Shore can internally account for SLR-driven shoreline retreat at each time step by activating the Bruun rule (see e.g., Robinet et al., 2020a). However, in the coupled LX-ST configuration used here, the Bruun rule is deactivated within LX-Shore, and cross-shore sediment transport is also switched off. Instead, all SLR-induced shoreline and profile adjustments are captured through explicit coupling with the ShoreTrans model (see Section 2.3).

For clarity, results shown in Section 3 include both the fully coupled LX-ST configuration (with Bruun OFF in LX-Shore), and, for comparison, simulations with stand-alone LX-Shore where the Bruun rule is activated. Longshore transport is computed using the Larson formula, which better suits morphologically active coasts with oblique wave incidence.

## 2.3. Coupling between LX-shore and ShoreTrans

Fig. 3 illustrates the coupling methodology between LX-Shore and ShoreTrans (LX-ST). This approach employs a time-splitting strategy,

acknowledging the differing temporal scales of processes: wave-driven longshore sediment transport occurs at short timescales (hours to days) and is addressed by LX-Shore at frequent intervals ($\Delta t_{LX}$), whereas slower processes such as sea-level rise (SLR) and shoreface profile translation are managed by ShoreTrans at longer intervals ($\Delta t_{ST}$, typically annual to decadal).

At each coupling step, LX-Shore (2) independently computes the reference shoreline position $S_{ref}(t_{i-1})$ (2a), using its dedicated input set (1a). For the coupling, the reference shoreline is discretized into shore-normal transects spaced consistently according to the LX-Shore grid resolution ($d_{xy}$). These transects are subsequently used to extract cross-shore profiles from the provided topobathymetric grid (3), introduced explicitly to support ShoreTrans operations. The wave-driven sediment volume change per unit alongshore distance is computed (5) based on the difference between the coupling shoreline, $S_{cpl}(t_i)$ (4a), and the reference shoreline, $S_{ref}(t_{i-1})$ (2a):

$$ \frac{dV}{ds} = -dR \times h_a \qquad (1) $$

where $dV/ds$ is the wave-driven volume change per unit alongshore distance $s$, $dR$ is the shoreline change induced by wave-driven longshore transport, and $h_a$ is the height of the active profile.

ShoreTrans (6) then updates the cross-shore profiles based on this sediment volume change and the projected sea-level rise (1c). As part of this update, the depth of Closure (DoC) is dynamically recalculated using the Hallermeier (1980) formula. The resulting time-varying DoC defines the lower boundary of the active coastal profile and is applied directly within ShoreTrans. The updated DoC is also passed back to LX-Shore.

From the updated profiles, a new shoreline, $S_{ST}(t_i)$ (7), is extracted, and the sediment fraction grid, $F_{ref}(t_i)$ (8), is recalculated accordingly. This updated sediment fraction grid is returned to LX-Shore, providing the updated reference shoreline $S_{ref}(t_i)$. Concurrently, the topobathymetric data is interpolated and adjusted (9) to reflect the newly calculated profiles and prepare for subsequent coupling cycles, depending on the chosen coupling mode.

At each subsequent ShoreTrans interval ($\Delta t_{ST}$), this coupling procedure – comprising shoreline extraction, volume calculation, profile updating, and sediment fraction grid recalculation – is repeated until the simulation concludes.

The interpolation of the topobathymetry (step 9 in Fig. 3) follows a novel interpolation-based method that we developed, which generates a dense, domain-wide point-cloud to ensure spatial consistency and accuracy in subsequent coupling iterations (Fig. 4).

This process begins with the identification and refinement of shoreline points (SPs) along the transects (Step 1). By default, SPs are defined at the Z-contour corresponding to the mean sea level, though users can modify this Z-value. A high-resolution shoreline is then generated from these points using the Akima interpolation method (Akima, 1970). Akima is preferred for handling sharp transitions without overshooting, unlike spline interpolation, which, while smooth, can be computationally intensive and less suited for abrupt changes.

Next, equidistant polylines (Step 2) are constructed within the interpolation domain, spaced uniformly at a distance $dI$ from the shoreline. Each point on these polylines is assigned a Z-value interpolated from the topobathymetric grid, ensuring that the spacing is small enough to capture detailed profile variations, such as those caused by sea walls or other coastal structures. These newly interpolated points are then merged with the existing point cloud (Step 3) by masking the interpolation region and retaining points outside this region from the original dataset. This approach ensures that the shoreline evolution is properly captured over time.

LX-ST provides a flexible coupling framework that adapts to varying levels of coastal complexity and computational constraints. At its most advanced, the model dynamically updates both the position of cross-shore transects and their associated profiles as the shoreline evolves. This configuration – referred to as coupling level 3 – ensures that
<figure><img src="image_5.png" /><figcaption>Fig. 3. Flowchart illustrating the coupling process between LX-Shore and ShoreTrans. The reference shoreline is denoted by $S_{ref}(t_{i-1})$, while $S_{cpl}(t_i)$ represents the coupling shoreline. The dashed line highlights periods of idle computation. Individual cross-shore profiles are indicated by $p_k$.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Top-view image of the interpolation method used to create the point cloud.</figcaption></figure>

morphological feedback are accurately captured in settings with strong curvature or rapidly changing shoreline geometry, making it ideal for simulating complex coastal systems. However, because this level involves higher computational costs, especially over long time periods or large domains, LX-ST also offers two streamlined alternatives.

Coupling level 2 maintains fixed transect positions while still incorporating shoreline feedback into profile updates. This intermediate configuration is conceptually similar to recent models such as IH-LANSloc, and strikes a balance between realism and efficiency, making it suitable for moderately complex coastlines. In Fig. 3, this corresponds to skipping step 9, meaning that ShoreTrans is applied to the original

shore-normal profiles at each update, without adjusting their spatial position.

Finally, coupling level 1 excludes shoreline feedback entirely and assumes fixed transects, with profile changes driven solely by long-shore sediment transport and sea-level rise. While this approach is less suited for dynamic coastlines, it offers significant gains in speed and is particularly useful for sensitivity analyses and comparison with other reduced-complexity models. In Fig. 3, this corresponds to skipping both step 8 (shoreline feedback update) and step 9 (topobathymetry interpolation), resulting in purely forward-driven updates.
<figure><img src="image_7.png" /><figcaption>Fig. 5. The profile used to generate the topobathymetry for the synthetic test cases.</figcaption></figure>

# 3. Synthetic test cases: Description and results

## 3.1. Test cases description

The main objective of these synthetic test cases is to illustrate the coupling capabilities and investigate the sensitivity of the results to the coupling procedure. To achieve this, we consider an idealized beach-dune profile (Fig. 5) and design three test cases (Fig. 6): (1) diffusion of a bulge under nearly shore-normal waves, (2) the effect of a longshore seawall under obliquely incident waves, and (3) the effect of a groyne under obliquely incident waves.

These test cases were selected to systematically assess the ability of the LX-ST coupling to handle varying degrees of shoreline planform evolution. Test case 1 (bulge) represents a scenario with strong temporal evolution of the shoreline planform, where significant added value from full coupling (level 3) is expected due to pronounced changes in shoreline orientation. Test case 2 (seawall) examines the effect of a seawall on an initially rectilinear shoreline, where levels 3 and 2 are anticipated to yield similar results, and level 1 is expected to deviate more significantly, highlighting the role of shoreline feedback in the presence of a fixed structure. Test case 3 (groyne) features a situation where only moderate changes in shoreline orientation occur and no seawall effect is present, so limited differences are expected among the three coupling levels. This selection enables a direct evaluation of the LX-ST coupling's performance across contrasting scenarios of planform change and management intervention. All cases use identical sediment properties and impose a linear 1 m SLR over their respective durations (5–100 y; see Table 1 for the key case parameters, and Supplementary Table S1 for the full configuration).

In all synthetic test cases, sediment bypassing around hard structures is represented using the shoreline-only bypassing (SB) scheme (Durand et al., 2024), wherein sediment is transported around an obstacle only when the shoreline itself extends beyond the tip of the structure. This choice is consistent with the simplified, idealized design of the test cases, and facilitates benchmarking against previous studies using comparable assumptions.

We run each case with both ShoreTrans modes (barrier rollover vs. encroachment) and LX-ST's three coupling levels (Section 2.3). Case 1 employs a realistic time series representative of a high-energy, wave-dominated coast (Castelle et al., 2017); Cases 2 and 3 use constant wave height and period with normally distributed incidence angles. By comparing coupling levels 1–3 across these management-relevant setups, we assess when and why dynamic transects (level 3) become essential to reproduce alongshore morphology.

To isolate decadal-scale trends, we run LX-ST with cross-shore transport turned off (ShoreFor deactivated, storm impact deactivated) and constant wave height and period, thereby removing all storm- and seasonal-scale fluctuations. Consequently, only longshore sediment transport and linear SLR drive shoreline change.

A comparison of the final shoreline positions for all test cases and a benchmark – LX-Shore (with Bruun rule activated) – is provided in Table 2. In the coupled LX-ST runs, the Bruun rule is deactivated in LX-Shore and SLR effects are instead handled by ShoreTrans (see Section 2.3).

## 3.2. Test case 1: Shoreline bulge

This test case explores how an initial shoreline bulge evolves under the combined influence of nearly shore-normal waves and an imposed sea-level rise of 1 meter over five years. The domain is 3 km long and 1.6 km wide, discretized with 100 m shoreline cells and a Topobathymetry resolution of 10 m (see Table 1). Wave forcing is prescribed using a realistic time series representative of a high-energy, wave-dominated coast (Castelle et al., 2017). To isolate the effects of longshore transport and sea-level rise, all simulations assume uniform sediment characteristics and cross-shore processes are deactivated.

As shown in Fig. 7a–b, the shoreline straightens as the bulge diffuses laterally, and the model captures this behavior with high spatial detail. The outcomes differ depending on the ShoreTrans translation mode. In the rollover mode, the dune system persists but exhibits strong alongshore variability: dunes narrow in the alignment of the former bulge due to localized sediment loss, while adjacent sectors widen from net sediment gain (see also supplementary Fig. S2). This results in a heterogeneous morphology shaped by the interaction of SLR and sediment redistribution. In contrast, the encroachment mode results in a more uniformly distributed coastal morphology. Here, shoreline diffusion and straightening dominate, and the central dune in the alignment of the initial shoreline bulge is completely eroded. This highlights the combined impact of SLR and diverging longshore sediment transport on the erosion and decay of the dune crest and the sensitivity to the rollover mode.

Using coupling level 2 (Fig. 7c–d), with fixed transect positions but retained shoreline feedback, the model still captures the overall trend toward straightening. However, it struggles to resolve finer details of erosion and accretion, particularly near the former bulge where shoreline curvature is greatest. This demonstrates the importance of allowing transects to move when simulating complex or rapidly changing coastlines.

In coupling level 1 (Fig. 7e–f), with both feedback and transect updates disabled, the model produces the greatest errors. Here, erosion in the bulge region is consistently overestimated, and the predicted shoreline is much less reliable.

## 3.3. Test case 2: Seawall

This test explores the coastal evolution of a straight shoreline with a localized 1-km-long seawall (Fig. 6b), subjected to obliquely-incident waves (30° from shore normal) and a linear SLR of 1 m over 100 years. The model domain is 5 km long and 1.4 km wide, discretized using 100 m shoreline cells and a topobathymetry resolution of 10 m (see Table 1). Wave height and period are held constant, while the angle of incidence follows a normal distribution.

In the absence of SLR, wave action is expected to induce minimal changes to the straight shoreline. However, with SLR, progressive erosion is anticipated along the entire coastline, while the presences of the seawall disrupts the alongshore sediment transport pathway. As shown in Table 2 and Fig. 8a–b, the shoreline evolves asymmetrically: updrift of the seawall, sediment accumulates due to wave-driven transport being blocked by the structure, partially offsetting erosion from sea-level rise. Downdrift, however, sediment supply is reduced, resulting
<figure><img src="image_8.png" /><figcaption>Fig. 6. Initial topobathymetry for test cases: (a) Bulge, (b) Seawall, and (c) Groyne.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Results for Case 1: Columns display two rollover modes – full rollover and encroachment– while the rows correspond to the three coupling levels offered by LX-ST (see Section 2.3). The thick black line indicates the shoreline at Z = MSL (Mean Sea level), and the dashed red line represents the shoreline derived from stand-alone LX-Shore with the Bruun rule activated (see Section 2.2).</figcaption></figure>
<caption>**Table 1**</caption>

Summary of key parameters for the three synthetic test cases with ST: ShoreTrans Resolution, TB: Topobathymetry Resolution, LTF: Longshore Transport Formula, Dw: Depth at which waves are imposed, BC: Boundary Condition (H: Horizontal).

<table><thead><tr><th>Test case</th><th>(1) Bulge</th><th>(2) Seawall</th><th>(3) Groyne</th></tr></thead><tbody><tr><td colspan="4">Computational grid</td></tr><tr><td>Grid (km): x × y</td><td>3 × 1.6</td><td>5 × 1.4</td><td>4 × 1.4</td></tr><tr><td>Cell size (m)</td><td>100</td><td>100</td><td>50</td></tr><tr><td>TB (m)</td><td>10</td><td>10</td><td>10</td></tr><tr><td>ST (m)</td><td>0.1</td><td>0.1</td><td>0.1</td></tr><tr><td colspan="4">Simulation settings</td></tr><tr><td>LTF</td><td>Kamphuis (1991)</td><td>Kamphuis (1991)</td><td>Kamphuis (1991)</td></tr><tr><td>Wave model</td><td>Larson et al. (2010)</td><td>Larson et al. (2010)</td><td>Larson et al. (2010)</td></tr><tr><td>Dw (m)</td><td>35</td><td>35</td><td>35</td></tr><tr><td>BC</td><td>Periodic H</td><td>Periodic H</td><td>Periodic H</td></tr><tr><td>SLR (m)</td><td>1 Linear</td><td>1 Linear</td><td>1 Linear</td></tr><tr><td>Hs (m)</td><td>μ = 1.14 ± 0.3</td><td>1</td><td>1.5</td></tr><tr><td>Tp (s)</td><td>μ = 11.13 ± 2.19</td><td>8</td><td>8 N'(-5, 20)<sup>b</sup></td></tr><tr><td>θ (°)</td><td>μ = 12.5 ± 0.36<sup>a</sup></td><td>N'(30, 15)<sup>b</sup></td><td>10</td></tr><tr><td>Duration (y)</td><td>5</td><td>100</td><td>3</td></tr><tr><td>Δt<sub>LX</sub> (h)</td><td>1</td><td>3</td><td>1</td></tr><tr><td>Δt<sub>ST</sub> (y)</td><td>0.25</td><td>1</td><td>1</td></tr><tr><td>Δt<sub>TR</sub></td><td>0.25</td><td>20</td><td></td></tr></tbody></table>

<caption>**Table 2**</caption>

Summary of maximum erosion (in meters) for each synthetic test case and coupling level, under two shoreline translation modes. Results from stand-alone LX-Shore (with Bruun rule activated) are shown for reference.

<table><thead><tr><th>Test</th><th>Mode</th><th>LX-Shore + Bruun</th><th>Level 1</th><th>Level 2</th><th>Level 3</th></tr></thead><tbody><tr><td rowspan="2">1- Bulge</td><td>Rollover</td><td>247 m</td><td>241 m</td><td>264 m</td><td>272 m</td></tr><tr><td>Encroachment</td><td>247 m</td><td>240 m</td><td>248 m</td><td>245 m</td></tr><tr><td rowspan="2">2- Seawall</td><td>Rollover</td><td>18 m</td><td>15 m</td><td>37 m</td><td>40 m</td></tr><tr><td>Encroachment</td><td>18 m</td><td>4 m</td><td>10 m</td><td>11 m</td></tr><tr><td rowspan="2">3- Groyne</td><td>Rollover</td><td>70 m</td><td>130 m</td><td>120 m</td><td>120 m</td></tr><tr><td>Encroachment</td><td>70 m</td><td>110 m</td><td>100 m</td><td>70 m</td></tr></tbody></table>

in pronounced erosion that is amplified by the SLR. In the rollover mode, this leads to a maximum downdrift retreat of 37 m, while in the encroachment mode, erosion is more limited, reaching only 10 m. In front of the seawall, the absence of accommodation space causes a lowering of the upper profile, consistent with the 'wall effect' shown in Fig. 1e.

In coupling level 2 (Fig. 8c-d), which includes shoreline feedback but uses fixed transect positions, the model reproduces the same trends observed previously (see also the supplementary material, Fig. S3). The maximum deviations between levels 3 and 2 remain below 2.5 m, suggesting that coupling level 2 provides sufficient accuracy for relatively linear coasts with limited temporal changes in curvature. For such cases, the additional computational cost of implementing dynamic transects may not be necessary.

In contrast, for coupling level 1 (Fig. 8e-f), i.e disabling both shoreline feedback and transect updates. Both updrift sediment trapping and downdrift erosion are under-represented: the model does not account for the blocking and redistribution of sediment caused by the structure, leading to an overly simplified erosion pattern under sea-level rise.

### 3.4. Test case 3: Groyne

The test case investigates the evolution of a straight sandy shoreline disrupted by a single groyne, extending 20 m in width and 200 m offshore (Fig. 6c). The scenario involves obliquely-incident waves at a -5° angle and a linear SLR of 1 m over a decade (Table 1). The domain spans 4 km in length and 1.4 km in width, discretized with 50 m shoreline cells and a topobathymetry resolution of 10 m. Wave height and period are fixed while wave direction follows a normal distribution

to account for natural variability. The primary objective is to examine how wave-driven sediment transport interacts with structures, such as groynes, in shaping beach-dune morphology under the combined influence of incident waves and SLR.

Initially, the groyne disrupts longshore sediment transport, causing sediment accumulation on the updrift side and erosion on the downdrift side. As sea level rises over time, these patterns of deposition and erosion become more pronounced. As shown in Fig. 9a-b, both ShoreTrans translation modes show similar shoreline behavior: accretion occurs updrift, while downdrift erosion increases. However there are two main differences. First, dune morphology diverges substantially: in the rollover mode, the dune migrates landward while maintaining volume; in contrast, the encroachment mode leads to rapid dune erosion due to limited accommodation space. Second, shoreline retreat is more pronounced in the rollover mode compared to encroachment (mean shoreline position: 490 m vs. 473 m from the offshore boundary).

This scenario exhibits low sensitivity to the coupling level. Level 1 uses fixed transects without shoreline feedback and already captures the main features of shoreline and dune evolution. Level 2 adds shoreline feedback while keeping transects fixed, slightly improving agreement with level 3. Level 3 dynamically updates both transects and profiles, but offers negligible benefit in this case due to minimal shoreline curvature change. Alongshore-averaged differences remain below 2 m across all levels (See Table 2).

A summary of final shoreline positions for all coupling levels and modes is provided in Table 2, including the LX-Shore + Bruun rule benchmark.

## 4. Real beach test case: Lacanau, southwest France

### 4.1. Test case description

Lacanau is a seaside resort located on the southwest coast of France along the Atlantic Ocean. The study site spans a 5-km meso- to macrotidal sandy shoreline exposed to high-energy waves predominantly coming from the west-northwest. Incident wave energy varies seasonally, with monthly mean significant wave height and peak wave period ranging from approximately 1.1 m and 8.5 s in July to 2.4 m and 13 s in January. Erosion rates range from 0.3 m/y to 3 m/y depending on the dataset and methodology used (Castelle et al., 2018; Nicolae Lerma et al., 2022; Castelle et al., 2022).

Lacanau was selected as a representative test case because it exemplifies common challenges faced by managed sandy coasts, including

<footnote>a Based on a realistic time series of a high-energy wave-dominated coast (see Figure S1).</footnote>

<footnote>b Normal distribution.</footnote>
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Results for Case 2: Columns display two rollover modes – full rollover and encroachment – while the rows correspond to the three coupling levels offered by LX-ST (see Section 2.3). The thick black line indicates the shoreline, and the dashed red line represents the shoreline derived from stand-alone LX-Shore with the Bruun rule activated (see Section 2.2).</figcaption></figure>

chronic erosion, sediment supply deficits, and the use of hard engineering structures that disrupt longshore transport. While the site is relatively straight, it offers a realistic setting for evaluating model coupling behavior under conditions of human intervention. The availability of high-resolution topographic and bathymetric data further supports its use as a benchmark case for assessing the LX-ST coupling approach, which simulates the interaction between alongshore, chronic erosion and sea level rise processes under coastal management constraints. This application is not intended as a predictive forecast of future shoreline change, but rather as a test of the coupling framework's ability to capture key morphodynamic feedback under realistic, data-informed conditions.

Initial topobathymetry was constructed using LiDAR topography collected in 2011 (Nicolae Lerma et al., 2019), complemented by bathymetric data from the Litto3D initiative – a collaboration between the French Hydrographic and Oceanographic Service (SHOM) and IGN

– acquired over campaigns from Sep 2020 to Sep 2022. These datasets were interpolated onto a 10 (longshore) × 1 m (cross-shore) grid to generate a coherent topobathymetric surface. For modeling purposes, the shoreline was approximated by the 1.5 m elevation contour above mean sea level, serving as a proxy for the shoreline position and simplified as a straight line. Beyond this, the subaqueous profile was reconstructed using a longshore-averaged Dean profile calibrated with the observed topobathymetry surface mentioned earlier. For qualitative validation of coastal dune evolution, additional LiDAR data collected in autumn 2023 by OCNA were used.

Wave forcing data (1940–2024) were sourced from ERA5 (Hersbach et al., 2020), a global reanalysis product by the European Centre for Medium-Range Weather Forecasts (ECMWF). ERA5 provides hourly wave conditions at a 0.5° spatial resolution. For this study, data were extracted at a nearshore point offshore of Lacanau (approx. 50 m water depth; coordinates: -1.5°E, 44.5°N), covering the period from 2011 to
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Results for Case 3: Columns display two rollover modes – full rollover and encroachment – while the rows correspond to the three coupling levels offered by LX-ST (see Section 2.3). The thick black line indicates the shoreline, and the dashed red line represents the shoreline derived from stand-alone LX-Shore with the Bruun rule activated (see Section 2.2).</figcaption></figure>

2024 (Fig. 10). To extend the dataset to 2100, the 1940–2024 time series was duplicated. A one-week moving average was applied at the duplication boundary to smooth the transition. This method preserves the statistical properties of the local wave climate while avoiding artificial discontinuities, enabling a controlled, stationary wave forcing input consistent with the illustrative scope of the Lacanau test case.

To simulate sediment transport around the seawall, we used the “full bypassing” (FB) method described in Durand et al. (2024). Unlike the “shoreline bypassing” (SB) approach used in idealized Test Case 2, the FB method accounts for subaqueous transport both inside and outside the surf zone. It allows sand to bypass coastal structures even when the shoreline does not reach the structure’s tip.

The computational domain (Fig. 11a) spans 15 km (longshore) × 2.45 km (cross-shore), but analysis focuses on a 5 km central section (Supplementary table 2 summarizes the main parameters). The additional 10 km (not shown) is included to minimize the influence of open boundary conditions. The depth of closure is set to 13.5 m (estimated using the average depth of closure using the Hallermeier, 1980

formula), and the dune height is 17 m. The time step for longshore transport ($\Delta t_{LX}$) is 1 h. The shoreline is updated annually ($\Delta t_{ST} = 1$ y) using encroachment mode and LX-ST level 2 coupling. We use the median sea-level rise projection from the CMIP6 SSP5-8.5 scenario (Intergovernmental Panel On Climate Change (Ipcc), 2023; Garner et al., 2021; Kopp et al., 2023). Shared Socioeconomic Pathways (SSPs) are scenarios used in climate modeling to describe possible future developments in demographics, economics, technology, and policy. SSP5-8.5 corresponds to a high-end emission scenario characterized by rapid economic growth, continued fossil fuel use, and limited climate policy, leading to a radiative forcing of 8.5 W/m$^2$ by 2100. The median SLR trajectory is used as the baseline forcing in the simulations, while the 17th–83rd percentile envelope are used to illustrate the uncertainty range of the SLR input scenarios (Supplementary figure S5). This is combined with a steady erosion rate of 1.4 m/y, based on observed shoreline retreat over the period 1950–2023. This trend reflects the site’s long-term sediment deficit and chronic erosion (Nicolae Lerma et al., 2022).
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Significant Wave Height (Hs), Peak Period (Tp), and Mean Wave Direction (MWD) from ERA5 wave data (1940–2024), extended to 2100 with duplication and one-week smoothing (vertical bands). MWD is in local coordinates, relative to the shore-normal.</figcaption></figure>

## 4.2. Validation

To evaluate the performance of the LX-ST coupling, we performed a simulation covering the 2011–2023 period and compared the modeled results with annual dune front positions derived from LiDAR topographic surveys conducted between 2014 and 2023. Validation focused on the 10-m elevation contour, used here as a proxy for the dune front, and analyzed across 100 shore-normal transects. This proxy was selected to reduce the influence of short-term cross-shore fluctuations and better isolate decadal-scale morphodynamic trends, consistent with the model’s intended scope. LiDAR data are available for each year within this period except 2015, allowing for nearly continuous year-by-year validation.

The box plots (Fig. 11b) show the distribution of these metrics across the domain. Overall, RMSE and MAE remain below 10 m, with median values around 8 m and 6 m, respectively, indicating robust performance for a reduced-complexity model. While most years exhibit stable errors, some outliers contribute to the upper whiskers – particularly 2014 and 2019 – coinciding with major storm events that caused abrupt morphological changes (Castelle et al., 2015, 2017; Laporte-Fauret et al., 2020). These short-term dynamics are not captured by the LX-ST coupling, which is designed to represent long-term trends. The moderate to high Nash–Sutcliffe Efficiency (NSE) values (median > 0.6) further suggest that the model performs well in simulating decadal shoreline evolution, despite omitting high-frequency processes.

We emphasize that no site-specific calibration was performed for this application. The reported metrics therefore reflect the model’s ability to reproduce interannual shoreline evolution without tuning. Despite its reduced complexity and long-term focus, LX-ST shows good agreement with annual dune front positions derived from LiDAR data, suggesting its capability to capture observed trends across the 2014–2023 period.

In addition to assessing shoreline change, we qualitatively evaluated model performance in reproducing dune face evolution using 2023 LiDAR data (Fig. 11a). We focused on the upper dune face

(elevation Z > 5 m), where the influence of cross-shore processes and short-term hydrodynamics is limited. Model predictions for 2023 were compared with observed topographic profiles along selected transects. Results show a reasonable agreement, with modeled (observed) landward shifts of 22 m (18 m) and 20 m (12 m) (Fig. 11c,e). Although high-resolution, multi-decadal LiDAR data are lacking to validate shoreface dynamics, the model’s ability to capture upper dune face retreat provides confidence in its applicability for long-term morphodynamic simulations.

## 4.3. Results

Fig. 12a shows the final topobathymetry in 2100 from a simulation covering the 2011–2100 period, with the seawall initially aligned with the shoreline (see initial condition in Fig. 11a). Over time, the seawall evolves into a rigid feature protruding seaward within the profile due to chronic erosion, disrupting longshore sediment transport and effectively acting as a groyne. By 2100, three distinct zones emerge: (i) updrift of the seawall, sediment accumulation reduces shoreline retreat and preserves the dune system; (ii) in front of the seawall, the absence of accommodation space leads to intense scouring and complete beach erosion; and (iii) downdrift, limited sediment supply and ongoing erosion cause significant profile lowering and complete dune loss

Fig. 12b illustrates the projected shoreline position under the SSP5–8.5 scenario, showing the 50th percentile (median) and 17%–83% confidence interval. Downdrift of the seawall, maximum retreat exceeds 230 m, with an uncertainty band of 35 m — reflecting the compounded effects of sediment trapping, evolving topobathymetry, and nonlinear feedback captured by the model. Updrift of the seawall, erosion is partially mitigated by sediment accumulation, leading to a narrower envelope (~12 m) and moderate erosion (~110 m).

Cross-shore transects (Fig. 12c–e) provide detailed insights into profile evolution at representative positions downdrift, in front of, and updrift of the seawall. These panels compare the initial profile
<figure><img src="image_13.png" /><figcaption>Fig. 11. (a) Initial topobathymetry with validation transects (dashed lines) and seawall location (solid black polygon); (b) Model performance from 2014–2023 based on 10-m contour, aggregated over the 5-km domain: RMSE, MAE, and Bias (left axis), NSE (right axis); (c–e) Cross-shore profiles at downdrift, seawall, and updrift transects showing the 2011 initial state, 2023 model output, and 2023 LiDAR.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. (a) Final topobathymetry showing cross-shore transects and shoreline orientation; (b) Projected shoreline position in 2100 under SSP5-8.5, showing the median (black line) and 17%–83% confidence envelope (gray shading); (c–e) Cross-shore profile evolution from 2011 to 2100 at the downdrift, seawall, and updrift transects, respectively, comparing the initial topography (2011) with simulated profiles from LX-ST, ShoreTrans, and LX-Shore (with Bruun activated).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 13.** (a) Shoreline evolution timestack with the -20 m value (seawall position) highlighted in black. (b) Alongshore shoreline position variability, calculated as the deviation of shoreline position from the longshore-averaged shoreline at each time step — the seawall section is masked for clarity.</figcaption></figure>

(2011) with simulations from LX-ST (coupled), ShoreTrans (cross-shore only), and LX-Shore (Bruun). The comparison highlights the necessity of coupling both longshore, erosion and sea-level rise processes to resolve spatially complex morphodynamic responses.

At the updrift transect (Fig. 12e), shoreline retreat is more limited (110 m), and erosion of the upper profile is reduced due to sediment accumulation against the seawall. LX-ST captures both the retreat and the modified profile. Compared to LX-ST, ShoreTrans overestimates retreat as it lacks representation of longshore sediment inputs. LX-Shore underestimates retreat and does not reflect the internal redistribution of sediment across the profile.

At the seawall transect (Fig. 12d), LX-ST simulates localized scouring in front of the structure, leading to the development of a steep nearshore slope, consistent with the expected wall effect. ShoreTrans also reproduces this feature, which arises from the displacement of erosion seaward in the absence of accommodation space. LX-Shore does not resolve this process, as it lacks cross-shore adjustment capability.

At the downdrift transect (Fig. 12c), shoreline retreat exceeds 230 m, accompanied by a broad landward shift of the beach-dune system. LX-ST reproduces both the retreat magnitude and the evolving profile shape. ShoreTrans underpredicts retreat, as it does not account for the reduction in sediment supply due to longshore transport gradients. LX-Shore captures the retreat distance but fails to reflect the accompanying reshaping of the coastal profile.

Fig. 13 further illustrates a two-stage sequence with a clear trajectory shift around 2065 in the current scenario of SLR, chronic erosion, and steady wave climate. Before 2065, erosion remains quasi-uniform alongshore, primarily driven by SLR and sediment deficit, except near the seawall sector. After 2065, erosion progressively intensifies downdrift. This shift coincides with the point at which the updrift shoreline becomes sufficiently eroded that not all sediment bypasses the structure. As a result, less sediment reaches the downdrift area, leading to accelerated erosion in that region.

# 5. Discussion

## 5.1. Coupling strategy and benchmark

LX-ST is built around a fully dynamic coupling strategy which combines dynamic transect repositioning with feedback between shoreline evolution and shoreface profile translation. This approach is designed to simulate complex coastal geometries where both shoreline orientation and cross-shore morphology evolve over time. While the present study focuses on simplified configurations, the model structure remains applicable to more complex environments (e.g. rotating embayed beaches, migrating megacusps).

To balance realism and computational demand, LX-ST also includes level 2 and level 1 as simplified alternatives. Level 2 retains shoreline feedback but fixes transect positions, providing a compromise suited for moderately dynamic coastlines with limited curvature change. Level 1

omits both shoreline feedback and dynamic transects, making it computationally efficient but appropriate only for simple, linear coastlines.

Runtime performance reflects the increasing complexity of coupling. Normalizing the computation time of the Lacanau simulations to 100 years per kilometer of the longshore domain, levels 1, 2, and 3 require 0.74 min, 3 min, and 16–20 min, respectively. This flexibility allows users to match model configuration to site-specific morphological complexity and computational constraints. In comparison to other models, LX-ST performs competitively (see Table S1, with runtimes converted to computation time for 100 y/km). GENESIS (Hanson, 1989) is highly efficient but does not include profile coupling and lacks standardized runtime reporting. CoSMoS-COAST (Vitousek et al., 2017) enables rapid regional simulations (0.03–0.04 min per 100 y/km) but omits dynamic bathymetric updates and feedback between shoreline change and wave conditions. IH-LANSloc (Álvarez-Cuesta et al., 2023), which shares conceptual similarities with LX-ST level 2, is physically robust but more computationally demanding. It couples with SWAN for wave propagation, and to reduce runtime, long-term simulations are based on a single SWAN run per year, representing mean wave conditions. With this simplification, runtimes typically reach several hours for 10-year simulations over 1–10 km domains (i.e., up to 10–100 h per 100 y/km). In contrast, LX-ST level 2 uses the Larson formulation (Larson et al., 2010) for wave breaking and completes a 90-year simulation over 15 km in 30 min (3 min/100 y/km). Of course, running LX-ST with SWAN activated in the LX-Shore model would significantly increase the computation time of the LX-ST coupling, but would also allow better representing the wave dynamics (e.g. on rotating embayed beaches).

## 5.2. Trajectory shift

The future of sandy beaches under sea-level rise remains a subject of active debate. While there is broad consensus on their vulnerability, the literature offers contrasting perspectives on long-term outcomes. For example, Vousdoukas et al. (2020) project widespread shoreline retreat and the potential disappearance of many sandy coasts based on extrapolated trends and global-scale SLR scenarios. In contrast, Cooper et al. (2020) argue that beach survival depends not solely on retreat rates, but also on factors such as beach width and the availability of accommodation space. According to this view, beaches that are backed by dunes capable of rolling landward may persist, while those constrained by hard structures, such as seawalls or cliffs, are at a greater risk of extinction.

These perspectives frame the interpretation of our Lacanau test case, which explores a scenario driven by SLR and a chronic sediment deficit (encroachment mode). LX-ST's approach reveals that erosion patterns are not spatially uniform: the beach fronting the seawall is expected to completely disappear by 2050 due to the lack of accommodation space, consistent with the mechanisms described by Cooper et al. (2020). Meanwhile, the dune system downdrift, although initially resilient, is
already significantly impacted by 2050 and is projected to vanish by the end of the century.

Interestingly, the model captures a noticeable shift in coastal trajec-
tory around 2065, driven by the combined effect of SLR and longshore
sediment transport gradients. What starts as a relatively uniform re-
treat gradually transitions into an acceleration of erosion downdrift of
the seawall. This highlights how long-term forcing can lead to non-
linear, location-specific responses. The results also show that dunes and
roll-back systems, when unconstrained, remain relatively resilient, re-
inforcing the importance of available accommodation space in shaping
shoreline evolution. While this scenario is not intended as a prediction
for Lacanau, it illustrates how the LX-ST coupling can help identify key
transitions and feedback in coastal morphology. Rather than aiming for
global generalization, the model provides a complementary approach
to large-scale assessments like Vousdoukas et al. (2020), offering more
detailed insights at local to regional scales.

5.3. *Limitations and model assumptions*

Several simplifications (in the coupling strategy itself or inherited
from ShoreTrans and LX-Shore) constrain the current implementation
of LX-ST.

While ShoreTrans permits user-defined cross-shore sediment inputs – such as imposed dune growth rates – it does not internally simulate aeolian transport. As a result, wind-driven sand exchanges between the beach and dunes are not dynamically coupled to modeled beach morphology. This limits LX-ST's ability to capture feedback between beach width, fetch conditions, and dune accretion. In systems where aeolian processes contribute to dune maintenance and post-storm recovery, their exclusion may lead to an underestimation of the system's long-term buffering capacity (Elko et al., 2016). Incorporating a dynamic aeolian transport module that responds to evolving beach-dune geometry and wind forcing is a key direction for future development.

An important simplification of LX-Shore is the assumption of uni-
form sediment properties, such as grain size and sediment transport
parameters. This is a common approach in reduced-complexity mod-
els (e.g Vitousek et al., 2017), but it may not hold in settings with
significant sediment variability, where spatial changes in grain size
could influence transport gradients and shoreline response. Incorpo-
rating variable sediment properties into LX-Shore would require sub-
stantial changes to the current framework. As a practical alternative,
we recommend sensitivity testing where heterogeneity is suspected. For
the Lacanau case, sediment characteristics are assumed to be relatively
uniform, and targeted sensitivity tests confirm that grain size variations
within plausible bounds have limited influence on model results (see
Supplementary Material S6).

LX-ST is best suited for sandy, wave-dominated coasts and does not explicitly simulate key processes found in more dynamic environments such as deltaic systems, tidal inlets, or barrier islands affected by overwash and inlet migration. In these cases, more specialized models that resolve tidal flows, inlet morphodynamics, or storm-driven overwash are likely to be more appropriate (Hanson, 1989; Larson et al., 1989). Applying LX-ST to low-energy settings where longshore transport dominates, such as the Great Lakes, could increase its practical relevance. However, this presents challenges. Mean water levels in the Great Lakes can fluctuate by over 1 meter within a few decades, driven by variability in precipitation and evaporation (Gronewold et al., 2013). These relatively fast changes in water level fall outside the assumptions of gradual, long-term sea-level rise embedded in models like ShoreTrans. Addressing this limitation may require smoothing of water level input or adapting the SLR component to better reflect regional hydrological variability. Until then, use of LX-ST in such environments should be done cautiously and with a clear understanding of its constraints.

Currently, the LX-ST coupling uses a fixed time step for updat-
ing shoreline and profile positions. While simple and consistent, this

approach ignores variations in forcing intensity. Implementing an adap-
tive time step – triggered by thresholds in shoreline change or sea-level
rise – could improve computational efficiency and model stability,
focusing resources on high-gradient periods.

Finally, while LX-ST has been applied to synthetic cases and a
real beach-dune system (Lacanau), complete model validation remains
limited. Without multi-decadal topobathymetric data isolating sea-level
rise impacts, long-term validation remains challenging. LiDAR compar-
isons offer a partial check, but future applications should test the model
across diverse settings and forcing scenarios using both planform and
profile datasets.

Despite these limitations, LX-ST's modular design allows extension as needed — supporting the integration of dynamic dune modules, probabilistic forcings, or alternative sediment transport formulations. Rather than aiming to represent all processes, LX-ST serves as a flexible framework adaptable to evolving research and management needs. For practical applications requiring insight into both short- and long-term shoreline changes, a first approach could involve combining the LX-ST coupling with satellite or in situ data to estimate short-term statistical characteristics (e.g., daily, seasonal, interannual), which can then be integrated with the long-term projections from LX-ST.

6. Conclusion

This study introduced LX-ST, a modular and computationally ef-
ficient framework to simulate coastal evolution over decadal to cen-
tennial timescales. LX-ST bridges planform and profile-scale dynamics
by coupling the two-dimensional shoreline model LX-Shore with the
transect-based profile model ShoreTrans. Through this coupling, LX-
ST enables dynamic feedback between longshore sediment transport,
evolving shoreline curvature, and shoreface response to sea-level rise.

The framework provides three levels of coupling to accommodate different modeling requirements and computational resources. Level 3, the fully dynamic configuration, updates both shoreline position and transect orientation at each timestep, enabling the model to resolve feedback between evolving shoreline geometry and shoreface response. Level 2 retains shoreline feedback but employs fixed transect positions, representing a computationally efficient compromise for scenarios where changes in shoreline curvature are moderate. Level 1 is the most simplified option, omitting both shoreline feedback and transect updating; it is best suited for idealized or rectilinear shorelines where the effects of feedback are minimal and computational cost is a primary concern.

A suite of synthetic test cases demonstrates that model performance
is strongly influenced by the choice of coupling level. In the bulge test
case, designed to simulate a shoreline with significant planform vari-
ability, only the fully dynamic approach (level 3) accurately captures
the feedback between evolving curvature and sediment redistribu-
tion. Lower coupling levels either misrepresent local erosion patterns
(level 2) or fail to track shoreline realignment altogether (level 1). In
contrast, for the seawall test case, where shoreline curvature evolves
more modestly, level 2 provides a sufficiently accurate response while
reducing computational cost. Finally, in the groyne test case, which pri-
marily involves alongshore redistribution without substantial changes
in shoreline geometry, level 1 yields results comparable to higher
coupling levels. These findings underscore the importance of adapting
the coupling strategy to site-specific morphodynamic complexity. Ap-
plication to the Lacanau site, using level 2, further demonstrates the
framework's capacity to resolve feedback and capture a trajectory shift
driven by sea-level rise and sediment trapping updrift of the seawall.

A key next step is to run ensemble simulations with the LX-ST model to explore how uncertainty in sea-level rise and erosion rates affects long-term shoreline change. This will provide a more robust basis for scenario planning, without requiring changes to the existing model framework.
In summary, LX-ST provides a transparent and flexible methodology for coastal morphodynamic modeling, enabling the exploration of long-term shoreline trajectories, the identification of emergent feedback mechanisms, and the formulation of risk-based coastal management strategies in the context of climate change.

### CRediT authorship contribution statement

**Mohammad Traboulsi:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Déborah Idier:** Writing – review & editing, Writing – original draft, Validation, Supervision, Software, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. **Bruno Castelle:** Writing – review & editing, Writing – original draft, Validation, Supervision, Software, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. **Arthur Robinet:** Writing – review & editing, Validation, Software, Resources, Methodology, Investigation, Data curation, Conceptualization. **Vincent Marieu:** Writing – review & editing, Validation, Software, Resources, Methodology, Investigation, Data curation, Conceptualization. **Elsa Durand:** Writing – review & editing, Software. **R. Jak McCarroll:** Writing – review & editing, Software.

### Code and data availability

The LX-ST code and its core component LX-Shore are not publicly available due to proprietary restrictions but may be shared upon reasonable request. Public release is planned within the next few years to support broader use and collaboration. The original ShoreTrans model is open-source and available at https://github.com/jakmccarroll/ShoreTrans. A Fortran implementation of ShoreTrans, adapted for use within LX-ST, is available at https://github.com/user689/ShoreTrans-fortran. The input data for all test cases, along with the MATLAB function used for shoreline-based topobathymetric interpolation, are publicly archived at https://doi.org/10.5281/zenodo.15586306. Topographic LiDAR data can be accessed through the Observatoire de la Côte de Nouvelle-Aquitaine (OCNA) at https://observatoire-cote-aquitaine.fr, and bathymetric data are available from the SHOM Litto3D database at https://diffusion.shom.fr.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This work was carried out in the framework and was funded by Agence Nationale de la Recherche (ANR) grant number ANR-21-CE01-0015 and BRGM. Elsa Durand is funded by an ANRT/CIFRE contract (n° 2021/0579) between Waeles Marine Consultants, Bordeaux University, and BRGM. The authors thank Rémi Thiéblemont (BRGM) for providing the sea level rise projection datasets used for the SSP scenario simulations. ERA5 wave data is produced by the Copernicus Climate Change Service (C3S) at ECMWF. LiDAR topography data were provided by the Observatoire de la Côte de Nouvelle-Aquitaine (OCNA), while bathymetric data were sourced from the Litto3D initiative, a collaboration between the French Hydrographic and Oceanographic Service (Shom) and the French National Institute of Geographic and Forest Information (IGN). The authors gratefully acknowledge the constructive and thoughtful feedback provided by the four anonymous reviewers. Their comments significantly improved the clarity, rigor, and overall quality of this manuscript.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.envsoft.2025.106624.

### Data availability

I have included a section explaining what data is available and what data needs permission.

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