# Temporal scales of variability in Regions Of Freshwater Influence on the French continental shelf over two decades

Maud Martinez Almoyna, Guillaume Charria, Marc Sourisseau, Anne Gaymard, Xavier Couvelard, Sebastien Theetten, Jean-François Le Roux

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Maud Martinez Almoyna, Guillaume Charria, Marc Sourisseau, Anne Gaymard, Xavier Couvelard, et al. Temporal scales of variability in Regions Of Freshwater Influence on the French continental shelf over two decades. Journal of Marine Systems, 2025, 249, 104068 (18p.). 10.1016/j.jmarsys.2025.104068. hal-05105696

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Temporal scales of variability in Regions Of Freshwater Influence on the French continental shelf over two decades

Maud Martinez Almoyna<sup>a,*</sup>, Guillaume Charria<sup>a</sup>, Marc Sourisseau<sup>b</sup>, Anne Gaymard<sup>a</sup>, Xavier Couvelard<sup>c</sup>, Sébastien Theetten<sup>a</sup>, Jean-François Le Roux<sup>a</sup>

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ARTICLE INFO

Keywords:

ROFI

Rivers

Numerical modelling

Shelf dynamics

Bay of Biscay

English Channel

A B S T R A C T

The Regions Of Freshwater Influence (ROFIs) are defined as the area on the continental shelf in the vicinity of estuaries, where freshwater from the river significantly influence water properties and circulation. These regions are subject to a variety of dynamic forcings, including tides, winds and river runoffs, which exhibit considerable variability. The objective of this study is to identify the dominant time scales of variability of the three major ROFIs (Seine, Loire, and Gironde) of the French continental shelf and their evolution over the last two decades. In order to address these questions, we developed a high-resolution numerical simulation of the physical dynamics of the Bay of Biscay and the English Channel. The results demonstrate that the three ROFIs oscillate on the same two cycles: the semidiurnal cycle, caused by tides, and the annual cycle, linked to the seasonal variation in runoff. At the weekly and monthly time scales, two contrasting dynamics emerge. The Seine ROFI, situated in the eastern English Channel, is predominantly influenced by tides and exhibits a third oscillatory cycle, namely the fortnightly cycle. In the Bay of Biscay, the Loire and Gironde ROFIs are more influenced by wind events that shape their monthly variations. The interannual variations are primarily driven by runoff, with an observed reduction in ROFIs extension over the twenty years simulated correlated with a decrease in runoff. However, the combination of shorter timescale events impacts the interannual variability, leading to years with distinctive dynamics of the ROFIs.

**1. Introduction**

The Regions Of Freshwater Influence (ROFIs) are the areas of the
coastal ocean located on the continental shelf in close proximity to
estuaries, that are characterised by significant freshwater inflow. The
freshwater inflows exert a significant influence on the dynamics and
living conditions of these regions. Due to their location, they are the
first regions of the ocean to be affected by river inputs, both in terms
of the quantity of freshwater and the variety of inputs, including nutri-
ents and contaminants, transported along the land-ocean continuum.
Consequently, they form vulnerable regions, impacted by the climate
change and human pressures.

A formal definition of ROFI is given by Simpson (1997) as the
region on the shelf where the local input of freshwater buoyancy is
comparable with, or exceeds, the seasonal input of buoyancy as heat
which occurs all over the shelf. This definition refers to the region
where salinity exerts a predominant influence on variations in density.
The ROFI region encompasses the river plumes and their associated

area of dilution on the shelf, and is therefore significantly influenced by
their dynamics (Horner-Devine et al., 2015). A single ROFI may contain
the plumes of multiple rivers, as observed in the case of the Liverpool
Bay ROFI (Sharples and Simpson, 1995; Verspecht et al., 2009).

The continental shelf of the Bay of Biscay and the English Channel are two coastal regions with contrasting dynamics (Fig. 1). Both regions are subject to significant influence from freshwater fluxes from land, distributed through three major rivers along the French coast: the Loire and the Gironde rivers, situated within the Bay of Biscay, with average runoffs exceeding 700 m³s⁻¹, and the Seine river, located within the Eastern Channel, whose average runoff exceeds 450 m³s⁻¹.

The Bay of Biscay opens in the north-east Atlantic ocean and is
located between the north coast of Spain and Brittany. The continental
shelf along the French coast is a meso-tidal environment, characterised
by an average depth of 100 m and a shelf variable width ranging from
60 km in the south of the bay to 160 km in front of the Loire river.
The seasonal complex circulation on the shelf have been studied for

<footnote><sup>a</sup> Ifremer, Univ. Brest, CNRS, IRD, Laboratory for Ocean Physics and Satellite remote sensing (LOPS), Technopole Brest Iroise, Ctr Brest, 29280, Plouzane, France</footnote>

<footnote>b Ifremer, DYNECO Pelagos, Technopole Brest Iroise, Ctr Brest, 29280, Plouzane, France</footnote>

<footnote>c Service Hydrographique et Océanographique de la Marine (SHOM), 29200, Brest, France</footnote>

<footnote>* Corresponding author.
E-mail address: maud.martinez.almoyna@ifremer.fr (M. Martinez Almoyna).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Bathymetry of the Bay of Biscay and the English Channel in numerical simulation (A) and the three regions under the influence of the Seine (B), the Loire (C) and the Gironde (D) rivers. Runoff discharge of the three rivers from 2001 to 2020 (E).</figcaption></figure>

several years, using both in-situ data and numerical models (Puillat et al., 2006; Lazure et al., 2009; Charria et al., 2013; Le Boyer et al., 2013; Kersalé et al., 2016). The hydrology of the Bay of Biscay shelf has been reviewed and completed by Puillat et al. (2004). In winter, the water column is generally homogeneous. However an inversion of the vertical temperature gradient may occur due to the influx of fresher and colder water masses originating from the estuaries. In spring, thermal stratification establishes, progressing from south to north along the French shelf. This process is reinforced during the summer, resulting in strong vertical temperature gradients.

The plumes of the Loire and Gironde rivers have already been the subject of several studies. Toublanc et al. (2023) demonstrated that variations in runoff discharge or winds and the existence of tides have a predominant effect on the shape of the Gironde plume at the estuary outlet. Moreover, Ayouche et al. (2021) showed that tides and winds also impact the internal and frontal dynamics of the plume. According to Lazure and Jegou (1998), the river plumes generally turn to the right as they exit the estuary and follow the coastline northwards, resulting in the formation of a coastal current as expected from a balanced river plume in the northern hemisphere (Horner-Devine et al., 2015). In such circumstances, the Gironde plume may merge with the Loire plume on a long coastal current. However, the wind may modulate this dynamic. A south-easterly wind, which favours downwellings, will have the effect of constraining the plume to the coast and reinforcing the circulation of the coastal current. Conversely, a north-westerly wind, favouring upwellings, will stop the propagation of the plumes and disperse them offshore (Puillat et al., 2006). Lazure and Jegou (1998) showed that winter winds tend to favour plume confinement at the coast, while a change in wind direction at the end of March or early April favours southwards propagation offshore of the plumes. Both (Lazure and Jegou, 1998) with numerical simulations from 1990

to 1996 and Puillat et al. (2004) with hydrographic measurements from 1992 to 2000 have demonstrated that the Loire and Gironde river plumes exhibit significant interannual variability. In particular, Puillat et al. (2004) demonstrated that wind and runoff events occurring on a monthly timescale have the potential to influence the interannual variability of the salinity distribution in the Bay of Biscay. Nevertheless, the study concludes that, given the mesoscale activity, it is necessary to employ a higher sampling resolution, both spatial and temporal, to obtain a better understanding of the interdependence of processes and their variability.

The English Channel is a semi-enclosed shelf sea, with openings to the west towards the Bay of Biscay and the Atlantic Ocean, and to the north-east towards the North Sea via the Dover Strait. The Channel is separated into two regions by the Cotentin peninsula. This macro-tidal environment has an average depth of 50 m where the tides have a significant influence on the overall dynamics. In the western part of the Channel, the tide may be described as a propagating wave while the tidal wave is more characteristic of a standing oscillation in the eastern Channel (Pingree, 1980). The tides generate strong residual currents (Pingree and Maddock, 1977; Salomon and Breton, 1993; Sentchev et al., 2006) that cross the Channel from west to east, with numerous nested gyres in the vicinity of islands and capes (Ménesguen and Gohin, 2006). In this shallow environment, the tide also plays an important role in mixing. Inducing bottom friction, the barotropic tidal currents homogenise the water column, drastically limiting any stratification (Pingree, 1978).

The Seine river discharges into the Bay of Seine, which is located in the eastern English Channel (Fig. 1B). The Seine estuary and its plume have been mostly studied from the perspective of sediment dynamics (Grasso et al., 2018; Schulz et al., 2018; Chapalain et al., 2019; Verney et al., 2024; Poppeschi et al., 2024). At the outlet of the
estuary, Chapalain et al. (2019) and Verney et al. (2024) observed the development of a haline stratification at low tide. The strength of the stratification is influenced by the tidal range and runoff. During neap tides or periods of high runoff discharge, the stratification becomes more pronounced. The plume then splits seawards from the river mouth, with the larger part heading north-west, while the remainder follows the south coast of the Bay westwards. Subsequently, the northward plume follows the coast towards the Dover Strait. It forms a broad band of fresher water associated with a haline front between waters of estuarine origin and coastal waters (Sentchev and Korotenko, 2004). Using a 3D numerical model, Cugier and Le Hir (2002) have shown that the dynamics of the Seine plume in the bay of Seine depend mainly on bathymetry and tides, and to a lesser extent on wind.

As shown in the literature, ROFIs are under the influence of several forcing mechanisms, including tide, wind, and river runoff discharge, which operate at different time scales. The primary objective of this study is to identify the dominant time scales of variability for the Bay of Biscay and English Channel ROFIs and to explain their differences. A second objective is to study the variations in the ROFIs over the last two decades to evaluate their interannual variability and the impacts of climate change on the coastal circulation. To answer these questions, we produced and analysed a realistic numerical simulation with fine spatial and temporal resolutions. The paper is organised as follows: the model configuration, data and methods are described in Section 2. The model assessment is presented in Section 3. The different scales of variability of ROFIs are identified in Section 4.1 and then detailed in Sections 4.2, 4.3, 4.4 and 4.5. Section 4.6 focuses on some extreme years. The main results are then discussed in Section 5 and followed by the main conclusions and perspectives.

# 2. Ocean model, data and methods

## 2.1. Modelling framework

### 2.1.1. GAMAR model configuration

CROCO is an ocean numerical model that solves the primitive hydrostatic equations in a generalised terrain-following vertical coordinate system. This model is designed to resolve very fine scales and their interactions with larger scales, which makes it particularly well suited to the study of coastal areas (Auclair et al., 2024).

To study ROFIs of major rivers along the French Atlantic coast, a configuration, named GAMAR configuration, has been set up for the Bay of Biscay and the English Channel. In order to accurately represent the sub-mesoscale processes, a fine horizontal resolution of 1 km with 40 vertical levels is implemented with the following vertical S-coordinate parameters: $\theta_s = 6$, $\theta_b = 4$ and $h_c = 15$ m (Jullien et al., 2005). This vertical discretisation, refined at the surface and at the bottom, provides, for a 50 metre deep water column, a sampling of 4 sigma levels in the first metre at the surface, and a one-metre-thick bottom level. The geographical domain extends from the Spanish coast in the south at 43° 17′N latitude, to the north at 50° 52′N, with a western boundary at 8° W longitude and an eastern limit at 1° 40′E. The open boundaries are at the north and west of the domain, towards the North Atlantic and the North Sea via the Strait of Dover. The Fig. 1 illustrates the bathymetry of the simulated area, including a focus on three specific regions of interest: the Eastern Channel, the Armorican shelf south of Brittany and the Aquitaine shelf. The simulated period runs from January 2000 to December 2020. The first year is let as a spin-up period and analyses began in 2001.

Particular attention has been devoted to the development of the model configuration based on several assessment indicators (refer to the 3 section for further details). The RSUP3 advection scheme was chosen to limit spurious diapycnal mixing in terrain-following coordinate models, as described by Marchesiello et al. (2009). A generic length-scale parametrisation (GLS mixing) boundary layer scheme parameterise the subgrid-scale vertical mixing processes (Umlauf and

Burchard, 2003), and ECUME V6 (Exchange Coefficients from Unified Multi-campaigns Estimates) is used for the sea-air exchanges at the atmospheric surface boundary layer (Belamari, 2005). The time step is set to 45 s, with instantaneous fields saved every hour.

### 2.1.2. Open boundary conditions and external forcings

The hourly atmospheric forcings (air temperature, relative humidity, 10 m wind, and radiative fluxes) are extracted for the study area from the ERA5 reanalysis (Hersbach et al., 2020) produced by the Copernicus Climate Change Service (C3S) at the European Centre for Medium-Range Weather Forecasts (ECMWF). The open boundary conditions in the western and the northern regions of the model configuration are defined from prescribed fields extracted from the Global Reanalysis GLORYS12V1 (CMEMS, 2024). The tidal sea surface elevation and currents with 8 harmonic constituents are imposed along the boundaries using the FES2014 ocean tide atlas (Lyard et al., 2021). The daily river runoffs used for the 23 rivers within the configuration are estimated from observations at gauging stations of the French hydrology database (http://www.hydro.eaufrance.fr). If the river gauging stations are located upstream of the river mouth, the river flow intensities are multiplied by the ratio of the total catchment area to the catchment area at the gauging station. The Spanish rivers observations are collected from Emodnet Physics (https://emodnet.ec.europa.eu/) and the Gipuzkoako Foru Aldundia (https://www.gipuzkoa.eus/en/web/obrahidraulikoak/hidrologia-eta-kalitatea/aforaleku-iraunkorren-sarea). River runoffs from South of United Kingdom are provided by the In Situ Thematic Centre from Copernicus Marine Service (https://marine.copernicus.eu/about/producers/insitu-tac). In the event of missing runoff values, a computed weekly climatology is employed to fill the gaps.

## 2.2. Observations used for model assessment

### 2.2.1. Remotely sensed sea surface temperature

The product considered for remotely sensed Sea Surface Temperature (SST) is the gridded European North West Shelf/Iberia Biscay Irish Seas - High Resolution L4 Sea Surface Temperature Reprocessed (CMEMS, 2023). This product is derived from Sea Surface Temperature Analysis from the European Space Agency Sea Surface Temperature Climate Change Initiative (ESA SST CCI) L3 products (covering the period 1982–2016) and from the Copernicus Climate Change Service (C3S) L3 product (covering the period 2016–2019). The gridded SST products are designed to represent a daily mean SST field at 20 cm depth.

### 2.2.2. In situ time series from COAST-HF network

Long-term in situ observations providing a reference for the evolution of the temperature and the salinity are measured from sensors on buoys from the Coastal OceAn observing SysTem - High Frequency, COAST-HF (http://www.coast-hf.fr) network (Farcy et al., 2019; Cocquempot et al., 2019; Simon et al., 2023). This network is part of the research infrastructure named ILICO for coastal and nearshore observations (Cocquempot et al., 2019). Following regions under river influence and available data, the observations from 7 COAST-HF stations have been analysed and compared with model simulation: Carnot (https://doi.org/10.17882/39754), SCENES (https://doi.org/10.17882/99434) and Smile (https://doi.org/10.17882/53689) stations in the eastern English Channel, Iroise (https://doi.org/10.17882/74004) and SMART (https://doi.org/10.17882/86020) in the Bay of Brest, Molit (https://doi.org/10.17882/46529) in the Bay of Vilaine, and Ferret (https://doi.org/10.17882/100119) in the Arcachon Bay entrance. Due to gaps in observations, only 4 stations can be considered for the salinity analysis.
### 2.2.3. CORA-IBI in situ profiles dataset

The in situ vertical profiles are aggregated in the Coriolis Ocean Dataset for Reanalysis for the Ireland-Biscay-Iberia region (hereafter CORA-IBI) product (Szekely et al., 2017). This regional dataset of in situ temperature and salinity profiles covers the period 1950–2014. In the CORA-IBI database, compiled observations are acquired by research or opportunity vessels (CTDs, XBTs, ferrybox, fishery observing system from the RECOPESCA program) and autonomous platforms (Fixed moorings, gliders, Argo profilers).

### 2.2.4. Tide gauge network

Sea level observations are collected by tide gauges from the REF-MAR network (http://refmar.shom.fr) accessed through the Copernicus In Situ TAC (Thematic Assembly Centre) of CMEMS (European Copernicus Marine Service). Hourly observations are considered before the harmonic analysis. For each ROFI, one tide gauge is processed (Le Havre for the Seine river, Saint-Nazaire for the Loire river, and Port-Bloc for the Gironde river).

### 2.3. ROFI characterisation methods

In order to study ROFIs and monitor their evolution over time, it is first necessary to define them in a way that allows for their identification in the numerical simulation. In this study, we conventionally use surface salinity to define the limits of ROFIs. Although it is not easy to define a threshold value that is both meaningful and applicable in this context, it is a necessary element in understanding the evolution of these structures over time. In consideration of the salinity of Bay of Biscay Central Waters (35.6 psu) (Lazure et al., 2006) and prior researches on plumes in the region (Lazure and Jegou, 1998; Puillat et al., 2004; Ayouche et al., 2021; Toublanc et al., 2023), the threshold has been defined at Sea Surface Salinity < 33 psu. However, a preliminary investigation has revealed that the proximity of the Loire and Gironde estuaries makes it challenging to distinguish between their two ROFIs. A straightforward zonal border (located at 46° 45'N) is insufficient for differentiating the two ROFIs, as the Loire frequently encroaches upon the region of interest designated for the Gironde (Fig. 1). Furthermore, these two regions frequently are the locations of low-salinity lenses that have detached from the plumes (Puillat et al., 2006) and that we want to exclude from our definition. Consequently, we incorporated a connectivity criterion for these two ROFIs, defining the ROFI as the contiguous surface matching the SSS criterion in contact with the estuary mouth.

Based on this definition, we defined a number of characteristics which facilitates the monitoring of changes in ROFI over time. The extent of the ROFI is calculated by summing the areas of the cells within the ROFI boundary. In addition, we used the formula (1) from Hetland (2005) to calculate freshwater volume ($V_f$) contained within isohaline surfaces of different salinity ($s_A$) between 28 psu and 33 psu.

$$V_f(s_A) = \iiint_{s<s_A} \frac{s_0 - s}{s_0} dV \quad (1)$$

The background salinity $s_0$ is taken at 35.6 psu. This variable enables the monitoring of alterations in the volume of freshwater within the ROFI, as well as its distribution between different salinity classes. The extent of the ROFI surface and the freshwater volume are calculated at each hour, over the twenty years of the simulation. A wavelet analysis was applied on the signals to identify the dominant frequencies over the period. We used the wavelet analysis method described by Torrence and Compo (1998). Finally, to study the evolution of the three-dimensional structure of the ROFI, we used the depth of the 33 psu isohaline within the ROFI. In order to analyse the wind patterns, the zonal and meridional wind speeds were averaged spatially for each region of interest. Subsequently, the favourable downwelling and upwelling winds were defined as the quarter sector of wind parallel to the coast, directed with the coast to the right and to the left, respectively.

## 3. Model simulation assessment

The interannual simulation used in this study has been validated through a comparison with in situ observations and remotely sensed data. The model assessment is comprehensive, providing an overview of model's capabilities in reproducing temperature, salinity and tidal dynamics. In order to assess the model at different scales, comparisons have been performed using different reference products.

### 3.1. Regional sea surface temperature: a modelled domain scale assessment

At the basin scale, the Sea Surface Temperature serves as an initial indicator of the model's capacity to reproduce observed coastal dynamics. On average (Fig. 2 top), the model displays a cold bias, compared with observations, less than 1 °C. This bias is constrained to the continental shelf with a maximum value over the continental slope, which is attributed to an excessively strong vertical mixing. Off the Brittany region, we also observe a bias dipole, whereby temperatures were found to be uncharacteristically warmer in coastal areas and significantly cooler offshore. This phenomenon is believed to be linked to the dynamics of the tidal Ushant front, a tidal front that has proven challenging to simulate with kilometre-scale resolutions in numerical models (Fig. 7, Petton et al. (2023)). Indeed, this frontal activity is subject to significant fluctuations at the shelf submesoscale, occurring at a range of 10 to 100 metres. When basin-scale biases are analysed, a warm bias (less than 1 °C except in estuaries) is also observed. This bias in shallow regions does not exceed 1 °C except in estuaries where the model resolution is insufficient to accurately reproduce estuary dynamics.

The spatially averaged temporal evolution of the SST (Fig. 2 bottom) exhibits a close correspondence with observations with similar interannual variations. For example, the model simulation reproduces the occurrence of exceptionally high temperatures during summers 2003 and 2018. Furthermore, the model demonstrates the ability to reproduce interannual variability during the winter season. Some discrepancies are observed but they are mainly explained by the higher temporal resolution in the model compared with observations where the short-term temporal variability is smoothed compared with modelled events. Both the model and the observations are associated with a warming trend. The temperature increase in the model simulation is slower (0.14 °C/decade) than in observations (0.21 °C/decade) over the two decades. A number of analyses have been conducted to elucidate the discrepancy between the coastal model configuration and observed trends. Our findings indicate that the divergence in temperature trends can be attributed to the influence of external forcing at open boundaries and atmospheric forcing.

### 3.2. Temporal evolution of temperature and salinity in ROFIs from coastal moorings

ROFI dynamics is associated with local high-frequency fluctuations in the circulation. In order to evaluate the model's ability to reproduce such features, model simulations are compared with observed time series from the buoys of the COAST-HF network (Farcy et al., 2019; Cocquempot et al., 2019; Simon et al., 2023) in temperature (Fig. 3) and salinity (Fig. 4). An overview of these features is presented through the application of principal statistical techniques, including correlation, standard deviation, bias, and centered Root Mean Square deviation (uRMSD), as illustrated in Taylor and target diagrams.

The correlation between observed and modelled temperature remains higher than 0.9 with a ratio of modelled and observed standard deviation close to 1 when seven stations along the coast are considered, extending from the south of the Bay of Biscay to the eastern English Channel (Fig. 3 left). The biases do not exceed 0.5 °C, with a uRMSD below 1.5 °C, with the exception of the SMART station (Fig. 3 right). It is notable that the SMART station is situated within a semi-enclosed bay
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Sea Surface Temperature biases between model simulation and satellite observations average between 2001 and 2020 (top). Time Series of the modelled (blue line) and observed (orange line) Sea Surface Temperature. Dashed lines are representing the linear trend over the period.</figcaption></figure>

(the Bay of Brest) in close proximity to a river mouth that is no wider than 2 km. It can be concluded that the resolution of the model is not optimal for accurately reproducing the observed variability, resulting in an underestimation of the latter.

Considering the salinity, model skills are locally more limited than for the temperature. The measured correlations range from 0.5 to 0.8 considering four stations with observations (other stations are associated with significant gaps in observations and are thus excluded from consideration). With regard to biases, these remain confined below 1 psu (Fig. 4). However, the uRMSD can exceed 3 psu, as evidenced by the SCENES station located in proximity to the Seine river mouth. The low correlations and large uRMSD can be attributed to the fact that the model simulations underestimate the amplitude of short-term low salinity events related to river floods (Poppeschi et al., 2021).

### 3.3. Spatial and vertical structure of salinity in ROFIs

ROFI can be defined in terms of their salinity distribution. The vertical structure of the simulated ROFIs is validated based on in situ vertical profiles extracted from the CORA-IBI database (Szekely

et al., 2017). Fig. 5 illustrates distributions of biases between observed and modelled vertical profiles for the three ROFIs. At the surface, between 0 and 20 m depth, the majority of the discrepancies are confined to a range of -1 to 1 psu, with half of the distribution falling below 0.5 psu for the Loire and Gironde ROFIs. The model exhibited an overestimation of salinity on average (with a median value a approximately +0.1 psu) for the Gironde. The aforementioned overestimation is diminished when deeper sections of the profiles are taken into consideration, with a median bias approaching zero between 40 and 100 m metres depth. With regard to the Loire ROFI, the median salinity bias is approximately zero for all depths. However, a peak in the distribution is observed around +0.1 psu, which suggests that the model simulations also exhibit a limited degree of overestimation. Conversely, in the Seine ROFI, the model demonstrates a tendency to underestimate salinity, with median values reaching approximately -0.4 psu between the surface and 40 m depth. The median bias is observed to be smaller between 40 and 100 metres depth. As the deeper profiles are situated further offshore, it highlights that the largest biases are located in proximity to the coastline. The distribution of the biases for the Seine is uniformly distributed between -1.3 and +0.4 psu. The larger range
<figure><img src="image_6.png" /><figcaption>Fig. 3. Taylor (left) and target (right) diagrams with statistics for the seven COAST-HF stations considered for comparisons in temperature. All in situ data available for the two considered decades are considered in statistics computation.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Taylor (left) and target (right) diagrams with statistics for the four COAST-HF stations considered for comparisons in salinity. All in situ data available for the two considered decades are considered in statistics computation.</figcaption></figure>

of biases observed for the Seine can be attributed to the influence of large-scale, short-term spatial variations driven by semi-diurnal tidal activity. Consequently, the locations of salinity fronts are undergoing rapid changes, which results in the phenomenon of collocated profiles sampling disparate sides of the fronts both in the model and in the observations. This can result in significant discrepancies between profiles. Nevertheless, biases persist within a constrained range for a model configuration tailored to diverse coastal dynamical regimes.

### 3.4. Model comparison with observations from tide gauges

In the context of the studied region, tides play a major role in the coastal circulation. This section presents an overview of the simulated tides in comparison with the data obtained from tide gauges. One station is considered by region of interest (Le Havre for the Seine river, Saint-Nazaire for the Loire river and Port-Bloc for the Gironde river). All tide gauges are located within the immediate vicinity of the river plume. For the purposes of this validation, six principal tidal constituents are considered (Fig. 6). In all three regions, the observed and modelled tide features are in close agreement with amplitude differences of less than 0.12 m. It is observed that these differences for M2 tides are more pronounced at the Seine and Gironde ROFIs. For the Loire, the largest discrepancies are observed in the case of the S2 tides. With regard to phase lags, the discrepancies do not exceed 9°, with a maximum phase lag difference of 3.81° (at the Port-Bloc station) for the largest M2 tidal constituent.

## 4. Results

### 4.1. Temporal scales of variability

In order to explore temporal scales of ROFI variability and identify the dominant frequencies over the 20-year simulation period, we analysed the wavelet spectra of the surface area (Fig. 7) and freshwater volume (not shown) time series.

The main detected period for the three ROFIs is the annual cycle, which dominates throughout the spectrum with some variations in intensity during the analysed time period. The annual period band is more pronounced for the Loire and Gironde ROFIs (Fig. 7C and E), although there is a decrease in the power spectra intensity between 2010 and 2011. Upon examination of the periods above the annual period for these two spectra, no discernible periodicity pattern emerges on the spectrum for the interannual time scales. The annual period band on the Seine ROFI wavelet spectrum (Fig. 7A) is clearly identifiable during the first decade with an energy exceeding $10^{-4}$ km$^4$, as it is the case for the other ROFIs. However, between 2012 and 2014, there is a decrease in the energy of this annual peak, as well as an increase in the intensity of the spectrum over the 6-month period (182 days). Following this time period, the annual signal intensity is seen to increase once more. Concurrently, the power of the spectrum increases in the periods between the annual and biennial periods during the second decade.
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Violin diagram representing the observed biases between the modelled and observed CORA-IBI vertical profiles. Three ROFIs are represented, with consideration given to three depth ranges: 0–20 m (blue), 20–40 m (orange), 40–100 m (green). The grey rectangle represents the distribution of biases between the first and third quartiles. The white segment represents the median value. Only the computed biases between 5th and 95th percentiles are displayed.</figcaption></figure>

For the periods shorter than the annual period, the wavelet spectra of the Loire and Gironde ROFIs exhibit a high degree of similarity, whereas that of the Seine is markedly distinct. The annual cycle exerts a profound influence on the Loire and Gironde spectra, manifesting as a decline in the intensity of the high-frequency spectrum each year during the summer months. This seasonal decline is especially notable for the Gironde ROFI.

The different years in these two spectra are distinguished by intensity variations occurring at multi-monthly periods, corresponding to periods of between 30 and 182 days. These variations are more contrasted on the Gironde spectrum. For this river, certain years exhibit heightened intensity (2001, 2004, 2008, 2009, 2013, 2014, 2015, 2018 and 2020). The Loire spectrum displays comparable patterns, albeit with less pronounced interannual variations. However, some years exhibit lower intensities, with values less than $10^{-5} \text{ km}^4$ observed at the multi-monthly periods (2005, 2010, 2011, 2012, 2017 and 2019). The Gironde spectrum also displays a decline in intensity for these same years. For periods between 15 and 30 days, we also observed few occurrences in the two spectra with intensity exceeding $10^{-4} \text{ km}^4$, such as the energy peak observed at the monthly period observed in 2014. In the case of these two ROFIs, the year 2001 exhibits a peak in energy that is equivalent in intensity to the annual signal, occurring at a frequency ranging from twice monthly to monthly, and even reaching the fortnightly scale in the case of the Gironde. One noteworthy aspect of these spectra is the observation of an occasional connection between the multi-monthly periods, typically 60 to 90 days, and annual period. This phenomenon is evident in the Loire data for the years 2004, 2006, 2008, and 2014, while in the Gironde data, it is prevalent in 2008 and 2014.

In comparison to the others, the spectrum of the Seine ROFI exhibits a markedly reduced intensity in the period between 30 and 365 days, with energy rarely exceeding $10^{-5} \text{ km}^4$, and minimal interannual variation. However on the spectrum, two periodic signals can be discerned at the weekly and monthly scales: the fortnightly period and the monthly period. The fortnightly signal is present throughout the 20 studied years, with several events when its intensity increases, such as in 2002, 2013 and 2018. The monthly signal is less regular, manifesting intermittently throughout the time period. It is present and particularly intense when the intensity of the fortnightly signal increases. These signals are present throughout the 20 simulated years

and are also discernible in the global wavelet spectrum (corresponding to the time-average of the wavelet power spectrum) (Fig. 7B). The year 2002 is notable because of a particular event. For a brief period, the power spectrum exhibited a pronounced increase in intensity on the weekly and bi-weekly scales. This peak in intensity extended to the lower frequency scales, thereby establishing a connection between the variability of the scales, from the weekly scale to the yearly scale.

Finally, another periodic signal is evident in all the wavelet power spectra (Fig. 7A, C and E) and global wavelet spectra (Fig. 7B, D and F), namely the semi-diurnal period. This period is present throughout the whole time period, with a decrease observed in summer for the Loire and Gironde spectra.

The three ROFIs therefore share a semi-diurnal signal as well as the annual signal. However, their variations differ between the diurnal and annual periods. Giving the diversity of detected temporal scales in the evolution of ROFI features, detailed analyses are provided for intra-annual, annual and inter-annual scales.

## 4.2. Diurnal variability

As we observed in the wavelet spectra presented in Fig. 7, the semi-diurnal signal is the smallest period to emerge clearly in all the ROFIs. However, in the Fourier spectrum of the surface area (Fig. 7 B,D and F) and the freshwater volume (not shown) of the ROFIs, the harmonics of this period are also found at higher frequencies. At semi-diurnal periods, the Fourier spectra reveal the presence of peaks corresponding to the main tidal components (e.g. M2, S2, N2, K2). The same frequency peaks are observed in the Fourier spectra of the freshwater volume. The Fourier spectra of the Seine ROFI displays greater energetic intensity across these different frequency peaks. There are also more tidal components present at the semi-diurnal scale (e.g. MU2) and more high-frequency harmonics.

An analysis of the semi-diurnal oscillation of surface area and freshwater volume reveals discrepancies in phase lag between the ROFIs (Fig. 8). For the three ROFIs, the area increases during ebb and is reaching a local maximum during low tide, before decreasing during the flood until the next high tide. These variations in surface area are of the order of $600 \text{ km}^2$ for the three ROFIs. The freshwater volume operates in a manner that is distinct for each of the ROFIs. In the case of the Gironde ROFI, the oscillation is in phase with the surface area, reaching a local maximum at low tide and a local minimum at high tide. In contrast, the ROFI of the Loire exhibits a different pattern, evolving in quadrature with the surface area. During low tide, the ROFI increases until reaching its maximum at the middle of the flood, after which it declines during high tide. The Seine ROFI also demonstrates a similar lag, however, with an asymmetry. During high tide, the freshwater volume reaches its minimum, then increases throughout low tide until reaching its maximum at the middle of the flood.

At the diurnal timescale, the three ROFIs studied are therefore mainly influenced by the semi-diurnal tidal cycle, although there are slight differences in their response to this forcing.

## 4.3. Weekly and monthly variability

The diurnal variability of the ROFI may be superposed, modulated or masked by a longer-term variability. One of the main sources of variability is the variability of river runoff. As it can be seen from Fig. 1E, the runoff of the three rivers varies greatly over the course of a season. In winter and spring, in addition to the average increase, runoffs follow a highly intermittent pattern, with episodes of flooding that can momentarily double the freshwater input. This episodic flooding behaviour is more prevalent on the Gironde, with intense floods lasting between a few days and a week, and much less so on the Seine, where the increases in flow are less marked and generally spread over several weeks. As for the Loire, its behaviour is intermediate, with floods as numerous as those of the Gironde, but smoother.
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Comparison of amplitudes (left) and phase lags (right) of the six main tidal constituents between the observed (blue) and modelled (orange) sea levels at the positions of three tide gauges: Le Havre (top), Saint-Nazaire (middle) and Port-Bloc (bottom). Comparisons are performed for August and September 2020.</figcaption></figure>

These events trigger a more or less rapid response from the ROFI, from few days to a month, as illustrated in Fig. 9 for February and March 2003. At the beginning of February, flooding occurred in all three rivers. In the ROFI of the Loire and Gironde, a flood event is followed one or two days later by an increase in the freshwater volume in the lowest salinity class. The freshwater volume will then increase in the higher salinity classes with a delay of a few days. The increase in freshwater input leads to an expansion of the ROFI, accompanied by a corresponding increase in surface area. This signature is less

immediate in the Seine ROFI. In Fig. 9, the increase in runoff does not generate an extension of the ROFI. The freshwater volume was already increasing at the beginning of February and this increase did not accelerate after the runoff peak. The ROFI of the Seine shows a slower response to runoff changes. A high runoff event causes a gradual increase in freshwater volume and surface area in the month following the flood. The ROFI surface area increases a week after the flood in mid-February, but a similar event takes place a month later without being preceded by an increase in runoff. It is more probable that this
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Left panels, wavelet power spectra of the surface area of the Seine (A), Loire (C) and Gironde (E) ROFIs. Right panels, global wavelet spectra, corresponding to the time-average of the wavelet power spectrum (dark line) and Fourier spectra (grey line) of the ROFI surface area of the Seine (B), Loire (D) and Gironde (F) ROFIs.</figcaption></figure>

extension is predominantly the consequence of the spring and neap tide cycle.

As observed in the wavelet spectra (Fig. 7 A), the Seine ROFI surface area exhibits a biweekly periodicity as well as a lesser degree of monthly periodicity. The variations in the Seine ROFI surface area are in accordance with the oscillations of the spring and neap tidal cycle. During neap tides, the surface area increases, with a notable rise when the tidal range is particularly low. Indeed, one neap tide out of two has a lower tidal range than the other, over a period of one lunar month, i.e. 28 days, with weaker tidal current associated. Furthermore, the extent of the ROFI is amplified when neap tides occur after a flood event. During these periods, the surface area of the Seine rises sharply, reaching a maximum before returning to its original level at the subsequent spring tide. During spring tides, the mean surface area of the ROFI decreases. The freshwater volume increases continuously throughout the cycle until the beginning of the spring

tide. It is predominantly contained within the highest salinity class, corresponding to the 33 psu isohaline contour. At the onset of the spring tide, the freshwater volume decreases in all salinity classes as the surface area decreases.

These extensions of the ROFI surface area during neap tides are one of the dominant characteristics of the Seine ROFI. However, the ROFIs for the Loire and Gironde regions do not show such a marked response to the spring and neap tide cycles. Indeed, the fortnightly and monthly periodic signals are not visible in the Loire and Gironde area spectra (Fig. 7). The amplitude of the semi-diurnal oscillations caused by the tide is reduced during neap tides, as tidal currents become weaker. However, no signature of ROFI surface area extensions is observed, as it is the case for the Seine.

On the Loire and Gironde ROFIs, the impact of the wind is dominant on the scale of weekly and monthly variability. The Fig. 10 illustrates, for the Loire ROFI, the effect that two opposing wind directions can
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** For respectively the Seine ROFI (A), the Loire ROFI (B) and the Gironde ROFI (C) : ROFI surface area and freshwater volume contain inside the 33 psu isohaline surface and surface elevation between 2 March 2003 and 6 March 2003.</figcaption></figure>

have on the surface and freshwater volume of the ROFI. The effects of wind on Gironde ROFI are similar, but not discussed here to avoid redundancy. From February to April, the wind to the south of Brittany is predominantly south-easterly, which correspond to a downwelling wind. The same conditions were observed off the Gironde estuary during the same period.

When the downwelling wind is set up, the ROFI is pushed along the coast. While it was quite spread out before this wind episode, this has the effect of slightly reducing its surface area. The ROFI is then constrained to the coast, which tends to maintain the coastal current. Downwelling favourable winds also tend to deepen the ROFI, making it more stable and less likely to dissipate. In Fig. 11B, we observe that in February 2003, the ROFI forms a long narrow band along the coast. The 33 psu isohaline follows the bathymetry contours and in some locations exceeds 30 meter depth. The freshwater volume and surface area of the ROFI remain relatively constant at high values for as long as the downwelling wind episode lasts.

However, in January of the same year, the situation was very different. A flood similar to the one in February is followed 2 weeks later by an intense episode of north-westerly winds, favourable to upwellings (Fig. 10). Initially, this wind episode will have no impact on the freshwater volume, but it will stretch the ROFI offshore, increasing its surface area while reducing its depth over this extension (Fig. 11A). As ROFI is stretched into a thin layer on the surface, it loses stability and becomes much more sensitive to mixing. This extension is then dissipated into the surrounding coastal waters by the wind, causing the surface area of the ROFI and its freshwater volume to drop abruptly. These wind events on the scale of a few days can shape the ROFI and have an impact on the whole month ahead. Similar patterns of increases in the ROFI surface area followed by sudden decreases in surface area and freshwater volume, corresponding to offshore extensions, were observed for the Loire and Gironde ROFIs over the 20 simulated years.

These events occurred between the end of January and June, with 0 to 2 events per season depending on the year. However, for the ROFI of the Seine, the wind rarely has an impact except during neap tides. During these periods, only strong upwelling favourable wind can enhance the ROFI extent.

Therefore, weekly to monthly variability of ROFIs is dominantly driven by tidal dynamics for the Seine region and by wind and runoff dynamics in Loire and Gironde regions.

## 4.4. Annual cycle

The annual cycle is the time scale of largest intensity in the wavelet spectrum (Fig. 7). As illustrated in Figs. 12 and 13, this is the periodic signal that produces the most significant variations in the surface area and freshwater volume of the ROFI. These variations align with the seasonal pattern of river runoffs.

ROFIs exhibit two distinct regimes throughout the year. In December, there is an increase in both the area and the volume of freshwater, in accordance with the increase in runoff (Fig. 1). The ROFIs reach their maximum extension and volume during the winter and spring months. The mean surface area for these months is 3707 km² for the Seine ROFI, 3567 km² for the Loire ROFI and 3526 km² for the Gironde ROFI with an equivalent freshwater volume of 5.7 km³, 4 km³ and 3.8 km³, respectively. The ROFIs of the Loire and Gironde can exhibit one to three peaks of rapid increase in surface area and freshwater volume, which contribute to the dynamic of the winter and spring ROFI. In contrast, the ROFI of the Seine displays a much more gradual evolution, with the only notable exceptions being the fortnightly extensions described above.

In the early summer period, as the river runoffs decrease, we observe a notable reduction in the size of ROFIs. The ROFIs in the Bay of Biscay, and in particular the Gironde ROFI, tend to dissipate during
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** For respectively the Seine ROFI (A), the Loire ROFI (B) and the Gironde ROFI (C) : in the upper panel, ROFI surface area, runoff discharge of the associated river and surface elevation between 1 February 2003 and 31 March 2003. In the lower panel, ROFI freshwater volume distributed among the different salinity classes over the same period. The pronounced fluctuations in the Loire ROFI surface area and freshwater volume between 15 and 22 February are due to a separation of a part of the ROFI at the level of a peninsula at each tidal cycle, breaking the connectivity criterion.</figcaption></figure>

this period, as the limit of the 33 psu isohaline moves back into the estuary. In contrast, the Seine ROFI, with its more gradual annual cycle, exhibits fewer differences between the winter and summer regimes. The ROFI does not disappear in summer and remains present in the Bay of the Seine throughout the year with a minimum surface area of 172 km².

## 4.5. Interannual variability

Having looked at the different temporal scales of variability, we now turn to what happens on an inter-annual scale. Whatever the ROFI considered, there is marked inter-annual variability with contrasting years.

The Seine ROFI exhibits a slight downward trend between 2001 and 2020. This is evidenced by a decrease in both surface area at a rate of -69.7 km² per year, and freshwater volume at a rate of -0.131 km³ per year. Due to the stronger runoff during the initial years in the times series, a recalculation of the trends was undertaken, with the years 2001 and 2002 being excluded from the analysis. The trend is -47 km² per year between 2002 and 2020 and -34 km² per year between 2003 and 2020 respectively for the surface area, and -0.08 km³ per year between 2002 and 2020 and -0.048 km³ per year between 2003 and 2020 respectively for the freshwater volume. The trend is less pronounced for the Loire ROFI, with a surface area decrease of -34

km² per year between 2001 and 2020 (respectively -10 km² per year between 2002 and 2020 and -14 km⁴ per year between 2003 and 2020) and a freshwater volume decrease of -0.041 km³ per year between 2001 and 2020 (respectively -0.008 km³ per year between 2002 and 2020 and -0.011 km³ per year between 2003 and 2020). The trend is almost none for the Gironde ROFI, with a surface area decrease of -5 km² per year from 2001 to 2020 with however an increase between 2002 and 2020 (+18 km² per year) and between 2003 and 2020 (+14 km² per year). The freshwater volume does not exhibit a significant trend from 2001 to 2020 and otherwise shows a slight increase between 2002 and 2020 (+0.021 km³ per year) and between 2003 and 2020 (+0.24 km³ per year).

The year 2001 stands out for its extreme extent and a freshwater volume exceeding 10 km³ for all three ROFIs. For the other simulated years, the Loire and Gironde ROFIs have very similar variations, while the Seine ROFI follows a different dynamic. In the Seine region (Fig. 12), the extent of the ROFI in summer is limited with the exception of the summer of 2001 which shows an extension exceeding 2500 km², close to the maxima simulated in winter. Following this extreme summer, the winter of 2002 shows the largest extension simulated over the 20 years (above 9000 km²) and a freshwater volume of 13 km³ (Fig. 13).
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** From top to bottom: first panel, Loire ROFI surface area (blue line) and tidal range (grey line). Second panel, Loire ROFI freshwater volume distributed among the different salinity classes. Third panel, Runoff discharge of the Loire river. Fourth panel, Mean wind speed and direction at 10 m spatial mean over the Loire sub-region. Downwelling winds are coloured blue and upwelling winds are coloured red (see Section 2).</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Maps of the depth of the 33 psu isohaline surface on 24 January 2003 (A) and 25 February 2003 (B).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 12.** From top to bottom: the Seine, the Loire and the Gironde ROFI area between 2001 and 2020, respectively.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 13. From top to bottom: the Seine, the Loire and the Gironde ROFI freshwater volume contain inside the ROFI between 2001 and 2020, respectively.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 14. Maps of the sea surface salinity over the Bay of Biscay on 19 April 2001 (A) and 25 April 2001 (B). The black line represents the 33 psu isohaline contour.</figcaption></figure>

Over the entire simulated period, we observe the 2010 winter as a minimum, both in terms of extent and freshwater volume. Apart from these extreme years, the dynamic of the Seine ROFI shows little variation between years. The wavelet spectrum shows a peak of energy at the level of the 1.5-year period from year 2014 onwards which may be associated with the presence of an intense winter in 2018 followed and preceded by two winters of low extent. In the Loire and Gironde regions, each year shows a particular dynamic. The winters with the largest extensions are those of 2001, 2014 and 2020. We also note a succession of minimum expansions in the years 2011 and 2012. Conversely, the last 5 years of the period show alternating winters of small and large extensions. This interannual dynamic is also observed in the freshwater volume.

Following this strong interannual variability built up by a succession of different and potentially extreme years, each dynamic is analysed with a special focus on extreme years.

## 4.6. Focus on extreme events for the ROFI extent

### 4.6.1. The year 2001

The year 2001 is identified as the year with the highest freshwater volume in the Loire and Gironde regions and with the second highest freshwater volume in the Seine region. This year is characterised by high river runoffs throughout the winter and spring (Fig. 1 E). In

the Seine, this results in a large extension of the ROFI, which exceeded 5000 km² for two months. This situation persists throughout the summer of 2001, which preconditioned the extension of the ROFI at the beginning of the winter of 2001–2002 (see Section 4.6.2). In the Loire and Gironde regions, the remarkable event takes place in several phases. At the beginning of the winter, the ROFIs of the Loire and Gironde form a continuous coastal current stretching from the mouth of the Gironde to the tip of Brittany. Subsequently changes in wind direction to north-easterly favour the extension of the ROFI seaward. The large amount of freshwater volume that was constrained along the coast extends over a wide region of the shelf, including the two sub-regions studied (Fig. 14). This extension subsequently dissipates, forming numerous low-salinity lenses.

### 4.6.2. The year 2002, in the eastern channel

At the beginning of the winter season of 2002 in the eastern Channel, the ROFI of the Seine was already markedly extended following the slight reduction during the preceding summer (Fig. 15). In addition, the considerable runoff of the Seine river, which exceeded 1000 m³s⁻¹ for most of the winter (Fig. 1), contributed to an increase in the freshwater volume contained in the ROFI, causing it to reach its maximum value of 13 km³. At the beginning of April, an upwelling wind episode occurred during a period of neap tide. The resulting wind current displaced a portion of the water mass offshore, extending along the entire length
<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Subfigure A, from top to bottom : first panel, Seine ROFI surface area (blue line) and tidal range (grey line), in 2002. Second panel, Seine ROFI freshwater volume distributed among the different salinity classes. Third panel, runoff discharge of the Seine river. Fourth panel, wind speed and direction at 10 m spatial mean over the Seine sub-region. Downwelling inds are coloured blue and upwelling winds are coloured red (see Section 2).
Subfigures B and C: Maps of the depth of the 33 psu isohaline surface in the Seine sub-region on 3 April 2002 and 8 April 2002, respectively.</figcaption></figure>

of the ROFI. This water mass, as it spread out into a thin surface layer, created the largest extension of the ROFI observed over the entire period, covering an area of 9790 km². The following day, the return of the intense spring tides homogenised this surface layer over the column, resulting in a sharp reduction of the surface area and the freshwater volume, which were both halved.

The formation of this extensive extension can be attributed to two key factors: the accumulation of freshwater volume in the ROFI due to high runoff discharges during the preceding months and the occurrence of a windy episode during a period of neap tide. These two elements have contributed to an extreme extension that is estimated to be approximately three times larger than the winter average surface area of the ROFI.

### 4.6.3. The year 2014, in the Bay of Biscay

At the end of January 2014, the Gironde experienced floods in excess of 5000 m³s⁻¹ (Fig. 16). During the following months, river runoffs remained at a high level, approximately 2000 m³s⁻¹. At the same time, the winds were predominantly directed towards the coast, which inhibited upwellings. This resulted in a relatively constrained and deep ROFI (Fig. 16B), with a depth of isohaline 33 psu greater than 25 m in the northern part of the region and a freshwater volume exceeding 9 km³. In March, the wind direction changed, becoming an upwelling favourable wind. The freshwater volume was then transported offshore, forming a large extension of the ROFI that exceeded 10000 km². The surface extension then dissipated into the coastal ocean, spreading over a thin surface layer. A similar situation occurred in the Loire ROFI during the same year.

## 5. Discussion

We have seen that the ROFIs of the Seine, Loire and Gironde react in different ways and at different timescales to the drivers to which they are subjected. In this section, we will discuss these variations from the perspective of the different drivers involved.

### 5.1. ROFIs and tides

On intra-annual scales, the three ROFIs are influenced by the tides, although the degree of influence varies according to the specific location.

The Seine ROFI differs from the other two in that all its intra-annual dynamics, from the diurnal to the monthly scale, are primarily governed by the tide. This can be explained by its geographical location. The Seine ROFI is located along the French coast in the Eastern English Channel, in an area with an average depth of less than 20 m. Tidal currents in this region are of the order of 1 m s⁻¹ (Pingree, 1980) generating significant vertical mixing. As a result of this mixing and the shallow depth, the majority of the ROFI is evenly distributed throughout the water column. This explains why the ROFI of the Seine, which typically has a surface area of less than or equal to that of the Loire or Gironde (Fig. 12), has a freshwater volume that is generally greater than that of the Loire or Gironde (Fig. 13). Indeed, the 33 psu isohaline generally follows the bathymetric contours across the entire surface of the ROFI (Fig. 15B), as described in Cugier and Le Hir (2002) for the Seine plume inside the Bay of Seine. Consequently, the Seine ROFI extends over the entire water column, resulting in a more substantial volume.
<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Subfigure A, from top to bottom : first panel, Gironde ROFI surface area (blue line) and tidal range (grey line), in 2014. Second panel, Gironde ROFI freshwater volume distributed among the different salinity classes. Third panel, runoff discharge of the Gironde river. Fourth panel, wind speed and direction at 10 m spatial mean over the Gironde sub-region. Downwelling winds are coloured blue and upwelling winds are coloured red (see Section 2).
Subfigures B and C: Maps of the depth of the 33 psu isohaline surface in the Gironde sub-region on 10 March 2014 and 19 March 2014, respectively.</figcaption></figure>

While the Seine ROFI is predominantly influenced by tidal forces, it is important to note that all three ROFIs are subject to these tidal effects. As we saw in Section 4.2, the tide generates an oscillation in the surface area and freshwater volume of the ROFI. During the ebb until low water, the tidal currents stretch the ROFI seaward, increasing its surface area and volume. However, with this mechanism alone, the oscillations of the freshwater volume should be in phase with those of the surface of the ROFI, as is the case for the Gironde ROFI (Fig. 8C). Another process is needed to explain the phase shift between the surface area oscillations and the freshwater volume oscillations observed for the ROFI of the Loire and the Seine.

The phase shift is probably caused by the tidal straining described by Simpson et al. (1990). This phenomenon has been observed in other locations, including the Rhine ROFI (Simpson and Souza, 1995) and the Liverpool ROFI (Sharples and Simpson, 1995), which share similarities with the Seine ROFI in terms of depth and tidal amplitude. The tidal straining is a consequence of the horizontal salinity gradient in the ROFI combined with the barotropic tidal currents in a shallow environment. During the ebb, the bottom stress induces shear in the tidal current, which then moves fresher and lighter water over the denser oceanic water, enhancing stratification. During the flood tide, the current shear is reversed and surface water is brought back to its initial position and can even pass over lighter water. This situation creates unstable density gradients within the water column which generate convective mixing. Consequently, the freshwater leaves the ROFI by mixing into coastal waters and the ROFI freshwater volume decreases. This mechanism should create an asymmetric M2 cycle of dissipation of the freshwater volume, with a maximum dissipation during flood tide.

This could explain the phase shift in the semi-diurnal oscillations of the freshwater volume observed in the Seine ROFI and the more moderate phase shift observed in the Loire ROFI.

Finally, tides exert a weekly influence on the Seine ROFI. As previously stated, the ROFI of the Seine was observed to be predominantly homogeneous vertically. However, during neap tides, the tidal currents weaken to the extent that they are no longer sufficient to completely homogenise the ROFI. A circulation process driven by the density gradient then occurs in the Bay of Seine, resulting in the formation of surface extensions of the ROFI to the north of the bay. When the tidal currents reintensify at the next spring tide, the water column undergoes rehomogenisation. Therefore, the surface area of the ROFI is reduced and it loses a portion of its freshwater volume as it mixes with the surrounding coastal waters. As far as the Gironde and the Loire ROFIs are concerned, while the tides have an influence on the dynamics and shape of the plume, especially in the near-field, as shown by Toublanc et al. (2023) for the Gironde, they do not have a dominant influence on the variability of the ROFI surface area or the freshwater volume at the ROFI scale, apart from the diurnal variability. This suggests that other factors, more important than the tides, modulate the extension and dissipation of these ROFIs on the weekly and monthly timescales.

## 5.2. ROFIs and winds

It has been demonstrated that wind exerts an influence on the ROFIs, resulting in fluctuations that are discernible on weekly and monthly timescales and occasionally generating visible variations on an interannual scale.
Nevertheless, wind exerts a relatively minor influence on the Seine ROFI. The vertical mixing of the ROFI resulting from tides attenuates the impact of wind stress at the surface. It is only during neap tides, when this mixing is reduced, that wind can exert a notable effect, enhancing or limiting the offshore extensions of the ROFI.

Conversely, the dynamics of the Loire and Gironde ROFIs are signifi-
cantly impacted by wind between January and June, during the periods
of highest runoff. However, wind exerts minimal influence when river
runoff is insufficient to generate a substantial ROFI. Consequently, wind
has a negligible impact in years characterised by low runoffs, such as
2011 and 2012. When the runoff is sufficient to develop ROFI outside
the estuary yet the winds are conducive to upwellings, the ROFIs
typically exhibit modest dimensions. The freshwater is directed offshore
and mixes rapidly with the coastal waters. When the winds are weak or
downwelling favourable, the ROFIs extend northwards along the coast.
Once they have spread out along the coast, they are very sensitive to
changes in the wind. A downwelling wind tends to constrain the ROFI
at the coast and preserve its freshwater volume, whereas an upwelling
wind is enough in a few days to spread the ROFI offshore and disperse
it in the coastal ocean. These dispersions lead to the formation of low-
salinity lenses as observed by Puillat et al. (2004, 2006) based on in
situ measurements from different cruises between 1992 and 2000. Once
the ROFI has dispersed, it has the potential to reform along the coast,
provided that the prevailing conditions are met.

This dynamic of low salinity waters in the face of winds has been
observed on the Loire and Gironde plumes between 1990 and 1996
by Lazure and Jegou (1998) using realistic numerical modelling. They
observed that river flows and winds favoured the development of a
coastal current in winter. In their study, a change in wind between
late March and early April was responsible for a change in the be-
haviour of the plumes, with freshwater spreading offshore and mixing
with seawater. Nevertheless, they also demonstrated that this seasonal
dynamic is subject to significant interannual variability in wind and
runoff, which results in high interannual variability in the plumes.
However, the duration of the studied period (six years) is insufficient to
adequately evaluate this seasonal pattern within the context of a highly
interannual dynamics. Finally, they observed in 1994 and 1995 that
Loire and Gironde plumes connected and formed large offshore extents
of low-salinity across a large part of the shelf, similar to the extent we
observed in 2001.

The transition between a winter dynamics characterised by the
presence of Loire and Gironde ROFIs along the coast, and a spring
dynamics marked by the offshore spreading of ROFIs, does not emerge
clearly when the period from 2000 to 2020 is considered. Of all the
offshore extensions observed for the both Loire and Gironde ROFIs over
the 20 years simulated, only two-thirds occurred during the months of
March and April, with only half of these occurring between 15 March
and 15 April. The remaining extensions occurred primarily during
February, May and June, and with one instance occurring at the end of
January in 2003 (Fig. 10). Furthermore, in certain years, two offshore
extensions have been observed in the same year, with a time interval
of one to three months between them (in 2004, 2008, 2014 and 2018)
for the Gironde ROFI. This suggests that the interannual variability
of the occurrence of conditions conducive to offshore extensions is
predominant over the seasonality of a regime change between 2001
and 2020

5.3. ROFIs and river runoffs

The primary process regulating the variability of ROFIs is the same
one that caused them to exist in the first place: the runoff discharge of
freshwater from the rivers.

The three rivers exhibit distinct dynamic characteristics (Fig. 1E).
The Gironde river exhibits a high degree of variability in its flow,

with the potential to experience floods that are two or three times the
normal discharge, but which last only two or three days. Similarly,
floods on the Loire are intense in terms of flow, but generally last at
least one week. In contrast, the Seine is less event-driven, with few
winter flooding episodes. Winter flow increases are spread over several
weeks. These differences in dynamics can be explained by the specific
dynamics of each catchment, both from a hydrological point of view
and in terms of human regulation with river developments and dams.
The dynamics of the river shape the ROFI on a weekly and monthly
scale, particularly as a result of the winter and spring floods. The less
event-driven dynamic of the Seine already limit the impact of the runoff
on the ROFI on a weekly scale. In addition, the vertical distribution
of the ROFI over the water column gives it an inertia in its response
to runoff variations. Rapid variations in flow are therefore reflected
throughout the ROFI on a monthly scale, with notably larger surface
extensions during the neap periods following a flood. In contrast, the
Loire and Gironde ROFIs demonstrate a more rapid response to floods.
An increase in flow in the Loire results in an expansion of the surface
area and the freshwater volume of the ROFI over the subsequent 24-
hour period. In the case of the Gironde, this increase is observed three
days later due to the extensive size of the estuary, which results in
a delay in the arrival of freshwater in the coastal ocean. The two
ROFIs are thus susceptible to abrupt alterations in runoff, which are
contingent upon the event dynamics of their respective rivers. This
sensitivity corroborates the observations documented by Nguyen et al.
(2024) regarding the necessity for the use of high-frequency runoff data
rather than climatologies for the accurate simulation of temporal and
spatial variations in salinity in the vicinity of estuaries.

On an interannual scale, variations in runoff are the primary driver
of changes in the magnitude of ROFIs. While wind events influence
the ROFI and are responsible for extreme events of surface extension
visible on an interannual scale, these expansions can only occur when
the runoff discharge is sufficiently elevated. In years with low runoff
throughout the winter and spring seasons, the ROFIs remain relatively
limited in size. Apart from the years 2001 and 2002, the relatively
minor interannual fluctuations in the Seine runoff contribute to the
moderate interannual variations in the ROFI. The observed trends in
the surface and freshwater volume of the ROFIs are correlated with the
corresponding trends in river discharge over the same period. The Seine
runoff is observed to decrease by 7.2 m³ s⁻¹ per year between 2001 and
2020, representing a 1.5% reduction in its mean annual flow of 489
m³ s⁻¹. The Loire runoff decreases by 12.7 m³ s⁻¹ per year, representing
a 1.7% reduction in its mean annual flow of 758 m³ s⁻¹ over the same
period. The Gironde runoff did not exhibit a statistically significant
trend for the two studied decades. The interannual variations of runoff
and the hydrological cycle are predominantly driven by the interannual
and multidecadal variations of large-scale atmospheric circulation. The
average and, even more so, the maximum river flows in Europe are
found to be strongly correlated with the climatic indices (Bouwer et al.,
2008). Studies have demonstrated that river flows in France exhibit
multi-decadal variations that are driven by large-scale atmospheric
circulation (Boé and Habets, 2014; Bonnet et al., 2020). In the case of
the Seine flow, Bonnet et al. (2020) showed that over the last 150 years,
this multi-decadal variation was responsible for a relative difference of
more than 25% in spring. In addition, studies on the regional impact
of climate change on the hydrological cycle predict a decrease in mean
river flows over France, with a greater decrease for the Gironde (Dayon
et al., 2018; Di Sante et al., 2021). The observed variations in ROFIs
driven by the decreases in runoffs for the Seine and the Loire, as well
as the absence of a significant decrease in the Gironde ROFIs and
runoff, should be contextualised within the broader context of climate
change, which is likely to cause a decrease in average river flows,
and a multidecadal internal variability that could temporarily limit or
exacerbate these long-term variations.
## 6. Conclusion

In order to study the variability of regions of freshwater influence (ROFIs), we developed a high-resolution simulation of the Bay of Biscay and the English Channel. We found that ROFIs display variability at different temporal scales. The main source of temporal variability in the three ROFIs is the annual cycle of river runoffs. The large winter and spring runoff discharges are at the origin of large ROFIs with significant variations. In summer, the reduction in runoffs leads to important limitations of the ROFI extent. The ROFI of the Seine is maintained only in the bay of Seine and the ROFIs of the Loire and Gironde disappear from the shelf of Bay of Biscay. All regions are also subject to semi-diurnal oscillations observed in ROFI surface area and volume.

While the semi-diurnal and annual cycles are detected to all three ROFIs of the French continental shelf, certain scales of variability differ due to the influence of processes specific to each region. The eastern Channel is characterised by a shallow depth and a strong tidal influence, particularly along the French coastline, resulting in a limited impact of rapid wind variations on ROFI dynamics. In contrast, the Loire and Gironde exhibit a more pronounced response to wind and flood events. During upwelling events, the ROFIs spread offshore in a thin surface layer, contributing to their dilution in the coastal waters.

On annual and interannual scales, the extent of all three ROFIs is significantly influenced by runoff. The reduction in runoff over the 20-year period has resulted in a slight decrease in the size of ROFIs. The surface areas of the ROFIs for the Seine, the Loire and the Gironde have exhibited a decrease of 70 km² per year, 34 km² per year and 5 km² per year, respectively. These variations are likely the consequence of a reduction in precipitation resulting from climate change, coupled with a multidecadal shift in river flows. However, it should be noted that variations in river runoffs are not the only factors impacting ROFIs on an interannual scale. Weekly or monthly time scale events, explained by a combination of wind and runoff events and sometimes tide amplitude, can affect annual or interannual variability. It therefore becomes evident that each year is a particular combination of events (runoffs, wind events, tides) that lead to ROFI singular dynamics, which are difficult to predict.

By the year 2100, climate simulations for Europe indicate a downward trend in average river flows in France, accompanied by an increase in the intensity and frequency of floods (Di Sante et al., 2021). These changes, in conjunction with potential alterations in wind regimes and the occurrence of storms, are likely to exert an influence on ROFIs, resulting in shifts in their seasonal and interannual fluctuations. Given the intricate and vulnerable nature of these ecosystems, a future priority will be to anticipate prospective changes that could affect them.

### CRediT authorship contribution statement

**Maud Martinez Almoyna:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Conceptualization.
**Guillaume Charria:** Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization.
**Marc Sourisseau:** Writing – review & editing, Supervision, Methodology, Investigation, Conceptualization.
**Anne Gaymard:** Writing – review & editing, Validation, Software.
**Xavier Couvelard:** Writing – review & editing, Validation, Software.
**Sébastien Theetten:** Writing – review & editing, Software.
**Jean-François Le Roux:** Writing – review & editing, Software.

### 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.

## Acknowledgements

This study is part of the RiOMar project (from the national Ocean and Climate research priority program - PPR Océan et Climat and funded by the French National Research Agency - grant ANR-22-POE-0006) and the SCOPEUS project (SWOT science team program) funded by the CNES. The PhD Thesis of M. Martinez Almoyna is funded by the RiOMar project. This project was provided with computing HPC and storage resources by GENCI at TGCC thanks to the grant 2024-A0160107096 on the supercomputer Joliot Curie's ROME partition. We acknowledge the COAST-HF (http://www.coast-hf.fr) national observing network component of the ILICO national research infrastructure. This study is part of the State-Region Plan Contract ObsOcean - ROEC-ILICO.

## Data availability

Data will be made available on request.

## References

Auclair, F., Benshila, R., Bordois, L., Boutet, M., Brémond, M., Caillaud, M., Cambon, G., Capet, X., Debreu, L., Ducousso, N., Dufois, F., Dumas, F., Ethé, C., Gula, J., Hourdin, C., Illig, S., Jullien, S., Corre, M.L., Gac, S.L., Gentil, S.L., Lemarié, F., Marchesiello, P., Mazoyer, C., Morvan, G., Nguyen, C., Penven, P., Person, R., Pianezze, J., Pous, S., Renault, L., Roblou, L., Sepulveda, A., Theetten, S., 2024. Coastal and Regional Ocean Community model. Zenodo.

Ayouche, A., Charria, G., Carton, X., Ayoub, N., Theetten, S., 2021. Non-linear processes in the gironde river plume (North-East Atlantic): Instabilities and mixing. Front. Mar. Sci. 8.

Belamari, S., 2005. Report on Uncertainty Estimates of an Optimal Bulk Formulation for Surface Turbulent Fluxes. Marine EnviRonment and Security for the European Area—Integrated Project (MERSEA IP), Deliverable d.4.1.2.

Boé, J., Habets, F., 2014. Multi-decadal river flow variations in France. Hydrol. Earth Syst. Sci. 18 (2), 691–708, Publisher: European Geosciences Union.

Bonnet, R., Boé, J., Habets, F., 2020. Influence of multidecadal variability on high and low flows: the case of the Seine basin. Hydrol. Earth Syst. Sci. 24 (4), 1611–1631, Publisher: European Geosciences Union.

Bouwer, L.M., Vermaat, J.E., Aerts, J.C.J.H., 2008. Regional sensitivities of mean and peak river discharge to climate variability in Europe. J. Geophys. Res.: Atmospheres 113 (D19), eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2008JD010301.

Chapalain, M., Verney, R., Fettweis, M., Jacquet, M., Le Berre, D., Le Hir, P., 2019. Investigating suspended particulate matter in coastal waters using the fractal theory. Ocean. Dyn. 69 (1), 59–81.

Charria, G., Lazure, P., Le Cann, B., Serpette, A., Reverdin, G., Louazel, S., Bati-foulier, F., Dumas, F., Pichon, A., Morel, Y., 2013. Surface layer circulation derived from Lagrangian drifters in the Bay of Biscay. J. Mar. Syst. 109–110, S60–S76.

CMEMS, E.C.M.S.I., 2023. European North West Shelf/Iberia Biscay Irish Seas - high resolution L4 sea surface temperature reprocessed.

CMEMS, E.C.M.S.I., 2024. Global ocean physics reanalysis.

Cocquempot, L., Delacourt, C., Paillet, J., Riou, P., Aucan, J., Castelle, B., Charria, G., Claudet, Conan, J., P. Coppola, L., Hocdé, R., Planes, S., Raimbault, P., Savoye, L., Vuillemin, R., 2019. Coastal ocean and nearshore observation: A French case study. Front. Mar. Sci. 6.

Cugier, P., Le Hir, P., 2002. Development of a 3D hydrodynamic model for coastal ecosystem modelling. Application to the plume of the Seine river (France). Estuar. Coast. Shelf Sci. 55 (5), 673–695.

Dayon, G., Boe, J., Martin, E., Gailhard, J., 2018. Impacts of climate change on the hydrological cycle over France and associated uncertainties. Comptes Rendus Géoscience 350 (4), 141–153, Publisher: Elsevier.

Di Sante, F., Coppola, E., Giorgi, F., 2021. Projections of river floods in Europe using EURO-CORDEX, CMIP5 and CMIP6 simulations. Int. J. Climatol. 41 (5), 3203–3221, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/joc.7014.

Farcy, P., Durand, D., Charria, G., Painting, D.J., Tamminen, T., Collingridge, K., Grémare, A.J., Delauney, L., Puillat, I., 2019. Toward a European coastal observing network to provide better answers to science and to societal challenges; the JERICO research infrastructure. Front. Mar. Sci. 6 (529).

Grasso, F., Verney, R., Le Hir, P., Thouvenin, B., Schulz, E., Kervella, Y., Khojasteh Pour Fard, I., Lemoine, J.-P., Dumas, F., Garnier, V., 2018. Suspended sediment dynamics in the macrotidal Seine Estuary (France): 1. Numerical modeling of turbidity maximum dynamics. J. Geophys. Res.: Ocean. 123 (1), 558–577, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/2017JC013185.
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., De Chiara, G., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R.J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., Thépaut, J.-N., 2020. The ERA5 global reanalysis. Q. J. R. Meteorol. Soc. 146 (730), 1999–2049, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/qj.3803.

Hetland, R.D., 2005. Relating river plume structure to vertical mixing. J. Phys. Oceanogr. 35 (9), 1667–1688, Publisher: American Meteorological Society Section: Journal of Physical Oceanography.

Horner-Devine, A.R., Hetland, R.D., MacDonald, D.G., 2015. Mixing and transport in coastal river plumes. Annu. Rev. Fluid Mech. 47 (1), 569–594.

Jullien, S., Gaillaud, M., Benshila, R., Bordois, L., Gambon, G., Dufois, F., Dumas, F., Gula, J., Corre, M.L., Gac, S.L., Gentil, S.L., Lemarié, F., Marchesiello, P., Morvan, G., Pianezze, J., Renault, L., Schreiber, M., Theetten, S., 2005. Croco Documentation.

Kersalé, M., Marié, L., Le Cann, B., Serpette, A., Lathuilière, C., Le Boyer, A., Rubio, A., Lazure, P., 2016. Poleward along-shore current pulses on the inner shelf of the Bay of Biscay. Estuar. Coast. Shelf Sci. 179, 155–171.

Lazure, P., Garnier, V., Dumas, F., Herry, C., Chifflet, M., 2009. Development of a hydrodynamic model of the Bay of Biscay. Validation of hydrology. 100 Years of Research within the Bay of Biscay, Cont. Shelf Res. 100 Years of Research within the Bay of Biscay, 29 (8).985–997,

Lazure, P., Jegou, A.-M., 1998. 3D modelling of seasonal evolution of Loire and Gironde plumes on Biscay Bay continental shelf. Oceanol. Acta 21 (2), 165–177.

Lazure, P., Jegou, A.-M., Kerdreux, M., 2006. Analysis of salinity measurements near islands on the French continental shelf of the Bay of Biscay. Sci. Mar. 70 (1), 7–14, Publisher: Institut de Ciències del Mar de Barcelona, CSIC.

Le Boyer, A., Charria, G., Le Cann, B., Lazure, P., Marié, L., 2013. Circulation on the shelf and the upper slope of the Bay of Biscay. Cont. Shelf Res. 55, 97–107.

Lyard, F.H., Allain, D.J., Cancet, M., Carrere, L., Picot, N., 2021. FES2014 global ocean tide atlas: design and performance. Ocean Science 17 (2), 615–649, Num Pages: 35 Place: Gottingen Publisher: Copernicus Gesellschaft Mbh Web of Science ID: WOS:000648484500001.

Marchesiello, P., Debreu, L., Couvelard, X., 2009. Spurious diapycnal mixing in terrain-
following coordinate models: The problem and a solution. Ocean. Model. 26 (3),
156-169.

Ménesguen, A., Gohin, F., 2006. Observation and modelling of natural retention structures in the English channel. J. Mar. Syst. 63 (3-4), 244-256.

Nguyen, T.T., Staneva, J., Grayek, S., Bonaduce, A., Hagemann, S., Pham, N.T., Kumar, R., Rakovec, O., 2024. Impacts of extreme river discharge on coastal dynamics and environment: Insights from high-resolution modeling in the German Bight. Reg. Stud. Mar. Sci. 73, 103476.

Petton, S., Garnier, V., Caillaud, M., Debreu, L., Dumas, F., 2023. Using the two-
way nesting technique AGRIF with MARS3D V11.2 to improve hydrodynamics and
estimate environmental indicators. Geosci. Model. Dev. 16 (4), 1191–1211.

Pingree, R.D., 1978. Mixing and stabilization of phytoplankton distributions on the northwest European continental shelf. In: Steele, J.H. (Ed.), Spatial Pattern in Plankton Communities. Springer US, Boston, MA, pp. 181–220.

Pingree, R.D., 1980. Chapter 13 physical oceanography of the celtic sea and English channel. In: Banner, F.T., Collins, M.B., Massie, K.S. (Eds.), Elsevier Oceanography Series. In: The North-West European Shelf Seas: The Sea Bed and the Sea in Motion II. Physical and Chemical Oceanography, and Physical Resources, vol. 24, Elsevier, pp. 415–465.

Pingree, R.D., Maddock, L., 1977. Tidal residuals in the English channel. J. Mar. Biol. Assoc. UK 57 (2), 339–354.

Poppeschi, C., Charria, G., Goberville, E., Rimmelin-Maury, P., Barrier, N., Petton, S., Unterberger, M., Grossteffan, E., Repecaud, M., Quemener, L., Theetten, S., Le Roux, J.-F., Treguer, P., 2021. Unraveling salinity extreme events in coastal environments: A winter focus on the Bay of Brest. Front. Mar. Sci. 8 (705403).

Poppeschi, C., Verney, R., Charria, G., 2024. Suspended particulate matter response to extreme forcings in the Bay of Seine. Mar. Geol. 472, 107292.

Puillat, I., Lazure, P., Jégou, A., Lampert, L., Miller, P., 2004. Hydrographical variability on the French continental shelf in the Bay of Biscay, during the 1990s. Cont. Shelf Res. 24 (10), 1143–1163.

Puillat, I., Lazure, P., Jegou, A.-M., Lampert, L., Miller, P., 2006. Mesoscale hydrological variability induced by northwesterly wind on the french continental shelf of the Bay of Biscay. Sci. Mar. 70 (S1), 15–26, Number: S1.

Salomon, J., Breton, M., 1993. An atlas of long-term currents in the channel. Oceanol. Acta.

Schulz, E., Grasso, F., Le Hir, P., Verney, R., Thouvenin, B., 2018. Suspended sediment dynamics in the macrotidal Seine Estuary (France): 2. Numerical modeling of sediment fluxes and budgets under typical hydrological and meteorological conditions. J. Geophys. Res.: Ocean. 123 (1), 578–600, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/2016JC012638.

Sentchev, A., Korostenko, K., 2004. Stratification and tidal current effects on larval transport in the eastern english channel: Observations and 3D modeling. Environ. Fluid Mech. 4 (3), 305–331.

Sentchev, A., Yaremchuk, M., Lyard, F., 2006. Residual circulation in the English channel as a dynamically consistent synthesis of shore-based observations of sea level and currents. Cont. Shelf Res. 26 (16), 1884–1904.

Sharples, J., Simpson, J.H., 1995. Semi-diurnal and longer period stability cycles in the Liverpool Bay region of freshwater influence. Cont. Shelf Res. 15 (2), 295–313.

Simon, A., Poppeschi, C., Plecha, S., Charria, G., Russo, A., 2023. Coastal and regional marine heatwaves and cold spells in the northeastern Atlantic. Front. Mar. Sci. 19, 1339–1355.

Simpson, J.H., 1997. Physical processes in the ROFI regime. J. Mar. Syst. 12 (1), 3–15.

Simpson, J.H., Brown, J., Matthews, J., Allen, G., 1990. Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries 13 (2), 125.

Simpson, J., Souza, A., 1995. Semidiurnal switching of stratification in the region of freshwater influence of the Rhine. J. Geophys. Res. 100, 7037–7044.

Szekely, T., Bezaud, M., Pouliquen, S., Reverdin, G., Charria, G., 2017. CORA-IBI, Coriolis Ocean Dataset for Reanalysis for the Ireland-Biscay-Iberia region. SEANOE.

Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 61–78.

Toublanc, F., Ayoub, N.K., Marsaleix, P., 2023. On the role of wind and tides in shaping the Gironde River plume (Bay of Biscay). Cont. Shelf Res. 253, 104891.

Umlauf, L., Burchard, H., 2003. A generic length-scale equation for geophysical turbulence models. J. Mar. Res. 61 (2), 235–265.

Verney, R., Le Berre, D., Repecaud, M., Bocher, A., Bescond, T., Poppeschi, C., Grasso, F., 2024. Suspended particulate matter dynamics at the interface between an estuary and its adjacent coastal sea: Unravelling the impact of tides, waves and river discharge from 2015 to 2022 in situ high-frequency observations. Mar. Geol. 471, 107281.

Verspecht, F., Rippeth, T.P., Howarth, M.J., Souza, A.J., Simpson, J.H., Burchard, H., 2009. Processes impacting on stratification in a region of freshwater influence: Application to Liverpool Bay. J. Geophys. Res.: Ocean. 114 (C11), _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2009JC005475.