F Toublanc

I Brenon

T Coulombier

Formation and structure of the turbidity maximum in the macrotidal Charente estuary (France): influence of fluvial and tidal forcings

Keywords: Estuary, Turbidity maximum, Numerical Modelling, Sediment dynamics, Tidal asymmetry, Density gradient

    Formation and structure of the turbidity maximum in the macrotidal Charente estuary (France): Influence of fluvial and tidal forcing F Toublanc, I Brenon, T Coulombier

Introduction

Because of their unique location at the interface between land and sea, estuaries are critical ecosystems subject to strong anthropogenic pressures. Macrotidal estuaries characterized by the presence of fine cohesive sediments frequently exhibit the formation of a highly turbid zone. This compact suspended sedimentary mass is called a turbidity maximum, and it is sensitive to variations in the tidal and fluvial regime. Understanding the dynamics and characteristics of turbidity maxima is important for the ecology as well as the economy of nearby coastal areas. For example, fine cohesive sediments are noted carriers of pollutants that endanger water quality [START_REF] Eyre | Implications of sedimentological studies for environmental pollution assessment and management : examples from fluvial systems in North Queensland and Western Australia[END_REF]. They are also related to strong siltation rates near harbours or other infrastructure, necessitating regular dredging. For instance, [START_REF] Owens | Fine-grained sediment in river systems: environmental significance and management issues[END_REF] report that 50 × 10 6 tons/year of sediment are dredged from coastal areas in the UK. They also show that dredging reaches 4 to 5 ×10 6 m 3 /year in the Elbe river and Hamburg harbour in Germany.

Turbidity maximum processes have been studied in several estuaries [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF][START_REF] Brenon | Modelling the turbidity maximum in the Seine estuary (France): Identification of Formation Processes[END_REF][START_REF] Cancino | Hydrodynamic and sediment suspension modelling in estuarine systems Part II : Application to the Western Scheldt and Gironde estuaries[END_REF][START_REF] Dyer | Estuaries: a Physical Introduction[END_REF][START_REF] Sottolichio | Modeling mechanisms for the stability of the turbidity maximum in the gironde estuary, france[END_REF][START_REF] Uncles | The freshwater-saltwater interface and its relationship to the turbidity maximum in the Tamar estuary , United Kingdom[END_REF][START_REF] Uncles | Runoff and tidal influences on the estuarine turbidity maximum of a highly turbid system : the upper Humber and Ouse Estuary, UK[END_REF]. The suspended sediment concentration in the turbidity maximum varies on several time scales (following the ebb-flood cycle, spring-neap cycle, seasonal variations, and so forth). On the 12 h scale of a semi-diurnal tidal cycle, slack waters tend to favour sedimentation and deposition, whereas flood and ebb phases favour erosion and resuspension, with mobile bed sediments feeding the turbidity maximum [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF]. Fluctuations on the larger time scale of a spring-neap tidal cycle, induced by changes in the current velocities intensities, are also important [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF][START_REF] Dyer | Estuaries: a Physical Introduction[END_REF]. From spring to neap tides, current velocities decrease and sedimentation takes place. The turbidity maximum zone is then reduced, and fluid mud appears (or is supplemented) at the bottom. Seasonal variations related to river discharge also occur. For example, floods can induce a seaward movement of the turbidity maximum [START_REF] Allen | Suspended sediment transport from the Gironde estuary (France) onto the adjacent continental shelf[END_REF][START_REF] Uncles | Runoff and tidal influences on the estuarine turbidity maximum of a highly turbid system : the upper Humber and Ouse Estuary, UK[END_REF].

The formation of a turbidity maximum in an estuary is mainly attributed to two processes: density circulation and tidal asymmetry [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF]. Density gradients may generate two-layer circulation (density circulation), with freshwater moving seaward at the surface and saltwater moving landward at the bottom. A turbidity maximum can appear at the density nodal point, where the flow becomes entirely seaward-oriented [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF][START_REF] Dyer | Estuaries: a Physical Introduction[END_REF].

Tidal asymmetry, characterized by uneven current velocities and slack waters [START_REF] Aubrey | A study of non-linear tidal propagation in shallow inlet / estuarine systems part I : observations[END_REF][START_REF] Friedrichs | Non-linear tidal distortion in shallow estuaries : a synthesis[END_REF], can generate a turbidity maximum at the tidal nodal point. According to [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF] and [START_REF] Dyer | Estuaries: a Physical Introduction[END_REF], the tidal nodal point is often located upstream from the density nodal point. [START_REF] Uncles | The freshwater-saltwater interface and its relationship to the turbidity maximum in the Tamar estuary , United Kingdom[END_REF] showed that positions of the turbidity maximum sometimes corresponds to the freshwater-saltwater interface.

The relative importance of both processes depends on estuary characteristics. [START_REF] Li | Modélisation numérique du transport des sédiments remis en suspension dans un estuaire -Application à la Gironde[END_REF] suggested that turbidity maximum dynamics are mainly driven by the tides. This behaviour was confirmed by [START_REF] Brenon | Modelling the turbidity maximum in the Seine estuary (France): Identification of Formation Processes[END_REF] and [START_REF] Sottolichio | Modeling mechanisms for the stability of the turbidity maximum in the gironde estuary, france[END_REF] in the Seine and Gironde estuaries, respectively. However, both studies showed that density gradients are essential to the stability of the turbidity maximum by maintaining a compact sedimentary mass in suspension and preventing strong sediment export.

The Charente estuary (Figure 1), located on the French Atlantic coast, is a useful site in which to study estuarine dynamics. In the recent years, the area has experienced droughts and also hosts a broad spectrum of economic activities (oyster farming, agriculture, tourism, port operations, and so forth), making this estuary particularly sensitive to water quality and siltation issues. Local features, such as the inversion of tidal asymmetry as a function of the spring-neap tidal cycle [START_REF] Toublanc | Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente, France)[END_REF] are also interesting. More generally, although numerous studies have investigated large macrotidal estuaries, smaller systems such as the Charente remain poorly understood. However, many of these small estuaries strongly influence their surroundings. This study focuses on the turbidity maximum and suspended sediment dynamics in the Charente, at different time scales and under various fluvial and tidal regimes.

Several indicators are used to quantify the impact of these forcings on the horizontal and vertical distribution of S S C (suspended sediment concentration), and to identify the mechanisms that drive the formation of the turbidity maximum. Changes in its structure are also investigated numerically, to delineate the processes controlling sediment escape to the connected bay.

Study site

The Charente estuary (45˚96N, 1˚00W, Fig. 1) is located on the French Atlantic Coast. The river flows into the Marennes-Oléron Bay, in the southern part of the pertuis Charentais. The river's catchment is 10550 m 2 and its length is 365 km. A dam is located in Saint-Savinien, 50 km from the river mouth. The mean river discharge is estimated to be 70 m 3 /s. Discharge can reach extreme values of 600 to 700 m 3 /s during flood events, and drop to less than 10 m 3 /s during the summer. Exceptional floods can have caused discharges of up to 1000 m 3 /s. The river is shallow, with a maximum depth of 10 m below mean sea level, and the estuary mouth is funnel-shaped.

The Marennes-Oléron Bay's total surface area covers nearly 150 km 2 , with 60% composed by intertidal areas.

The sediments in the estuary and in the eastern part of the Marennes-Oléron Bay are entirely cohesive, with a very fine grain size [START_REF] Strady | Spatial and temporal variations in trace metal concentrations in surface sediments of the Marennes Oléron Bay. Relation to hydrodynamic forcing[END_REF]. In the western part of the bay, sediments are sandier [START_REF] Tesson | Aspects dynamiques de la sédimentation dans la baie de Marennes-Oléron (France)[END_REF][START_REF] Bertin | Tidal inlet response to sediment infilling of the associated bay and possible implications of human activities: the Marennes-Oléron Bay and the Maumusson Inlet, France[END_REF]. The mud ratio decreases and the mean gran size tends to increase upstream, but the latter remains less than 20 µm and the mud ratio is always greater than 80% [START_REF] Coulombier | Seasonal monitoring of sediments dynamics in a highly turbid estuary (Charente Estuary, France): source and sink of the turbidity maximum[END_REF].

The estuary and the bay are affected by semidiurnal tides. At the river mouth, the mean and maximum tidal ranges are 4.5 m and 6.5 m, respectively. This macrotidal regime is also characterized by the influence of quarterdiurnal constituents (M4, MS4 and MN4), which are strongly amplified shoreward by resonance along the Bay of Biscay shelf [START_REF] Le Cann | Barotropic tidal dynamics of the Bay of Biscay shelf[END_REF]. [START_REF] Bertin | Importance of wave age and resonance in storm surges: The case Xynthia, Bay of Biscay[END_REF] verified this phenomenon numerically and showed that the largest amplification by resonance occurred for the MS4 constituent. In combination with the internal tidal distortion of the estuary, these externally generated overtides result in fortnightly inversions of the tidal asymmetry [START_REF] Toublanc | Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente, France)[END_REF]. Depending on the timing of the spring-neap tidal cycle, and the position in the estuary, the estuary can be dominated either by the flood or the ebb.

Prior to this study, few data were available on the turbidity maximum of the Charente estuary, including only The characteristics and movements of the turbidity maximum are very important to management of the area. This is especially true in Rochefort where the harbour is often dredged to compensate for strong sediment accumulation: reports estimate that 160,000 m 3 /year of sediment is dredged. Tourism, as well as oyster and mussel farming in the Marennes-Oléron Bay also strongly depend on outflows from the Charente river.

Materials and methods

Numerical modelling

The numerical model MARS-3D (Modelling for Applications at Regional Scales) used in this study has been described in previous work [START_REF] Lazure | An external-internal mode coupling for a 3D hydrodynamical model for applications at regional scale (MARS)[END_REF]. It is a finite differences model that solves the Navier-Stokes equations under hydrostatic and Boussinesq assumptions when used in 3D mode. The configuration presented here consists of two nested grids. The first one, with 100 m horizontal resolution, is forced by tides computed using the SHOM CST-France model (Le [START_REF] Roy | Réalisation et validation d'un modèle de marée en Manche et dans le Golfe de Gascogne. Application à la réalisation d'un nouveau programme de réduction des sondages bathymétriques[END_REF]. It runs in 2D and provides open boundary conditions at the seaward limit for the second grid. This grid has a 30 m horizontal resolution and runs in 3D with 8 sigma levels. Daily river discharges are prescribed. Bathymetric data (Fig. 2) were provided by several organizations (SHOM, Ifremer, EPTB Charente). Upstream of L'Houmée, the grid resolution is insufficient to accurately represent the dynamics of the river. Consequently, an artificial canal is created, with bathymetric values extracted from the real data. This allows us to prescribe the estimated daily discharge at the Saint-Savinien dam.

Atmospheric forcing is provided by the ARPEGE model from Météo-France(15 kilometres, 6 hours). The model includes the wind speed 10 meters above the sea surface, the atmospheric pressure and the temperature 2 meters above the sea surface.

A two equation k-kl turbulence closure model is used (Warner et al., 2005b). This model, which resembles the Mellor-Yamada level 2.5 scheme (1974;[START_REF] Mellor | Development of a turbulence closure model for geophysical fluid problems[END_REF], solves the vertical eddy viscosity and diffusivity by calculating the turbulent kinetic energy and the turbulence length scale. The horizontal eddy viscosity and diffusivity are computed by using the Smagorinsky method, to take the local shear conditions into account (1963).

Considering the relative homogeneity of the sediment and its granulometry measured along the estuary, one sedimentary class is used in the model. Settling velocity is variable (between 0.05 and 1 mm/s) and depends on concentration, salinity and turbulence, according to a semi-empirical formulation (Le [START_REF] Hir | Application of the continuous modeling concept to simulate high-concentration suspended sediment in a macrotidal estuary[END_REF]. The concentration and turbulence dependence for settling is crucial to take into account the flocculation processes that occur in areas of strong S S C with cohesive sediment [START_REF] Blake | Sediment trapping and transport in the ACE Basin, South Carolina[END_REF][START_REF] Milligan | Flocculation and sedimentation in the ACE Basin, South Carolina[END_REF][START_REF] Milligan | Flocculation and the loss of sediment from the Po River plume[END_REF]. The sedimentary module mudsand in MARS-3D was fully described by [START_REF] Hir | Dynamics of sand and mud mixtures: A multiprocess-based modelling strategy[END_REF] and takes into account suspended sediment transport (no bedload transport) associated with fine sediments. Consolidation processes are not considered in this study. In the absence of relevant measurements at the Saint-Savinien dam that would allow us to establish a runoff/concentration relationship, a fixed input of 0.05 g/L is prescribed at the upstream boundary. This value was chosen according to upstream data presented by [START_REF] Modéran | Organic matter exploitation in a highly turbid environment: Planktonic food web in the Charente estuary, France[END_REF]. Moreover, cores and surface sediments sampled on the estuarine banks show little variation in the mud fraction and mean grain size. Thus, variations in river flow do not necessarily imply a strong fluvial sediment input, because the sediment characteristics remain very similar.

In-situ measurements for model validation

Model validation is performed using in-situ data recorded for different periods and at different locations, as shown in Figure 1.

Sea surface elevation and current velocities are validated using continuous tide gauge data from Rochefort and the Aix Island (from the REFMAR portal) and ADCP data (Sentinel-RDI instruments, 1200 kHz, 5-minute sampling frequency, February to April 2011) at the river mouth (Port-des-Barques). Current velocities are also validated using ADV measurements (Argonaut-ADV, Sontek) carried out at Rochefort (November 2012 to August 2013, 30 seconds averaged every 5 minutes), approximately one meter above the sediment bed.

Simulated salinity levels are compared to datasets obtained from multi-parameter probes (YSI 6600V2) located at the mouth, surface (February to March 2011, 10-minute sampling frequency) and bottom (October to December 2012, 5-minute sampling frequency). Turbidity data were also recorded with the same probes (5-minute sampling frequency), at the mouth (approximately two meters above the bed) and at Rochefort (approximately one meter above the bed). Salinity and turbidity probes were laboratory calibrated using standard solutions (12880 microS iemens.cm -1 , and formazin at 1000 and 4000 NTU, respectively). Wet sediments collected from the intertidal banks of the Charente were diluted at several concentrations in a 40 L black bucket to calibrate the turbidity sensors. Validation of suspended sediment concentrations was performed after filtration on GF/C filters [START_REF] Coulombier | Seasonal monitoring of sediments dynamics in a highly turbid estuary (Charente Estuary, France): source and sink of the turbidity maximum[END_REF].

Results

This section focuses on the results obtained by numerical modelling. The S S C levels are analysed and displayed for various fluvial and tidal conditions. Prior to this analysis, the performance of the model is validated to several variables (water surface elevation, current velocities, salinity levels and S S C).

Model validation

Mean absolute (MAE) and root mean square (RMSE) errors are calculated to compare the modelled and observed water surface elevation, current velocities and salinity levels. Model accuracy is also evaluated using the skill parameter (Eq. 1) developed by [START_REF] Willmott | On the validation of models[END_REF] and used in several recent estuarine dynamics studies [START_REF] Li | Simulations of Chesapeake Bay estuary: Sensitivity to turbulence mixing parameterizations and comparison with observations[END_REF][START_REF] Ma | Hydrodynamic modeling of Changjiang Estuary: Model skill assessment and large-scale structure impacts[END_REF]Warner et al., 2005a;[START_REF] Xing | A three-dimensional hydrodynamic and salinity transport model of estuarine circulation with an application to a macrotidal estuary[END_REF]. This parameter takes into account the modelled (X mod ) and observed (X obs ) deviations around the observed mean (X obs ) to estimate model performance, and varies between 0 (no agreement) and 1 (perfect agreement), as follows:

S kill = 1 - Σ |X mod -X obs | 2 Σ X mod -X obs + X obs -X obs 2 (1)
All calculations are presented in Table 1. The stations used for validation are shown in Figure 1. Water surface elevations are well reproduced by the model (skill > 0.99 for all locations). Figure 3 shows a graphical representation of the results at the estuary mouth and at Rochefort. A period of two tidal cycles (24 h) is shown for the water surface elevation at Port-des-Barques, close to the estuary mouth.

In MARS-3D, bottom friction is calculated using a roughness length z0, derived from the Nikuradse coefficient [START_REF] Nikuradse | Laws of flow in rough pipes[END_REF]. The hydrodynamic results showed in Figure 3 and Table 1 required adjusting this parameter, which was reduced within the estuary. This issue was particularly important in the Rochefort area, because of fluid mud in the channel, which can cause a significant increase in current velocities, the physical roughness of the sediment bed being very low. [START_REF] Hamm | Morphodynamic coupling of bottom roughness and fluid mud for modelling tidal propagation in the Loire estuary (France)[END_REF] and [START_REF] Walther | Modélisation tridimensionnelle de la salinité et de la turbidité dans l'estuaire de la Loire : couplage des processus[END_REF] showed that hydrodynamic models often fail to reproduce this effect and overestimate low water levels. [START_REF] King | Bottom friction reduction in estuaries[END_REF] made similar observations. After calibration of our model, the Chézy coefficient corresponding to the roughness length is estimated to reach 100 to 110 m 1/2 /s, depending on the water depth. These values are within the range of those obtained in other studies: according to [START_REF] Winterwerp | Introduction to the physics of cohesive sediment dynamics in the marine environment[END_REF], Chézy values of 110 m 1/2 /s were found in the Yangtze and the Amazon rivers, due to the presence of fluid mud.

Current velocities are better reproduced in the direction of flow (zonal in Port-des-Barques, meridional in Rochefort (Figure 3)) than in the perpendicular direction. However, the model still agrees well with observational data (skill > 0.92). The highest errors occurred at Rochefort, both for current velocities and water surface elevation. Model performance on salinity is within the range of the two previous parameters (skill > 0.95). Errors mainly occur during the transition from spring to neap tide (and vice versa).

Concerning sediment dynamics, [START_REF] French | Critical perspectives on the evaluation and optimization of complex numerical models of estuary hydrodynamics and sediment dynamics[END_REF] noted that it was difficult to validate modelled suspended sediment Following this calibration/validation, the turbidity maximum is well reproduced by the model, and its position and movements are coherent with field observations. The background concentration is higher in the model than in observations. This difference could be explained by the tendency of numerical models in sigma coordinates to smooth the S S C, the volume integrated in the modelled cell being more important than the volume of the measurement cell [START_REF] Sottolichio | Evolution hydrosédimentaire récente de l'estuaire de la Gironde. Apport d'un modèle de transport[END_REF]. A different tuning of the settling velocity could also improve the results, but the values for the maximum and minimum settling velocities were chosen to obtain satisfying results, both at the river mouth and at Rochefort. Higher S S C are obtained during neap tides in the model. This period in the tidal cycle favours the presence of the fluid mud. As shown by [START_REF] Ross | On the mechanics of lutoclines and fluid mud[END_REF], density stratification caused by fluid mud and its interface with the water column (lutocline) can reduce mixing and suppress resuspension. This is not yet taken into account in the model and could explain the differences obtained during neap tides.

The skill parameter equals 0.62 at the river mouth and 0.74 at Rochefort. These results are within the range of those obtained in recent studies on 3D hydrosedimentary modelling of estuaries: [START_REF] Cheng | Generation of an estuarine sediment plume by a tropical storm[END_REF] obtained skill values of 0.66 and 0.88 for surface and bottom S S C, respectively; [START_REF] Van Maren | Fine sediment transport into the hyper-turbid lower Ems River : the role of channel deepening and sediment-induced drag reduction[END_REF] obtained skill values greater than 0.6. Figure 4 shows that the order of magnitude of suspended sediment concentrations and the spring-neap variability are well reproduced. Particularly, the transition from neap to spring tides occurs gradually, following the same pattern as the observations. We also note that the ebb/flood asymmetry, which is a crucial feature in this study, is well-represented: during spring tide, the S S C is higher during the flood than during the ebb, and the high water slack favours deposition more than the low water slack. Thus, the model is suitable for the study of sediment dynamics conducted here, because it reproduces well the two main timescales considered (semi-diurnal and spring-neap tidal cycles).

Semi-diurnal variability

In this section, the evolution of suspended sediment concentrations during a 12 h spring tidal cycle is presented.

The river discharge is set at 50 m 3 .s -1 . Four indicators are used to discuss the modelling results: S S C, which represents the mean suspended sediment concentration in the estuary (from the river mouth to the upstream limit of the domain); ∆S S C, the mean bottom-surface difference in S S C, which is used to evaluate the overall vertical S S C stratification; S S C max , the spatial maximum suspended sediment concentration and ∆S S C max , the spatial maximum bottom-surface difference in S S C. For the last two parameters, the distance from the estuary's mouth is also calculated. These values are extracted from the model at four times: low water, three hours after low water (or mid-flood), high water, and three hours after high water (or mid-ebb) (Table 2). The variations in S S C are also shown in Figure 5. The results are displayed using a logarithmic colour scale to include the over the entire range of concentrations. This logarithmic scale is particularly important for the results approximately 4 kilometres downstream from the reference point chosen as the river mouth (see Figure 1). As the tidal cycle progresses, S S C decreases by more than 35% in 3 hours, while ∆S S C remains stable. S S C max and ∆S S C max are obtained 3 km upstream from the mouth, and their values increase between low water and mid-flood. Transects 3 and 4 (Figure 5) show that the turbidity maximum extension is close to 60 km and does not vary significantly.

Suspended sediment concentrations remain high during this phase of the tidal cycle.

Between mid-flood and high water, the mean S S C is halved. S S C is three times higher at low water than at high water. However, ∆S S C remains nearly constant, suggesting that stratification is high. Strong S S C max and ∆S S C max values (more than 14 g/L) that occur 13 km from the river mouth support this assumption. An overall decrease in S S C is also observed in transect 1 (Figure 5), even though strong concentrations still exist close to the bottom. The turbidity maximum extension is almost 45 km.

Between high water and mid-ebb, S S C is nearly halved, and ∆S S C is reduced by 70 %. The S S C and ∆S S C maxima reach their lowest values (Table 2). The difference in distance between high water and mid-ebb is 2 km, compared to 7 km between low water and mid-flood. The turbidity maximum extension at mid-ebb (Transect 2, Figure 5) is estimated to be between 35 and 40 km.

From mid-ebb to low water, mean S S C and ∆S S C increase sixfold and threefold, respectively. Maximum values also increase and occur 15 km downstream from their mid-ebb location.

These results suggest that the most dynamic periods in the tidal cycle are the first hours of flood and the last hours of ebb. These periods are associated with strong increases in S S Cs in the estuary, and with the highest differences in distance for S S C max and ∆S S C max . In contrast, from mid-flood to mid-ebb, suspended sediment concentrations decrease significantly.

Spring-neap variability

The indicators presented in the previous section (S S C, ∆S S C, S S C max and ∆S S C max ) are extracted from modelling results and presented in Table 3, for spring and neap tides. S S C and ∆S S C are calculated over two tidal cycles (approximately 24 h). The corresponding distances from the mouth are indicated for S S C max and ∆S S C max , as well as the time in the tidal cycle when these values are reached. Figure 6 shows the distribution of S S C for high and low water during spring and neap tides. The indicators S S C, S S C max and ∆S S C max are reduced by an order of magnitude between spring and neap tides.

Maxima occur at high water during spring tides and at low water during neap tides. The ∆S S C is less than 0.1 g/L during neap tides, and close to 1 g/L during spring tides.

These values show a large reduction of the suspended sedimentary mass between spring and neap tides, which is also shown in Figure 6. The 1 g/L contour line (in black) is non-existent during the high water period of neap tides and barely visible at low water (approximately 45 km from the river mouth). It appears to be difficult to define a turbidity maximum zone under these conditions. For spring tides, the highest S S Cs are obtained close to the downstream

Runoff variability

To estimate the impact of river discharge on the turbidity maximum dynamics and characteristics, the same indicators are presented in Table 3, for a high runoff of 400 m 3 /s and a low runoff of 5m 3 /s. Figures 7 and9 show the corresponding transects along the estuary, as in the previous sections.

High runoff

The spring tide mean S S C decreases between the 50 m 3 /s and the 400m 3 /s simulations (by more than 20%).

Similar results are obtained for ∆S S C, S S C max and ∆S S C max (which decrease between 18% and 26%). In contrast, during neap tide the S S C increases by more than 50% when the river runoff increases. Transects 3 and 4 (Figure 7) demonstrate this difference, especially at low water: while the 1 g/L contour line was almost non-existent in Figure 6, it is well defined in Figure 7.

The S S C max and ∆S S C max both occur three hours after low water during spring tide (three hours sooner than mean runoff conditions), and relatively close to the mouth (3.09 km and 1.64 km, respectively). Both maxima occur 22 km from the river mouth during low water during neap tides (and at the same time as the mean runoff). At low water during spring tides, the downstream "limit" of the turbidity maximum shifts seaward by a few kilometres. If the limit is considered to be point of maximum S S C, this constitutes a 2.1 km difference. However, the turbidity maximum does not seem to be fully advected from the estuary into the bay. S S C measurements confirm this behaviour (Figure 8): river discharge is increasing from 150 m 3 /s to 400 m 3 /s and S S C decreases at Rochefort while it stays high at the river mouth. Moreover, S S C values greater than 1 g/L are recorded during neap tides.

Low runoff

Estuarine turbidity consistently decreases when the river runoff is very low (5 m 3 /s). All of the values in the final two columns of Table 3 (representing low runoff conditions) are lower than those for mean runoff. The transects (Figure 9)confirm this behaviour graphically.

The S S C and ∆S S C maxima occur at different times during the tidal cycle: 4 hours after low water for spring tide and five hours after high water for neap tide. Positions and extensions are similar to those for mean river discharge. For high water during spring tides (Figure 9, transect 1), S S C is however higher upstream during low runoff conditions. During neap tide, the same remark made for mean runoff holds true for low runoff conditions: it is difficult to define a suspended sedimentary mass.

Discussion

Flood/ebb variability: deposition and resuspension

The semi-diurnal tidal cycle induces variations in current velocities, which directly impact the bed shear stress.

Along with the nature and state of the sedimentary bed, bed shear stress is one of the parameters that control erosion processes [START_REF] Mehta | Surface erosion of fine-grained sediment revisited[END_REF][START_REF] Tolhurst | A comparison and measurement standardisation of four in situ devices for determining the erosion shear stress of intertidal sediments[END_REF]. The results of this study demonstrate the impact of these current variations on the turbidity maximum over a tidal cycle during spring tides.

The difference between high and low water slack is particularly important. The latter is short and current velocities remain high within the estuary (more than 1 m/s). Around high water, current velocities are weaker for a longer period of time, allowing sedimentation. This behaviour affects S S C and ∆S S C. The S S C is three times higher at low water that at high water.

At high water, the maximum S S C is high (over 10 g/L) and so is stratification. Calculating a stratification ratio (∆S S C/S S C) allows comparison between the results. This ratio is greater than 1 at high water, showing that suspended sediments are not well distributed throughout the water column; the transects in Figure 5 confirm this result. In contrast, the stratification ratio is 0.34 at low water. Three hours after high water (mid-ebb), S S C is halved, suggesting that deposition occurred for the last three hours, causing an overall decrease in estuarine S S C.

The S S C decreases between low water and mid-flood as well, but it remains higher than around high water: S S C is almost four times greater at mid-flood than at mid-ebb. This difference also suggests that deposition occurred, but for a shorter period of time. Sediments also begin to become resuspended due to the increase in current velocities, because S S C max , ∆S S C max and ∆S S C increase three hours after low water. The turbidity maximum extension, defined by the 1 g/L limit, is greater at low water and mid-flood (60 to 55 km) than at high water and mid-ebb (40 to 45 km).

Sediments are maintained in suspension by strong velocities at the end of the ebb and at the beginning of the flood, making this period in the tidal cycle more dynamic than the high water slack. This behaviour has been observed in other estuaries including the Tamar, the Humber-Ouse [START_REF] Uncles | The freshwater-saltwater interface and its relationship to the turbidity maximum in the Tamar estuary , United Kingdom[END_REF][START_REF] Uncles | Runoff and tidal influences on the estuarine turbidity maximum of a highly turbid system : the upper Humber and Ouse Estuary, UK[END_REF], the Gironde [START_REF] Sottolichio | Modélisation de la dynamique des structures turbides (bouchon vaseux et crème de vase) dans l'estuaire de la Gironde[END_REF] and the Seine [START_REF] Brenon | Modelling the turbidity maximum in the Seine estuary (France): Identification of Formation Processes[END_REF].

The S S C variations in the Charente turbidity maximum are mainly driven by the successive phases of deposition, advection and resuspension, caused by current velocity fluctuations. [START_REF] Uncles | Seasonal variability of mobile mud deposits in the Tamar Estuary[END_REF] showed, that the turbidity maximum in the Tamar estuary primarily results from local resuspension, and that seasonal variability is partly due to the migration of mud deposits that move the bed-source of sediments. These observations can be transposed to the Charente estuary, where both the modelling results presented in this study and field measurements [START_REF] Coulombier | Seasonal monitoring of sediments dynamics in a highly turbid estuary (Charente Estuary, France): source and sink of the turbidity maximum[END_REF] show the same type of behaviour.

Fortnightly and seasonal variability: does the turbidity maximum always exist ?

Results show a strong variability in the dynamics and characteristics of the turbidity maximum in the Charente estuary. The spring-neap tidal cycle and the fluctuations in river runoff cause significant variations in suspended sediment concentrations throughout the estuary.

The mean S S C decreases nearly ninefold between spring and neap tide. Bottom shear stress is significantly reduced during neap tide because of the decrease in current velocities. As shown in the previous section, these fluctuations strongly impact resuspension and deposition processes. Turbulence and tidal mixing keep sediments in suspension during spring tide, whereas weak neap tide currents favour sedimentation [START_REF] Dyer | Estuaries: a Physical Introduction[END_REF].

For mean runoff, it is difficult to define a turbidity maximum during neap tides, because no clear high concentration area stands out. The maximum S S C (1.8 g/L) occurs approximately 30 km upstream, at low water, and probably results from local resuspension due to bathymetric variations as opposed to tidal straining. Dual frequency echo sounding performed during average tidal conditions [START_REF] Coulombier | Seasonal monitoring of sediments dynamics in a highly turbid estuary (Charente Estuary, France): source and sink of the turbidity maximum[END_REF] showed the presence of a turbidity maximum, confirmed by high S S C recorded from mid-depth to the bottom, meaning that the turbidity maximum was not extended throughout the water column. These observations testify of an intermediate state between spring and neap tide, when the turbidity maximum still exists but begins to weaken. In contrast, echo sounding performed during spring tide showed no interface in the water column with high S S C recorded throughout the water column and over the entire area covered during the survey (from the river mouth to approximately 5 km downstream from L'Houmée). Modelling results are coherent with these observations. In the Loire estuary, [START_REF] Marchand | The influence of seasonal salinity and turbidity maximum variations on the nursery function of the Loire estuary (France)[END_REF] mentions that during neap tide, the turbidity maximum settles and induces the formation of a mud layer at the bottom, which can cover a large area (20 km in the case of the Loire). The dual frequency echo sounding mentioned before also showed a net interface near the bottom at Rochefort, interpreted as a fluid mud patch of high concentration, with a thickness reaching 1.5 m in the deepest part of the channel. Fluid mud at the bottom can significantly reduce friction and tidal dissipation, which was taken into account in our model. This phenomenon has also been observed at the Amazon outlet [START_REF] Gabioux | Tidal propagation over fluid mud layers on the Amazon shelf[END_REF][START_REF] Kineke | Fluid-mud processes on the Amazon continental shelf[END_REF]. Other highly turbid macrotidal estuaries are likely to display this type of behaviour, and [START_REF] Marchand | The influence of seasonal salinity and turbidity maximum variations on the nursery function of the Loire estuary (France)[END_REF] highlights its negative effect on water quality, which is essential to the ecology of these areas.

The same behaviour is observed for low runoff conditions (Figure 9), which often prevail during the summer; even lower concentrations exist in the water column (mean S S C is less than 0.1 g/L and maximum S S C is less than 1.5 g/L). A shift in the time occurrence of maximum S S C and ∆S S C is also observed. They occur one hour earlier during neap tide (five hours after high water), and two hours earlier during spring tide (four hours after low water).

In the absence of significant river discharge, the sediment dynamics of the estuary are essentially driven by the tidal forcing. [START_REF] Toublanc | Fortnightly tidal asymmetry inversions and perspectives on sediment dynamics in a macrotidal estuary (Charente, France)[END_REF] showed that tidal asymmetry inversions occur in the estuary, following the spring-neap tidal cycle. For spring tide, the estuary is flood-dominant (shorter flood, stronger flood velocities). During neap tide, it is ebb-dominant (shorter ebb, stronger ebb velocities). These inversions could explain the difference we find in this study, with higher S S C during the ebb for neap tides, and higher S S C during the flood for spring tides.

High runoff simulations show that a turbidity maximum can also appear during neap tide. The joint action of high river discharge and the tides leads to the formation and maintenance of a well-defined suspended sedimentary mass, with significant longitudinal S S C gradients, in contrast to the mean and low runoff simulations. During spring tide, S S C max and ∆S S C max occur three hours earlier (mid-flood) than for the mean runoff simulation (high water). This difference can be explained by the tidal damping caused by a strong river discharge. Because the hours defined as for low and high water are extracted from predictions, they cannot reflect the shift in the estuarine dynamics due to runoff variability. As explained by [START_REF] Horrevoets | The influence of river discharge on tidal damping in alluvial estuaries[END_REF], high runoff induce higher low water levels upstream, especially when the cross-section is narrow. Friction is modified and the estuarine flow is more quickly by the river discharge than for mean conditions. [START_REF] Godin | Modification of river tides by the discharge[END_REF] indicated that in the downstream part of the estuary, low water will be slowed and high water will be accelerated. The three-hour shift observed during spring tide and high runoff conditions could correspond to this river discharge effect.

Although S S C levels vary between the mean and low runoff simulations, the position and extension of the turbidity maximum between low and high water during spring tide are similar. These results suggest that, for this range of river discharge, turbidity maximum dynamics are mainly driven by the tides. In the following subsection, the relative importance of the tides and the density gradients are discussed further.

Impact of density gradients on turbidity maximum characteristics

Two principal mechanisms dictate the formation of a turbidity maximum in an estuary: tidal asymmetry and density circulation [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF][START_REF] Brenon | Modelling the turbidity maximum in the Seine estuary (France): Identification of Formation Processes[END_REF][START_REF] Uncles | Seasonality of the turbidity maximum in the Humber-Ouse estuary , UK[END_REF]. The characteristics and dynamics of this sedimentary mass often result from the joint action of these two phenomena. [START_REF] Uncles | The freshwater-saltwater interface and its relationship to the turbidity maximum in the Tamar estuary , United Kingdom[END_REF] explain that the position of the turbidity maximum sometimes corresponds to the position of the saline intrusion, and varies according to changes in tidal and fluvial forcings. The transects for mean and high river runoff conditions (Figures 6 and7) show that, even if the turbidity maximum shifts seaward when the runoff is high, it does not seem to be exported from the estuary.

Maintenance of the turbidity maximum within the limits of the estuary could be explained by interactions between this sedimentary structure and salinity gradients, which are also subject to variations in the tides and the river discharge. Figure 10 shows the S S C along with modelled salinity levels for different tidal and fluvial conditions.

The saline intrusion limit, defined by the 1 psu contour line, is located upstream of the maximum S S C zone for the mean runoff simulation. However, the downstream limit of 1g/L corresponds to the area where the salinity levels change rapidly, i.e when the horizontal salinity gradient is stronger, especially at low water. Under a strong runoff, the saline intrusion moves downstream and the horizontal salinity gradient is stronger. The association with the turbidity maximum is clearer than for mean runoff conditions. Given these observations, we hypothesize that density gradients associated with the salinity variations play a crucial role in maintaining the turbidity maximum inside the estuary.

In the Gironde estuary, according to [START_REF] Sottolichio | Modeling mechanisms for the stability of the turbidity maximum in the gironde estuary, france[END_REF], density gradients are essential to the stability of the turbidity maximum and prevent a massive export of sediments. [START_REF] Brenon | Modelling the turbidity maximum in the Seine estuary (France): Identification of Formation Processes[END_REF] showed that tidal influence is predominant in the Seine estuary, but that density gradients also play a significant role in shaping the structure of the turbidity maximum and keeping fine sediments in the estuary. The relative importance of both mechanisms was also studied by [START_REF] Allen | Effects of tides on mixing and suspended sediment transport in macrotidal estuaries[END_REF] and [START_REF] Uncles | Seasonality of the turbidity maximum in the Humber-Ouse estuary , UK[END_REF], who consider that tidal asymmetry is predominant at low to mean runoff conditions and that sediment trapping strongly depends on density circulation at high runoff conditions. Simulations that do not consider the density gradients related to salinity are presented in Figure 11. The results

show that even when the density gradients are not taken into account, the turbidity maximum stays within the estuary for both mean and high river runoff conditions. However, density gradients seem to play a significant role in defining the extension and concentration of the turbidity maximum. At low water, the downstream end of the turbidity maximum is sharper when density gradients are considered, and the longitudinal S S C gradient is much stronger (3.75 g/L/km versus 1.25 g/L/km for the high runoff simulation). Vertical density gradients also impact the structure of the turbidity maximum. For the mean runoff simulation, the downstream 1g/L limit is closer to the bottom when density gradients are considered, both at high and low water. Without these gradients, suspended sediments are better distributed throughout the water column, and the maximum concentrations are reduced. This behaviour is also observed for high runoff conditions. Figure 10 shows that salinity stratification is strong in this area, which reduces turbulent mixing and traps sediments near the bottom.

This phenomenon was investigated and proved numerically by [START_REF] Geyer | The importance of suppression of turbulence by stratification on the estuarine turbidity maximum[END_REF] and [START_REF] Burchard | The formation of estuarine turbidity maxima due to density effects in the salt wedge. A hydrodynamic process study[END_REF]. [START_REF] Blake | Sediment trapping and transport in the ACE Basin, South Carolina[END_REF] observed the same behaviour in the ACE Basin.

As in other macrotidal and/or highly turbid estuaries (Gironde, [START_REF] Sottolichio | Modeling mechanisms for the stability of the turbidity maximum in the gironde estuary, france[END_REF]; Humber-Ouse, [START_REF] Uncles | Seasonality of the turbidity maximum in the Humber-Ouse estuary , UK[END_REF][START_REF] Uncles | Runoff and tidal influences on the estuarine turbidity maximum of a highly turbid system : the upper Humber and Ouse Estuary, UK[END_REF] and Seine [START_REF] Brenon | Modelling the turbidity maximum in the Seine estuary (France): Identification of Formation Processes[END_REF]), tidal asymmetry is the dominant mechanism leading to the formation of a turbidity maximum, but its structure and sediment trapping inside the estuary also depend on density circulation.

Conclusion

The Charente estuary is a highly turbid macrotidal system characterized by strong S S C variations throughout the semi-diurnal and the spring-neap tidal cycles. River discharge also strongly influences S S C.

The results of this study show that tidal forcing dominantly governs the dynamics and characteristics of the turbidity maximum in the Charente estuary. Resuspension and deposition cycles are the main source and sink for suspended sediments. Conditions during spring tide ensure that sediments are eroded and trapped in a highly turbid area for all river runoff situations. However, weak neap tide currents are insufficient to maintain a well-defined sedimentary mass in suspension. In this case, the river discharge can play a key role in the formation of the turbidity maximum; when runoff is high, a compact suspended sedimentary mass is obtained. Under low and mean runoff during neap tide, strong sedimentation is likely to induce the formation of a fluid mud layer at the bottom, or to reinforce is presence.

The turbidity maximum is not advected out of the estuary during high runoff conditions. Simulations without density gradients show that the core of the turbidity maximum remains within the estuary, although its structure and stability are significantly modified. The downstream end of the suspended sedimentary mass is less sharp, which could lead to greater sediment export, especially at low water during spring tides. Preliminary sediment fluxes results suggest a 12% net sediment export increase, after a 14 day simulation. Sediments are also more distributed throughout the water column, suggesting that vertical density stratification traps sediment at the bottom. Thus, tidal asymmetry is mostly responsible for the formation of the turbidity maximum, but density gradients help define its shape and the vertical and longitudinal S S C stratifications.

Bed consolidation was not taken into account in the model and is a perspective for future research. This mechanism could be particularly important for the transition between neap and spring tides. As mentioned before, neap tides favour sedimentation, generating deposits that may not be resuspended for several days. In this situation, consolidation could occur, making it more difficult for currents to erode sediments during the neap to spring transition. The impact of fluid mud also merits further investigation. For this study, friction does not vary through time. The development of coupling between deposits and the roughness length could be considered to improve model performance. Moreover, the reduction of mixing caused by density stratification in the lutocline could favour the stabilisation of fluid mud and suppress resuspension. Future developments of sediment component of the model could include this phenomenon.

Figure 1 :

 1 Figure 1: The Charente River, from the Saint-Savinien dam to the mouth, including locations of sampling stations

Figure 2 :

 2 Figure 2: Bathymetric data used for numerical modelling

Figure 3 :

 3 Figure 3: Measured and modelled water surface elevations at the river mouth (Port-des-Barques) over 24 h (a) and at Rochefort over 14 days (b). Measured and modelled current velocities at Rochefort (c)

Figure 4 :

 4 Figure 4: Measured (using a YSI probe) and modelled suspended sediment concentrations at the river mouth

Figure 5 :

 5 Figure 5: Transects of modelled suspended sediment concentrations for a tidal cycle of spring tides and mean river discharge -The black line represents the 1g/L contour

Figure 6 :

 6 Figure 6: Transects of modelled suspended sediment concentrations for high and low water during spring and neap tides under mean river discharge. The black line indicates the 1g/L contour.

Figure 7 :

 7 Figure 7: Transects of modelled suspended sediment concentrations for high and low water during spring and neap tides under high river discharge. The black line indicates 1g/L contour.

Figure 8 :

 8 Figure 8: Observed S S C at the river mouth (Port-des-Barques) and Rochefort under flood conditions

Figure 9 :

 9 Figure 9: Transects of modelled suspended sediment concentrations for high and low water during spring and neap tides under low river discharge. The black line indicates the 1g/L contour.

Figure 10 :

 10 Figure 10: Transects of modelled suspended sediment concentrations and salinity for high and low water during spring tide under mean river discharge conditions (1 & 2) and for low water under high river discharge conditions (3).

Figure 11 :

 11 Figure 11: Transects of modelled suspended sediment concentrations for high and low water during spring tide, at mean (transects 1 & 2) and high (transects 3 & 4) river discharges. Density gradients are not taken into account.

Table 1 :

 1 Model -data comparison calculations for water surface elevation, current velocities and salinity

	Variable	Location	MAE	RMSE	Skill (no unit)
	Water surface elevation	Aix Island	9.92	12.3	0.9974
	(cm)	Port-des-Barques	12.66	15.38	0.9976
		Rochefort	13.26	16.73	0.9969
	Current velocities (u;v) Port-des-Barques (averaged)	12.4 ; 7.06	16.2 ; 8.78	0.9802 ; 0.9344
	(cm/s)	Rochefort (bottom)	10.04 ; 12.47 12.48 ; 15.79 0.9255 ; 0.9473
	Salinity	Port-des-Barques (surface)	2.71	3.39	0.9708
	(psu)	Port-des-Barques (bottom)	1.91	2.26	0.9620
		Rochefort (bottom)	2.23	2.75	0.9506

Table 2 :

 2

	S S C	3.78	2.41	1.21	0.620
	∆S S C	1.29	1.44	1.41	0.425
	S S C max	9.07	9.80	14.7	2.87
	Distance	-3.76	2.97	13.3	11.4
	∆S S C max	5.27	8.24	14.4	2.26
	Distance	-4.31	2.97	13.3	11.4

Indicators S S C, ∆S S C, S S C max , ∆S S C max (g/L) and distances from the river mouth for S S C max and ∆S S C max

(km)

.

Low water Low water + 3 h High water High water + 3 h

Table 3 :

 3

		Mean river discharge	High river discharge	Low river discharge
		Spring tides Neap tides Spring tides Neap tides Spring tides Neap tides
	S S C	1.63	0.183	1.29	0.307	1.22	0.091
	∆S S C	1.11	0.080	0.880	0.141	0.697	0.037
	S S C max	14.7	1.81	12.0	2.74	5.58	1.14
	Distance	13.3	29.8	3.09	22.1	11.7	22.3
	Tide hour	HW	LW	LW+3	LW	LW+4	HW+5
	∆S S C max	14.4	1.44	10.6	2.22	4.21	0.887
	Distance	13.3	29.8	1.64	22.1	12.2	22.3
	Tide hour	HW	LW	LW+3	LW	LW+4	HW+5

The indicators S S C, ∆S S C, S S C max , ∆S S C max (g/L), and their associated distances from the mouth (km) and times during the tidal cycle at mean, high and low river discharge (50 m 3 /s, 400 m 3 /s, 5 m 3 /s)

Acknowledgments

The authors gratefully acknowledge funding from the Conseil Général of Charente Maritime, the Poitou-Charentes Region, the CNRS, the FEDER and the University of La Rochelle. We also acknowledge the REFMAR portal for the tide gauge data provided, as well as Ifremer for bathymetry and the MARS-3D code.

Appendix A. Sediment dynamics modelling

The sediment module implemented in MARS-3D solves an advection/diffusion equation, taking into account erosion and deposition processes. A full description is available in previously cited studies [START_REF] Hir | Application of the continuous modeling concept to simulate high-concentration suspended sediment in a macrotidal estuary[END_REF][START_REF] Hir | Dynamics of sand and mud mixtures: A multiprocess-based modelling strategy[END_REF]. A brief summary follows.

For pure mud, the erosion law of Partheniades-Ariathurai is chosen to calculate the erosion flux:

τ cem is the critical shear stress for erosion and E 0,mud is a constant.

The deposition flux is following the Krone law:

τ cd is the critical shear stress for deposition, C is the suspended sediment concentration, and W s is the settling velocity. W s is determined through a semi-empirical relationship with C (Le [START_REF] Hir | Application of the continuous modeling concept to simulate high-concentration suspended sediment in a macrotidal estuary[END_REF], to take into account flocculation processes:

W min and W max are the minimum and maximum settling velocities, respectively. C W max is the concentration at which W s = W max . α 1 and α 2 are constants chosen to reach a given maximum settling velocity at C W max . Beyond this value of C, hindered settling velocity occurs. β 1 and β 2 are chosen to take into account this behaviour. C W cr is a critical value of concentration, which corresponds conceptually to the gel point (concentration from which the water-sediment mixture is classified as fluid mud). Turbulence is also taken into account according to Van Leussen (1994).


Tatiana Escovedo
email: tatiana@ele.puc-rio.br

André Vargas
email: andrev@ele.puc-rio.br

Abs Da Cruz

Marley Vellasco
email: marley@ele.puc-rio.br

Adriano Koshiyama
email: adriano@ele.puc-rio.br

NEVE: A Neuro-Evolutionary Ensemble for Adaptive Learning

Keywords: adaptive learning, concept drift, neuro-evolutionary ensemble, quantum-inspired evolution

This work describes the use of a quantum-inspired evolutionary algorithm (QIEA-R) to construct a weighted ensemble of neural network classifiers for adaptive learning in concept drift problems. The proposed algorithm, named NEVE (meaning Neuro-EVolutionary Ensemble), uses the QIEA-R to train the neural networks and also to determine the best weights for each classifier belonging to the ensemble when a new block of data arrives. After running eight simulations using two different datasets and performing two different analysis of the results, we show that NEVE is able to learn the data set and to quickly respond to any drifts on the underlying data, indicating that our model can be a good alternative to address concept drift problems. We also compare the results reached by our model with an existing algorithm, Learn++.NSE, in two different nonstationary scenarios.

INTRODUCTION

The ability for a classifier to learn from incrementally updated data drawn from a nonstationary environment poses a challenge to the field of computational intelligence. Moreover, the use of neural networks as classifiers makes the problem even harder, as neural networks are usually seen as tools that must be retrained with the whole set of instances learned so far when a new chunk of data becomes available.

In order to cope with that sort of problem, a classifier must, ideally, be able to [START_REF] Schlimmer | Incremental learning from noisy data[END_REF]:

• Track and detect any sort of changes on the underlying data distribution;

• Learn with new data without the need to present the whole data set again for the classifier; • Adjust its own parameters in order to address the detected changes on data;

• Forget what has been learned when that knowledge is no longer useful for classifying new instances.

A more successful approach consists in using an ensemble of classifiers. This kind of approach uses a group of different classifiers in order to be able to track changes on the environment. Several different models of ensembles have been proposed on the literature [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF][START_REF] Kuncheva | Classifier ensemble for changing environments[END_REF][START_REF] Kuncheva | Classifier ensemble for detecting concept change in streaming data: Overview and perspectives[END_REF]:

• Ensembles that create new classifiers to each new chunk of data and weight classifiers according to their accuracy on recent data; • Unweighted ensembles which can cope with new data that belongs to a concept different from the most recent training data;

• Ensembles that are able to discard classifiers as they become inaccurate or when a concept drift is detected.

Most models using weighted ensembles determine the weights for each classifier using some sort of heuristics related to the amount of mistakes the classifier does when working with the most recent data [START_REF] Ahiskali | Learning concept drift in non-stationary environments using an ensemble of classifiers based approach[END_REF]. Although in principle any classifier can be used to build the ensembles, the ones which are most commonly used are decision trees, neural networks and naive Bayes [START_REF] Oza | Online Ensemble Learning[END_REF].

In this work, we present an approach based on neural networks which are trained by means of a quantum-inspired evolutionary algorithm. Quantum-inspired evolutionary algorithms [START_REF] Da Cruz | Quantum-inspired evolutionary algorithms for numerical optimization problems[END_REF][START_REF] Da Cruz | Algoritmos evolutivos com inspiração quântica para otimização de problemas com representação numérica[END_REF][START_REF] Han | Quantum-inspired evolutionary algorithm for a class of combinatorial optimization[END_REF][START_REF] Han | On setting the parameters of QEA for practical applications: Some guidelines based on empirical evidence[END_REF][START_REF] Han | Quantum-inspired evolutionary algorithms with a new termination criterion, He gate, and two-phase scheme[END_REF] are a class of estimation of distribution algorithms which present, for several benchmarks, a better performance for combinatorial and numerical optimization when compared to their canonical genetic algorithm counterparts. We also use the quantum-inspired evolutionary algorithm for numerical optimization (QIEA-R) to determine the voting weights for each classifier which is part of the ensemble. Every time a new chunk of data arrives, a new classifier is trained on this new data set and all the weights are optimized in order for the ensemble to improve its performance on classifying this new set of data.

Therefore, we present a new approach for adaptive learning, consisting of an ensemble of neural networks, named NEVE (Neuro-Evolutionary Ensemble). To evaluate its performance and accuracy, we used 2 different datasets to execute several simulations, varying the ensemble settings and analysing how do they influence the final result. We also compare the results of NEVE with the results of Learn++.NSE algorithm [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF], an existing approach to address adaptive learning problems.

This paper is organized in four additional sections. Section 2 details the Quantum-Inspired Neuro-Evolutionary algorithm and the proposed model, the Neuro-Evolutionary Ensemble Classifier. Section 3 presents and discusses the results of the experiments. Finally, section 4 concludes this paper and present some possible future works.

2

The Proposed Model

The Quantum-Inspired Neuro-Evolutionary Model

Neuro-evolution is a form of machine learning that uses evolutionary algorithms to train artificial neural networks. This kind of model is particularly interesting for reinforcement learning problems, where the availability of input-output pairs is often difficult or impossible to obtain and the assessment of how good the network per-forms is made by directly measuring how well it completes a predefined task. As training the weights in a neural network is a non-linear global optimization problem, it is possible to minimize the error function by means of using an evolutionary algorithm approach.

The quantum-inspired evolutionary algorithm is a class of "estimation of distribution algorithm" (EDA) that has a fast convergence and, usually, provides a better solution, with fewer evaluations than the traditional genetic algorithms [START_REF] Kuncheva | Classifier ensemble for changing environments[END_REF][START_REF] Oza | Online Ensemble Learning[END_REF]. In this model, quantum-inspired genes are represented by probability density functions (PDF) which are used to generate classical individuals through an observation operator. After being observed, the classical individuals are evaluated, as in traditional genetic algorithms, and, by means of using fitness information, a set of quantuminspired operators are applied to the quantum individuals, in order to update the information they hold in such a way that on the next generations, better individuals will have a better chance to be selected. Further details on how this optimization method works can be found in [START_REF] Da Cruz | Quantum-inspired evolutionary algorithms for numerical optimization problems[END_REF][START_REF] Da Cruz | Algoritmos evolutivos com inspiração quântica para otimização de problemas com representação numérica[END_REF][START_REF] Han | Quantum-inspired evolutionary algorithm for a class of combinatorial optimization[END_REF][START_REF] Han | On setting the parameters of QEA for practical applications: Some guidelines based on empirical evidence[END_REF][START_REF] Han | Quantum-inspired evolutionary algorithms with a new termination criterion, He gate, and two-phase scheme[END_REF].

Based on this algorithm, the proposed quantum-inspired neuro-evolutionary model consists in a neural network (a multilayer perceptron (MLP)) and a population of individuals, each of them encoding a different configuration of weights and biases for the neural network. The training process occurs by building one MLP for each classical individual using the genes from this individual as weights and biases. After that, the full training data set (or the set of tasks to be performed) is presented to the MLP and the average error regarding the data set is calculated for each MLP. This average error is used as the fitness for each individual associated to that MLP, which allows the evolutionary algorithm to adjust itself and move on to the next generation, when the whole process will be repeated until a stop condition is reached.

This subsection presented the quantum-inspired neuro-evolutionary model. This model will be the basis for the algorithm proposed in this paper, to be presented in the next subsection.

NEVE: The Neuro-Evolutionary Ensemble Classifier

To some applications, such as those that use data streams, the strategy of using simpler models is most appropriate because there may not be time to run and update an ensemble. However, when time is not a major concern, yet the problem requires high accuracy, an ensemble is the natural solution. The greatest potential of this strategy for detecting drifts is the ability of using different forms of detection and different sources of information to deal with the various types of change [START_REF] Kuncheva | Classifier ensemble for detecting concept change in streaming data: Overview and perspectives[END_REF].

One of the biggest problems in using a single classifier (a neural network, for example) to address concept drift problems is that when the classifier learns a dataset and then we need it to learn a new one, the classifier must be retrained with all data, or else it will "forget" everything already learned. Otherwise, using the ensemble, there is no need to retrain it again, because it can "retain" the previous knowledge and still learn new data.

Hence, in order to be able to learn as new chunks of data arrive, we implemented an ensemble with neural networks that are trained by an evolutionary algorithm, pre-sented in section 2.1. This approach makes the ensemble useful for online reinforcement learning, for example. The algorithm works as shown in figure 3 and each step is described in detail on the next paragraphs.

On step 1 we create the empty ensemble with a predefined size equal to s. When the first chunk of data is received, a neural network is trained by means of the QIEA-R until a stop condition is reached (for example, the number of evolutionary generations or an error threshold). If the number of classifiers in the ensemble is smaller than s, then we simply add this new classifier to the ensemble. This gives the ensemble the ability to learn the new chunk of data without having to parse old data. If the ensemble is already full, we evaluate each classifier on the new data set and we remove the one with the highest error rate (including the new one, which means the new classifier will only become part of the ensemble if its error rate is smaller than the error rate of one of the classifiers already in the ensemble). This gives the ensemble, the ability to forget about data which is not needed anymore. Finally, we use the QIEA-R to evolve a voting weight for each classifier. Optimizing the weights allows the ensemble to adapt quickly to sudden changes on the data, by giving higher weights to classifiers better adapted to the current concepts governing the data. The chromosome that encodes the weights has one gene for each voting weight, and the population is evolved using the classification error as the fitness function. It is important to notice that when the first s-1 data chunks are received, the ensemble size is smaller than its final size and thus, the chromosome size is also smaller. From the s data chunk on, the chromosome size will remain constant and will be equal to s.

In this work, we used only binary classifiers but there is no loss of generality and the algorithm can also be used with any number of classes. For the binary classifier, we discretize the neural network's output as "1" or "-1" and the voting process for each instance of data is made by summing the NN's output multiplied by its voting weight. In other words, the ensemble's output for one instance k from the i-th data chunk is given by: [START_REF] Schlimmer | Incremental learning from noisy data[END_REF] where P(Dik) is the ensemble's output for the data instance Dik, wj is the weight of the j-th classifier and cj(Dik) is the output of the j-th classifier for that data instance. If P(Dik) < 0, we assume the ensemble's output is "-1". If P(Dik) > 0, we assume the ensemble's output is "1". If P(Dik) = 0, we choose a class randomly.

3

Experimental Results

Datasets Description

In order to check the ability of our model on learning data sets with concept drifts, we used two different data sets (SEA Concepts and Nebraska also used at [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF]) upon which we performed several simulations in different scenarios.

The SEA Concepts was developed by [START_REF] Street | A streaming ensemble algorithm (SEA) for large-scale classification[END_REF]. The dataset consists of 50000 random points in a three-dimensional feature space. The features are in the [0; 10] domain but only two of the three features are relevant to determine the output class. Class labels are assigned based on the sum of the relevant features, and are differentiated by comparing this sum to a threshold.

Nebraska dataset, also available at [START_REF] Polikar | Benchmark Datasets for Evaluating Concept drift/NSE Algorithms[END_REF], presents a compilation of daily weather measurements from over 9000 weather stations worldwide by the U.S. National Oceanic and Atmospheric Administration since 1930s, providing a wide scope of weather trends. As a meaningful real world dataset, [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF] choosed the Offutt Air Force Base in Bellevue, Nebraska, for this experiment due to its extensive range of 50 years and diverse weather patterns, making it a longterm precipitation classification/prediction drift problem. Class labels are based on the binary indicator(s) provided for each daily reading of rain: 31% positive (rain) and 69% negative (no rain). Each training batch consisted of 30 samples (days), with corresponding test data selected as the subsequent 30 days. Thus, the learner is asked to predict the next 30 days' forecast, which becomes the training data in the next batch. The dataset included 583 consecutive "30-day" time steps covering 50 years.

Running Details

On each simulation, we used a fixed topology for the neural networks consisting of 3 inputs for SEA Concepts dataset and 8 inputs for Nebraska dataset, representing the input variables for each dataset. In both datasets, we used 1 output, and we varied the number of the neurons for the hidden layer. Each neuron has a hyperbolic tangent activation function and, as mentioned before, the output is discretized as "-1" or "1" if the output of the neuron is negative or positive, respectively. The evolutionary algorithm trains each neural network for 100 generations. The quantum population has 10 individuals and the classical population 20. The crossover rate is 0:9 (refer to [START_REF] Da Cruz | Algoritmos evolutivos com inspiração quântica para otimização de problemas com representação numérica[END_REF][START_REF] Han | Quantum-inspired evolutionary algorithm for a class of combinatorial optimization[END_REF] for details on the parameters). The same parameters are used for evolving the weights for the classifiers. The neural network weights and biases and the ensemble weights are allowed to vary between -1 and 1 as those values are the ones who have given the best results on some pre-evaluations we have made.

The first experiment was conducted in order to evaluate the influence of the variation of the parameters values in the results (number of the hidden layer neurons and the size of the ensemble). We used 4 different configurations for each dataset. After running 10 simulations for each configuration, we performed some an Analysis of Variance (ANOVA) [START_REF] Montgomery | Design and analysis of experiments[END_REF]. In order to use ANOVA, we tested the Normality assumption for the noise term with Shapiro-Wilk's test [20] and the homogeneity of variances with Bartlett's test [START_REF] Montgomery | Design and analysis of experiments[END_REF]. All the statistical procedures were conducted in R package [START_REF] Development | R: A language and environment for statistical computing[END_REF], admitting a significance level of 5%.

The second experiment, in turn, aimed to compare the results found by NEVE and Learn++.NSE algorithms and we used, for each dataset, the best configuration found by first experiment (ensemble size and number of neurons at hidden layer values). After running one simulation for each dataset, we made statistical comparisons between the results found by NEVE and Learn++.NSE algorithms. The results of Learn++.NSE can be found at [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF]. Then, to evaluate NEVE we made 10 runs for each dataset used, due to the stochastic optimization algorithm used to train NEVE. Based on these runs, we calculate some statistical parameters (mean, standard deviation, etc.) that were used to compute the Welch t-test [START_REF] Montgomery | Design and analysis of experiments[END_REF] to evaluate which algorithm had, in average, the best performance in test phase. The normality assumption necessary for Welch t-test was verified using Shapiro-Wilk test [START_REF] Royston | An extension of Shapiro and Wilk's W test for normality to large samples[END_REF]. All the statistical analyses were conducted in R statistical package [START_REF] Development | R: A language and environment for statistical computing[END_REF].

First Experiment

Based on the past subsections, we made 40 simulations using SEA dataset and 40 simulations using Nebraska dataset, using 4 different configurations on each dataset. Table 1 displays number of neurons at hidden layer and ensemble size with different levels (5 and 10) and the output (average error in test phase for 10 runs) for each configuration.

In order to evaluate which configuration provided a significant lower error, we have to perform multiple comparisons between the results of each configuration. For each dataset if we decide to use t-test [START_REF] Montgomery | Design and analysis of experiments[END_REF] for example, we have to realize 6 comparisons between the configurations, and thus, the probability that all analysis will be simultaneous correct is substantially affected. In this way, to perform a simultaneous comparison between all configurations we fitted a one-way Analysis of Variance (ANOVA) [START_REF] Montgomery | Design and analysis of experiments[END_REF] for each dataset, described by:

Yij = µ + CFj + εij; εij ~ N(0, σ 2 ) ( 1
)
where Yij is the i-th ouput for the j-th configuration, µ is the global mean, CFj is the run configuration with j-levels (j =1,2,3,4) for each dataset (A, B, C and D, and E, F, G, H, for SEA and Nebraska respectively) and εij is the noise term, Normal distributed with mean zero and constant variance (σ 2 ). If CFj is statistically significant, then some configuration demonstrated an average error different from the others. To verify which configuration has the average error less than other configuration we used Tukey's test [START_REF] Montgomery | Design and analysis of experiments[END_REF]. Analyzing the results displayed in Table III, in both datasets the errors variance is homogeneous (Bartlett's test, p-value > 0.05). After verifying these two assumptions (Normal distribution and homogeneity of variances), we fitted the one-way ANOVA. In both datasets, some configurations (A, B, C and D for SEA, and E, F, G and H for Nebraska) demonstrated an average error different from the others (p-value < 0.05). In addition, in both fitted models, the noise term follows a Normal distribution (Shapiro-Wilk's test, p-value > 0.05).

In order to identify which configuration performed, in average, better than other, we made Tukey's test for difference of means. Table 3 present the results of this analysis. It seems that in SEA dataset the D configuration performed significantly better than A and C, although its results is not statistically different than configuration B. In Nebraska the E and H configurations obtained error measures substantially lower than F and G. In fact, we can choose the configuration D as the best configuration to SEA and H to Nebraska dataset, considering the fixed parameters displayed in table II. This choice is based on two criterias: lower average error and computational cost to train these models.

3.4

Second Experiment.

Aiming to enable a better comparison with the results of the algorithm Learn +. NSE [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF] in SEA Concepts dataset, we used 200 blocks of size 25 to evaluate the algorithm in the test phase. The best configuration previously achieved was 5 neurons in hidden layer and the size of the ensemble equal to 5 (see table 4). Also, with the results of Learn +. NSE in Nebraska dataset, we performed similarly to that used in [START_REF] Elwell | Incremental Learning of Concept drift in Nonstationary Environments[END_REF]. The best configuration previously achieved was 10 neurons in hidden layer and the size of the ensemble equal to 10. Then, NEVE and Learn++.NSE results were displayed in Table 4. As can be seem, the mean accuracy rate of Learn++.NSE is lower than the best configuration of NEVE, and thus this difference is statistically significant (tcrit = -41.07, p-value < 0.0001), demonstrating that NEVE perrformed better in the test phase on SEA Concepts dataset.

However, in Nebraska the mean accuracy rate of NEVE is lower than the best configuration of Learn++.NSE, and thus this difference is statistically significant (tcrit = 18.26, p-value < 0.0001), demonstrating that NEVE performed better, in average, than Learn++.NSE. Figures 4 and5 illustrates the hit rate on each test block obtained by NEVE on SEA and Nebraska, respectively.

Conclusions and Future Works

This paper presented a model that uses an ensemble of neural networks trained by a quantum-inspired evolutionary algorithm to learn data sets (possibly with concept drifts) incrementally. We analyzed the ability of the model using two different datasets and conducting two different experiments. In the first experiment, we found a good configuration for both datasets and demonstrated how the number of neurons and the ensemble size affect the average error produced by the model. As stated in the results, the ensemble size affected almost two times more the results of NEVE than the number of neurons. In the second experiment, the NEVE algorithm have demonstrated a better performance in SEA dataset compared to Learn++.NSE and yet lower accuracy when comparing with Learn++.NSE in Nebraska dataset.

Although the NEVE algorithm have demonstrated satisfactory performance for the datasets used in the analysis of this study, it is strongly recommended to perform further tests -using different configurations, different datasets and performing different analysis -to confirm the results presented here. We also intend in the future to continue this work, analyzing other existing approaches, such as [START_REF] Kolter | Dynamic weighted majority: An ensemble method for drifting concepts[END_REF] and [START_REF] Jackowski | Fixed-size ensemble classifier system evolutionarily adapted to a recurring context with an unlimited pool of classifiers[END_REF], and performing new experiments in comparison with these and other algorithms. We still need to investigate other factors related to QIEA-R fine tunning (genetic operators, population size, etc.).

Fig. 1 .

 1 Fig. 1. The neuro-evolutionary ensemble training algorithm.

Fig. 4 .

 4 Fig. 4. Evolution of NEVE hit rate in SEA testing set.

Fig. 5 .

 5 Fig. 5. Evolution of NEVE hit rate in Nebraska testing set.

Table 1 .

 1 Results for SEA and Nebraska dataset.

			SEA dataset
	Neurons	Ensemble	Config	Error in test phase
	Number	Size		Mean	Std. dev.
	10	10	A	24.99%	0.17%
	5	5	B	24.88%	0.19%
	10	5	C	25.06%	0.21%
	5	10	D	24.75%	0.17%
			Nebraska dataset
	Neurons	Ensemble	Config	Error in test phase
	Number	Size		Mean	Std. dev.
	10	10	E	32.30%	0.48%
	5	5	F	32.85%	0.43%
	10	5	G	33.04%	0.37%
	5	10	H	32.10%	0.46%
	Then, we performed the analysis for both dataset and exhibit the main results in
	Table 2.

Table 2 .

 2 Results for SEA and Nebraska dataset.

	ANOVA -SEA dataset
	Method	Test Statistic	p-value
	Bartlett's test	0.4443	0.9309
	Config	5.4360	0.0035
	Shapiro-Wilk's test	0.9260	0.2137
	ANOVA -Nebraska dataset
	Method	Test Statistic	p-value
	Bartlett's test	0.6537	0.8840
	Config	11.5900	< 0.0001
	Shapiro-Wilk's test	0.9708	0.3803

Table 3 .

 3 Tukey's test for SEA and Nebraska dataset.

	SEA dataset	Nebraska dataset

Table 4 .

 4 Results of SEA and Nebraska experiments.

	Dataset	Algorithm	Mean	Standard Deviation
	SEA	NEVE Learn++.NSE (SVM)	98.21% 96.80%	0.16% 0.20%
	Nebraska	NEVE Learn++.NSE (SVM)	68.57% 78.80%	0.46% 1.00%