Journal of Sedimentary Research, 2011, v. 81, 138–152

Research Article

DOI: 10.2110/jsr.2011.8

PATTERN OF SEDIMENT TRANSPORT IN A MICROTIDAL RIVER MOUTH USING GEOSTATISTICALSEDIMENT-TREND ANALYSIS

GREGOIRE M. MAILLET,*1 EMMANUEL POIZOT,2 FRANCOIS SABATIER,3 CLAUDE VELLA,3 AND YANN MEAR2

1Faculty of Sciences, University of Angers, 02 Boulevard Lavoisier, F-49045 Angers cedex 01, France

e-mail: gregoire.maillet@univ-angers.fr

, 2Cnam-Intechmer, BP 324, F-50103 Cherbourg, France3Aix Marseille Universite, CEREGE, UMR 6635CNRS, BP 80, F-13545 Aix en Provence cedex 04, France

ABSTRACT: We perform a grain-size trend analysis (GSTA) to investigate sediment-transport mechanisms in the Grand Rhonemicrotidal mouth during various hydroclimatic conditions. The objective is to determine the efficiency of this method to explainthe directions of residual transport pattern and mode of distribution of the fluvial sediment input in an environment that is verydifficult to equip with instrumentation during extreme events. The known biases of this sedimentological approach are reducedby using enriched geostatistical processing and choosing periods of sampling subject to unequivocal hydrodynamic forcings. Themodeling results and grain-size distributions of surface sediments clearly show three vector fields during periods of low riverdischarge. The first vector field corresponds to an upstream zone under fluvial influence. The second field is characteristic of amixing zone, confined inside the river mouth and marked by heterogeneous sedimentation. This sector is interpreted as theconfrontation zone between alluvial and marine dynamics. Farther offshore, the vectors are oriented towards the river and atcounter slope. In deeper zones, the vectors reflect the sediment-transport generated by wave refraction at the top of the mouthbar. At the delta front (bathymetry from 25 m to 220 m), the vectors are interpreted as representing a lag deposit. The periodsof medium and extreme floods are associated with storms. The marine dynamic regime generates a longshore drift current,which brings sediments onto the mouth bar. During medium flood events, only the inner part of the mouth bar is highlyinfluenced by the river. During extreme flood events, the river influences both the eastern part of the mouth and the wave regimein the central part. Consequently, the GSTA method shows that, even during flood events, the river solid discharge is nottransferred towards the adjoining upper shoreface. In the context of a wave-dominated delta, the distribution of surfacesedimentation in a microtidal mouth remains controlled mainly by the swell, even in periods of flood when the intensity of riverdynamics is exacerbated. Finally, all these results are similar to the known hydro-sedimentological behaviours of the RhoneRiver mouth. Nevertheless, GSTA results seem not self-sufficient to explain all the processes, but this method proposes analternative approach to traditional methods used to measure bed-load sediment transfer during extreme events.

INTRODUCTION

River mouths are located at the interface between zones of fluvial andmarine dynamics. The shape of these mouths and the transfer of alluvialsediment load towards the adjoining upper shoreface thus depend primarilyon marine and river hydrodynamic forcing (Bhattacharya and Giosan2003). In deltaic environments, coarse sediment discharge passes throughthe river mouth to feed the nearby beaches and leads to delta progradation.Because sand transport is linked with the high-energy hydrodynamiccontext, flood events are key periods for understanding the mechanisms ofbed-load (. 4 w , 63 mm) transfer from fluvial to coastal zones. In theMediterranean climatic context, these characteristics are particularlyexacerbated due to the rainfall regime, which generates intensive flash-floods with high rates of increase in discharge (. 250 m3 s21 h21). TheRhone River is characterized by a typical Mediterranean regime(Bethemont 1972) ideal for the study of such phenomena.

During these extreme events, in situ measurements are always difficult toperform because (1) the shortness of the event, (2) the dangerousnavigation conditions, and (3) difficulty of accurate bed-load measure-ments due to strong currents. All of these constraints together are strong

limitations to the study of the sediment dynamics in such an area. Hence,number of samples collected cannot be large, sub sampling is often notpossible, and the in situ instrumentation is quite limited, above all in thecase on Rhone river mouth, which is a non-navigable zone.

That is the reason why only few studies have tried to perform directmeasurements during flood events. These hydrodynamic conditionsgenerally lead to analysis of sediment-transport through indirectmethods. On the one hand, bed-load transport mechanisms are studiedthrough the short-term measurement of hydrodynamic processes, and arethen extrapolated spatially and temporally by mathematical modeling.Following this way, Poulos and Collins (1994) used mathematical modelsto simulate the density of a river plume in a microtidal river mouth inGreece. However, this approach is not always appropriate. Indeed, theflow dynamics and sediment concentrations are liable to strongfluctuations in time and space, and it is not always possible to reconstructa suitable scenario that combines realistically all the data from specificand localized measurements.

On the other hand, a more reliable approach consists of studying theresidual sediment budgets using bathymetric surveys, assuming that the

Copyright E 2011, SEPM (Society for Sedimentary Geology) 1527-1404/11/081-138/$03.00

variations in bottom morphology reflect the cumulative effects ofsedimentary processes (on the Rhone Delta: Suanez et al. 1998; Mailletet al. 2006b; Maillet et al. 2006c; Sabatier et al. 2006; Sabatier et al. 2009).Thus, the first approach (i.e., mathematical modeling) enables us toobtain a detailed analysis of the dynamics, but without yielding an overallunderstanding of the processes. Alternatively, bathymetric surveys allowus to study the resulting evolution, but incorporate a large uncertaintylinked to the inevitable interpretation of different factors that modify themorphologies.

These limitations explain why the study of sediment dynamics incoastal environments has turned towards simple statistical models,based on the spatial evolution of the sedimentological parameters.Indeed, an analysis of the spatial characteristics of sediment distribu-tions can help to understand the processes generating sedimentmovement as well as ascertain the origin of the sediments. Amongother factors, sediment-transport is influenced by grain properties suchas shape, nature, hydraulic behaviour, and density, but size distributionremains the most important parameter (Larson et al. 1997). As show byKrumbein (1938), Russell (1939), McCave (1978), Harris et al. (1990),Guillen and Hoekstra (1997), Flemming (2007), Wang et al. (2009) andother studies, grain-size trends seem to be a result of sediment-transportprocesses. Most applications of grain-size trend analysis (GSTA) arerelated to the open marine environment in cases where there is no apriori assumption on transport direction. In this context, a 2-Dapproach appears to be relevant for taking into account the spatialscale (Gao and Collins 1991, 2001; Masselink 1992; Rios et al. 2002;Rios et al. 2003). Whatever the time evolution of the sediment trend, ithas been shown that a particular evolution of sedimentologicalstatistical parameters can be more significant (showing the best fit withresults obtained through other methods like side-scan sonar and tracers)of a specific sedimentary environment (Lanckneus et al. 1992; Mohd-Lokman et al. 1998; Ehrhold 1999; Wu and Shen 1999; Van Wesenbeckand Lanckneus 2000; Le Bot et al. 2001; Lucio et al. 2002). Accordingto many authors (Pandarinath and Narayana 1993; Stevens et al. 1996;Asselman 1999; Le Bot et al. 2001; Garnaud 2003), the evolution ofgrain-size parameters is influenced by the energy level of thehydrodynamic system.

In river-mouth environments, GSTA was tested by scientists withinteresting results. Marion et al. (2005) provided a comparative study ofmulti-technique surveys of sediment distribution in the Authie estuary(France) and obtained relevant and comparable results with GSTAapproach. Duc et al. (2007) used sediment distribution and associatedtransport pathways to understand the accretionary and erosional patternsin the coastal zone of the Red River mouth (North Vietnam). But, to ourknowledge, no study has already been performed in a microtidal rivermouth. Thus, the present study concerns the microtidal system of theRhone River mouth. Until recently, the characteristics of its sedimentarycover were not very well documented, which has considerably restrictedthe study of sediment-transport between the Rhone River and its delta. Inthis area, we performed a 2D sediment trend analysis enhanced with ageostatistical approach (Poizot et al. 2006). The aim of this work is to tryto understand the mechanisms of river sediment input to the proximalcoastline, taking into account the limitations mentioned above (shortnessof the events and dangerous navigation conditions). To achieve this, wecompare the results of three sediment sampling campaigns, each of thembeing characteristic of a specific energy condition. This allows to obtain astrict temporal framework to constrain the method and therefore toelucidate the dominant processes governing the sediment dynamics at theRhone River mouth. The selected values of the liquid discharges aresuccessively low, medium, and exceptional. This study is given anadditional interest by the short interval of time separating these threecampaigns (less than six months), and the rareness of high marinephenomena occurring between them.

Site Description

The Grand Rhone is located in the eastern part of the Rhone Delta(Figs. 1A, B), in south-east France. It is the more important of the twodistributaries of the river (85% to 90% of the water flow).

Morphology and Sediment Cover of the Rhone Inlet

The mouth zone is characterized by major storage of the sediment loadand a weak lateral redistribution of the fluvial input (Suanez et al. 1998;Maillet et al. 2006a; Sabatier et al. 2006). Many authors have shown aprogressive reduction in solid load of the river over 200 years, inparticular the sandy load (Pont et al. 2002; Antonelli et al. 2004; Mailletet al. 2006c; Sabatier et al. 2006). Despite this, the present-day lobe ismade up mainly of sands in the 0–15 m depth zone (Suanez et al. 1998).The morphology of the mouth zone (Figs. 1A, C) was described in detailby Maillet et al. (2006b). The channel of the Rhone at its downstreamtermination is 800 m wide and is barred on its west bank by a small sandspit. The mouth bar forms the top part of the subaqueous lobe, andoccurs as a shallow flat (3.5 km2 between 0 m and 22 m water depth) witha slope opposite to the flow of the Rhone River. The top of the bar iscrescent-shaped, and is sub-emergent 2 km downstream from the mouthof the river. The river channel displays a morphological continuitythrough the mouth bar (bypass channel), while bending towards the east.The delta front extends from the outer edge of the bar until 20 m waterdepth, and is characterized by a very steep slope (. 4u). Beyond this, wefind the more gently sloping prodelta sensu stricto (Lansard 2004; Mailletet al. 2006b).

Hydrodynamic Conditions at the River–Sea Interface

The respective influences of the river, waves, and sea level lead us toclassify the Rhone delta in the category strongly influenced by swell(wave-influenced delta; Galloway 1975). At Beaucaire station (Fig. 1A),the mean annual river discharge is 1715 m3s21, but ranges over a largeamplitude related to the high seasonal variability of the Mediterraneanclimate (6% of the year Q . 3500 m3s21 and 15% of the yearQ , 800 m3s21). The annual, decadal, and centennial flood returnperiods correspond to discharges of 3300, 8390, and 11300 m3s21,respectively. The Rhone mouth is characterized by a very smallastronomic tidal range of about 0.3 m, and can therefore be classifiedas a microtidal (almost atidal) environment. The wave regime is dividedinto three dominant directions: SW (30% calm waves generated byoffshore winds), SSE (16%), and SE (11% storm waves generated byonshore winds). The modal, annual, and decennial recurrent significantwave heights (Hsig) are 0.6 m, 3.3 m, and 4.6 m, with significant periods(Tsig) of 4 s, 6.5 s, and 7.5 s, respectively.

Sediment Transfers

Waves coming into the mouth from the SW to the SSE inducelongshore sediment-transport towards the east, while waves from the SEsector produce a moderate longshore drift in the opposite direction (to thewest), due to the effect of refraction on the modern lobe topography.Consequently, the net longshore drift is oriented from west to east, butthe mouth is considered as a sediment sink (Blanc 1977; Suanez andProvansal 1998; Sabatier et al. 2009). The predominant longshore drifttowards the east results morphologically in the lengthening of the mouthspit in the same direction on the west bank. This also produces a netsediment-transport from west to east in the medium to long term (Suanezet al. 1998; Sabatier and Suanez 2003), leading to the formation of theGracieuse spit (Fig. 1B). Both at sea and close to the mouth area, thepattern of currents has been investigated to describe the behavior of theriver plume. These studies made use of dredges (Pauc 1971), satellite

PATTERN OF SEDIMENT-TRANSPORT IN A RIVER MOUTH 139J S R

images (Demarcq and Wald 1984; Forget et al. 1990; Forget and Ouillon1998), analysis of radar data (Devenon et al. 1992; Arnoux-Chiavassa etal. 1995; Broche et al. 1998), and modeling approaches (Arnoux-Chiavassa et al. 2003; Reffray et al. 2004; Dufois 2008 and referencestherein, Ulses et al. 2008). All of these studies concluded that the extentand thickness of the Rhone river plume depend on the river discharge, themeteorological conditions, and the surrounding circulation pattern. Theplume extends offshore towards the southwest during north westerlywinds, whereas it is constrained to the coast on the western side of theRhone mouth during south easterly winds (storms). However, in mostcases, the previous studies describe the sea-surface currents on a large gridcell ($ 1km 3 1km) or at the scale of the Gulf of Lions at water depthsgreater than 20 m. On the other hand, Marsaleix et al. (1998) forced theirmodel by ignoring the wind forcing factor in order to describe the plumecirculation offshore. They found evidence for a strong induced bottomcurrent flow in the vicinity of the mouth converging toward the rivermouth, in the direction opposite to the river current. Although thisbehaviour is surprising, it has been theoretically predicted (Chao andBoicourt 1986), and physically observed around the Rhone river mouthby Pauc (1971), Vassas et al. (2008), and Arnaud (2009). Recently, Ulseset al. (2005) investigated the current circulation between the mouth andthe Gulf of Fos (to the east; Fig. 1) with a 3D model and a grid size of200 m 3 200 m. Their study focuses on freshwater displacements at seaunder mean river discharge (1700 m3s21), but also gives information onaverage currents under southeasterly winds (5 ms21) and bottom currentsduring northwesterly winds (8 ms21). In the case of SE winds, they notethat the current (0.6–1.1 ms21) is directed to N340u between the river andthe mouth bar, and turns towards N270u 2 km offshore (0.4–0.7 ms21).On the eastern part of the mouth, the current is directed to the north-east,while on the western part it is towards the north-west. In the case of NWwinds, the current (0.3–0.6 ms21) is oriented towards N340u between theriver and the mouth bar, intercepting a general longshore current flowingnorth-east (, 0.10 ms21). Under both wind regimes, the river current isstrongly modified in the first kilometer towards the sea, down to a water

depth of 20 m. In this zone, at around 13 m to 15 m depth, Garcıa-Garcıaet al. (2006) carried out ADCP measurements during low river discharge(1200 m3s21) associated with calm conditions (wave height around 0.2 m),showing homogeneous velocities in the water column (around 0.2 ms21)oriented offshore.

To conclude, although the existence of this opposite slope current soclose from the river is surprising, the various studies on hydrodynamicsclose the Rhone River mouth zone suggest that the phenomenon is likely.Nevertheless these studies deal only with investigations of plumeformation, dilution, salinity, temperatures, and hydrodynamics at a largescale. Then, in the area of the mouth, where fluvial sands are thought tobe deposited, the bedload sediment distribution and transport have notbeen investigated in detail.

METHODOLOGY

Acquisition of Sediment Data

Three sampling campaigns were performed to characterize sedimentdynamics during low-stage discharge (17 March 2003, calm sea, Rhonedischarge: 898 m3s21), medium flood event (25 October 2002: 2470 m3s21)and extreme flood event (22 November 2002, during a lull in the middle ofthe flood event: 4735 m3s21) (Table 1). For each of these campaigns, 38samples were collected by SCUBA divers, making sure that the sedimentsample does not reflect a localized small-length-scale bedform, and using aPVC tube corer. All of the core samples were dissected, and only the topmostcentimeter was stored for analysis. This sampling of the core top was carriedout while visually making sure that the sediment was homogeneous.Offshore positions were fixed by differential global positioning system(6 5m) on a grid pattern (Fig. 2A) designed to be as regular as possibleconsidering the hydrodynamic conditions and the morphology of the zone.

All samples were analyzed using a Coulter particle-size laser counter(IFREMER/SHOM, Brest, France). A limited number of grain-sizeanalyses were performed on the total sediment fraction using a lasermicrogranulometer (Coulter counter LS230; size range 0.4 mm to 1 mm),

FIG. 1.—A) Location map of the Rhone Delta, showing B) the mouth zone (bathymetry in m). The zone consists of C) a mouth bar forming a half-circle opposite theriver, and double offshore bars along the adjoining beaches (photo courtesy of IGN, France). The dominant littoral drift and associated sediment-transport is directedtowards the east (Sabatier and Suanez 2003).

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which did not involve chemical destruction of the sample (preservationof organic matter and CaCO3). We used the software v. 3.0 provided bythe Coulter Corporation to calculate statistical parameters of mean,sorting, and skewness with the arithmetic method (Coulter Corporation1992).

Modeling of Marine Dynamics

Due to the lack of in situ measurements of meteorological forcedmarine dynamics in the study zone, and because we needed tocharacterize the hydrodynamic conditions before sampling campaigns,

FIG. 2.—A) Location of surface sediment sampler. B) Semi-variogram of the data points from the sample grid (study carried out on the mean grain-size). C) Sketchmap showing position of the 93 interpolated pseudo-samples. D) Semi-variogram of the new grid. The geostatistical characteristic distance (Dg) between two sedimentsamples corresponds to the limit of the influence of one observation on its neighbors, and is defined here in terms of stabilization of the semi-variance.

TABLE 1.—Characteristics of 2002 flood events at the Beaucaire measuring station, 60 km upstream of the river mouth.

BEAUCAIRE STATION September 2002 October 2002 November 2002

Probability of occurrence Fifty-year flood event One-year flood level Fifty-year flood eventGeographical origin Cevenol flash flood Generalized flood Generalized floodPeak discharge (m3s21) 10,500 3,102 10,200Mean daily maximum discharge (m3s21) 6,800 2,500 7,000Date of peak 10/09/2002 25/10/2002 26/11/2002Rate of flood increase (m3s21h21) 350 10 80Duration of discharge . 8.000 m3s21 (hr) 16 / 74Duration of discharge . 10.000 m3s21 (hr) 8 / 23

Max liquid volume discharged (109 m3) 2 days 1.3 0.4 2.56 days 1.7 1.2 4.7

Bed load* Total (106 T) 1.18 ? 7.15Instantaneous (gl21) 1.9 ? 3

Data from Compagnie Nationale du Rhone (CNR), except * from Ollivier (2006).

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we used outputs from a wave propagation model. There are two maintypes of models: those capable of replicating offshore wave conditions butthat yield results for the nearshore zone that are less reliable, and thosethat are, in contrast, robust for modeling of nearshore conditions but areless reliable for offshore conditions. As a result, we have had recourse totwo types of embedded models in order to obtain reliable data that cancharacterize the state of the sea prior to sampling.

As far as the offshore data for our study area are concerned, we firstused output from the WW3 model (Wave Watch 3, Tolman 1999) at thescale of the NW Mediterranean basin for a depth of about 150 m(GlobeOcean 2007). This model is a third-generation one, which signifiesthat non-linear interactions between frequency bands are integrallysolved. WW3 is widely used to propagate waves at the regional scale, andits reliability is well established (Padilla-Hernandez et al. 2007). The inputfor atmospheric forcing of the WW3 model comes from output from theECMWF model (European Centre for Medium Range Weather Forecast,UK) for wind, and from the NCEP (National Center for EnvironmentalPrediction, USA) for atmospheric pressure covering the entire Mediter-ranean Sea with a spatial resolution of 0.5u 3 0.5u. Output from WW3 iscompared for validation and calibration, if necessary, with altimetricsatellite sensors provided by TopexPoseıdon (CNES–Centre Nationald’Etudes Spatiales France). WW3 output comprises wave directionalspectra from which are derived the usual basic parameters such as Hsig

(significant wave height), Tp (peak period), and qp (direction).

To compute a temporal series of swell characteristics in shallow waters(20 m depth), the output from WW3 were used as input to the STWAVEmodel (Steady-State Spectral Wave Model; McKee Smith et al. 2001).This depth value is adopted here because it corresponds approximately tothe maximum depth attained by our sampling and allows an accuratedescription of the wave conditions preceding the sampling campaigns.STWAVE is a steady-state, finite-difference spectral model based on thewave-action balance equation. STWAVE simulates depth-induced waverefraction and shoaling, current-induced refraction and shoaling, depth-and steepness-induced wave breaking, diffraction, wave growth due towind forcing, and wave–wave interactions and white capping thatredistribute and dissipate energy in a growing wave field. As a finalword, we have used only classical wave data (height, period, anddirection) in order to obtain a three-hour time series between November2002 and March 2003 (Fig. 3). Indeed, it was not reasonable to attempt touse STWAVE to replicate interactions between river flow and waves dueto the lack of reliable bathymetric data for the seabed, and especially forthe river channel.

Procedure for Sediment Trend Modeling

Following the direction of transport, the grain-size can decrease(Pettijohn and Ridge 1932; Self 1977) or increase (McCave 1978;Nordstrom 1981). Because of remaining uncertainties, later investigatorspreferred using a model based on a combination of statistical grain-sizeparameters, i.e., mean size, sorting, and skewness, and several methodshave been developed to define sediment-transport path:

N 1D (one dimensional) approach where main assumption is that thesediment-transport is by unidirectional currents,

N 2D (two dimensional) is based on the fact that the sediment-transporttakes place across a unidirectional front rather than from point topoint.

McLaren (1981) and McLaren and Bowles (1985) proposed a 1-Dmodel to determine the grain-size trend. This latter approach proposesseveral possible configurations, but distinguishes two main scenarios(combined evolution of the three statistical parameters considered).Taking two samples, d1 and d2, let us consider a transport direction fromd1 to d2 in cases where the sediment deposited at d2 is (1) finer, better

sorted, and more negatively skewed (and so noted FB2) than d1 or (2)coarser, better sorted, and more positively skewed (noted CB+) than d1.This model has been validated for many types of environments and forvery varied objectives: monitoring of dredging (McLaren and Powys1989), transfer of pollutants (McLaren and Little 1987; McLaren et al.1993a), self-clearing of a navigation channel (McLaren et al. 1993b), anddetermining the origin of sedimentary sources (De Falco et al. 2003). Themodel has also been tested on a large spatial scale to identify the directionof littoral drift, leading to some interesting conclusions (McLaren andBowles 1985) with controversial results in certain cases (Masselink 1992,1993; McLaren 1993; Masselink et al. 2008). It can also be applied tomany types of marine settings, but it has been used more commonly inenvironments influenced by a significant tidal range (De Mayer andWartel 1988; Nordstrom 1989; Van Lancker et al. 2004) than inmicrotidal zones (Flemming 1988; Masselink 1992). This model hasrarely been used in microtidal environments, mainly due to themultiplicity of dynamic processes controlling sedimentary dispersion insuch zones. Conversely, on a large scale, it is sometimes possible todisregard the other parameters (swell, longshore drift, etc.) in tidallyinfluenced environments where tidal currents are dominant, thusfacilitating the interpretation of the distribution of morphometric indices.Hence, the 1-D approach is very sensitive to the confrontation ofmultidirectional dynamics, which creates uncertainty in the determinationof current directions in environments with multiple sources of input,particularly in river-mouth zones and estuaries (Gao and Collins 1991;Wu and Shen 1999).

Advocating a 2D approach, Gao and Collins (1991) used a grid ofsampling stations and defined trends by comparing the grain-sizeparameters of each sample with it is nearest neighbours in any directionlying within a characteristic distance (noted Dcr). This latter is defined byGao and Collins (1992) as the spatial scale of sampling that can beconsidered as the maximum sampling interval. These trends aretransformed into a ‘‘residual model’’ representing the direction ofsediment-transport vectors between two points of the sampling grid.The method assumes that the grain-size trends between two points, basedon the FB2 and CB+ evolution proposed by McLaren (1981), have ahigher frequency of occurrence in the direction of transport than in theopposite direction. This approach has been used to good effect withdiverse objectives in the study of different littoral environments: spread ofcontaminants (Chang et al. 2001), human impact on a river and its delta(Carriquiry and Sanchez 1999), foreshore dynamics (Balouin et al. 2005;Pedreros et al. 1996), and modeling of sedimentary basins (Gao andCollins 1994; Gao et al. 1994; Stevens et al. 1996). More recent studieshave focused successfully on the dynamics of estuaries (Mallet et al. 2000;Jia et al. 2003; Yang et al. 2004), including microtidal environments(Duman et al. 2004).

Le Roux’s method (1994a, 1994b) is also based on a 2D approach.Considering a central station, it uses the four nearest stations todetermine transport vectors. Because the creation of a regular grid (samedistance between sampling stations) by interpolation is not required tocompute the data, Le Roux and Rojas (2007) consider their approach tobe more realistic.

Differences observed between two or more grain-size frequencydistributions and their derived statistical descriptors are spatially closelyassociated and should contain process-related information (Flemming2007). The geostatistical approach offers an analysis framework thatallows considering, during a grain-size trend analysis (GSTA), spatialdifference criteria of the grain-size parameters. In this context, Asselman(1999) and Poizot et al. (2006) proposed enhancements of the GSTAmethod. The main concerns are (1) the optimization of the sedimentsample grid and (2) the choice of the sediment samples to consider asbeing in relation according to the studied statistical parameter evolution.

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Sampling and Re-Gridding Approach

Asselman (1999) and Poizot et al. (2006) showed that when thesampling interval is not in relation with the sedimentological processes,errors can occur. When the sampling scale is too small, errors introducedby the grain-size analysis may destroy any ordered patterns in the grain-size trends (Asselman 1999; Gao and Collins 2001). On the other hand,when the sampling scale is too large, samples may be taken in differentenvironments. Consequently, interpretation of data from the nearestsamples may not provide the best trend (McLaren and Bowles 1985; Gaoand Collins 1991; Gao and Collins 1992; Asselman 1999; Poizot et al.2006; Masselink et al. 2007) if samples are not spatially dependent. Ifthese authors are considered, the 2D approach advocated by Gao and

Collins (1991), Gao and Collins (1992), Le Roux (1994a, 1994b), Wu andShen (1999), Rios et al. (2002), and Rios et al. (2003) seems to be the bestto use when the sampling scheme is not regular enough, when the studiedarea is under the influence of complex morphology and processes, andcontains several sediment sources and sinks. More recently, Plomaritis etal. (2008) showed for their studied area that the transition from a regulargrid with random sampling does not destroy the information contained inthe dataset and does not sufficiently alter it to make it unusable. Using adataset distributed over a regular grid seems then to be the best choice fordetermining the transport-vectors field (Cheng et al. 2004; Friend et al.2006; Bourrin et al. 2008).

Through the theory of regionalized variables (geostatistics), introducedby Matheron (1965), the semi-variogram analysis allows to take into

FIG. 3.—Hydrodynamic conditions duringsampling period. A) Hydrograph of Rhone Riverat the Beaucaire station. Dates and dashed linecorrespond to sampling campaigns. B, C) Gen-eral characteristics of waves and winds at themouth of the Grand Rhone River (after Globe-Ocean 2007). Horizontal gray bars indicatedirections. D) Changes of sea level linked tobarometric conditions.

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account the structural characteristics of a studied natural phenomenon.Asselman (1999) and Poizot et al. (2006) proposed to use this approach.Firstly, it allows building and optimizing the creation of a regular gridthrough the use of one of the geostatistic interpolators such as kriging(ordinary, universal, etc.) (Fig. 2C). Secondly, the semi-variogramanalysis allows determining the best distance to consider neighbouringpoints for a central station where trend vectors are defined (Poizot et al.2006) (Fig. 2D).

In a recent review paper, Poizot et al. (2008) considered two kinds offlaws concerning the GSTA approach. The first type, related to the inputdata, is linked to good practice in sedimentological analysis (physicalproperties of sediment, mechanical and chemical modification of particlesduring and after transport, sampling method, depth and density, etc.).Not taking into account these uncertainties leads to determiningerroneous sediment trend pathways. The second type of uncertainty isrelated to the GSTA model implementation (changes in nomenclature,choice of the characteristic distance, data smoothing, etc.). The main oneto be addressed is to consider grain-size trends that are adapted to thesedimentary environment studied. As advocated by these authors, resultsobtained through a GSTA approach can be considered only if quality-assurance concepts are followed all along the GSTA procedure.

Users of the GSTA approach are confronted with the problem ofscaling the sampling grid. In most cases, it is not easy to determine inadvance the ideal interval between sampling points. As a consequence,this method may not be applicable to areas where sedimentaryenvironments are highly variable over short distances (Gao and Collins1992). Obviously, whatever the sedimentological method used, itsmodifications and optimizations taken into account, the result can bevalidated only if the samples are representative of the sedimentaryprocesses that we seek to highlight (Wu and Shen 1999). The choice ofscale sampling is guided by the confrontation of empirical knowledge ofsedimentologist, technical resources used, and environmental conditions.

To minimize these concerns, Poizot et al. (2006) proposed a protocolbased on a five-step approach:

(1) Perform a regular grid based on the sampling scheme. A semi-variographic study allows to determine a geostatistical model(Webster and Olivier 1992a; Webster and Olivier 1992b) used tointerpolate the sedimentological statistical parameters (mean,sorting, and skewness).

(2) Study the special variation of the statistical parameters definingthe geostatistical characteristic distance (Dg). This determination ismade through a new semi-variographic study.

(3) Choose the studied trend (i.e., CB+ or FB2).

(4) Compute the vector field within the framework of Gao and Collinsapproach using the interpolated dataset and the Dg parameter inplace of Dcr.

(5) Perform a non-parametric statistical test validating the computedvector field.

During this procedure no smoothing of the vector field is performedbecause this operation can produce altered results (Le Roux et al. 2002;Poizot et al. 2008). The final step of the analysis concerns the significanceof the results. To determine this, a significant statistical test needs to beapplied. Because the field vector distribution is not always assumed tofollow a normal distribution, a nonparametric test (Watson test) shouldbe employed (Watson 1961; Watson 1962). Following Gao and Collins(1992), this significant test is placed at the end the GSTA procedure.

In the method proposed by Poizot and Mear (2008), the length of thearrows drawn in the resulting map is not a function of the sediment-transport intensity, but is related to the confidence which can beattributed to the computed direction. The higher the vector length, thehigher the confidence of the computed vector trends.

RESULTS

Hydrodynamic Context during Sampling

During the study period, from October 2002 to March 2003, fluvialdischarges display considerable heterogeneity, which allows us to measurebottom-sediment grain-size under representative river conditions(Fig. 3A).

The campaign of 17 March 2003 followed on from medium dischargeslasting several weeks. It corresponds to a period of hydrological calmsince the discharge (898 m3s21) is lower than the mean annual value. Themarine conditions during the month prior to sampling are of rather lowenergy and indicate a period of good weather (only three very shortstorms, of less than 24 hours). Consequently, the campaign of 17 March2003 is representative of a low-stage situation following the period offlood that generally precedes the low water levels of summer. Thesampling on 25 October 2002 was performed during an annual floodevent (2470 m3s21). It occurred after many months of low river levels(summer discharge , 1500 m3s21), but was influenced by a fifty-yearflood event in September (Table 1) consistent with an annual stormreturn period (Hsig 5 2.15 m). Consequently, the campaign of 25October 2002 is representative of the annual floods taking place at thebeginning of autumn, after the calm period of summer. During thesampling of 22 November 2002, the discharge of the Rhone was4,735 m3s21, but this had risen to 10,200 m3s21 a few days before(Table 1). This campaign thus characterizes a flood with a 50-year returntime, which is accompanied by a south easterly storm with a wind speed(15 ms21), swell height (Hsig 5 3.26 m) and duration (. 72 hours)(Fig. 3B, C) indicating a biannual periodicity. The bed load during theflood event of November is particularly high. The first estimates yield atotal net budget of 7.15 3 106 tons, with instantaneous suspended matterconcentrations of up to 3 gel21 (Olivier 2006). The sampling during thecampaign of 22 November 2002 thus reflects an exceptional floodassociated with a relatively important marine storm. This type of event isrepresentative of the episodes of concomitant floods and extreme storms,since these two sorts of events are caused by a regional weather situationaffecting the whole of the French Mediterranean basin (Moron andUllman 2005).

General Characteristics of the Rhone Mouth Sedimentary Cover

Figure 4 presents the distribution of the grain-size parameters, i.e.,mean, sorting index, and skewness (Folk and Ward 1957) calculated fromthe sampling grids carried out during low river discharge, medium flood,and extreme flood events. Generally speaking, the river compartmentshows a marked contrast between the east bank, characterized by fine-grained surface sediments (mean grain size: 5 w), and the west bank withmuch coarser deposits (mean grain size: 3.8 w). This strong contrast insuch a reduced space is related mainly to the morphology of the riverchannel, which is deeply incised on the east bank (216 m). Moreover, thepresence of a coastal spit in the west (Fig. 1C), partially barring thechannel, leads to the build-up of a longitudinal mega dune in the river,which owes its stability to the tendency of the Rhone to migrate towardsthe east during extreme floods (Maillet et al. 2006b). The position of thepass is clearly marked by a decrease in the grain-size of surface sedimentslocated in the channel. In the marine sector, the surface sediments becomeprogressively finer offshore, forming an arc-like pattern around the outletof the river. The decrease in grain-size is very rapid (mean . 1.3 w on thetop of the mouth bar to , 4 w beneath water depth of 30 m) and iscorrelated with the gradient opposite the mouth.

Sedimentation on the mouth bar is related to the coarse clastic inputmoving in the river by rolling or saltation. This material accumulates onthe top of the bar because its extension farther offshore is limited by theaction of swells that absorb the energy of the river. This exposure to

144 G.M. MAILLET ET AL. J S R

marine dynamics prevents the deposition of finer particles. The uppershoreface and shoal environments are dominated by fine sands (, 2.3 w).In a general way, the calcium carbonate content of the samples isinversely proportional to the particle size, but never exceeds 15%, thusreflecting the erogenous origin of sedimentation on the present-day deltalobe and adjoining beaches. Maillet et al. (2006b) have shown that thesurface sedimentation beneath 220 m results mainly from the settling outof the fine particles making up the plume, including during periods offlood. The prodelta zone is dominated largely by muds. The presence of abottom nepheloid layer (Aloısi et al. 1982; Naudin et al. 1997) makes itdifficult to determine the exact position of the ‘‘surface’’, which is situatedevidently between the base of the nepheloid layer and the top of a layer ofsurface mud with very high water content (20% to 80%, Courp 1990;Lansard 2004). However, a sandy fraction (ca. 10%) is present in theprodelta deposits, which is explained by the sliding of sandy masses andchannelled flows on the slope of the delta front (Maillet et al. 2006b). Inthe method proposed here, we are justified in restricting the study of floodimpact to the 0 m to 220 m zone, due to the relative sedimentologicalhomogeneity of the sector deeper than 220 m, which is no longer subjectto the influence of waves.

Impact of Flood Events on Surface Sedimentation

The sedimentary pattern in the mouth zone, as described above andillustrated in Figure 4 by the distribution of median grain-size duringperiods with no floods, is more or less well preserved during flood events.The sedimentation regime thus appears not very sensitive to variations ofliquid discharge alone. Despite a tendency to increased particle size

towards the open sea during flood events, the sedimentary cover remainsappreciably the same during low river-discharge events and extremehydrological conditions, as shown through the observations of Maillet etal. (2006b) based on bathymetric measurements, and the modeling withMARS 3D software by Dufois (2008) during Rhone River 2003centennial flood event (neither specific accumulation nor erosion onprodeltaic slope during flood periods ). Moreover, we find a broadlysimilar spatial pattern of sediment sorting during no-flood and low-river-discharge periods. Taking into account the marine dynamics affectingshallow waters, the best-sorted sediments are found on the top of themouth bar and on the west bank of the river. Conversely, the deepestzones (east bank of the river channel and foot of the delta front) exhibitthe least homogeneous sedimentation. Ultimately, there appears to be anegative correlation between sorting and water depth. During both floodevents, the zone of well-sorted sediment is reduced to the inner part of thebar. All the same, the trend is towards a general degradation of sorting,visible mainly in the channel which is most exposed to the violence offlood dynamics. This general behaviour is illustrated particularly by thesedimentation regime on the west bank of the channel. During low-river-discharge, this sector is characterized by coarse deposits, which are wellsorted and display particle shapes approaching a Gaussian distribution(symmetry). During flood events, the sediment remains coarse but poorlysorted and enriched in fine particles (positive skewness). This tendencyreflects the impact of a very high-energy event on the sedimentarymaterial, expressed in the flood regime by bimodal deposits andresuspension mechanisms (large median grain-size but very poor sorting).More homogeneous deposits are formed during low-discharge periods,reflecting the grain-size homogeneity of the solid discharge. During low-

FIG. 4.—Surface sedimentology of the mouth zone: evolution of the three sedimentological parameters depending on fluvial and marine dynamics.

PATTERN OF SEDIMENT-TRANSPORT IN A RIVER MOUTH 145J S R

river-discharge events, the inner part of the mouth bar exhibits a specificenrichment in poorly sorted fine particles. This probably results from theinteraction between sorting by the swell surge (high significant waveheight) and the flocculation of fine particles in the mixing zone betweenfresh and salt water (Eisma 1986; Thill et al. 2001). During the extremeflood event, while marine conditions are also dominated by highsignificant wave height, they are additionally influenced by a very highsea level (Fig. 3D). Thus, the mixing zone and resulting sedimentaryprocesses are transferred upstream in the Rhone channel. Consequently,the surface sedimentary cover of the main part of the mouth bar and deltafront is weakly influenced by extreme fluvial dynamics.

Pattern of Net Sediment-Transport

Following the procedure previously explained, we created a regulargrid on which new values are defined. Theoretically, because the semi-variogram model chosen is continuous, the grid could be made as fine aswanted. Whatever the grid density, it needs to be in accordance with theoriginal information. To define our grid spacing, we created multiplegrids with an increasing number of points (decreasing distance betweenpoints). As the number of points increases (grid becoming finer), the testresults decrease in quality, showing a departure from the originalinformation. The finest grid (close to 300 m step) satisfying the test wasselected and used for further computations. The non-normality of all thestudied grain-size dataset (Shapiro test: p-value always lower that 0.05 fora 5 0.99) needed to use a nonparametric test, i.e., the Wilcoxon Ranksum test, to compare the independent unpaired dataset. No difference wasdetected between parameters from the raw and the interpolated data(Table 2).

An analysis of the semi-variograms (Fig. 2D) of the interpolated grain-size parameters allows defining a characteristic distance of 0.025 decimaldegrees (approximately 2800 m).

Six vector fields were then computed for the three hydrological periods(low-river-discharge, medium flood event, and extreme flood event).Because each trend can be in relation to a specific environment, we choseto study the two trends, denoted CB+ (coarser, better sorted, morepositively skewed) and FB2 (finer, better sorted, more negativelyskewed), separately avoiding to mix, on a single vector field, vectorscorresponding to each environment. Only the result based on CB+evolution satisfied the Watson test. This signifies that the nonrandomnesshypothesis of the vector field cannot be rejected at a confidence level of95% and can therefore be used to study hydrodynamic processes. Becausethe FB2 evolution failed the Watson test, it is no longer considered inthis study.

For each case defined here, Figure 5 shows the vector fieldscharacteristic of sediment-transport.

Low-River-Discharge Case.—Based on the study of the vectordirections and length, three areas are highlighted, denoted as A, B, andC. Zone A is confined to the more upstream part of the river channel.Transport vectors directed towards the south are observed only in asector where the banks are closer together. The high values of the lengthof these vectors indicate an anisotropy in the direction of transport. Thispattern of the vectors is consistent with the direction of flow of the river.Zone B develops at the outlet of the fluvial channel, elongated in an east–west direction and extending from the upper shoreface of Piemanson tothe upper shoreface of La Gracieuse (between 0 m and 22 m), includingall of the inner part of the mouth bar. In the north, it occupies thelowermost part of the Rhone River channel. The southern boundary ofzone B exhibits some more or less well-marked indentations with north–south elongation. It is characterized by a set of vectors of low length,indicating a strong isotropy. The majority of these vectors convergetowards the center of the mouth. A third zone, denoted as C (between

22 m and 220 m), occupies all the southernmost part of the mouth zone.It corresponds globally to the prodelta front, which is characterized by amaximum homogeneous slope greater than 4u, and is incised by slumpsand several channels subparallel to the slope (Maillet et al. 2006b). Theset of vectors is perpendicular to the isobaths, and shows concordantdirections towards the center of the mouth. The high values of the vectorlength highlight the strong anisotropy of the transport directions.

Medium Flood Event.—During the medium flood event (peak of2540 m3s21), zone A (river channel) shows a greater downstreamextension than in the case of low river discharge. The homogeneity ofthe vector field for the medium flood event highlights a strong anisotropyin this zone, which reflects a unimodal transport direction towards thesouth-southeast. This vector field characterizes the fluvial transport of theRhone. The vectors of direction converge towards zone B, which has areduced area compared to the situation during low discharge. While zoneB extends more towards the open sea, as far as the top of the mouth bar(22 m isobath), it is confined to the eastern sector of the river mouth. Theindentations of the southernmost limit no longer appear so well marked.The vectors exhibit the same pattern (in terms of both direction andlength) than during the period of low river discharge. This central flatarea, currently lies at a water depth of between 1.5 m and 2.5 m. Zone C(between 22 m and 220 m) shows the greatest spatial extent. Comparedto the situation during low river discharge, this zone expands to occupyall of the eastern part of the study zone, thus rimming zone B in the eastand the south. Its boundary with the upstream vector field appears moreregular. The smoothing out of the indentations is associated with thedevelopment of a greater intrusion of zone C within the mouth bar.Farther west, the geographical extent of zone C is limited by theappearance of a new zone, referred to here as D. The characteristics of thevectors calculated for zone C are on the whole identical to the situationduring low river discharge, although the vectors appear more isotropic inthe western part of the zone. The period of flood thus favors theappearance of two new vector fields. In the east, one of the new vectorfields can be associated with zone C, since it appears sufficientlyconcordant with the already observed pattern. In the western mouthzone, zone D appears at the eastern end of the Piemanson shoreface,bordering the southernmost extent of zone A. The vectors are directedtowards the east until the center of the mouth. This vector field can beobserved from the coast to a water depth of 22.0 m, and occupies a widthof approximately 500 m. It represents the longshore drift currentidentified from the morphology of the coastline (Sabatier and Suanez2003).

TABLE 2.—Wilcoxon tests results (test of independence) performed foreach mission (a 5 0.99). For the three missions, parameters from regulargrids are tested against parameters from the same irregular grids. None ofthe tests give any evidence of a difference between parameters of the two

data sets (p-value . 0.01). Reg. refers to data from regular grid, and irreg.to data from irregular grid.

Mission Parameters p-value

One-year flood event Mean reg. versus mean irreg. 0.3255Fifty-year flood event Mean reg. versus mean irreg. 0.6339Low river discharge Mean reg. versus mean irreg. 0.1865One-year flood event Sorting reg. versus sorting irreg. 0.7638Fifty-year flood event Sorting reg. versus sorting irreg. 0.5229Low river discharge Sorting reg. versus sorting irreg. 0.1067One-year flood event Skewness reg. versus skewness irreg. 0.0275Fifty-year flood event Skewness reg. versus skewness irreg. 0.2841Low river discharge Skewness reg. versus skewness irreg. 0.0254

146 G.M. MAILLET ET AL. J S R

Extreme Flood Event.—With an extreme flood discharge at the mouth(peak 6099 m3s21), the five zones defined during the medium flood eventare also present. In the bed of the river (zone A), the transport vectorsremain parallel to the banks. In the downstream part of the channel, thefield vectors bear towards the southeast, thus forming a general S-shapedpattern. This is superimposed on the configuration of the principalchannel of the Rhone, which continues offshore as a bypass channel.Zone B preserves the same characteristics as during the medium floodevent, but its surface area is doubled, while progressing towards the east.During an extreme flood event, zone B extends towards the marinedomain as far as water depths of 25 m, by expanding across the top ofthe mouth bar. Zone C occupies all of the southern part of the maritimedomain. Its characteristics (strong anisotropy and direction of vectorfield) remain unchanged compared to the preceding situations (lowdischarge and medium flood event). Zone D is strongly reduced to half inits width but preserves the same extension towards the east.

DISCUSSION

Based on hydrodynamic conditions specific to the sampling campaignand the overall configuration of the sedimentary cover, we can proposean interpretation of the vector fields in terms of sedimentary dynamics.

The inner part of the river channel displays a characteristic sedimentsignature (sample 6, Fig. 6). The grain-size distribution is wide (poorsorting) and polymodal, with a median close to 6 w (, 15 mm). Theinfluence of the increase in discharge on the sedimentary transfer in zoneA is clearly shown by GSTA. In periods of low river discharge, the marinedynamic regime influences the fluvial dynamics as far as the channel. Thegrain-size distribution of sample 16 (Fig. 6) is similar to that of sample 6,but the median is higher, because of an enrichment in the coarsest fraction(. 3.3 w , 100 mm) due to the marine inputs. When the dischargeexceeds the threshold of the medium flood event, a reinforcement of riverdynamics is seen both in the spreading of zone A towards the sea (Fig. 5)and in the increase of the significance of the transport vectors.Nevertheless, we note that the effect of river dynamics never extendsbeyond the coastline, including during extreme flood events. During theseperiods, the vectors show that sedimentary transfers are more strictlyguided by the morphology of the channel (S-shaped). Maillet et al.(2006b) also showed that, in this downstream zone, the channel couldundergo downcutting of more than 5 m during an extreme flood event.Thus, GSTA allows us to highlight the transport by traction of coarserparticles (until 1 w , 500 mm), which occurs when the discharges aresufficiently high, in agreement with the liquid discharge values proposedby Antonelli et al. (2004).

For the three trends considered here, zone B (Fig. 5) shows a strongisotropy of the vector field, being located at the junction between twotypes of transport: fluvial (zone A) and longshore drift along theshoreface of Piemanson (zone D in Fig. 5, sample 75 in Fig. 6).Moreover, zone B is affected by a complex swell derived from themodification (shoaling, breaking, or diffraction) of the principal swells(southeast and southwest) on top of the mouth bar.

In the inner sector of the mouth bar (samples collected around station30, Fig. 6), the deposits result clearly from a mixture of sediments comingfrom different sources. Examining the grain-size distribution of sample51, we can easily identify three modes: (1) coarse sands brought in byerosion of the mouth bar (similarities with sample 75, peak around 1.5 w

r

FIG. 5.—Results of geostatistical sediment trend analysis (GSTA) during lowriver discharge, medium flood event and extreme flood event. Zones were drawnusing a combination of length and direction of GSTA vectors. The arrows indicatethe direction of transport. The longer the arrow, the greater the anisotropy of thevector bearing. Numbers refer to EPSHOM bathymetric contours in meters.

PATTERN OF SEDIMENT-TRANSPORT IN A RIVER MOUTH 147J S R

, 350 mm), (2) fine sands transported by the current coming from thewest (characteristic peak at 2.7 w , 150 mm), and (3) a fine fraction,coming from the upstream part of the river and similar to the sample atstation 6.

The enhancement of fluvial dynamics is also reflected by the change inthe position and extent of this zone. At low discharge, zone B extendsover the entire inner part the bar (, upper shoreface), thus expressing thezone of influence of longshore drift and coastal wave action. The largeindentations on the southern boundary are in continuity with the bypasschannel through the mouth-bar (see concordance between shape of thezone-B boundary and the 22 m bathymetric contour).

Thus, for periods of low river discharge, the influence of the swell onsediment transport is expressed as far as the center of the mouth bar,owing to a smaller influence of depth on the swell at the level of thebypass channels. Because of this strong influence of the swell on the topof the mouth bar, there is an excellent grain-size sorting of the depositedsediments (sorting index , 0.15) and a very coarse median grain-size(Q50 5 1.3 w , 400 mm for sample 123, Fig. 6). For a medium floodevent, the effects of the river currents increase. Thus, the mixing zone isshifted towards the sea. The increased height of the swells does not seemsufficient to compensate for the sedimentary transfers towards the opensea caused by the river current. The mixing zone thus remains locatedinside the mouth bar, but in the part nearest to the top to the bar. Theouter part of the bar and the delta front remain dominated by transportof marine origin, directed towards the coast. Sample 39 displays a grain-size distribution characteristic of a high-energy sedimentation zone.

Nevertheless, it evidently differs from samples taken on the top of themouth bar by having a slightly finer grain-size (Q50 5 1.5 w , 350 mm),due to the remobilization of deposits from the adjacent beaches.When river and marine dynamics increase (extreme-flood case), themixing zone shifts eastwards under the effect of the river current, and ispushed back in the central part of the mouth bar by strong swells(2.5 , Hsig , 3.5m). Displacement of the mixing zone towards theeast is also controlled by swell with prevailing directions from the SSWand SE which induce a current directed towards the eastern part of themouth.

It is noteworthy that the appearance of zone D is synchronous with theincrease in discharges. However, the vector field parallel to the coastline isclearly related to the transport of littoral drift, as proposed by Sabatierand Suanez (2003) and confirmed by the grain-size distribution of sample75 (Fig. 6). This hypothesis is more likely because the significant heightsof swell increase during the medium and extreme flood events, while thiszone corresponds to depths characteristic of the surge swell. Nevertheless,it is possible that the existence of this zone is favoured by the riverdynamics. In fact, this could be partially explained by a siphoning effectcreated by the river water current entering the sea (Orton and Reading1993). This highly localized current causes a depression at the rivermouth, which is compensated by a lateral input of water.

The development of zone C towards the sea is accompanied by aconsiderable increase in the length of the associated transport vectors.Offshore, these vectors are directed towards the mouth of the Rhone,running against the slope and perpendicular to the depth contours. At

FIG. 6.—Use of the sedimentary signatures of surface samples to interpret sediment dynamics during periods of medium flood. Each sedimentary environment ischaracterized by a specific grain-size pattern. The grain-size distribution of the samples collected in the mixing zone, inside the mouth bar, reflects a combination ofvarious components, i.e., material from several different sources of input. The arrows indicate the various directions of sediment input identified by sedimenttrend analysis.

148 G.M. MAILLET ET AL. J S R

first sight, this direction is surprising on a prodelta lobe advancingoffshore and subject to gravity slides (Maillet et al. 2006b). However,Marsaleix et al. (1998) used numerical modeling based on the work ofChao (1988) to infer a possible convergence of the bottom currentstowards the mouth related to baroclinic circulation, which is associatedwith the exchange of fresh and salt water. Nevertheless, taking intoaccount the particular conditions of the model (low discharge, less than1000 m3s21, absence of wind and waves, very simplified channel, etc.) andthe absence of in situ measurements, we remain prudent about such ahypothesis. Even though our analysis appears to support such amechanism, it is not, at this stage, completely convincing to explain thedirections of the transport vectors in this zone. The asymmetry of theswell and the orbital velocities could explain our results, but thisphenomenon has never been directly observed and the classical butrecognized mechanisms for the formation of delta lobes define a sedimentflux directed offshore. In conclusion, these vectors do not seem to reflectthe existence of sediment transport from offshore towards the mouth,except between 25m and the top of the mouth bar, where they are linkedto transport by refraction of the swell, On the other hand, Maillet et al.(2006b) have identified the prodelta front deeper than the 25 m isobathas a settling zone during the 2003 extreme flood event and explained thatmost of sediment transfers from the top of the bar to the prodelta aregenerated by slides occurring out of flood periods. Moreover, accordingto McLaren (1981) and McLaren and Bowles (1985), CB+ trends can beinterpreted as resulting from either a transport process (Case C) or a lagdeposit (Case A). Thus, we conclude that, although the vectors observedin this zone are not influenced by specific events, they can be interpretedas a lag deposit influenced by the grain-size gradient depending on thedistance from the sediment source. A similar mechanism has already beenproposed in a high-energy estuary dominated by tidal currents (Chang etal. 2001).

Is GSTA Alone Sufficient to Support the Conclusions?

In order to estimate sediment-transport at a river mouth or inlet,another alternative is to use a 2D morphodynamic model (De Vriend etal. 1993), but, notwithstanding numerous examples in the literature, thenumerical simulation of waves and currents on a prodelta lobe remainsvery complex (Sutherland et al. 2004). The numerical models already usedfor the Rhone (see site description) do not envisage bedload sediment-transport, and our results cannot therefore be directly compared to thoseof previous studies. As a matter of fact, numerical modeling of river-mouth currents should reproduce wave blocking generated by theconjunction of marine dynamics (essentially waves and wave-inducedcurrents) and river outflow. In order to apprehend these mechanisms,preliminary investigations were conducted for the mouth of the Rhoneusing a 2DV model (Sabatier et al. 2009). At the river-mouth bar, wherewaves are liable to break, numerical modeling replicates longshoretransport to the northeast, and this is in agreement with our results, butthis modeling does not provide elements of comparison with what weobserve at the front of the delta lobe. Moreover, for river mouths,modeling of currents and sediment-transport is hampered by problems ofrealistic representation of the difference in water level between the riverflow and the ocean. Some progress in this regard has been achieved usingSTWAVE, but this concerns relatively simple cases (Reed and Militello2005) that are hardly comparable with the Rhone. To our knowledge,only Giosan (2007) has attempted to model waves at a river mouth similarto that of the Rhone (St Georges, Danube), but the results concern onlywave height, and neglected river flow. In addition to these problems ofintegration of physical processes in numerical models, modeling of thedynamics at the mouth of the Rhone is hampered by the lack of reliablebathymetric data. At present, data in agreement with our sampling resultsdo not exist for the lower Rhone. Moreover, recent bathymetric

measurements conducted at the terminus of the river (Maillet et al.2006b) and over a 500 m grid 4 km from the mouth (Vassas et al. 2008)indicate, respectively, very rapid river-bed incision processes and settlingprocesses on the delta front during flood events, and the occurrence ofhighly mobile hydraulic dunes. In order to model the current, we wouldneed bathymetric data that are contemporaneous with our sampling,without which it would be illusory to attempt 3D modeling of sediment-transport. Most studies (Estournel et al. 1997; Marsaleix et al. 1998;Guan et al. 1999; Estournel et al. 2001; Arnoux-Chiavassa et al. 2003;Reffray et al. 2004) circumvent this difficulty by using a grid that is solarge that sedimentary processes related to rapid variations in morphol-ogy (bars and delta front) disappear. Modeling of currents and sediment-transport is hampered in this zone by the complex morphology, whichnecessitates a much finer grid. Improper model replication of river-induced flow will yield unreliable results on wave flow interactions (waveblocking processes) near the river mouth bar and in the upper part of theprodelta lobe. These shortcomings constitute a challenge for futurestudies, but our intent, in this study, was simply to provide a statisticalestimation of sediment flux in a microtidal river mouth.

CONCLUSION

This study takes an upstream place in a global project leading to gain abetter understanding of how sediment particles are transported fromrivers to the continental shelf, across the slope, and into deep-seaenvironments. Moreover, it is crucial to understand the mechanisms offormation of prodelta lobe for developing ways of exploiting thesubmarine environment in a responsible and sustainable manner.Therefore, by investigating hydro-sedimentary processes during majorperiods of solid inputs (flood events), the GSTA method aims to improvethe knowledge of sediment transfer in a microtidal fluviomarinetransition zone.

To acquire a better understanding of these sediment dynamics, weapplied sedimentary trend analysis to three datasets obtained at threeriver-flow regimes: low-river-discharge, medium flood event, and extremeflood event. During low-river-discharge, sediment transport is detectedonly in the inner part of the Rhone mouth.

The inner part of the mouth bar appears as the confrontation zone ofmarine and river dynamics. The sediment deposits are heterogeneousbecause they are supplied both by river inputs and material coming fromthe top part of the mouth bar. No residual direction of transport can beclearly identified. Inside the mouth bar, the influence of swell-relatedtransport is observed mainly at the level of the bypass channels. Theentire top part of the mouth bar is subject to grain-size sorting (erosion ofthe finest particles) characteristic of high-energy conditions associatedwith the surge of the swell. At water depths greater than 25 m, the GSTAgenerates transport vectors running against the slope that clearly expressthe importance of settling mechanisms in the supply of sediments to theprodelta front. The medium flood event is characterized by more markedfluvial transport, whose influence extends up to the center of the mouthbar. The mixing zone is spatially restricted because of the increasedinfluence of the swell, and is also fed by transport from west to eastappearing on the Piemanson shoreface. Following the reinforcement ofmarine dynamics, the swell influences the sedimentary cover morehomogeneously inside the mouth bar. The extreme flood event does notlead to a clear modification of sediment transport regime compared to thesituation during a medium flood event. The input of coarser fluvialsediments is highlighted by an increase in the area of the zone subject toriver dynamics, in agreement with the bathymetry of the channel (S-shape). The influence of the littoral drift on the Piemanson shore isreduced by the increase in the intensity of the swell, which coincides withthe extreme flood event. Thus, it appears that medium flood events(, 2500 m3s21) are sufficient to modify sediment dynamics in the

PATTERN OF SEDIMENT-TRANSPORT IN A RIVER MOUTH 149J S R

proximal zone of the mouth of the Rhone. The more extreme events(. 8000 m3s21) do not modify the overall scheme established in this way.The action of swell, even during periods of calm, is a major hydrodynamicfactor controlling the redistribution of sediments on the upper part of themouth bar (down to a maximum depth of 25 m). This influence of theswell extends well within the mouth bar. In view of the hydrodynamiccontext selected for this study, and the question of whether the fluvialsolid load supplies sand to the adjoining beaches, it is noteworthy that novector field indicates the existence of sediment transfer beyond the mouthbar. It also appears that the periods of flood, although favoring thetransfer of sand in the river, do not lead to the direct supply of theadjacent offshore bars, as demonstrated by Maillet et al. (2006a) andSabatier et al. (2009) on a century-time-scale.

To conclude, the GSTA method proves to be suitable for thedetermination of sediment dynamics in a context where several sourcesof input are clearly identified and several hydrodynamic factors coexist ina restricted geographical area, although it cannot replace the collection ofmorphological and hydrodynamical data. In such a complex area, the useof the geostatistical characteristic distance (Dg) defined by a variographicanalysis (Poizot et al. 2006) is particularly well adapted. This is becausethe method of determining Dg integrates the diversity of environmentsand mechanisms present in the studied zone, taking into account scalerestrictions provide by Masselink et al. (2008). The optimization of GSTAnecessarily involves the individual analysis of the various possible grain-size trends. Thus, in this study, we validated trend CB+ statistically onlywhen it could be considered individually. However, even if it can bestatistically validated, the sediment transport so defined should beinterpreted according to the local environmental context (swell, currents,bathymetry, bottom morphology, etc.). It is important to reconsider theremarks made by McLaren (1981) and McLaren and Bowles (1985) onthe validity of trend CB+ (transport or lag deposit). The failure to takethese remarks into account could explain some discrepancies pointed outby many authors in comparing the results obtained by the GSTAapproach with environmental knowledge acquired elsewhere. Theinterpolation of grain-size parameters on a regular grid proves to be apowerful method in areas where it is difficult or even impossible to collecta sufficient number of samples in a short period of time (since this is afunction of the period of the hydrodynamic agents) or in zones with veryactive hydrodynamics. However, it is necessary to validate theinterpolation by a statistical analysis based on a nonparametric test(i.e., Wilcoxon test).

ACKNOWLEDGMENTS

This study benefits from the support of the national programme ELM, theFrench GDR on ‘‘Margins’’ and the CARMA project financially supportedby Provence–Alpes–Cote d’Azur Region. It is also a part of the FrenchNational Research Agency (ANR) EXTREMA project (ANR-06-VULN-005, 2007–2010) supported by the competitive poles ‘‘Mer PACA (ProvenceAlpes Cote d’Azur)’’ and ‘‘Gestion des Risques et Vulnerabilite desterritoires.’’ We acknowledge Editor Paul McCarthy and Associate Editor(AE) Jackie Huntoon for their excellent recommendations. The authors alsothank IFREMER/DRO/GM and the ‘‘Domaine de la Palissade’’ through itsdirector J.C. Briffaud, for their technical and logistic support. O. Samat, E.Ribes, and M. Martin are thanked for their help during sampling missions, C.Cerboni, Captain of the ‘‘Team Golfus,’’ for his substantial assistance.Finally, G.M. Maillet is especially grateful to P.L. Friend and T. Plomaritis(NOC, Southampton) for their valuable criticisms of our results. M.S.N.Carpenter is responsible for post-editing an early draft of the manuscript.

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Received 23 December 2008; accepted 3 June 2010.

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