Abstract: In this paper, data on longshore and cross-shore sediment transport

2130 ESTIMATION OF LONGSHORE AND CROSS-SHORE SEDIMENT TRANSPORT ON SANDY MACROTIDAL BEACHES OF NORTHERN FRANCE ADRIEN CARTIER 1,2, ARNAUD HEQUETTE 1,2 1. Laboratoire d Océanologie et de Géosciences, UMR CNRS 8187 LOG, Université du Littoral Côte d Opale, 32 Ave Foch, 62930 Wimereux, France. 2. Univ Lille Nord de France, F-59000 Lille, France. Adrien.cartier@univ-littoral.fr, Arnaud.hequette@univ-littoral.fr Introduction Abstract: In this paper, data on longshore and cross-shore sediment transport were obtained during six field experiments, on three sandy macrotidal barred beaches of northern France. This study is based on sediment trap experiments, following the method of Kraus (1987), and completed by wave and current measurements using a series of hydrodynamic instruments deployed across the intertidal zone. Results showed that longshore sediment transport increased with both wave height and mean flow, but no relation was found with wave angle which is probably due to the influence of tidal currents that interact with wave-induced longshore currents. Cross-shore sediment flux was generally higher than longshore flux, suggesting that shore-perpendicular sediment transport associated with wave oscillatory currents probably represents a major factor controlling the cross-shore migration of intertidal bars. Estimation of sand transport is needed for most coastal engineering designs and constitutes a major issue for a better understanding of the dynamics of sandy beaches. Longshore and cross-shore sediment transport are one of the most widely studied processes in the coastal literature because movement of sand in the nearshore zone by waves and currents is of fundamental importance to the longterm sediment budget of a stretch of coast and plays a key role in shaping coastline. Although, a large number of studies have been carried out on this topic, most of them were focused on measuring sand transport along micro- and mesotidal beaches (Bayram et al., 2001; Kumar et al., 2003). In comparison, only a few studies have been conducted on macrotidal beaches (e.g., Davidson et al., 1993; Levoy et al., 1994; Voulgaris et al., 1998; Corbau et al, 2002) where sediment transport results from the complex interactions of tidal currents with longshore currents generated by obliquely incident breaking waves, this complexity being further increased by the large variations in water level that induce significant horizontal translations of the surf zone. For a number of years, sediment transport studies were mostly focused on meso- to macroscale processes and estimated from beach morphology change, for example, or from fluorescent tracer experiments (Voulgaris et al., 1998). With the fast evolution of high frequency sensors technology, sediment transport has also

2131 been determined using optical backscatter sensors (Davidson et al., 1993; Tonk and Masselink, 2005) or more recently, acoustic backscatter profiler instruments that can provide high resolution suspended sediment concentration estimates. Proper calibration of acoustic or optical data is often problematic, however, due to the presence of organic matter in the water column or to grain size variability (Battisto et al., 1999). The use of optical or acoustic backscatter sensors for estimating sediment flux is further complicated in the highly-turbulent surf zone where breaking waves generate air bubbles that can induce erroneous sediment concentration estimates (Puleo et al., 2006). In this paper, we present the results of field measurements carried out on three macrotidal beaches of northern France for evaluating alongshore and cross-shore sediment transport in the surf zone under the action of wave and tidally-induced currents. In order to avoid the problems mentioned above in the turbid and organicrich coastal waters of northern France (Vantrepotte et al., 2007), this study was based on sediment trap experiments completed by wave and current measurements using a series of hydrodynamic instruments deployed across the intertidal zone. Study area Fig. 1. Location map showing the three study sites, northern France.

2132 This study has been conducted on three sandy macrotidal barred beaches of northern France (Figure 1). The first field experiment site (Zuydcoote) is located near the Belgian border, facing the North Sea; the second site (Wissant Bay) is on the shore of the Dover Strait, while the third study site (Hardelot) is located on the coast of the eastern English Channel. Mean sediment size is 0.20 mm at Zuydcoote, 0.22 m at Wissant and 0.23 mm at Hardelot. Tidal range increases from the Belgium border to the English Channel, spring tide amplitude ranging from approximately 5 m at Zuydcoote to nearly 10 m at Hardelot. Due to the large tidal range, tidal currents are strong along the coast of northern France, and flow almost parallel to the coastline. The region is dominated by waves from southwest to west, originating from the English Channel, followed by waves from the northeast to north, generated in the North Sea. Wave energy is strongly reduced at the coast due to significant wave refraction and shoaling over the shallow sand banks of the eastern Channel and southern North Sea. Methods Hydrodynamics measurements were carried out using electromagnetic wave and current meters (InterOcean S4 ADW and Midas Valeport current meters) and Acoustic Doppler Current Profilers (ADCP) deployed across the intertidal zone from the lower to the upper beach (Fig. 2). All instruments operated during 9 minutes intervals every 15 min, providing almost continuous records of significant wave height (H s ), wave period and direction, longshore (V l ) and cross-shore (V t ) current velocity components, and mean current velocity (V m ) and direction. Current velocity was measured at different elevations above the bed depending on each instrument. The S4 and Valeport current meters recorded current velocity at 0.4 m and 0.2 m above seabed respectively, while the ADCP measured current velocity at intervals of 0.2 m through the water column from 0.4 m above the bed to the surface. Current velocity at 0.2 m above the bed was estimated using the ADCP data by applying a logarithmic regression curve to the measured velocities obtained at different elevations in the water column. During one field experiment (Zuydcoote, 2009), one of the ADCP only measured current velocity. Longshore and cross-shore sediment fluxes were estimated using streamer traps, following the method proposed by Kraus (1987). The sediment traps consisted of a vertical array of five individual streamer traps with 63 µm mesh size sieve cloth that collected sand-size particles at different elevations above the bed, up to a height of approximately 1 m. These measurements were used to compute estimates of suspended sediment transport at discrete elevations above the bed as well as depthintegrated sediment flux. Calculations of the sediment flux from sand traps are clearly detailed in the paper of Rosati and Kraus (1989). Measurements of longshore sediment transport with the sediment traps were undertaken during 10 minutes at several locations across the intertidal zone during rising and falling tides in order to obtain

2133 estimates of longshore sediment flux from the lower to the upper beach during flood and ebb (Fig. 2). During three of the six field experiments, the sediment traps were deployed along two shore-perpendicular transects with a spacing of about 100 m to investigate the alongshore variability in longshore sediment transport (Figure 2). During five field experiments, a number of cross-shore sediment transport measurements were carried out simultaneously with longshore sediment sampling. During four of these experiments, the sediment traps were oriented for measuring onshore-directed transport, and during one experiment both onshore- and offshoredirected sediment flux were measured (Table 1). A total of 270 streamer trap deployments were carried out during the study. As shown in Figure 2, sediment traps were deployed in the vicinity of the wave and current meters, but also at other locations across the intertidal zone. Bivariate as well as multivariate statistical analyses were performed between measured sediment flux and hydrodynamic parameters (e.g., significant wave height, mean current velocity ) recorded simultaneously, but only for sediment transport measurements obtained close to hydrographic instruments. During each field experiment, beach morphology was surveyed using a very high resolution Differential Global Positioning System (DGPS) with horizontal and vertical error margins of ± 2 cm and ± 4 cm respectively. Two field measurement campaigns were conducted on each study site during conditions of low to moderate wave activity (H s ranging from approximately 0.1 to 0.7 m), as well as during spring and neap tides, to cover a range of different hydrodynamic conditions. Field experiments were conducted in November 2008 (ZY08) and in November-December 2009 (ZY09) at Zuydcoote, in March 2009 (WI09) and in March-April 2010 (WI10) at Wissant, and in May-June 2009 (HA09) and January- February 2010 (HA10) at Hardelot. Fig. 2. Representation of deployment of sediment traps and hydrodynamic instruments during the field experiments. Arrows represent the direction of measured sediment flux. Numbers refer to the successive positions of sediment traps during rising (1-5) and falling (6-10) tide.

2134 Results Range of longshore and cross-shore transport rates All the sediment trap measurements showed a classical bottomward increase in sediment transport, with a high variability in total sediment flux depending on wave energy and mean current strength. Longshore sediment flux reached values up to 2.1 x 10-1 kg.s -1.m -1 during the ZY09 experiment (Table 1), which was the most energetic event during which sediment sampling took place. Lower rates of sediment transport were measured in the vicinity of wave and current meters where sediment flux nevertheless exceeded 1.6 x 10-1 kg.s -1.m -1 for a mean flow velocity of 0.5 m.s -1. The maximum onshore sediment flux was observed during the same field experiment, reaching 1.8 x 10-1 kg.s -1.m -1 (Table 1). Close to the hydrodynamic instruments, lower onshore transport values were obtained with a maximum rate of about 3.2 x 10-2 kg.s -1.m -1. Offshore-directed sediment transport was also measured, but only during one experiment (WI10), reaching a maximum of 1.1 x 10-2 kg.s -1.m -1 when a significant wave height of 0.4 m and a mean flow velocity of only 0.15 m.s -1 were recorded. Table 1. Maximum and minimum values of longshore, onshore and offshore sediment transport for each field experiment (units in kg.s -1.m -1 ). Longshore On shore Off shore Max min Max min Max Min ZY08 1.0E-05 3.2E-05 3.9E-03 2.7E-04 - - ZY09 2.1E-01* 2.7E-05 1.8E-01 9.1E-05 - - WI09 2.8E-02 4.9E-05 2.6E-03 1.9E-04 - - WI10 9.4E-04 5.8E-05 8.9E-03 3.7E-04 1.1E-02 2.8E-04 HA09 1.7E-03 1.9E-05* 9.4E-04 7.2E-05 - - HA10 8.4E-03 3.9E-04 2.4E-02 3.9E-03 - - * Bold characters represent the highest values while italics correspond to the lowest. Relationship between longshore sediment transport and hydrodynamics During each experiment, longshore sediment transport increased with both significant wave height and mean current velocity. This positive relationship appeared extremely variable, however, from a site to another. Figure 3 represents longshore sediment transport related to significant wave height for all field experiments. In spite of some scatter in the data, the trend indicates that sediment transport increases with wave height. Low sediment transport (< 1.0 x 10-4 kg.s -1.m -1 ) is mainly associated with small wave heights (< 0.3 m), but only a small increase in wave height appears to induce significantly larger sediment transport. Sediment flux generally exceeds 1.0 x 10-3 kg.s -1.m -1 when H s reaches 0.4 m, representing a ten-fold increase in

2135 sediment transport for an increase in wave height of approximately 0.2 m. However, high sediment transport values can also be associated with low wave conditions, such as during the WI09 experiment when a sediment transport rate of 2.4 x 10-2 kg.s -1.m -1 was measured with a significant wave height of 0.19 m for example (Fig. 3). The variability in sediment flux values obtained during conditions of equivalent wave heights, and the fact that similar transport rates may be associated with different wave heights, even on the same beach and during the same field experiment (e.g., WI09), suggest that waves do not represent the only factor controlling sediment transport. Figure 4 shows the relationship between longshore sediment transport and mean current velocity. Least-square regression analyses show that longshore sediment flux is better correlated with current velocity than with wave height as revealed by higher determination coefficients. Low transport rates, which are ranging from 1.0 x 10-4 to 1.0 x 10-5 kg.s -1.m -1, are always associated with low current velocity (< 0.2 m.s -1 ), whereas sediment flux is always higher than 1.0 x 10-3 kg.s -1.m -1 when velocity exceeds 0.4 m.s -1, Fig. 3. Relationship between longshore sediment transport and significant wave height (H s) for each field experiment. Fig. 4. Relationship between longshore sediment transport and mean current velocity (V m) at 0.2 m (squares) and 0.4 m (circles) above the bed.

2136 Similarly to what was observed with wave heights, high sediment transport rates can also be observed with lower current velocities. The highest current velocity recorded during sampling reached 1.29 m.s -1 and was associated with a sediment flux of 7.2 x 10-3 kg.s -1.m -1, but the maximum longshore transport rate measured near a hydrodynamic instrument peaked at 1.6 x 10-1 kg.s -1.m -1, which is almost two orders of magnitude higher, for a mean flow of only 0.5 m.s -1 (Fig. 4). The range of sediment transport rates is particularly wide for V m under 0.2 m.s -1, but with increasing current speed, the range of values is narrowed, especially above 0.4 m.s -1. This current speed may correspond to a threshold value above which the transport is dominated by the mean flow. The higher variability in sediment transport rates observed for current velocities under 0.4 m.s -1, and especially for velocities less than 0.2 m.s -1, may be explained by a greater influence at low current velocities of other processes such as wave oscillatory flows that interact with the mean flow. This variability may also reflect the lower limit of the sampling method that could barely provide accurate estimates of sediment flux under low energy conditions. Longshore sediment flux appeared to be more closely related to the product of significant wave height and current velocities (H s* V m ) than to wave height or mean current velocity alone as shown by the better correlation coefficients obtained (R² 0.4m = 0.46 and R² 0.2m = 0.58), suggesting that the observed changes in sediment transport rates are better explained by the combined action of wave and current rather than by the action of wave or currents solely acting at the bed. In addition, results of multiple linear regression analyses using H s and V m at 0.2 m and 0.4 m above the bed showed that mean current velocity accounts for approximately 60% of the variance while wave height can explain about 30%. Conversely to what was observed in other studies (Komar and Inman, 1970), our correlation analyses showed no relation between longshore transport rates and wave angle (R² = 0.20), which is probably due to the influence of tidal currents that interact with wave-induced longshore currents on these macrotidal beaches. Alongshore variability in longshore sediment transport Figure 5 shows the comparison of longshore sediment flux simultaneously measured along two shore-perpendicular profiles (P1 and P2) spaced 100 m apart. In most cases, similar sediment transport rates were measured on both transects, except during the ZY08 field experiment during which more variability was observed. The consistency in longshore sediment transport from one transect to the other can be explained by a high degree of alongshore uniformity in hydrodynamic parameters as the comparison of wave height and mean current velocity measured on both transects revealed.

2137 Fig. 5. Comparison of longshore sediment fluxes measured on two shore-perpendicular beach profiles. Although longshore sediment transport flux was generally equivalent alongshore, large differences were observed in some occasions due to local variations in beach morphology. During the WI09 experiment, for example, variations in sediment transport rates reached 2.4 x 10-2 kg.s -1.m -1 between the two transects. These large differences in longshore sediment flux were observed during ebb when a sediment trap was located in the vicinity of a migrating intertidal channel in which flow canalization associated with runnel drainage locally increased sediment transport. Comparison between longshore and cross-shore sediment transport 85 cross-shore sediment trap deployments were carried out during longshore sediment sampling, among which 76 sampled onshore sediment flux and 9 were oriented for measuring offshore-directed transport. All these measurements were used for comparing the magnitude of cross-shore sediment flux with simultaneously measured longshore sediment flux, but only 47 cross-shore transport measurements, which were realized near hydrodynamic instruments, could be compared with hydrodynamic parameters. Onshore sediment transport Figure 6 shows the comparison between longshore and onshore-directed sediment transport. Although there is a good correspondence between longshore and onshore transport, our data show that approximately 70% of onshore sediment fluxes are higher than longshore sediment fluxes. The differences in sediment transport rates are generally significant as onshore sediment flux is on average 3 to 4 times higher than longshore flux and up to 30 times higher.

2138 Fig. 6. Comparison of longshore and onshore depth-integrated flux for each field experiment. Although one would expect that onshore sediment transport would be directly related to wave action and orbital velocities, no relation was found between onshore transport rate and H s. Onshore transport rates were also poorly correlated with V t, indicating a weak relationship with cross-shore currents. A slightly higher, but still poor correlation (R 2 = 0.2), was obtained with mean longshore current velocity (V l ) measured at 0.4 m above the bed. Moreover, only 40% of mean cross-shore velocities were greater than longshore velocities during sediment sampling, while 70% of the onshore fluxes measured near hydrodynamic instruments were higher than longshore sediment fluxes. Fig. 7. Example of cross-shore and longshore velocity variations recorded by a Valeport electromagnetic current meter during a one minute interval (HA09). These apparent contradictions can be explained by the different timescales corresponding to the sediment sampling interval, to the frequency rates of acquisition of hydrodynamic data, or to the length of time during which the processes responsible for sediment transport operate. Sediment transport rates represent 10-minute timeaveraged values while wave heights and current speeds are mean (or spectral) values

2139 computed from pressure and velocity components recorded at a frequency of 2 Hz during 9 minute bursts. As can be seen on Figure 7, representing an example of crossshore and longshore velocity variations recorded during a 1-minute interval, crossshore velocities are characterized by relatively large, high-frequency, onshore-offshore velocity fluctuations resulting from wave orbital motion. In this example, maximum cross-shore velocity reaches a value of 0.76 m.s -1 whereas maximum longshore velocity is only 0.18m.s -1. When averaged over this 1-minute interval, however, both cross-shore and longshore velocities approximately equal to zero, which obscures the fact that instantaneous cross-shore velocities are extremely variable and much higher than longshore velocities. Fig. 8. Example of differences between onshore (Q on) and longshore (Q l) sediment flux as a function of significant wave height (H s) and local beach slope (tanβ), HA09 field experiment. P 1 and P 2 refer to sampling transect 1 and 2 respectively. A number of studies showed that onshore sediment transport in the surf zone is largely controlled by high-frequency cross-shore velocity variations due to wave-induced oscillatory currents and by wave breaking processes that contribute to sand resuspension (e.g., Davidson et al., 1993; Austin et al., 2009), which are all dependent of beach slope. Beach slope (tanβ) was surveyed at the sediment sampling sites during each sediment trap deployment and the dominance of onshore or longshore transport was determined by subtracting longshore sediment flux from onshore sediment flux (Q on Q l ) where Q on is the onshore sediment flux and Q l is the longshore flux. The data collected during several experiments suggest that onshore transport tends to exceed longshore transport with increasing H s and tanβ (Figure 8). These results show that shoreward-directed sediment transport increases with wave energy, but also suggest that the relatively steeper slopes associated with the stoss side of intertidal bars may cause a rapid increase in shoaling wave height, which can favour asymmetrical, onshore-directed, wave oscillatory flows and hence onshore sediment transport.

2140 Offshore sediment transport Offshore sediment fluxes were measured during only one experiment (WI10), simultaneously with longshore and onshore sediment transport, representing a total of 9 seaward-directed transport measurements. In all cases but one, cross-shore sediment flux, which could be either onshore- or offshore-directed, was higher than the longshore flux (Figure 9a). Offshore sediment transport rates were always higher than longshore transport rates, offshore sediment transport being on average approximately 7 times greater than longshore fluxes. Fig. 9. Comparison of longshore sediment flux with (a) onshore (Q on), offshore (Q off), and (b) net cross-shore (Q net) sediment flux during the WI10 experiment. However, offshore-directed transport was sometimes higher or lower than onshore transport, which is likely due to differences in orbital velocity asymmetries of shoaling and breaking waves across the intertidal zone. Non-directional net crossshore sediment flux (Q net ) was estimated as: Q net ( Q = Q on on Q off Q off 2 ) (1) The results show that even net cross-shore sediment transport was generally higher than longshore transport (Figure 9b), revealing that under the hydrodynamic conditions encountered during this field experiment significant quantities of sand were transported across the beach. Conclusion Assessing the role of controlling hydrodynamic processes on longshore and crossshore sediment transport in the breaker and surf zone of macrotidal beaches appeared to be difficult to determine due to the complex interactions between several forcing

2141 parameters. In addition, several physical constraints did not allow us to measure sediment transport with high-frequency sensors, but using streamer traps that provide time-averaged transport rates. Moreover, for safety reasons, sand trapping was not conducted during high wave energy conditions (H s > 1m). During the low to moderate energy conditions that characterized our sand trap measurements, longshore sediment transport proved to be dependent on both significant wave height and mean current velocity (Figures 3 and 4), but appeared to be mainly controlled by the mean flow, especially beyond a velocity of 0.4 m.s -1.The lack of relationship between wave angle and sediment flux shows that the wave energetic approach is not adapted for estimating sediment transport on macrotidal beaches where tidal currents can modulate the magnitude of horizontal sediment transport. Although, longshore sediment flux can be very variable across the intertidal zone, sediment transport rates showed a low variability alongshore due to a high degree of longshore hydrodynamic uniformity. Higher sediment transport rates can locally be observed, however, near drainage channels associated with intertidal bartrough beach topography. It is generally accepted that sediment transport in the southern North sea and Dover strait is strongly controlled by shore parallel tidal currents, resulting in net longshore sediment transport on the shoreface (Héquette et al., 2008) and in the intertidal zone (Sedrati and Anthony, 2007). Our results show that onshore sediment transport in the surf zone can also be higher than longshore sediment transport. Based on fluorescent tracer experiments carried out on a macrotidal beach of Belgium, Voulgaris et al. (1988) also suggested that onshore transport may be higher than longshore transport, but this was restricted to the swash-dominated upper beach. The fact that macrotidal beaches appear to be either dominated by longshore- or cross-shore sediment transport can probably be explained by the differences in spatial and temporal scales associated with various measurement techniques used in different studies. Fluorescent tracers, for example, can be used for assessing residual sediment transport across the intertidal zone during a complete tidal cycle while streamer trap measurements provide timeaveraged estimates of local sediment flux over a time interval of only a few minutes. Although long-term residual sediment transport may be longshore-dominated on the macrotidal beaches of northern France, our results showing that important shoreperpendicular sediment transfer takes place across the beach at short timescales, suggesting that cross-shore transport may have been sometimes overlooked in these coastal environments. At near instantaneous timescale, cross-shore sediment transport associated with wave-induced oscillatory currents probably represents a major factor controlling the cross-shore migration of intertidal bars.

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