Aeolian sediment transport on a beach with a varying sediment supply

Aeolian Research 15 (2014) 235–244

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Aeolian sediment transport on a beach with a varying sediment supply S. de Vries a,⇑, S.M. Arens b, M.A. de Schipper a, R. Ranasinghe c,d,e a

Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands Arens Bureau voor Strand-en Duinonderzoek, Iwan Kantemanplein 30, 1060 RM Amsterdam, The Netherlands c Department of Water Engineering, UNESCO-IHE, PO Box 3015, 2601 DA Delft, The Netherlands d Harbour, Coastal and Offshore Engineering, Deltares, Delft, The Netherlands e Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia b

a r t i c l e

i n f o

Article history: Received 26 February 2014 Revised 4 August 2014 Accepted 4 August 2014 Available online 24 August 2014 Keywords: Aeolian transport Supply limited Beach Field measurements Fetch

a b s t r a c t Variability in aeolian sediment transport rates have traditionally been explain by variability in wind speed. Although it is recognised in literature that limitations in sediment supply can influence sediment transport significantly, most models that predict aeolian sediment transport attribute a dominant role to the magnitude of the wind speed. In this paper it is proposed that spatio-temporal variability of aeolian sediment transport on beaches can be dominated by variations in sediment supply rather than variations in wind speed. A new dataset containing wind speed, direction and sediment transport is collected during a 3 day field campaign at Vlugtenburg beach, The Netherlands. During the measurement campaign, aeolian sediment transport varied in time with the tide while wind speed remained constant. During low tide, measured transport was significantly larger than during high tide. Measured spatial gradients in sediment transport at the lower and upper beaches during fairly constant wind conditions suggest that aeolian sediment transport on beaches may be partly governed by the spatial variability in sediment supply, with relatively large supply in the intertidal zone when exposed and small supply on the upper beach due to sorting processes. The measurements support earlier findings that the intertidal zone can be significant source of sediment for sediment transport on beaches. Both a traditional cubic model (with respect to the wind speed) and a newly proposed linear model are fitted to the field data. The fit quality of both types of models are found to be similar. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction This paper aims to interpret aeolian sediment transport on beaches under supply limited conditions using field measurements. These interpretations can be of particular interest when predicting aeolian sediment transport on beaches or in other supply limited environments. Two general prerequisites for aeolian sediment transport are (1) the driving force of the wind and (2) the availability of sediment. The availability of sand or sediment supply is the amount of sediment that can be eroded by wind. Supply limited conditions arise when the wind driven transport capacity can not be reached due to the lack of sediment supply. Aeolian sediment transport on beaches is often stated to be supply limited (Nickling and Davidson-Arnott, 1990; Houser, 2009). Sediment supply on beaches can be governed by various phenomena such as surface moisture content (Davidson-Arnott ⇑ Corresponding author. Tel.: +31 152789220. E-mail addresses: [email protected] (S. de Vries), M.A.deSchipper@tudelft. nl (M.A. de Schipper). http://dx.doi.org/10.1016/j.aeolia.2014.08.001 1875-9637/Ó 2014 Elsevier B.V. All rights reserved.

et al., 2005), beach slope (Hardisty et al., 1988; de Vries et al., 2012), fetch length (Bauer and Davidson-Arnott, 2002), the presence of vegetation (Arens, 1996) and the presence of lag deposits armoring the sand surface layer (van der Wal, 1998). Some of these supply variables (e.g. moisture content) can vary on short timescales in the order minutes to hours. The fetch effect is an increase of the aeolian sediment transport rate with distance in the direction of the wind over an erodible surface (see for an overview Delgado-Fernandez (2010) and references therein). The fetch effect is often described as a supply limiting parameter due to a combination of wind direction and beach geometry. In some cases, the beach geometry can vary on short timescales due to tidal influences. The critical fetch distance (F c ) is the fetch distance (F) required for the sediment transport (q) to reach a certain maximum transport (qm ). This maximum transport represents a transport potential and is often determined assuming an equilibrium relation with the wind speed. The maximum transport is in these cases defined to be equal to the wind driven transport capacity. Fig. 1 gives a conceptual representation of the fetch effect after Bauer and Davidson-Arnott (2002).

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Linear parameterization of the Fetch effect

q(F)/qm

1

0.5

0

0

0.5

1

1.5 F/Fc

2

2.5

3

Fig. 1. Conceptual representation of the fetch effect, where transport increases with increasing fetch towards a certain limit. Reference is made to Bauer and DavidsonArnott (2002) who suggests comparable curves, on a conceptual level, including a smoother transition between the increasing and stable transport.

Various reports are available on the effect of fetch where the estimated critical fetch distances vary from 0 to 200 m (DelgadoFernandez, 2010; Lynch et al., 2008; Jackson and Cooper, 1999). Delgado-Fernandez (2011) state that critical fetch lengths could vary due to varying moisture content. This is in line with an earlier finding of Davidson-Arnott et al. (2008) which suggests that moisture content can influence fetch length but the maximum transport rate might also be influenced. At this point a distinction between maximum transport and wind driven transport capacity might be appropriate. Surface moisture content can influence the sediment entrainment and hence the maximum transport. Since the wind driven transport capacity is based on an equilibrium with wind speed, the surface moisture content (which is a supply limiter) does not influence the wind driven transport capacity. To what extent the maximum transport rate is related to wind driven transport capacity in supply limited conditions remains unclear. This complicates the applicability of the fetch model to predict aeolian sediment transport rates at an arbitrary beach. An alternative interpretation of fetch and aeolian sediment transport in supply limited conditions is provided by de Vries et al. (2014). They argue that, in supply limited conditions, both critical fetch length and maximum transport can be a function of supply rather than wind driven sediment transport capacity. Using this approach for predicting aeolian sediment transport relies heavily on the quantification of sediment supply rather than defining a critical fetch distance and a maximum transport rate. At the same time they consider sediment supply in a holistic way without differentiating between individual supply limiting factors. Ample evidence of aeolian sediment transport rates at a beach varying due to supply limiting effects can be found in field measurements presented by, among others, Davidson-Arnott et al. (2005), Bauer et al. (2009), Davidson-Arnott and Bauer (2009). On longer timescales the effects of limited sediment supply is reflected by the general over prediction of sediment transport by sediment transport formulations that do not account for supply limited conditions. (see for instance Sarre, 1988; Sherman et al., 1998; Kroon and Hoekstra, 1990; Sherman et al., 2013) In conditions where sediment supply is abundant (e.g. desert situations), rates of aeolian sediment transport can be estimated using the well established theory by Bagnold (1954). The theory by Bagnold (1954) relates a higher (often cubic) power of the wind speed to equilibrium sediment transport rates. For situations where supply is limited, such limitations are often accounted for in a pragmatic way by adding empirical parameters to Bagnold (1954) type formulations when fitting field data (e.g. Kroon and Hoekstra, 1990; Arens, 1996; Delgado-Fernandez, 2011). Generic models for these empirical parameters are unavailable and consequently the use of such formulations is highly site specific. Therefore, at present, the generic quantitative prediction capability of aeolian sediment transport rates on beaches is very limited (Sherman and Li, 2012; Bauer et al., 1996).

de Vries et al. (2014) consider sediment supply to be independent of wind conditions. In their model they propose to set a discrete limit to sediment supply as an alternative to correcting Bagnold (1954) type sediment transport formulations for supply limiting effects. In this approach, maximum transport and transport potential are unrelated in supply limited situations and can therefore be of different magnitude (where maximum transport is always smaller or equal to the transport capacity). While wind driven sediment transport capacity (qm ) used in fetch theories is not per se a function of supply, the application of the critical fetch approach seems ambiguous when predicting sediment transport under supply limited situations. Furthermore, de Vries et al. (2014) suggest that aeolian sediment transport on beaches could be linearly related to wind speed. This linear relation is based on the principle that sediment transport is a product of wind velocity and an average sediment concentration (in the air). It is argued that this average sediment concentration could be determined to a great extent by the available supply rather than the wind speed. At this stage the formulated linear model does not have predictive skill however, de Vries et al. (2014) have shown that for a synthetic case the linear fit could possibly be used to derive information on the magnitude of the sediment supply. The linear model could therefore provide a tool to assess the variability in supply magnitude during field experiments where sediment transport rates and wind velocities are measured. This study was driven by the desire to be able to interpret and predict aeolian sediment transport on beaches. A dedicated field experiment along the Dutch coast is undertaken with the specific aim of gaining insights into spatio-temporal variability of sediment supply on beaches. It is hypothesized that sediment supply governs aeolian sediment transport rates on the beach and that the linear model proposed by de Vries et al. (2014) can be used to describe supply limited aeolian sediment transport.

2. Field site and experimental design Field measurements were conducted from 6 to 10 December 2010 at Vlugtenburg beach located on the south west of the Holland coast (see Fig. 2). At the time of the measurements, beach slopes were are roughly between 1:40 and 1:50 and the mean grain size (D50 ) was in the order of 200–300 lm. The beach can generally be categorized as a dissipative beach according to the geographical framework presented by Short and Hesp (1982). The beach shape is partly the result of a major nourishment which was implemented (in 2008) two years before the measurements (de Schipper et al., 2012). The nourishment has resulted in an artificial beach, dune and foreshore. After the nourishment the coastal profile has been shaped by marine and aeolian forces. The nourished sand contains a relatively large amount of shell fragments. Due to sorting processes over time, the shell fragments form lag deposits at the upper beach. In the intertidal zone, the lag deposits are reworked. van der Wal (1998) reports on similar spatial distributions of lag deposits (consisting of shell fragments) at different nourishment sites along the Dutch coast. Figs. 3 and 4 illustrate the local morphology and surface characteristics at the measurement site. Generally, mean wave heights and periods along the Dutch coast are 1.2 m and 5 s respectively and alongshore differences in wave climate are small (Wijnberg and Terwindt, 1995). The tide is semi diurnal with a neap-, spring-tidal range of respectively 1.2–2.2 m. The horizontal cross shore excursion of the waterline due to the tide is around 80–100 m. As a result, the tide creates a significant temporal variability of beach width and therefore wind fetch during onshore and oblique onshore winds. Measurements of

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Fig. 2. The measurement location at Vlugtenburg beach in the Netherlands. The beach south west oriented and is located between Hoek van Holland and Scheveningen.

Fig. 3. Aerial photo of the measurement area taken 4 months before the field campaign. The intertidal zone the upper beach and the dune area visible. The ‘new’ artificial foredune (or sand dike) is indicated by the gray rectangle and is partly planted with vegetation. The older dunes are located landward from the ‘new’ dune where a valley lies in between. The location of the measurement array (indicated by the red box) is restricted to the intertidal area and the upper beach. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

water levels are available from a nearby tide gauge inside the harbour at Hoek van Holland. The wind climate is dominated by west to south west winds. The coastline is oriented south west to north east, 40° with respect to north (where the shore normal direction is 310° with respect to north). The dominant west to south west winds are thus oblique onshore. The intertidal zone generally has a concave morphology where the seaward side has a relatively mild slope which steepens toward the upper beach at the landward side (see Fig. 5). Intertidal morphology at the study site is characterized by dynamic intertidal bar systems and local topography changes are relatively large due to wave and tide forcing. The surface in the intertidal zone is relatively smooth containing no micro scale bed forms with the exception of runnels (intertidal troughs) in which sometimes bed ripples occur as a result of currents during high waters. Temporal changes of the bed level at the upper beach are relatively small when compared to the intertidal area (de Vries et al., 2011). The upper beach is characterized by a constant sloping surface from the waterline towards the dunes. At the measurement site, both the beach and the dunes are artificially constructed.

Fig. 4. Photo of the beach during the measurements taken facing the beach (with wind from the back). In the near view the relatively smooth surface of the intertidal zone is shown. At the upper beach, lag deposits (mainly shell fragments) at the surface and saltation are visible.

Fig. 5. Cross shore profile with the locations of the saltiphones (top view shown in Fig. 6). A fixed saltiphone and the wind station are situated at location C. The horizontal gray lines indicate the measured high water level and low water level at the tide station in Hoek van Holland (spring tide was just before the measurements on the 7th of December). The dashed black line indicates the vertical reference level (NAP) which is around mean sea level.

Generally, at Dutch beaches the dune foot is located around the +3 m NAP (where NAP is located around mean sea level). This level is empirically determined and corresponds to the break in slope between the beach and dune (Ruessink and Jeuken, 2002). At this artificial beach no clear break in slope and dune foot is present and since sediment transport on the beach is of interest we have chosen to introduce an artificial landward boundary of our

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Fig. 6. Left panel shows a schematized top view of the measurement locations. The x-axis is east–west and y-axis is north–south oriented. The circles indicate saltiphone locations. Filled circle indicates the co-location position of the wind station. The dashed line indicates the orientation of the waterline (approximated at the 0 m NAP contour) and the dashed dotted line indicates the landward reference (at 5 m NAP). The black solid line indicates the shore normal profile shown in Fig. 5. Right panel summarizes the measured wind conditions (in m/s) during the 4 days of the experiment. The dotted circles indicate the percentages of occurence. The black solid line indicates the shore normal direction.

measurement domain at the +5 m contour. Apart from the shell layer, micro scale bed forms are present on the upper beach. The micro-scale bed forms are significant and mainly anthropogenic, created by footsteps and tire tracks. A number of 4 saltiphones were used during the experiment. A saltiphone detects sediment transport by a microphone attached to a stainless steel tube (Spaan and van den Abeele, 1991). Particle counters allow for a prediction of sediment transport. The center of the saltiphones’ sensors was located 10 cm above the sand surface at all times. Locating the sensor closer to the bed would lead to more frequent saturation of the impact sensor due to more transport closer to the bed. Locating the sensor higher will exclude periods of modest saltation when the saltation layer is relatively small. To measure transport gradients in cross shore direction, the saltiphones were placed on the beach in a cross shore oriented array during part of the campaign. The saltiphones’ locations are indicated as locations A–D in Fig. 5 and the left panel of Fig. 6. During part of the experiment the saltiphones were located in and near the intertidal zone. Wind speed and direction were measured using a cup anemometer (Vector Instruments A100R) and wind vane (Vector Instruments W200P) at location C at 2 m height above the sand bed. The right panel of Fig. 6 shows the measured wind conditions at location C indicating the dominant cross shore wind direction. The saltiphones, wind vane and cup anemometers were wired to a Delta-T DL2e data logger which provided power for all instruments. The saltiphones were set to record cumulative counts per second. To synchronize instruments and to reduce the size of the data stream, the data of the saltiphones and the wind station were stored every 5th second only. Wind conditions are instantaneous values of speed and direction. One saltiphone is fixed at position C on the upper beach during the entire measurement campaign. Fig. 7 shows an overview of the measured data at location C. Additional to the measurements at point C, two separate Runs were done where the 3 remaining saltiphones were used at different locations (see Table 1 for details). Run I is for comparison purposes to ensure that all saltiphones give similar values when placed in a cluster (results are discussed in Appendix A). Run II is used to gain insight into spatio-temporal gradients in aeolian sediment transport over the beach. Saltiphones are impact sensors with an estimated sampling interval of 1 ms (Sterk et al., 1998). Therefore the maximum measurement capacity is around 1000 counts per second. Using Fig. 7 it can be estimated that this measurement capacity is in practice around 1200 counts per second. If measurements approach this measurement capacity, the validity of the measurements cannot be guaranteed since under-counting of impacts increases with increasing impacts (Yurk et al., 2013). To test this for our data,

Fig. 7. Collected data during the experiment at location C. The top panel shows the raw data of the wind velocity. The middle panel shows the data for the wind direction where the dashed line indicates the shore-normal direction. The bottom panel shows the saltiphone counts. The gray areas identify separate runs during which the location of the remaining saltiphones is varied.

the number of times that counts exceeded 1000 for each saltiphone was quantified. It is found that saltiphone counts exceeded 1000 counts in less than 5% of the individual samples where non-zero transport was measured. At this stage we cannot exclude the possibility that our data is influenced by the under-counting of impacts but, since the found percentage is rather small, we assume that all sensors are equally influenced to a limited extent and that total saltiphone counts can be used as a proxy for aeolian sediment transport rates. Additionally, a conservative approach is adopted when interpreting the results. 3. Results and discussion 3.1. Temporal variability of time averaged parameters Fig. 8 shows 30 min averaged time series of measured wind speed and saltiphone counts at location C during the full length of the experiment. After 4:00h on December 9th, the wind

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Table 1 Details of subsets where multiple saltiphones are analysed. During Run I the saltiphones are located in a cluster confined to 2 m2. During Run II the saltiphone locations vary in space. Meas.

Time interval at 9 December 2012

Remarks

Run I Run II

00.00–9.30 [CET] 10.00–15.20 [CET]

Saltiphones placed close to each other in a cluster at location C. Saltiphones placed in an array (locations A–D) covering the intertidal zone and beach. Tide is mid-tide and falling tide

5 0 12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00

Total counts

5

Tide elevation [m]

3.2. Spatial gradients in time averaged transports

2

x 10

1 0 12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00

2 0 −2 12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 Time

Fig. 8. Measured data aggregated over 30 min intervals at location C. The top panel shows average wind conditions. Middle panel shows total counts. Bottom panel shows vertical tide from a nearby tide station (at Hoek van Holland) with respect to NAP which is about mean sea level.

velocities and directions (see Fig. 7) are measured to be fairly stable (around 10 m/s and 310°) until the end of the measurement period. Although these wind conditions are fairly stable in this period, large variations in transport rates are observed (see the middle panel of Fig. 8). The variability in time of the total counts indicate a periodic signal where auto-correlation indicates a periodicity of 12.5 h. This periodicity coincides with the tidal period. Correlating the total counts per 30 min interval with the measured water level at Hoek van Holland (averaged over 30 min), a significant (95% confidence) negative correlation is found (R ¼ 0:68). This indicates that the variance in water level explains 46% (¼ R2  100) of the measured variance in total counts. The measurements show that approximately 90% of the total transport (at location C) occurred during the low tide (when water level was below 0 m NAP). The tidal variation induces a temporal variation of the beach width due to the wetting and drying of the intertidal zone. High tides correspond to a submerged intertidal zone and low aeolian transport whereas low tides correspond to an intertidal zone which is exposed to aeolian forcing and large aeolian sediment transport. During the observations, the intertidal zone may have been a dominant sediment source for aeolian transport on the beach. Many authors stress the importance of moisture content as a supply limiting parameter. Although not measured, the moisture content in the intertidal zone will vary due to the tide. The drying of the intertidal zone can be expected to influence the supply of sediment from the intertidal zone. Fig. 8 shows that during the low tide at mid day, sediment transports are higher than during the low tides during the night. Solar radiation and higher temperatures during the day may accommodate relatively fast drying of the beach during the day with respect to the night leading to a larger sediment supply from the intertidal zone during the day than during the night.

Spatial gradients in time averaged transports were derived using Run II (see Fig. 7) of the data-set. This run contains data from saltiphones placed in a cross shore array. The cross shore array is partially located in the intertidal zone and consists of 4 saltiphones (see Fig. 5). In accordance with the previous section, 30 min data intervals are used to derive transport parameters at each location. Fig. 9 shows the measured total counts for the 11 intervals of 30 min in Run II. During all 30 min intervals considered, no transport is measured at location A. Location A is the most seaward location which is located inside the intertidal zone. When considering locations A– C there is a clear positive gradient present in the direction of the wind for all the 30 min intervals. The increase ceases after a certain distance in the direction of the wind (locations C–D) where in some cases also a modest decrease in total saltiphone counts is shown. An increase in the direction of the wind is expected according to fetch and supply theories. The more or less stable sediment transport at the upper beach could be explained due to a possible lack of sediment supply at the upper beach. The measured decrease in sediment transport is difficult to explain. A decrease in sediment transport in downwind direction has been reported earlier by Bauer et al. (2009) who attribute this to the development of an internal boundary layer reducing the winds transport capacity near the bed. They implicitly assume that at the upper beach the wind driven transport capacity is satisfied. From Figs. 8 and 9 it is however clear that while winds are relatively stable, the sediment transport at the upper beach varies. The temporal variation of the sediment transport is possibly a result of varying upwind supply. This makes it unlikely that sediment transport capacity is reached and effects of an internal boundary layer are measured. While the measured decrease is modest, it could also be the result of difference in sensor accuracies described in Appendix A. 4. Relationship between wind speed and sediment transport rates The relationship between wind speed and sediment transport rates (saltiphone counts) is evaluated by fitting both conventional 3rd power models and alternative linear models to the collected data. It could be assumed that the fitting coefficients of the cubic 4

Total counts [counts/ 30 minutes]

u [m/s]

08−10 Dec 2010 10

15

x 10

10:00:00 − 10:30:00 10:30:00 − 11:00:00 11:00:00 − 11:30:00 11:30:00 − 12:00:00 12:00:00 − 12:30:00 12:30:00 − 13:00:00 13:00:00 − 13:30:00 13:30:00 − 14:00:00 14:00:00 − 14:30:00 14:30:00 − 15:00:00 15:00:00 − 15:30:00

10 5 0

90(A) 70(B) 50(C) 20(D) 0 Cross shore distance [m] (Saltiphone)

Fig. 9. Measurements of total counts for 11, 30 min intervals at 4 saltiphone locations during Run II. Colors and lines indicate corresponding time intervals. For interpretation of the saltiphone locations see Fig. 5. Winds are from left to right in the figure.

S. de Vries et al. / Aeolian Research 15 (2014) 235–244

In line with the work of Bagnold (1954), a 3rd power function between wind speed and sediment transport rates corrected with a threshold velocity is fitted. A generic form of such a 3rd power function is given by:

( Q s ðtÞ ¼

Acub  ðuðtÞ  ut cub Þ3

if u > utcub

0

if u < utcub

ð1Þ

where Q s [counts/(s m2)] is the measured sediment transport rate by the saltiphone. Acub [counts s2/m5] is an empirical constant representing environmental properties including grain size, density and supply. The utcub [m/s] is the threshold velocity which can also be governed by surface properties. Since time series of wind speed uðtÞ and sediment transport rates Q s ðtÞ are measured, the unknown constants Acub and ut cub can be derived using curve fitting procedures for the specific time intervals. It should be noted that the derived constants will be partly influenced by the height of the sensor (10 cm above the bed). Therefore, we discuss here the spatio-temporal changes in these derived constants rather than the absolute values. Additionally, a linear model such as proposed by de Vries et al. (2014) is fitted. Their linear model presents a description of aeolian sediment transport rates assuming that the sediment transport concentration is constant (within a certain period) and is governed by sediment supply. While wind speed is assumed proportional to sediment speed (us ðtÞ [m/s]) which is fluctuating on a timescale shorter than the average sediment concentration (C c [counts/ m3]). Sediment transport rates can be represented using:

Q s ðtÞ ¼ C c  us ðtÞ

ð2Þ

The sediment speed can theoretically be as large as the wind speed and is zero when wind speed is below threshold wind speed. Moreover, the sediment speed is also a function with respect to the height above the bed (Kok et al., 2012). Given this complexity the pragmatic approach of de Vries et al. (2014) is adopted which implicitly assume that the sediment velocity is proportional to the excess wind velocity beyond the threshold wind velocity:

 Q s ðtÞ ¼

Alin  ðuðtÞ  utlin Þ if u > ut lin 0

if u < ut lin

09−Dec−2010 09:30 − 10:00 1500 counts

4.1. Temporal differences when fitting linear and cubic models

procedure for fitting the relations discussed above for an arbitrary 30 min interval. For each wind speed bin, a binned average is calculated (see the middle panel of Fig. 10). Both the cubic (Eq. (1)) and the linear models (Eq. (3)) are fitted to the binned averaged transports using a curve fitting procedure. The curve fitting procedure optimizes the fit quality calculated by R2 . The measured wind speeds in each 30 min interval which deviate twice the standard deviation from the mean measured wind speed are discarded to minimize the possible influence of outliers on the fitting procedure. Results contain the value of the threshold velocities (ut lin and ut cub which are restricted to be larger than 0) and the empirical constants (Alin and Acub ) for both fits. Moreover, the fit quality (R2 ) is derived for both fits. Fig. 10 shows the linear and cubic fit indicating similar R2 -values for a particular 30 min time window. Applying the above for the full data-set (at location C), fitting parameters for every 30 min window are obtained. Fig. 11 shows the threshold velocity (ut), R2 and the (empirical) fitting constant (A) for the linear and cubic fit for all 70 measured 30 min intervals. The correlation coefficient is similar for both fitting methods with an average R2lin of 0.76 and an average R2cub of 0.72 (where infinite or negative values of R2 , are discarded). The derived threshold velocities using the linear fit show a relatively constant distribution with a mean threshold velocity of 8.8 m/s (standard deviation 1.5 m/s). For the cubic fit the average of the derived threshold velocities is 6.31 m/s (standard deviation 2.6 m/s). Overall, the derived threshold velocities using the cubic fit are smaller and fluctuate more with respect to the linear fit. Given our sensor was placed at 10 cm height from the bed, the derived threshold velocities using cubic fitting seem remarkably low. The derived threshold velocities using the cubic fitting seem small when comparing with earlier derived threshold velocities by Bagnold (1954) who finds a threshold velocity around 2.5 m/s

1000 500 0

6

8

10

12

14

12

14

12

14

1200 Binned data Linear Fit (R2 = 0.89)

1000 Avg counts [−]

and linear models represent the variability of the environmental parameters. In the previous section it is shown that environmental variables such as the measurement location and the time varying water level cause aeolian sediment transports to vary. When transport varies, fitting coefficients of the models will also vary. Following the wind tunnel results presented by Sterk et al. (1998) we assume for the moment that the total saltiphone count is linearly related to the total transport and the measured counts/s are proportional to sediment transport [kg/s]. This assumption might be compromised for field environments (with fluctuating winds) due to (amongst others) changes in the vertical concentration profile due to wind fluctuations. In the future, additional measurements or detailed modelling might shed more light on the degree of validity of this assumption for field situations.

Cubic Fit (R2 = 0.88) 800 600 400 200 0 6

8

6

8

10

20

ð3Þ

where Alin [counts/m3] is an empirical constant and utlin [m/s] is the threshold velocity. For the purpose of fitting, the full data-set is subdivided in 30 min intervals identical to the intervals of the derived aggregated parameters in Fig. 8. The 30 min intervals are selected since during this time the environmental conditions (such as fetch and moisture) will not vary significantly. For every time interval of 30 min, the measured sediment transports are binned with respect to wind speed. Wind speed bins are based on the discretization interval of the wind sensor (0.25 m/s). Fig. 10 illustrates the

Occurence [%]

240

10 0

10 Wind speed [m/s]

Fig. 10. Top panel shows the raw data of the measured counts for the saltiphone at location C. Middle panel shows mean counts for binned wind speeds together with their best linear and cubic fit. The bottom panel shows the wind speed mass distribution where the vertical line represents the mean. The dotted lines indicate the wind speed that corresponds to a deviation of two times the standard deviation with respect to the mean wind speed. The gray datapoints in the top and middle panel indicate data outside the range which is used for fitting.

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1200

Rlin & Rcub [−]

1

2

Data Loc. C (50 m) Data Loc. B (70 m) Linear Fit Loc. B (R2 = 0.65)

utcub & utlin [m/s]

15 10

Cubic Fit Loc. B (R2 = 0.64)

600

400

5 200 0 12:00 18:00 00:00 06:00 12:00 18:00 00:00

06:00 0

6

1500

7

8

9 10 Wind speed [m/s]

11

12

13

2

2

5

Cubic Fit Loc. C (R2 = 0.87)

800 06:00

Avg counts [−]

2

cubic linear 0 12:00 18:00 00:00 06:00 12:00 18:00 00:00

Acub [10 counts s /m ] 3 Alin [counts/m ]

Linear Fit Loc. C (R2 = 0.83)

1000

0.5

Fig. 12. Velocity binned data of average counts including linear fits for two locations measured simultaneously from 12.00 to 12.30 at 9 December 2010.

1000 500 0 12:00 18:00 00:00 06:00 12:00 18:00 00:00

06:00

Fig. 11. Overview of fitting data for every 30 min interval. Top panel shows linear correlation coefficients for both linear and cubic fits. Middle panel shows the derived threshold velocities. Bottom panel shows the fitting constants. Gray stars represent the cubic fit where black dots represent the linear fit. Table 2 The correlation coefficient R using linear correlations between parameters and the measured total counts during 30 min intervals. Significant correlation at pffiffiffi R > 2= n ð¼ 0:28Þ. Where n is the sample size of the time series.

This indicates a lack of dependence between average wind and total transport. The lack of dependence may be explained by the dominant effects on sediment transport due to supply limitations over effects due to fluctuating winds. Table 2 also shows that the time series of both fitting parameters of the cubic fit (Acub and ut cub ) show significant correlation with the time series of the total counts. With respect to the fitted parameters of the linear fit it is found that the empirical constant (Alin ) does not correlate significantly with the measured total counts. This implies that the empirical parameter derived using the linear model does not represent the variability in sediment transport rates. The derived threshold velocity (ut lin ) is significantly correlated with total counts. Fitting both relations (linear and cubic), the time series of the derived threshold velocities (ut lin and ut cub ) correlate with the time series of total counts. This indicates that in both cases variability in threshold velocity explains some variability in total counts during this particular experiment. During previous experiments presented by Arens (1996), significant variability in fitted threshold velocities (using a cubic fit) was also found. These varying threshold velocities found by Arens (1996) were attributed to varying environmental conditions including varying surface moisture content due to precipitation. 4.2. Spatial differences while fitting the linear and cubic model

for sand of 250 lm in a wind tunnel and 4 m/s for desert sand of 320 lm in the field. Davidson-Arnott and Bauer (2009) and Arens (1996) found threshold velocities in the field which are generally significantly larger than 5 m/s. After fitting the linear and cubic models, the relation between the averaged sediment transports and the derived model parameters can be tested. Table 2 shows the linear correlations between the derived parameters. Gray cells indicate significant linear correlation (at 95% confidence). A significant negative correlation is found between total transport and water level. This dependence is also illustrated in Fig. 8. No significant correlation is found between total transport and the average wind velocity.

Fig. 12 shows the binned distribution of measured wind speeds and averaged measured transports [counts/s] at locations B & C for an arbitrary interval. Although the measurements were obtained simultaneously, the fitting coefficients differ. Fig. 13 shows the fitting coefficients for Run II using the linear and third power fit for locations B, C and D. Both Alin and Acub are generally smaller at location B compared to locations C and D. Also ut cub and ut lin vary where the threshold velocities using the linear model show limited spatial variations compared to the threshold velocities using the cubic model. 5. Discussion 5.1. Aeolian sediment transport and the role of sediment supply The measured cross shore gradients in transport rates, shown in Fig. 9, are mostly on the lower beach and in the intertidal zone during low tide. Since a spatial transport gradient indicates an area

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of sediment entrainment, this (lower beach) area is a sediment source for aeolian transport. At the upper beach, the spatial gradients are less pronounced if not non-existent. This indicates that there is limited sediment entrainment on the upper beach. If no sediment is picked up at any part of the spatial domain, this could mean one of two things: (a) there is no supply in the corresponding spatial domain, or (b) the wind driven transport capacity has been reached. While there is limited sediment entrainment at the upper beach, the measured transport at the upper beach varies with time (see Fig. 9 locations C–D). Since wind conditions were fairly constant (see Figs. 7 and 8), this variation in sediment transport can hardly be explained by variation in wind conditions (and wind driven transport capacity). Therefore it seems unlikely that the wind driven transport capacity is satisfied during the presented measurements. It is even quite possible that the sediment transport capacity is of higher order than the measured transports and is not reached at any time during the measurements. In that case, the measurements would likely show only the variations in sediment transport rates which are governed by variations in sediment supply. The sediment entrainment at the lower beach and the limited sediment entrainment at the upper beach could be explained by a spatial varying supply. Supply might be relatively large in the intertidal area and small at the upper beach due to the presence of lag deposits at the upper beach. This would imply that during the measurements, the transport at the upper beach is governed by variability in upwind sediment supply rather than local wind driven transport capacity. This upwind supply is governed by the area in and around the intertidal area. Based on these measurements it can be hypothesized that, during the measurements, a large part of the aeolian sediment transport over the beach originates from the intertidal area. On the upper beach supply could be limited by the presence of lag deposits. The presence of these lag deposits could result from

sediment sorting at the bed surface by aeolian processes. In the intertidal area, no lag deposits are present due to the additional dynamics induced by marine processes continuously reworking the upper layer of the bed (Carter, 1976). As a result, the amount of sediment available at the bed for aeolian transport (sediment supply) is likely to vary spatially where a zone of supply is present near the intertidal zone and a zone of reduced supply at the upper beach. These measurements support the concept of spatially varying supply as a function of the tide. Such a concept has also been suggested by van der Wal (1998), stating that at low tide and during onshore winds, transport initiated at the intertidal zone could function as an important sediment source for sediment transport towards the dunes. A similar concept is also explored numerically by de Vries et al. (2014) using a spatial domain consisting of an explicit supply and no-supply zone. The spatial variability in sediment supply and aeolian transport in the intertidal zone could be governed by a variable moisture content of the sand surface, intertidal morphology (ridge and runnel systems, Anthony et al. (2009) in combination with salt crust formation. The range of these complex variables makes it at this stage difficult to quantify and predict the sediment supply at an arbitrary beach. Collecting more data or re-analysis existing data could possibly assist in gaining more insight in the complexities of spatial varying sediment supply on beaches. 5.2. The fetch effect or supply limitations Our measurements show an increase in transport in downwind direction until a certain maximum is reached in qualitative accordance with fetch theories. The observations show a maximum transport rate on the upper beach which seems to be governed by the relatively small sediment supply at the upper beach (due to lag deposits) in combination with a time varying sediment supply (due to the effects of the tide) in the upwind area. The ‘fetch effect’ measured in this case is likely to be driven by supply only. The explicit influence of supply on fetch effects complicates the prediction of aeolian sediment transport rates using traditional fetch theories. The current critical fetch models describe the effects of fetch and the realization of a wind driven transport capacity over the critical fetch distance. The critical fetch distance can be a function of supply and the maximum sediment transport could also be a function of supply. The current fetch theory can possibly benefit to account explicitly for a maximum sediment transport and critical fetch due to spatially and temporally varying supply. Data which contains spatial gradients in sediment transport measured on the beach might provide important information on spatial and temporal distribution of sediment supply in addition to information on fetch effects. 5.3. Transport capacity vs supply limitations Many transport formulations consider wind velocity as a measure of the amount of aeolian sediment transport. Given a certain wind velocity, the corresponding aeolian transport capacity can be calculated. However, this transport capacity cannot be reached if there is insufficient supply. This has major implications for current aeolian sediment transport formulations. Traditionally, supply limitations are being accounted for by modifying the empirical constants in the cubic ‘Bagnold type’ formulations (see for instance Sherman and Li, 2012). In this approach it is implicitly assumed that the variability in transport due to variability in wind conditions is dominant over that due to variability in supply. As indicated by the data herein, the variability of supply can indeed have a more dominant influence over the variability due to wind and therefore, the physics underlying ‘Bagnold type’ formulations are likely not representative for supply limited situations.

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Fig. 14. The left panel shows a schematized top view of the measurement locations. The x-axis is east–west and y-axis is north–south oriented. The square indicates saltiphones’ locations. The dashed line indicates the orientation of the waterline (approximated at the 0 m NAP contour) and the landward reference (at 5 m NAP). The black solid line indicates the shore normal profile shown in Fig. 5. Right panel summarizes the measured wind conditions (in m/s) during Run I. The dotted circles indicate the percentages of occurence.

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Exploring alternative transport formulations, such as the linear model presented by de Vries et al. (2014) could be useful for supply limited situations that commonly occur on beaches. While literature recognises the existence of various factors that limit sediment supply to aeolian transport on beaches, there is very limited knowledge on the quantification of sediment supply in beach situations. Additional knowledge on the quantification of the supply is of major interest when assessing the relevant importance between wind driven transport capacity and supply limiting effects on aeolian sediment transport on beaches. As a first step, a comprehensive collation of field data from previous studies may be used to evaluate the performance of linear and cubic models combined with applications of models by Delgado-Fernandez (2011) and de Vries et al. (2014).

6. Conclusions Results of a 3 day field campaign where sediment transport rates and wind speeds were measured at Vlugtenburg beach, The Netherlands are presented and analysed. The analysis shows that:  We have collected measurements where the effect of water level fluctuations due to the tide are clearly present in the temporal variability of the measured aeolian sediment transport. While wind conditions were fairly constant, 90% of the measured transport occurs during low tide during the measurements. Transport activity at the upper beach was relatively small when the intertidal area is inundated. Therefore, the water level and the intertidal zone governed the aeolian

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sediment transport on the beach to a large extent and the intertidal area played a governing role with respect to sediment supply and aeolian transport on the beach.  A significant gradient in sediment transport over the beach exists during onshore winds. Sediment transport increases in the direction of the wind until a certain distance. A strong increase of sediment transport is found at the lower beach during low tide. The increase in transport in downwind direction is attributed to an increase in upwind sediment supply. At the upper beach there is no significant increase of sediment transport. This can be explained by the presence of lag deposits on the upper beach. These lag deposits limit sediment supply at the upper beach and create a spatially varying sediment supply. The sediment transport on the beach is governed by this spatially varying supply rather than wind speed.  It is shown that supply limitations can have a dominant effect on aeolian sediment transport rates over effects due to fluctuating wind speed. Therefore, existing sediment transport formulations where sediment transport rates are taken to be proportional to a higher power of the wind speed are likely to be invalid in supply limited situations. Alternatively, a linear (supply limited) model is explored. Fitting linear relationships between wind and sediment transport magnitudes provide reasonable fits which are of equal quality compared to conventional cubic relationships.

Acknowledgements This work is partly funded by the ERC advanced Grant 291206NEMO. S. de Vries, M.A. de Schipper and S.M. Arens were partly funded by the innovation program Building with Nature. The Building with Nature program is funded from several sources, including the Subsidieregeling Innovatieketen Water (SIW, Staatscourant nrs 953 and 17009) sponsored by the Dutch Ministry of Transport, Public Works and Water Management and partner contributions of the participants to the Foundation EcoShape. The program receives co-funding from the European Fund for Regional Development EFRO and the Municipality of Dordrecht. R. Ranasinghe is supported by the AXA Research fund and the Deltares Coastal Maintenance Research Programme ‘Beheer & Onderhoud Kust’. Martijn Muller and Timon Pekkeriet are acknowledged for their support and assistance in the field. Robin Davidson-Arnott and one anonymous reviewer are thanked for their very valuable comments on the manuscript. Appendix A. saltiphone comparison In this appendix it is shown that all 5 saltiphones measure similar sediment transport amounts when placed at a similar position (within a 2 m radius). Data series Run I (see Table 1) is discussed. Saltiphones are placed close to each other and should produce similar output. Fig. 14 shows that measured wind is between 8 and 12 m/s from NW directions. Fig. 15 shows that total measured counts compare well to one another. Maximum variations in total counts between sensors are 10%. This 10% is small but significant, therefore when analysing the results a conservative approach has to be taken when inter-comparing data from different saltiphones. References Anthony, E.J., Ruz, M.-H., Vanhe, S., 2009. Aeolian sand transport over complex intertidal bar-trough beach topography. Geomorphology 105 (1–2), 95–105.

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