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The effect of wind gusts, moisture content and fetch length on sand transport on a beach
Geomorphology 68 (2005) 115 – 129 www.elsevier.com/locate/geomorph
The effect of wind gusts, moisture content and fetch length on sand transport on a beach Robin G.D. Davidson-Arnotta,*, Kelvin MacQuarriea, Troels Aagaardb b
a Department of Geography, University of Guelph, Guelph, ON, Canada N1G 2W1 Institute of Geography, Copenhagen University, aster Volgade 10, DK-1350, Copenhagen K., Denmark
Received 1 August 2003; received in revised form 25 February 2004; accepted 1 April 2004 Available online 19 December 2004
Abstract This paper reports on an analysis of instantaneous sediment transport in relation to wind gusts, moisture content and fetch length from a field study carried out at Skallingen, Denmark. Wind speeds were measured with cup anemometers and instantaneous sediment transport with vertical traps coupled to electronic balances. Moisture content was measured gravimetrically using samples taken along a beach profile at intervals of 1 to 2 h. Sediment transport and wind speeds were sampled at 1 Hz and a 5-s running mean was used to smooth the data from the trap because of limitations of the balance resolution. Three measures of the threshold of sediment motion—the intermittency threshold, minimum threshold and maximum threshold—were explored using data from five runs carried out on October 26, 2000. The intermittency threshold and maximum threshold were largely insensitive to wind speed but varied spatially along the fetch distance. The minimum threshold increased significantly with increasing mean wind speed as a result of reduced time for drying of the surface layer. Examination of time series for instantaneous wind speed and sediment transport for a number of runs on October 26 and November 6, 2000 showed close agreement between fluctuations in wind speed and fluctuations in sediment transport. Cross spectral analysis of instantaneous wind speed and sediment transport for one run on each day where there was continuous transport showed high coherence between the two variables over a range of frequencies from 0.2 Hz to b0.01 Hz. Plots of all non-zero instantaneous sediment transport values versus wind speed show considerable scatter. In general, transport rates are highest for traps located further from the upwind non-erodible boundary (i.e. along the fetch). Best fit power relationships show R 2 values generally ranging from 0.4 to 0.6 and exponents ranging from 4.5 to 6.94—i.e. much higher than the traditional value of 3 found in most transport equations. Traps located close to the upwind boundary had lower R 2 values and exponents b2.5. D 2004 Elsevier B.V. All rights reserved. Keywords: Aeolian sand transport; Intermittency; Threshold of motion; Moisture content
* Corresponding author. Fax: +1 519 837 2940. E-mail address: [email protected] (R.G.D. Davidson-Arnott). 0169-555X/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2004.04.008
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1. Introduction Sand transport by wind is the primary source of sediment supply for the building of foredunes on sandy beaches and thus a major component of sediment budget calculations for both the beach (the source) and the dune (the sink). Predictive models of foredune growth must therefore incorporate a parameter that quantifies the rate of sediment transport from the beach (Bauer and DavidsonArnott, 2002). Prediction of instantaneous sediment transport usually begins with (relatively) simple models such as those of Bagnold (1941), Kawamura (1951) and Lettau and Lettau (1977). They all assume uniform steady winds and a simple, dry sand surface with the result that the predicted transport rate is a function of the wind speed—i.e. transport-limited conditions prevail (Nickling and Davidson-Arnott, 1990). Sand transport rates are generally proportional to the cube of wind speed (U) or the wind shear velocity (U *), though the absolute predictions vary considerably between models, and field measurements often show considerable departures from predicted values even under relatively simple conditions (e.g. Greeley et al., 1996; Sherman et al., 1998). In turn, these models of instantaneous sand transport can be combined with wind data collected over periods of days or months to predict longer term sand transport into the dunes (Fryberger and Dean, 1979; Chapman, 1990). Here again, measured values can depart substantially from predicted values (Davidson-Arnott and Law, 1996). Laboratory and field studies have shown that the rate of sand transport by wind responds rapidly to fluctuations in wind speed so that unsteadiness or gustiness in the wind record is reflected in similar variations in the instantaneous sand transport rate on a time scale of a few seconds (Lee, 1987; Butterfield, 1991, 1993; McKenna Neuman et al., 2000). The spatial and temporal response of the system to wind gusts may be complicated by the difference in the response time for sand entrainment and for adjustment of the wind profile to changes in the mass of sand being transported (Bagnold, 1941; Owen, 1964; Anderson and Haff, 1991; Arnold, 2002). Where the wind gusts fluctuate around the threshold for sediment motion sand transport becomes intermittent, with periods of sand transport
associated with fluctuations above the threshold and periods of no transport being associated with variations below the threshold (Stout and Zobeck, 1997; McKenna Neuman et al., 2000). The proportion of time that the system is active during a given sampling time can be defined by c p such that a value of c p=0.0 reflects no transport and c p=1.0 reflects continuous transport (Stout and Zobeck, 1997). Actual sand transport rates on natural beaches are often much lower than predicted by the standard models noted above because of conditions such as the presence of moisture, or lags of gravel or shell that may act to limit the entrainment of sand from the surface. These factors result in transport rates that are supply limited (Nickling and Davidson-Arnott, 1990). There is considerable documentation of the effects of moisture on both the threshold of sediment motion and, to a lesser extent, on the flux rate (Belly, 1964; McKenna Neuman and Nickling, 1989; Namikas and Sherman, 1995). It also seems likely that the presence of small amounts of moisture will affect the operation of the saltation cascade both by reducing the number of grains initially ejected by fluid stresses and later by reducing the average number of grains dislodged by the impact of saltating particles. Thus, the presence of moisture may contribute to the fetch effect—the distance required to achieve full transport conditions (Chepil and Milne, 1939; Davidson-Arnott and Law, 1990; Gillette et al., 1996; Jackson and Nordstrom, 1998). It should be noted that moisture can also change the transport rate either positively through producing a harder rebound surface (McKenna Neuman and Maljaars Scott, 1998) or negatively by trapping some of the saltating grains. The presence of moisture on the beach may also contribute to the intermittency of sediment transport. This occurs whenever wind and/or solar radiation results in the drying of a thin surface layer of grains. The drying reduces the threshold of sediment motion to the point where transport is initiated and a cloud of particles is transported downwind. Transport may be enhanced by the impact of the saltating grains if the surface conditions downwind are such that the impact threshold is exceeded and a saltation cascade initiated. Thus, on a moist beach the drying effect can produce spatial/ temporal complexity in the continuity of sand transport (Davidson-Arnott and Dawson, 2001; Cornelis and Gabriels, 2003; Wiggs et al., 2004).
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A series of field experiments has been carried out recently at Skallingen, a large sandy spit on the Danish North Sea coast (Fig. 1a,b); the experiments have been designed to measure sedimentary processes in the nearshore, beach and dune systems and to develop a better understanding of the controls of the beach and dune sediment budgets (Aagaard et al.,
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1998, 2004). One part of the study was designed to explore the effects of varying wind speed and surface moisture conditions on the threshold of sediment motion, the intermittency function and instantaneous rates of aeolian sediment transport. This paper presents results from that field study which was carried out in October and November, 2000.
Fig. 1. Location of study area: (a, b) Location of Skallingen spit on the Danish North Sea Coast; (c) Geomorphic map of Skallingen. The experimental site was located at survey line 6420.
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2. Study area Skallingen is a large spit on the west coast of Jutland, Denmark (Fig. 1). The spit is part of a barrier chain that extends along the North Sea coast southward from the cuspate foreland of Bl3vand Huk and includes the islands of Fanb, Mandb and Rbmb as well as the German island of Sylt (Aagaard et al., 1995). The barrier chain is backed by an extensive lagoon, the Wadden Sea. Skallingen spit is about 12 km long and 2.5 km wide and consists of a beach and dune system as well as an extensive backbarrier marsh. The beach is 40–60 m wide with a slope of 0.025. The nearshore gradient out to about 400 m is 0.08 with the 6m depth contour located 3–4 km offshore. At the northern end of the spit the foredune is generally low and irregular but in the central and southern area the dunes have a height of 3–7 m above the beach and may exceed 10 m in places (Aagaard et al., 1995). The dunes have been breached by overwash in places during storms which produce large storm surges. The study site was located about two thirds of the way along the spit at survey line 6420 (Fig. 1c). Data were collected on 5 days when sediment transport occurred on the beach—October 26, 29, November 02, 03 and 06. At the beginning of the study there was considerable build-up of sand on the upper foreshore and a well-defined dune ramp with relatively dry, loose sand that could be transported by wind action (Fig. 2a). A severe storm between October 30 and November 01 produced a storm surge of 3m and significant wave heights N5 m, resulting in the erosion of the beach and removal of the dune
ramp, considerable erosion of the foredune along the length of the spit and a much more gentle foreshore slope (Fig. 2b).
3. Methodology Measurements of instantaneous sediment transport were made with vertical traps based on the design of Nickling and McKenna Neuman (1997). The traps have an opening at the front of 0.01 m. They are wedge shaped and the back opening is covered with 0.06 mm stainless steel wire mesh resulting in a nearly isokinetic trapping ability. Two versions of the traps were used-integrating traps and balance traps. Sediment collects in the bottom of the integrating trap and is led into a 4 cm diameter pipe which extends about 25 cm below the base of the trap and helps to stabilise the trap when it is deployed on the beach (Davidson-Arnott and Dawson, 2001). A labelled plastic bag is fixed in place over the base of the pipe before the start of a run to collect the trapped sediment. Each trap is buried in the sand so that the entrance is at, or just slightly below the sand surface, and the trap is oriented into the wind. The inlet to the trap is blocked by a strip of foam rubber, which can be pulled out quickly at the start of a run to begin sediment collection. At the end of a run the trap is turned 1808 to stop sand entering the trap and then the foam rubber strip is replaced. The trap is then removed from the sand. All the collected sand is shaken into the tube at the base and collected for later analysis. These traps thus integrate transport over the duration of the run.
Fig. 2. Photographs looking north of the study site: (a) October 26, 2000 prior to the storm. Note the dune ramp with three balance traps deployed at the top, middle and base of the ramp, and the damp area marking the limit of the previous high tide. Experimental set-up shown in Fig. 3; (b) November 3, 2000 after the storm. Note erosion of the dune ramp, scarping of the foredune and the low beach gradient.
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The balance traps were modified from the original design by mounting them on circular plastic containers which housed a Mettler electronic balance with a digital output. Sand caught in the trap was directed by a funnel into a collection pan on the electronic balance below, thus permitting a continuous measurement of the weight of sediment trapped. The balances have a precision of 0.1 g and a total range of 1200 g, thus permitting a number of runs to be carried out before the collection pan is emptied. Output from the balance was hard wired to a computer data logger through a serial cable and recorded at 1 Hz using DasyLabtm software. Since the balance records the accumulated weight, the rate of sand accumulation in the trap each second can be derived by subtracting the reading at t +1 from the reading at time t. The integrating traps have a height of 0.65 m and the balance traps 0.5 m. Wind speed at a height of 0.3 m was measured with R.M. Young three-cup anemometers which produce a DC voltage output. Wind direction on the beach was measured with a wind vane set at a height of 2 m. The signals from the anemometers and wind vane were also recorded on the data logger housed in the trailer. Regional wind speed and direction as well as other meteorological variables and water level in the backbarrier lagoon were measured at a 10 m high tower located on the back barrier about 1 km from the beach site over the duration of the study. Moisture content on the beach was measured gravimetrically using 5 cm diameter core samples taken along a profile perpendicular to the beach (Davidson-Arnott and Dawson, 2001). A 0.5-cm-thick sample was taken from the top and base of the core. The samples were double bagged and laboratory analysis carried out within 12 h of collection. Moisture content was analysed by weighing the field sample, drying it in an oven at 100 8C and weighing it again. Moisture content was calculated as: M¼
wf wd 100 wd
ð1Þ
where M is moisture content (%), wf is the weight of the field sample, wd is the weight of the dry sample. Profiles of the intertidal zone, beach and dune were surveyed using a total station and standard surveying techniques. Sediment size analysis was run on samples taken on the beach using a 2-m fall column.
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4. Results 4.1. Intermittency and sampling interval Sand transport measured over a period of seconds to hours is characteristically intermittent as a result of temporal fluctuations in wind speed (gustiness) and direction, and the spatial and temporal variability of factors such as moisture which act to limit sand supply from the beach surface. Periods of sand transport may ¯ bU t and periods with no occur during gusts when U transport may occur during periods of low wind ¯ NU t. As noted earlier, the speeds even though U temporal variability of transport can be defined by an intermittency function c p equal to the proportion of time the system is active (Stout and Zobeck, 1997). Rather than the complicated iterative procedure outlined by Stout and Zobeck (1997), c p was determined for each run by simply sorting wind speed values in a spread sheet in ascending order and determining the wind speed corresponding to the total number of zero transport data points recorded for that run. A photograph of beach conditions on October 26, 2000 is shown in Fig. 2a and the instrument layout for the experiment carried out on that day in Fig. 3. Three balance traps were set up at the top middle and bottom of the dune ramp, with the bottom trap being about 10 m landward of moist sand associated with the swash limit on the previous high tide (Figs. 2a and 3). Five sampling runs ranging in length from 18 to 25 min were carried out between 13:40 and 17:00. Winds were from the west–north–west blowing along the beach and slightly onshore. Wind speeds measured at 10 m at the back barrier station were about 11 m s1 for the first run, dropping to about 10 m s1 for runs 2–4 and then rising to 13 m s1 in a squall during the final run (Fig. 4). Winds were slightly less oblique during the final run (Fig. 4). Wind speed (m s1) recorded at anemometer 4 at a height of 0.3 m and transport (g s1) measured at trap 2 at the top of the dune ramp are shown in Fig. 5a for a 25-min run. Data were collected at 1 Hz and the calculated value for c p is 0.67. The spiky nature of the sediment transport data in Fig. 5a is in part an artefact of the 0.1 g resolution of the balance and this also affects the resolution of the transport rate. Assuming a 100% trapping efficiency, a 0.1 g s1 trapping rate with a trap opening of 0.01 m corresponds to a
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Fig. 3. Plan view of experimental set-up on October 26, 2002. No usable data were collected from anemometer 9.
transport rate of 0.0025 kg m1 s1. If the instantaneous rate falls below this value it takes longer than 1 s for sufficient weight to accumulate on the balance to change the value of the reading and thus to register transport for that 1-s period. Additionally, there is some variation in the length of time it takes for sediment to reach the balance. Sand entering the bottom of the trap reaches the balance slightly more quickly than sand travelling 30 cm above the bed which hits the wire mesh at the back of the trap and then falls to the bottom of the trap before going through the funnel to the balance tray. In order to reduce the effect of the balance resolution and the difference in time to reach the balance, the balance and wind data were smoothed using a 5-s running mean with each point equally weighted (Fig. 5b). Smoothing the data increases the resolution of the transport rate to 0.02 g s1. It clearly reduces the variation in the record, and the magnitude of the highest gusts and equivalent transport rates. However, as noted by Stout (1998), the definition of c p is affected by the sampling frequency and thus the smoothing process results in a decrease in the number of data points showing a zero transport rate and a
corresponding increase in c p from 0.67 to 0.91 for trap 2. The transport rate for trap 1 near the base of the ramp is also shown in Fig. 5b. The unsmoothed value of c p for trap 1 is 0.07 and this increases to 0.20 when the data are smoothed by the 5 s running mean. Clearly there is a trade-off between some loss of the signal and the errors introduced by the precision of the balances; the 5 s running mean used here represents the shortest time fraction that produced strong correlation with the wind record. 4.2. Thresholds of sediment transport Wherever sediment transport is intermittent, the instantaneous transport rates can be used to define and explore the nature of the sediment transport threshold and its relation to moisture content on the beach. The threshold wind speed can be calculated from the instantaneous data by requiring that the fraction of time that the wind exceeds the threshold value (c t) be equal to the fraction of time that saltation occurs in the record (Stout and Zobeck, 1997). This is termed here the intermittency threshold U tc . We can define two other estimates of the threshold wind speed based on
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Fig. 4. Mean wind speed and direction for October 26, 2000 measured at a height of 10 m in the back barrier. Shore perpendicular is approximately 2308.
the instantaneous record: (1) U tmin, the lowest wind speed for which transport is measured and (2) U tmax, the highest speed for which zero transport is measured. Initial examinations of the records for five
runs for all three traps deployed showed that there was considerable scatter based on a single point, and that a more consistent measure of the upper and lower bounds for the threshold could be obtained from
Fig. 5. Comparison of fluctuations in wind speed measured at anemometer 4 and sediment transport at trap 2 (top of dune ramp), (a) instantaneous record recorded at 1 Hz; (b) 5 s running mean for wind speed, trap 2 and trap 1 (bottom of ramp).
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averaging over several data points. Thus U tmin was estimated from the mean of the lowest five wind speed measurements associated with sediment transport and U tmax from the mean of the highest five speeds where there was no transport. The smoothed 1 Hz data for sediment transport (sand trapping rate) is plotted against wind speed measured at anemometer 4 for all non-zero values for trap 2 at the top of the dune ramp and trap 1 at the base of the ramp (Fig. 6) together with values for c p, U tc , U tmin, and U tmax. There are clear differences between the two traps, located only 10 m apart, in the relationship between sediment transport rates and wind speed (Figs. 5b and 6a,b), with transport rates showing a much greater tendency to increase with increasing wind speed at trap 2 than at trap 1. These differences are also evident in the mean transport rate, maximum transport rate and the proportion of time that sediment transport occurs (Figs. 5b and 6a,b), with the lower values at trap 1 reflecting closer proximity to the wet sand at the top of the swash line, and thus a much shorter fetch.
The intermittency threshold wind speed U tc and U tmax are both greater for trap 1 at the base of the ramp than for trap 2 at the top of the ramp but the values for U tmin are similar (Fig. 6). In order to explore the nature of the relationship between the various estimates of threshold wind speed and trap location the three parameters are plotted for all five runs carried out on October 26, 2000 (Fig. 7). Only trap 2 was deployed for the first run at 13:40. Run 5 (mean wind speed 8.5 m s1) is truncated after 500 s because the onset of rain in the squall led to clogging of the trap entrance. The intermittency threshold U tc shows no significant variation with mean wind speed (Fig. 7a). There is, however, a clear distinction between the values for each trap location, with U tc decreasing from the bottom of the ramp to the top of the ramp. The maximum threshold U tmax also shows a distinction based on location on the dune ramp, with lower values recorded at the top of the ramp compared to the bottom (Fig. 7b). Unlike the case for the intermittency threshold, the maximum threshold
Fig. 6. Plot of sediment transport (g s1) against wind speed at anemometer 4 for all non-zero transport values: (a) trap 2 at the top of the dune ramp; (b) trap 1 at the base of the ramp. Also shown are the values for the intermittency function c p, the lower and upper bounds for the threshold of transport U tmin, U tmax, and the calculated intermittency threshold U tc .
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Fig. 7. Estimates of the threshold wind speed plotted against mean wind speed (measured at 0.3 m) for five runs on October 26 for traps located at the top, middle and base of the dune ramp. Note that only the trap at the top of the ramp was deployed during the first run: (a) intermittency threshold, U tc ; (b) maximum threshold U tmax; and (c) the minimum threshold U tmin. Lines on (a) and (b) are extrapolations drawn by eye. The line on (c) is the linear best fit line which has an R 2 of 0.74—significant at the 95% confidence level.
U tmax does show some variation with mean wind speed, initially showing an increase with increasing wind speed to about 7.5 m s1 and then considerably lower values being recorded for the highest wind speed (Fig. 7b). By comparison with the other two threshold estimates, the values for U tmin (Fig. 7c) show very little differentiation by trap location but they do show a significant linear increase in the threshold value with increasing mean wind speed (R 2=0.74).
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The decrease in both U tc and U tmax up the dune ramp appears to reflect the effects of distance from the wet upwind boundary—i.e. increasing fetch length. The decrease in the values for the intermittency parameter c p and increase in the transport rate in this direction both suggest that the spatial dependency of U tc and U tmax can be attributed to the saltation cascade which is initiated at the edge of the damp surface (Fig. 2a), with the threshold increasingly being controlled by saltation impacts rather than fluid forces. The decrease in the values for U tmax at the highest wind speed is interpreted to be a reflection of an increase in the fetch length with the very high wind speed recorded during this squall. Observations during the run showed that sediment was mobilized on the damp foreshore out to 20 m seaward of the base of the dune ramp. The increase in U tmin with increasing wind speed is interesting. It may in part simply reflect the fact that as the mean wind speed increases there are fewer low wind speed values at which sediment transport occurs. However, at the highest mean wind speed there is little difference in the value recorded at the three traps yet the intermittency parameter ranged from a high of 0.99 at trap 2 at the top of the ramp to a low of 0.64 at trap 1 at the bottom of the ramp. It seems more likely that the explanation lies primarily in the drying effects of wind blowing over the surface layer, possibly aided by solar insolation, which results in a dynamic variation in the fluid threshold with time. At low wind speeds transport is highly intermittent, but drying of the surface layer in the comparatively long intervals between transport events eventually reduces the fluid threshold to the point where sediments can be entrained during a gust. At a high mean wind speed, gusts can remove a surface layer with a much higher moisture content and there is insufficient time during intervals of relatively low winds for the surface to dry out to the point where transport can be initiated. 4.3. Temporal variability of sand transport and wind speed Examination of the smoothed instantaneous transport rates and wind speed suggests that the temporal variability of sediment transport is similar to the pattern of wind gusts (e.g. Fig. 5b). It is difficult to compare many of the records statistically because the
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Fig. 8. Plan view of experimental set-up on November 6, 2000.
transport data is not continuous. However, continuous transport was measured over a period of 500 s at trap 2 during Run 5 on October 26 resulting from the high winds associated with a squall line. Similarly, continuous transport was recorded at trap 3 during an experiment on November 6th with winds blowing obliquely offshore and the traps set up onto the foreshore (see Fig. 8). Dry sand had accumulated near the base of the eroded foredune over the previous 5 days and this was blown alongshore and offshore across the exposed foreshore at low tide. The time series of wind speed for both days (Figs. 9a and 10a) show considerable fluctuation over a range of frequencies. In all cases, the sand transport rate responds rapidly to changes in wind speed and the two series appear very similar. Spectra for both days show no significant peaks and a relatively steady increase in energy towards lower frequencies (Figs. 9b and 10b). The cross-spectra also tend to increase towards the low frequency end (Figs. 9c and 10c). What is perhaps most significant is that the coherence between the two series on both days is generally high across the spectrum at frequencies lower than 0.2 Hz. Spectra for trap 1 on October 26 and trap 2 on November 6 show similar features. The similarity of the spectra and the high coherence over much of the spectrum on both days and at two different locations on the beach provide strong support for earlier studies
Fig. 9. Wind speed and sediment transport relationships October 26, Run 5: (a) instantaneous sediment transport and wind speed, trap 2 at the top of the ramp; (b) spectra for wind speed and sediment transport; (c) cross spectra and coherence. The spectral data are smoothed using Hamming weights over 15 frequency classes. Note that, because the original data were smoothed by a 5-s running mean, the spectra have been truncated at a frequency of 0.2 Hz.
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6. The locations of the instruments are shown in Figs. 3 and 8. These traps were selected because they were directly paired with an anemometer mounted at a height of 0.3 m adjacent to the trap. The mean wind speed and intermittency parameter, as well as the R 2 value and exponent for the best fit power curve are given in Table 1 for all observations and several examples are shown in Fig. 11. Trap 2 on October 26 and trap 3 on November 6 have the longest fetch on the respective days and the highest rates of transport recorded for all the runs. In general, the R 2 values for these traps are relatively high (0.4–0.6) and the exponent for the least squares power function lies between 4 and 6. Trap 2 on October 26 shows greater variability, with a low value of 1.1 for run 4 and a high of 6.94 for run 3. Trap 1 on October 26 and trap 2 on November 6 have a much shorter fetch: the R 2 values are generally lower than those for the traps with a longer fetch and the values Fig. 10. Wind speed and sediment transport relationships November 6, Run 4: (a) instantaneous sediment transport and wind speed trap, 3 near the low tide limit; (b) spectra for wind speed and sediment transport; (c) cross spectra and coherence. The spectral data are smoothed using Hamming weights over 15 frequency classes. Note that, because the original data were smoothed by a 5-s running mean, the spectra have been truncated at a frequency of 0.2 Hz.
that indicate that, where there is an abundant source of sediment, the transport system responds rapidly to fluctuations in the wind speed. 4.4. Prediction of sediment transport rate The relationship between wind speed or wind shear velocity and the resulting sand transport rates has usually been modelled using a power function with an exponent of 3 (Bagnold, 1941; Kawamura, 1951; Lettau and Lettau, 1977). Empirical measurements in wind tunnels and in the field have usually been based on integrated traps and the use of the balance traps permits an examination of the instantaneous response of transport to changing wind speeds. The relationship between instantaneous wind speed and the sand transport rate was explored by fitting power curves to all pairs of observations in a measurement run with non-zero transport data for traps 1 and 2 deployed on October 26 and traps 2 and 3 deployed on November
Table 1 Summary of statistics from best-fit power regression curve for instantaneous sediment transport measured by balance traps and wind speed measured at a co-located anemometer at 0.3 m above the bed for all runs on October 26, 2000 and November 06, 2000 U mean (m s1)
No. of observations
IP
R2
Exponent
October 26 Trap 1 1 2 3 4 5 Trap 2 1 2 3 4 5
6.91 6.31 6.94 9.16 7.31 6.7 6.12 6.74 8.41
1484 1492 1486 512 996 1484 1492 1486 512
0.18 0.13 0.07 0.87 0.84 0.91 0.33 0.95 1
0.4 0.13 0.06 0.24 0.47 0.54 0.32 0.03 0.74
1.02 2.56 1.31 3.29 5.18 4.44 6.94 1.1 5.21
November 6 Trap 2 3 4 5 6 Trap 3 3 4 5 6
8.68 8.13 8.56 7.79 7.97 7.61 8.2 7.66
827 804 771 890 827 804 771 890
0.99 0.99 1 0.99 1 1 1 0.99
0.13 0.6 0.17 0.24 0.35 0.65 0.63 0.48
1.96 4.45 1.98 2.34 3.97 4.97 4.88 4.3
Trap #
Run #
Values are for the entire run except for rune 5 on October 26, which is cut off after the onset of rain. The regression curve is fitted for all non-zero transport pairs.
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Fig. 11. Examples of plots of instantaneous wind speed and transport rate for pairs of traps for all non-zero transport conditions from runs on October 26 and November 6, 2000: (a) traps 1 and 2, October 26 run 2; (b) traps 1 and 2 October 26 run 5; (c) traps 2 and 3 November 6 run 6. The instrument layouts are shown in Figs. 3 and 8. Data from all runs on the two days are shown in Table 1.
of the exponent for the least squares power function lies between 1 and 2.5. An exception to this occurs for trap 1 on October 26 during run 5 where the exponent is 3.29. As noted earlier, during this run a squall mobilized sediment transport on the damp foreshore, resulting in much higher transport rates being recorded at trap 1 and in effect increasing the fetch in front of the trap. Similarly, results from trap 2 for run 4 on November 6 gave an R 2 value of 0.6 and an exponent of 4.45. At this time, small dunes were beginning to form on the foreshore and the high transport rate may reflect the development of a dune with considerable quantities of dry sand immediately in front of the trap.
5. Discussion Comparison of instantaneous wind speed and sediment transport records show that the sand trans-
port system on the beach responds rapidly to changes in wind speed and this is supported by the coherence of the cross spectra for two runs where there was continuous transport. This is in agreement with a number of other studies (e.g. Butterfield, 1993; McKenna Neuman et al., 2000; Davidson-Arnott et al., 2003) and the pattern is clear both for fluctuations in the rate of transport during conditions of continuous transport, as well as for the occurrence of bursts of transport during conditions of intermittent transport. Nevertheless, while the pattern of response of the sediment transport system closely follows that of the wind speed, plots of the instantaneous transport values show that there is considerable scatter in the magnitude of the transport response over periods of seconds to minutes at one location and spatially over distances of a few metres. Much of this temporal and spatial variability appears to reflect the availability of sediment for entrainment and the effects of moisture content and fetch length.
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Comparison of different estimates of sediment transport threshold (Fig. 7) show that in the field, particularly where there are strong gradients in the moisture content of surface samples, there can be no simple definition of a threshold related to moisture content (e.g. Belly, 1964). Clearly, sediment entrainment at a point depends not only on the local moisture conditions but also on moisture conditions and entrainment in the upwind area. The results from this study indicate that, during intermittent sediment transport, what is happening on the surface upwind of the point of interest is probably more important than the local fluid threshold related to moisture. The dependence of the minimum threshold U tmin on wind speed demonstrates the additional temporal complexity introduced by surface drying—in effect the threshold can vary over periods as short as tens of seconds in response to drying of the surface layer of grains by wind and by insolation. Similar results have been reported from a study carried out on a beach in Wales (Wiggs et al., 2004) and from work carried out in Prince Edward Island, Canada (Yang, 2003). Thus, intermittency in sediment transport is not just a reflection of variations in wind speed above and below a fixed threshold (Stout and Zobeck, 1997) but also of variations in the threshold itself as the moisture content of the surface layer changes. The complex pattern of sand streamer generation commonly observed on beaches therefore can be seen as a reflection of both the temporal and spatial fluctuations in wind speed and surface moisture content. The spatial variation in threshold effects and transport rates with distance downwind from the wet zone on both of the days reported here provides supporting empirical evidence for the role of the fetch effect in controlling the transport rate (Davidson-Arnott and Law, 1990; Greeley et al., 1996; Davidson-Arnott and Dawson, 2001). While recent wind tunnel studies show that with uniform dry sand fetch distances are only a few metres (e.g. Dong et al. 2004) field studies, including this one, have shown that it is more usually tens of metres (Davidson-Arnott and Law, 1990; Nordstrom and Jackson, 1992; Gillette et al., 1996) and it may be particularly significant on beaches where surface moisture contents are often N4%. These results reinforce the need for the explicit consideration of the
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fetch effect in modelling sand supply to coastal dunes (Bauer and Davidson-Arnott, 2002). Finally, the complexity of the transport system is reflected in the wide range of exponents obtained by fitting power curves to regressions between the instantaneous wind speed and transport rates (Table 1). The traditional cubic relationship between shear velocity U * or wind speed U and the sand transport rate has been derived largely from wind tunnel studies with steady uniform winds and dry, well sorted sand, with transport averaged over periods of 10 min or more (e.g. Bagnold, 1941; Kawamura, 1951). Fluctuating wind speeds introduce complexities because the cube of mean shear velocity for a given time period is generally not equal to the mean of the cube of instantaneous shear velocities (Namikas et al., 2003). The situation becomes more complex when transport is intermittent because the average transport rate integrates periods of transport and no transport ((Stout and Zobeck, 1997; Rasmussen and Sorensen, 1999; McKenna Neuman et al., 2000) and this probably accounts for some of the discrepancies observed in field studies between predicted transport rates and actual measured values (e.g. Sherman et al., 1998). The values of 4.5–6 for the exponent measured here for the two downwind traps are large, but measurements of transport intensity using a saltation probe which measures the impact of grains on a piezo-electric crystal have also shown similar high exponents when power curves are fitted to the data (Davidson-Arnott et al., 2003). Where the intermittency value is well below unity, the average transport rate over a period of minutes will be much lower and this will produce a better fit with predictive equations based on a cubic relationship between mean wind speed and transport rates. However, it should be noted that the high exponents were also obtained for conditions where there was continuous transport (c p=1). As we improve our ability to make high speed measurements of sediment transport in the field, the relationships between high frequency dynamics and the prediction of average transport rates over periods tens of minutes will need to be refined. There is considerable scatter in the data points relating transport rates to wind speed. Some of the scatter may be related to a tendency for a decrease
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in transport to lag slightly behind a decrease in wind speed (McKenna Neuman et al., 2000). Some of it may simply reflect the spatial and temporal variability of sand streamers, with higher transport rates associated with the streamers and lower rates between the streamers.
M. Christiansen, C. Houser, J. Nielsen and N. Vinther for their assistance in the field, and M. Finoro and M. Puddister for technical and cartographic assistance.
References 6. Conclusions The conclusions of the study can be summarized as follows: (1) Sand transport rates respond instantaneously to variations in wind speed at a range of frequencies from seconds to minutes for both intermittent and continuous sediment transport; (2) Surface moisture content on the beach greatly influences the threshold of movement at a point. However, the actual threshold is a dynamic one that is influenced by the rate of drying of the surface layer of grains. Moisture content influences both the fluid threshold and the impact threshold and entrainment of sediment from a point on the surface is controlled both by the conditions at that point and by events happening over the upwind surface; (3) Together with the intermittency threshold defined by Stout and Zobeck (1997) the minimum and maximum thresholds considered here provide different measures of the factors controlling sediment entrainment and transport; (4) The fetch effect influences the actual threshold at a point and, together with the availability of dry sand, it appears to influence the magnitude of the response of the transport rate to varying wind speed.
Acknowledgements The field study was supported by a research grant from the Danish Natural Sciences Research Council, Grant numbers 9701836 and 11-0925 (T. Aagaard Principal Investigator) and by a Natural Sciences and Engineering Research Council of Canada Research Grant to RD-A. We thank J. Dawson, B. Greenwood,
Aagaard, T., Nielsen, N., Nielsen, J., 1995. Skallingen—Origin and evolution of a barrier spit. Technical Memo No. 35, Institute of Geography, University of Copenhagen, 86 pp. Aagaard, T., Nielsen, J., Davidson-Arnott, R., Greenwood, B., Nielsen, N., 1998. Coastal morphodynamics at Skallingen, SW Denmark: high energy conditions. Geogr. Tidsskr. 98, 20 – 30. Aagaard, T., Davidson-Arnott, R., Greenwood, B., Nielsen, J., 2004. Sediment supply from shoreface to dunes: linking sediment transport measurements and long term morphological evolution. Geomorphology 60, 205 – 224. Anderson, R.S., Haff, P.K., 1991. Wind modification and bed response during saltation of sand in air. Acta Mech. (Suppl.) 1, 21 – 52. Arnold, S., 2002. Development of the saltation system under controlled environmental conditions. Earth Surf. Process. Landf. 27, 817 – 829. Bagnold, R.A., 1941. The Physics of Blown Sand and Desert Dunes. Methuen, London. 265 pp. Bauer, B.O., Davidson-Arnott, R.G.D., 2002. A general framework for modelling sediment supply to coastal dunes including wind angle, beach geometry, and fetch effects. Geomorphology 49, 89 – 108. Belly, P.-Y., 1964. Sand movement by wind. U.S. Army Corps of Engineers CERC, Tech. Memo. 1, 38 pp. Butterfield, G.R., 1991. Grain transport rates in steady and unsteady turbulent airflows. Acta Mech. (Suppl.) 1, 97 – 122. Butterfield, G.R., 1993. Sand transport response to fluctuating wind velocity. In: Clifford, N.J., French, J.R., Hardisty, J. (Eds.), Turbulence: Perspectives on Flow and Sediment Transport. John Wiley and Sons, Chichester, England, pp. 305 – 336. Chapman, D.M., 1990. Aeolian sand transport—an optimized model. Earth Surf. Process. Landf. 15, 751 – 760. Chepil, W.S., Milne, R.A., 1939. Comparative study of soil drifting in the field and in a wind tunnel. Sci. Agric., 249. Cornelis, W.M., Gabriels, D., 2003. The effect of surface moisture on the entrainment of dune sand by wind: an evaluation of selected models. Sedimentology 50, 771 – 790. Davidson-Arnott, R.G.D., Law, M.N., 1990. Seasonal patterns and controls on sediment supply to coastal foredunes, Long Point, Lake Erie. In: Nordstrom, K.F., Psuty, N.P., Carter, R.W.G. (Eds.), Coastal Dunes: Form and Process. John Wiley and Sons, pp. 177 – 200. Davidson-Arnott, R.G.D., Law, M.N., 1996. Measurement and prediction of long-term sediment supply to coastal foredunes. J. Coast. Res. 12, 654 – 663. Davidson-Arnott, R.G.D., Dawson, J.D., 2001. Moisture and fetch effects on rates of aeolian sediment transport, Skallingen,
R.G.D. Davidson-Arnott et al. / Geomorphology 68 (2005) 115–129 Denmark. Proceedings Canadian Coastal Conference, CCSEA. , pp. 309 – 321. Davidson-Arnott, R.G.D., Ollerhead, J., Hesp, P.A., Walker, I.J., 2003. Spatial and temporal variability in intensity of aeolian transport on a beach and foredune. Proc. Coastal Sediments ’03, ASCE. 11 pp. Dong, Z., Wang, H., Liu, X., Wang, X., 2004. The blown sand flux over a sandy surface: a wind tunnel investigation on the fetch effect. Geomorphology 57, 117–127. Fryberger, S.G., Dean, G., 1979. Dune forms and wind regime. In: McKee, E.D. (Ed.), Global Sand Seas, pp. 141 – 151. Gillette, D.A., Herbert, G., Stockton, P.H., Owen, P.R., 1996. Causes of the fetch effect in wind erosion. Earth Surf. Process. Landf. 21, 641 – 659. Greeley, R., Blumberg, D.G., Williams, S.H., 1996. Field measurements of the flux and speed of wind-blown sand. Sedimentology 43, 41 – 52. Jackson, N.L., Nordstrom, K.L., 1998. Aeolian transport of sediment on a beach during and after rainfall, Wildwood, NJ, USA. Geomorphology 22, 151 – 157. Kawamura, R., 1951. Study of sand movement by wind. University of Tokyo, Rept. Inst. Tech. 5, #314. Lee, J.A., 1987. A field experiment on the role of small scale wind gustiness in aeolian sand transport. Earth Surf. Process. Landf. 12, 331 – 335. Lettau, K., Lettau, H., 1977. Experimental and micrometeorological field studies of dune migration. In: Lettau, K., Lettau, H. (Eds.), Exploring the World’s Driest Climate, IES Report, vol. 101. University of Wisconsin Press, Madison, pp. 110 – 147. McKenna Neuman, C., Maljaars Scott, M., 1998. A wind tunnel study of the influence of pore water on aeolian sediment transport. J. Arid Environ. 39, 403 – 419. McKenna Neuman, C., Nickling, W.G., 1989. A theoretical and wind tunnel investigation of the effects of capillary water on the entrainment of sediment by wind. Can. J. Soil Sci. 69, 79 – 96. McKenna Neuman, C., Lancaster, N., Nickling, W.G., 2000. Effect of unsteady winds on sediment transport intermittency along the stoss slope of a reversing dune. Sedimentology 47, 211 – 226.
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Namikas, S.L., Sherman, D.J., 1995. A review of the effects of surface moisture content on aeolian sand transport. In: Tchakerian, V.P. (Ed.), Desert Aeolian Processes. Chapman and Hall, London, pp. 269 – 293. Namikas, S.L., Bauer, B.O., Sherman, D.J., 2003. Influence of averaging interval on shear velocity estimates for aeolian transport modelling. Geomorphology 53, 235 – 246. Nickling, W.G., Davidson-Arnott, R.G.D., 1990. Aeolian sediment transport on beaches and coastal sand dunes. In: DavidsonArnott, R.G.D. (Ed.), Proceedings Symposium on Coastal Sand Dunes. National Research Council of Canada, pp. 1 – 35. Nickling, W.G., McKenna Neuman, C., 1997. Wind tunnel evaluation of a wedge-shaped aeolian transport trap. Geomorphology 18, 333 – 345. Nordstrom, K.F., Jackson, N.L., 1992. Effect of source width and tidal elevation changes on aeolian transport on an estuarine beach. Sedimentology 39, 769 – 778. Owen, P.R., 1964. Saltation of uniform grains in air. J. Fluid Mech. 20, 225 – 242. Rasmussen, K., Sorensen, M., 1999. Aeolian mass transport near the saltation threshold. Earth Surf. Process. Landf. 24, 413 – 422. Sherman, D.J., Namikas, D.W.T., Wang, S.L., 1998. Wind blown sand on beaches: an evaluation of models. Geomorphology 22, 113 – 133. Stout, J.E., 1998. Effect of averaging time on the apparent threshold for aeolian transport. J. Arid Environ. 39, 395 – 401. Stout, J.E., Zobeck, T.M., 1997. Intermittent saltation. Sedimentology 44, 959 – 970. Wiggs, G.F.S., Baird, A.J., Atherton, R.J., 2004. The dynamic effect of moisture on the entrainment and transport of sand by wind. Geomorphology 59, 15 – 30. Yang, Y., 2003. The Effects of Surface Moisture Content on Aeolian Sediment Transport on a Beach. MSc thesis, University of Guelph, 105 pp.
The effect of wind gusts, moisture content and fetch length on sand transport on a beach Robin G.D. Davidson-Arnotta,*, Kelvin MacQuarriea, Troels Aagaardb b
a Department of Geography, University of Guelph, Guelph, ON, Canada N1G 2W1 Institute of Geography, Copenhagen University, aster Volgade 10, DK-1350, Copenhagen K., Denmark
Received 1 August 2003; received in revised form 25 February 2004; accepted 1 April 2004 Available online 19 December 2004
Abstract This paper reports on an analysis of instantaneous sediment transport in relation to wind gusts, moisture content and fetch length from a field study carried out at Skallingen, Denmark. Wind speeds were measured with cup anemometers and instantaneous sediment transport with vertical traps coupled to electronic balances. Moisture content was measured gravimetrically using samples taken along a beach profile at intervals of 1 to 2 h. Sediment transport and wind speeds were sampled at 1 Hz and a 5-s running mean was used to smooth the data from the trap because of limitations of the balance resolution. Three measures of the threshold of sediment motion—the intermittency threshold, minimum threshold and maximum threshold—were explored using data from five runs carried out on October 26, 2000. The intermittency threshold and maximum threshold were largely insensitive to wind speed but varied spatially along the fetch distance. The minimum threshold increased significantly with increasing mean wind speed as a result of reduced time for drying of the surface layer. Examination of time series for instantaneous wind speed and sediment transport for a number of runs on October 26 and November 6, 2000 showed close agreement between fluctuations in wind speed and fluctuations in sediment transport. Cross spectral analysis of instantaneous wind speed and sediment transport for one run on each day where there was continuous transport showed high coherence between the two variables over a range of frequencies from 0.2 Hz to b0.01 Hz. Plots of all non-zero instantaneous sediment transport values versus wind speed show considerable scatter. In general, transport rates are highest for traps located further from the upwind non-erodible boundary (i.e. along the fetch). Best fit power relationships show R 2 values generally ranging from 0.4 to 0.6 and exponents ranging from 4.5 to 6.94—i.e. much higher than the traditional value of 3 found in most transport equations. Traps located close to the upwind boundary had lower R 2 values and exponents b2.5. D 2004 Elsevier B.V. All rights reserved. Keywords: Aeolian sand transport; Intermittency; Threshold of motion; Moisture content
* Corresponding author. Fax: +1 519 837 2940. E-mail address: [email protected] (R.G.D. Davidson-Arnott). 0169-555X/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2004.04.008
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1. Introduction Sand transport by wind is the primary source of sediment supply for the building of foredunes on sandy beaches and thus a major component of sediment budget calculations for both the beach (the source) and the dune (the sink). Predictive models of foredune growth must therefore incorporate a parameter that quantifies the rate of sediment transport from the beach (Bauer and DavidsonArnott, 2002). Prediction of instantaneous sediment transport usually begins with (relatively) simple models such as those of Bagnold (1941), Kawamura (1951) and Lettau and Lettau (1977). They all assume uniform steady winds and a simple, dry sand surface with the result that the predicted transport rate is a function of the wind speed—i.e. transport-limited conditions prevail (Nickling and Davidson-Arnott, 1990). Sand transport rates are generally proportional to the cube of wind speed (U) or the wind shear velocity (U *), though the absolute predictions vary considerably between models, and field measurements often show considerable departures from predicted values even under relatively simple conditions (e.g. Greeley et al., 1996; Sherman et al., 1998). In turn, these models of instantaneous sand transport can be combined with wind data collected over periods of days or months to predict longer term sand transport into the dunes (Fryberger and Dean, 1979; Chapman, 1990). Here again, measured values can depart substantially from predicted values (Davidson-Arnott and Law, 1996). Laboratory and field studies have shown that the rate of sand transport by wind responds rapidly to fluctuations in wind speed so that unsteadiness or gustiness in the wind record is reflected in similar variations in the instantaneous sand transport rate on a time scale of a few seconds (Lee, 1987; Butterfield, 1991, 1993; McKenna Neuman et al., 2000). The spatial and temporal response of the system to wind gusts may be complicated by the difference in the response time for sand entrainment and for adjustment of the wind profile to changes in the mass of sand being transported (Bagnold, 1941; Owen, 1964; Anderson and Haff, 1991; Arnold, 2002). Where the wind gusts fluctuate around the threshold for sediment motion sand transport becomes intermittent, with periods of sand transport
associated with fluctuations above the threshold and periods of no transport being associated with variations below the threshold (Stout and Zobeck, 1997; McKenna Neuman et al., 2000). The proportion of time that the system is active during a given sampling time can be defined by c p such that a value of c p=0.0 reflects no transport and c p=1.0 reflects continuous transport (Stout and Zobeck, 1997). Actual sand transport rates on natural beaches are often much lower than predicted by the standard models noted above because of conditions such as the presence of moisture, or lags of gravel or shell that may act to limit the entrainment of sand from the surface. These factors result in transport rates that are supply limited (Nickling and Davidson-Arnott, 1990). There is considerable documentation of the effects of moisture on both the threshold of sediment motion and, to a lesser extent, on the flux rate (Belly, 1964; McKenna Neuman and Nickling, 1989; Namikas and Sherman, 1995). It also seems likely that the presence of small amounts of moisture will affect the operation of the saltation cascade both by reducing the number of grains initially ejected by fluid stresses and later by reducing the average number of grains dislodged by the impact of saltating particles. Thus, the presence of moisture may contribute to the fetch effect—the distance required to achieve full transport conditions (Chepil and Milne, 1939; Davidson-Arnott and Law, 1990; Gillette et al., 1996; Jackson and Nordstrom, 1998). It should be noted that moisture can also change the transport rate either positively through producing a harder rebound surface (McKenna Neuman and Maljaars Scott, 1998) or negatively by trapping some of the saltating grains. The presence of moisture on the beach may also contribute to the intermittency of sediment transport. This occurs whenever wind and/or solar radiation results in the drying of a thin surface layer of grains. The drying reduces the threshold of sediment motion to the point where transport is initiated and a cloud of particles is transported downwind. Transport may be enhanced by the impact of the saltating grains if the surface conditions downwind are such that the impact threshold is exceeded and a saltation cascade initiated. Thus, on a moist beach the drying effect can produce spatial/ temporal complexity in the continuity of sand transport (Davidson-Arnott and Dawson, 2001; Cornelis and Gabriels, 2003; Wiggs et al., 2004).
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A series of field experiments has been carried out recently at Skallingen, a large sandy spit on the Danish North Sea coast (Fig. 1a,b); the experiments have been designed to measure sedimentary processes in the nearshore, beach and dune systems and to develop a better understanding of the controls of the beach and dune sediment budgets (Aagaard et al.,
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1998, 2004). One part of the study was designed to explore the effects of varying wind speed and surface moisture conditions on the threshold of sediment motion, the intermittency function and instantaneous rates of aeolian sediment transport. This paper presents results from that field study which was carried out in October and November, 2000.
Fig. 1. Location of study area: (a, b) Location of Skallingen spit on the Danish North Sea Coast; (c) Geomorphic map of Skallingen. The experimental site was located at survey line 6420.
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2. Study area Skallingen is a large spit on the west coast of Jutland, Denmark (Fig. 1). The spit is part of a barrier chain that extends along the North Sea coast southward from the cuspate foreland of Bl3vand Huk and includes the islands of Fanb, Mandb and Rbmb as well as the German island of Sylt (Aagaard et al., 1995). The barrier chain is backed by an extensive lagoon, the Wadden Sea. Skallingen spit is about 12 km long and 2.5 km wide and consists of a beach and dune system as well as an extensive backbarrier marsh. The beach is 40–60 m wide with a slope of 0.025. The nearshore gradient out to about 400 m is 0.08 with the 6m depth contour located 3–4 km offshore. At the northern end of the spit the foredune is generally low and irregular but in the central and southern area the dunes have a height of 3–7 m above the beach and may exceed 10 m in places (Aagaard et al., 1995). The dunes have been breached by overwash in places during storms which produce large storm surges. The study site was located about two thirds of the way along the spit at survey line 6420 (Fig. 1c). Data were collected on 5 days when sediment transport occurred on the beach—October 26, 29, November 02, 03 and 06. At the beginning of the study there was considerable build-up of sand on the upper foreshore and a well-defined dune ramp with relatively dry, loose sand that could be transported by wind action (Fig. 2a). A severe storm between October 30 and November 01 produced a storm surge of 3m and significant wave heights N5 m, resulting in the erosion of the beach and removal of the dune
ramp, considerable erosion of the foredune along the length of the spit and a much more gentle foreshore slope (Fig. 2b).
3. Methodology Measurements of instantaneous sediment transport were made with vertical traps based on the design of Nickling and McKenna Neuman (1997). The traps have an opening at the front of 0.01 m. They are wedge shaped and the back opening is covered with 0.06 mm stainless steel wire mesh resulting in a nearly isokinetic trapping ability. Two versions of the traps were used-integrating traps and balance traps. Sediment collects in the bottom of the integrating trap and is led into a 4 cm diameter pipe which extends about 25 cm below the base of the trap and helps to stabilise the trap when it is deployed on the beach (Davidson-Arnott and Dawson, 2001). A labelled plastic bag is fixed in place over the base of the pipe before the start of a run to collect the trapped sediment. Each trap is buried in the sand so that the entrance is at, or just slightly below the sand surface, and the trap is oriented into the wind. The inlet to the trap is blocked by a strip of foam rubber, which can be pulled out quickly at the start of a run to begin sediment collection. At the end of a run the trap is turned 1808 to stop sand entering the trap and then the foam rubber strip is replaced. The trap is then removed from the sand. All the collected sand is shaken into the tube at the base and collected for later analysis. These traps thus integrate transport over the duration of the run.
Fig. 2. Photographs looking north of the study site: (a) October 26, 2000 prior to the storm. Note the dune ramp with three balance traps deployed at the top, middle and base of the ramp, and the damp area marking the limit of the previous high tide. Experimental set-up shown in Fig. 3; (b) November 3, 2000 after the storm. Note erosion of the dune ramp, scarping of the foredune and the low beach gradient.
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The balance traps were modified from the original design by mounting them on circular plastic containers which housed a Mettler electronic balance with a digital output. Sand caught in the trap was directed by a funnel into a collection pan on the electronic balance below, thus permitting a continuous measurement of the weight of sediment trapped. The balances have a precision of 0.1 g and a total range of 1200 g, thus permitting a number of runs to be carried out before the collection pan is emptied. Output from the balance was hard wired to a computer data logger through a serial cable and recorded at 1 Hz using DasyLabtm software. Since the balance records the accumulated weight, the rate of sand accumulation in the trap each second can be derived by subtracting the reading at t +1 from the reading at time t. The integrating traps have a height of 0.65 m and the balance traps 0.5 m. Wind speed at a height of 0.3 m was measured with R.M. Young three-cup anemometers which produce a DC voltage output. Wind direction on the beach was measured with a wind vane set at a height of 2 m. The signals from the anemometers and wind vane were also recorded on the data logger housed in the trailer. Regional wind speed and direction as well as other meteorological variables and water level in the backbarrier lagoon were measured at a 10 m high tower located on the back barrier about 1 km from the beach site over the duration of the study. Moisture content on the beach was measured gravimetrically using 5 cm diameter core samples taken along a profile perpendicular to the beach (Davidson-Arnott and Dawson, 2001). A 0.5-cm-thick sample was taken from the top and base of the core. The samples were double bagged and laboratory analysis carried out within 12 h of collection. Moisture content was analysed by weighing the field sample, drying it in an oven at 100 8C and weighing it again. Moisture content was calculated as: M¼
wf wd 100 wd
ð1Þ
where M is moisture content (%), wf is the weight of the field sample, wd is the weight of the dry sample. Profiles of the intertidal zone, beach and dune were surveyed using a total station and standard surveying techniques. Sediment size analysis was run on samples taken on the beach using a 2-m fall column.
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4. Results 4.1. Intermittency and sampling interval Sand transport measured over a period of seconds to hours is characteristically intermittent as a result of temporal fluctuations in wind speed (gustiness) and direction, and the spatial and temporal variability of factors such as moisture which act to limit sand supply from the beach surface. Periods of sand transport may ¯ bU t and periods with no occur during gusts when U transport may occur during periods of low wind ¯ NU t. As noted earlier, the speeds even though U temporal variability of transport can be defined by an intermittency function c p equal to the proportion of time the system is active (Stout and Zobeck, 1997). Rather than the complicated iterative procedure outlined by Stout and Zobeck (1997), c p was determined for each run by simply sorting wind speed values in a spread sheet in ascending order and determining the wind speed corresponding to the total number of zero transport data points recorded for that run. A photograph of beach conditions on October 26, 2000 is shown in Fig. 2a and the instrument layout for the experiment carried out on that day in Fig. 3. Three balance traps were set up at the top middle and bottom of the dune ramp, with the bottom trap being about 10 m landward of moist sand associated with the swash limit on the previous high tide (Figs. 2a and 3). Five sampling runs ranging in length from 18 to 25 min were carried out between 13:40 and 17:00. Winds were from the west–north–west blowing along the beach and slightly onshore. Wind speeds measured at 10 m at the back barrier station were about 11 m s1 for the first run, dropping to about 10 m s1 for runs 2–4 and then rising to 13 m s1 in a squall during the final run (Fig. 4). Winds were slightly less oblique during the final run (Fig. 4). Wind speed (m s1) recorded at anemometer 4 at a height of 0.3 m and transport (g s1) measured at trap 2 at the top of the dune ramp are shown in Fig. 5a for a 25-min run. Data were collected at 1 Hz and the calculated value for c p is 0.67. The spiky nature of the sediment transport data in Fig. 5a is in part an artefact of the 0.1 g resolution of the balance and this also affects the resolution of the transport rate. Assuming a 100% trapping efficiency, a 0.1 g s1 trapping rate with a trap opening of 0.01 m corresponds to a
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Fig. 3. Plan view of experimental set-up on October 26, 2002. No usable data were collected from anemometer 9.
transport rate of 0.0025 kg m1 s1. If the instantaneous rate falls below this value it takes longer than 1 s for sufficient weight to accumulate on the balance to change the value of the reading and thus to register transport for that 1-s period. Additionally, there is some variation in the length of time it takes for sediment to reach the balance. Sand entering the bottom of the trap reaches the balance slightly more quickly than sand travelling 30 cm above the bed which hits the wire mesh at the back of the trap and then falls to the bottom of the trap before going through the funnel to the balance tray. In order to reduce the effect of the balance resolution and the difference in time to reach the balance, the balance and wind data were smoothed using a 5-s running mean with each point equally weighted (Fig. 5b). Smoothing the data increases the resolution of the transport rate to 0.02 g s1. It clearly reduces the variation in the record, and the magnitude of the highest gusts and equivalent transport rates. However, as noted by Stout (1998), the definition of c p is affected by the sampling frequency and thus the smoothing process results in a decrease in the number of data points showing a zero transport rate and a
corresponding increase in c p from 0.67 to 0.91 for trap 2. The transport rate for trap 1 near the base of the ramp is also shown in Fig. 5b. The unsmoothed value of c p for trap 1 is 0.07 and this increases to 0.20 when the data are smoothed by the 5 s running mean. Clearly there is a trade-off between some loss of the signal and the errors introduced by the precision of the balances; the 5 s running mean used here represents the shortest time fraction that produced strong correlation with the wind record. 4.2. Thresholds of sediment transport Wherever sediment transport is intermittent, the instantaneous transport rates can be used to define and explore the nature of the sediment transport threshold and its relation to moisture content on the beach. The threshold wind speed can be calculated from the instantaneous data by requiring that the fraction of time that the wind exceeds the threshold value (c t) be equal to the fraction of time that saltation occurs in the record (Stout and Zobeck, 1997). This is termed here the intermittency threshold U tc . We can define two other estimates of the threshold wind speed based on
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Fig. 4. Mean wind speed and direction for October 26, 2000 measured at a height of 10 m in the back barrier. Shore perpendicular is approximately 2308.
the instantaneous record: (1) U tmin, the lowest wind speed for which transport is measured and (2) U tmax, the highest speed for which zero transport is measured. Initial examinations of the records for five
runs for all three traps deployed showed that there was considerable scatter based on a single point, and that a more consistent measure of the upper and lower bounds for the threshold could be obtained from
Fig. 5. Comparison of fluctuations in wind speed measured at anemometer 4 and sediment transport at trap 2 (top of dune ramp), (a) instantaneous record recorded at 1 Hz; (b) 5 s running mean for wind speed, trap 2 and trap 1 (bottom of ramp).
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averaging over several data points. Thus U tmin was estimated from the mean of the lowest five wind speed measurements associated with sediment transport and U tmax from the mean of the highest five speeds where there was no transport. The smoothed 1 Hz data for sediment transport (sand trapping rate) is plotted against wind speed measured at anemometer 4 for all non-zero values for trap 2 at the top of the dune ramp and trap 1 at the base of the ramp (Fig. 6) together with values for c p, U tc , U tmin, and U tmax. There are clear differences between the two traps, located only 10 m apart, in the relationship between sediment transport rates and wind speed (Figs. 5b and 6a,b), with transport rates showing a much greater tendency to increase with increasing wind speed at trap 2 than at trap 1. These differences are also evident in the mean transport rate, maximum transport rate and the proportion of time that sediment transport occurs (Figs. 5b and 6a,b), with the lower values at trap 1 reflecting closer proximity to the wet sand at the top of the swash line, and thus a much shorter fetch.
The intermittency threshold wind speed U tc and U tmax are both greater for trap 1 at the base of the ramp than for trap 2 at the top of the ramp but the values for U tmin are similar (Fig. 6). In order to explore the nature of the relationship between the various estimates of threshold wind speed and trap location the three parameters are plotted for all five runs carried out on October 26, 2000 (Fig. 7). Only trap 2 was deployed for the first run at 13:40. Run 5 (mean wind speed 8.5 m s1) is truncated after 500 s because the onset of rain in the squall led to clogging of the trap entrance. The intermittency threshold U tc shows no significant variation with mean wind speed (Fig. 7a). There is, however, a clear distinction between the values for each trap location, with U tc decreasing from the bottom of the ramp to the top of the ramp. The maximum threshold U tmax also shows a distinction based on location on the dune ramp, with lower values recorded at the top of the ramp compared to the bottom (Fig. 7b). Unlike the case for the intermittency threshold, the maximum threshold
Fig. 6. Plot of sediment transport (g s1) against wind speed at anemometer 4 for all non-zero transport values: (a) trap 2 at the top of the dune ramp; (b) trap 1 at the base of the ramp. Also shown are the values for the intermittency function c p, the lower and upper bounds for the threshold of transport U tmin, U tmax, and the calculated intermittency threshold U tc .
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Fig. 7. Estimates of the threshold wind speed plotted against mean wind speed (measured at 0.3 m) for five runs on October 26 for traps located at the top, middle and base of the dune ramp. Note that only the trap at the top of the ramp was deployed during the first run: (a) intermittency threshold, U tc ; (b) maximum threshold U tmax; and (c) the minimum threshold U tmin. Lines on (a) and (b) are extrapolations drawn by eye. The line on (c) is the linear best fit line which has an R 2 of 0.74—significant at the 95% confidence level.
U tmax does show some variation with mean wind speed, initially showing an increase with increasing wind speed to about 7.5 m s1 and then considerably lower values being recorded for the highest wind speed (Fig. 7b). By comparison with the other two threshold estimates, the values for U tmin (Fig. 7c) show very little differentiation by trap location but they do show a significant linear increase in the threshold value with increasing mean wind speed (R 2=0.74).
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The decrease in both U tc and U tmax up the dune ramp appears to reflect the effects of distance from the wet upwind boundary—i.e. increasing fetch length. The decrease in the values for the intermittency parameter c p and increase in the transport rate in this direction both suggest that the spatial dependency of U tc and U tmax can be attributed to the saltation cascade which is initiated at the edge of the damp surface (Fig. 2a), with the threshold increasingly being controlled by saltation impacts rather than fluid forces. The decrease in the values for U tmax at the highest wind speed is interpreted to be a reflection of an increase in the fetch length with the very high wind speed recorded during this squall. Observations during the run showed that sediment was mobilized on the damp foreshore out to 20 m seaward of the base of the dune ramp. The increase in U tmin with increasing wind speed is interesting. It may in part simply reflect the fact that as the mean wind speed increases there are fewer low wind speed values at which sediment transport occurs. However, at the highest mean wind speed there is little difference in the value recorded at the three traps yet the intermittency parameter ranged from a high of 0.99 at trap 2 at the top of the ramp to a low of 0.64 at trap 1 at the bottom of the ramp. It seems more likely that the explanation lies primarily in the drying effects of wind blowing over the surface layer, possibly aided by solar insolation, which results in a dynamic variation in the fluid threshold with time. At low wind speeds transport is highly intermittent, but drying of the surface layer in the comparatively long intervals between transport events eventually reduces the fluid threshold to the point where sediments can be entrained during a gust. At a high mean wind speed, gusts can remove a surface layer with a much higher moisture content and there is insufficient time during intervals of relatively low winds for the surface to dry out to the point where transport can be initiated. 4.3. Temporal variability of sand transport and wind speed Examination of the smoothed instantaneous transport rates and wind speed suggests that the temporal variability of sediment transport is similar to the pattern of wind gusts (e.g. Fig. 5b). It is difficult to compare many of the records statistically because the
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Fig. 8. Plan view of experimental set-up on November 6, 2000.
transport data is not continuous. However, continuous transport was measured over a period of 500 s at trap 2 during Run 5 on October 26 resulting from the high winds associated with a squall line. Similarly, continuous transport was recorded at trap 3 during an experiment on November 6th with winds blowing obliquely offshore and the traps set up onto the foreshore (see Fig. 8). Dry sand had accumulated near the base of the eroded foredune over the previous 5 days and this was blown alongshore and offshore across the exposed foreshore at low tide. The time series of wind speed for both days (Figs. 9a and 10a) show considerable fluctuation over a range of frequencies. In all cases, the sand transport rate responds rapidly to changes in wind speed and the two series appear very similar. Spectra for both days show no significant peaks and a relatively steady increase in energy towards lower frequencies (Figs. 9b and 10b). The cross-spectra also tend to increase towards the low frequency end (Figs. 9c and 10c). What is perhaps most significant is that the coherence between the two series on both days is generally high across the spectrum at frequencies lower than 0.2 Hz. Spectra for trap 1 on October 26 and trap 2 on November 6 show similar features. The similarity of the spectra and the high coherence over much of the spectrum on both days and at two different locations on the beach provide strong support for earlier studies
Fig. 9. Wind speed and sediment transport relationships October 26, Run 5: (a) instantaneous sediment transport and wind speed, trap 2 at the top of the ramp; (b) spectra for wind speed and sediment transport; (c) cross spectra and coherence. The spectral data are smoothed using Hamming weights over 15 frequency classes. Note that, because the original data were smoothed by a 5-s running mean, the spectra have been truncated at a frequency of 0.2 Hz.
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6. The locations of the instruments are shown in Figs. 3 and 8. These traps were selected because they were directly paired with an anemometer mounted at a height of 0.3 m adjacent to the trap. The mean wind speed and intermittency parameter, as well as the R 2 value and exponent for the best fit power curve are given in Table 1 for all observations and several examples are shown in Fig. 11. Trap 2 on October 26 and trap 3 on November 6 have the longest fetch on the respective days and the highest rates of transport recorded for all the runs. In general, the R 2 values for these traps are relatively high (0.4–0.6) and the exponent for the least squares power function lies between 4 and 6. Trap 2 on October 26 shows greater variability, with a low value of 1.1 for run 4 and a high of 6.94 for run 3. Trap 1 on October 26 and trap 2 on November 6 have a much shorter fetch: the R 2 values are generally lower than those for the traps with a longer fetch and the values Fig. 10. Wind speed and sediment transport relationships November 6, Run 4: (a) instantaneous sediment transport and wind speed trap, 3 near the low tide limit; (b) spectra for wind speed and sediment transport; (c) cross spectra and coherence. The spectral data are smoothed using Hamming weights over 15 frequency classes. Note that, because the original data were smoothed by a 5-s running mean, the spectra have been truncated at a frequency of 0.2 Hz.
that indicate that, where there is an abundant source of sediment, the transport system responds rapidly to fluctuations in the wind speed. 4.4. Prediction of sediment transport rate The relationship between wind speed or wind shear velocity and the resulting sand transport rates has usually been modelled using a power function with an exponent of 3 (Bagnold, 1941; Kawamura, 1951; Lettau and Lettau, 1977). Empirical measurements in wind tunnels and in the field have usually been based on integrated traps and the use of the balance traps permits an examination of the instantaneous response of transport to changing wind speeds. The relationship between instantaneous wind speed and the sand transport rate was explored by fitting power curves to all pairs of observations in a measurement run with non-zero transport data for traps 1 and 2 deployed on October 26 and traps 2 and 3 deployed on November
Table 1 Summary of statistics from best-fit power regression curve for instantaneous sediment transport measured by balance traps and wind speed measured at a co-located anemometer at 0.3 m above the bed for all runs on October 26, 2000 and November 06, 2000 U mean (m s1)
No. of observations
IP
R2
Exponent
October 26 Trap 1 1 2 3 4 5 Trap 2 1 2 3 4 5
6.91 6.31 6.94 9.16 7.31 6.7 6.12 6.74 8.41
1484 1492 1486 512 996 1484 1492 1486 512
0.18 0.13 0.07 0.87 0.84 0.91 0.33 0.95 1
0.4 0.13 0.06 0.24 0.47 0.54 0.32 0.03 0.74
1.02 2.56 1.31 3.29 5.18 4.44 6.94 1.1 5.21
November 6 Trap 2 3 4 5 6 Trap 3 3 4 5 6
8.68 8.13 8.56 7.79 7.97 7.61 8.2 7.66
827 804 771 890 827 804 771 890
0.99 0.99 1 0.99 1 1 1 0.99
0.13 0.6 0.17 0.24 0.35 0.65 0.63 0.48
1.96 4.45 1.98 2.34 3.97 4.97 4.88 4.3
Trap #
Run #
Values are for the entire run except for rune 5 on October 26, which is cut off after the onset of rain. The regression curve is fitted for all non-zero transport pairs.
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Fig. 11. Examples of plots of instantaneous wind speed and transport rate for pairs of traps for all non-zero transport conditions from runs on October 26 and November 6, 2000: (a) traps 1 and 2, October 26 run 2; (b) traps 1 and 2 October 26 run 5; (c) traps 2 and 3 November 6 run 6. The instrument layouts are shown in Figs. 3 and 8. Data from all runs on the two days are shown in Table 1.
of the exponent for the least squares power function lies between 1 and 2.5. An exception to this occurs for trap 1 on October 26 during run 5 where the exponent is 3.29. As noted earlier, during this run a squall mobilized sediment transport on the damp foreshore, resulting in much higher transport rates being recorded at trap 1 and in effect increasing the fetch in front of the trap. Similarly, results from trap 2 for run 4 on November 6 gave an R 2 value of 0.6 and an exponent of 4.45. At this time, small dunes were beginning to form on the foreshore and the high transport rate may reflect the development of a dune with considerable quantities of dry sand immediately in front of the trap.
5. Discussion Comparison of instantaneous wind speed and sediment transport records show that the sand trans-
port system on the beach responds rapidly to changes in wind speed and this is supported by the coherence of the cross spectra for two runs where there was continuous transport. This is in agreement with a number of other studies (e.g. Butterfield, 1993; McKenna Neuman et al., 2000; Davidson-Arnott et al., 2003) and the pattern is clear both for fluctuations in the rate of transport during conditions of continuous transport, as well as for the occurrence of bursts of transport during conditions of intermittent transport. Nevertheless, while the pattern of response of the sediment transport system closely follows that of the wind speed, plots of the instantaneous transport values show that there is considerable scatter in the magnitude of the transport response over periods of seconds to minutes at one location and spatially over distances of a few metres. Much of this temporal and spatial variability appears to reflect the availability of sediment for entrainment and the effects of moisture content and fetch length.
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Comparison of different estimates of sediment transport threshold (Fig. 7) show that in the field, particularly where there are strong gradients in the moisture content of surface samples, there can be no simple definition of a threshold related to moisture content (e.g. Belly, 1964). Clearly, sediment entrainment at a point depends not only on the local moisture conditions but also on moisture conditions and entrainment in the upwind area. The results from this study indicate that, during intermittent sediment transport, what is happening on the surface upwind of the point of interest is probably more important than the local fluid threshold related to moisture. The dependence of the minimum threshold U tmin on wind speed demonstrates the additional temporal complexity introduced by surface drying—in effect the threshold can vary over periods as short as tens of seconds in response to drying of the surface layer of grains by wind and by insolation. Similar results have been reported from a study carried out on a beach in Wales (Wiggs et al., 2004) and from work carried out in Prince Edward Island, Canada (Yang, 2003). Thus, intermittency in sediment transport is not just a reflection of variations in wind speed above and below a fixed threshold (Stout and Zobeck, 1997) but also of variations in the threshold itself as the moisture content of the surface layer changes. The complex pattern of sand streamer generation commonly observed on beaches therefore can be seen as a reflection of both the temporal and spatial fluctuations in wind speed and surface moisture content. The spatial variation in threshold effects and transport rates with distance downwind from the wet zone on both of the days reported here provides supporting empirical evidence for the role of the fetch effect in controlling the transport rate (Davidson-Arnott and Law, 1990; Greeley et al., 1996; Davidson-Arnott and Dawson, 2001). While recent wind tunnel studies show that with uniform dry sand fetch distances are only a few metres (e.g. Dong et al. 2004) field studies, including this one, have shown that it is more usually tens of metres (Davidson-Arnott and Law, 1990; Nordstrom and Jackson, 1992; Gillette et al., 1996) and it may be particularly significant on beaches where surface moisture contents are often N4%. These results reinforce the need for the explicit consideration of the
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fetch effect in modelling sand supply to coastal dunes (Bauer and Davidson-Arnott, 2002). Finally, the complexity of the transport system is reflected in the wide range of exponents obtained by fitting power curves to regressions between the instantaneous wind speed and transport rates (Table 1). The traditional cubic relationship between shear velocity U * or wind speed U and the sand transport rate has been derived largely from wind tunnel studies with steady uniform winds and dry, well sorted sand, with transport averaged over periods of 10 min or more (e.g. Bagnold, 1941; Kawamura, 1951). Fluctuating wind speeds introduce complexities because the cube of mean shear velocity for a given time period is generally not equal to the mean of the cube of instantaneous shear velocities (Namikas et al., 2003). The situation becomes more complex when transport is intermittent because the average transport rate integrates periods of transport and no transport ((Stout and Zobeck, 1997; Rasmussen and Sorensen, 1999; McKenna Neuman et al., 2000) and this probably accounts for some of the discrepancies observed in field studies between predicted transport rates and actual measured values (e.g. Sherman et al., 1998). The values of 4.5–6 for the exponent measured here for the two downwind traps are large, but measurements of transport intensity using a saltation probe which measures the impact of grains on a piezo-electric crystal have also shown similar high exponents when power curves are fitted to the data (Davidson-Arnott et al., 2003). Where the intermittency value is well below unity, the average transport rate over a period of minutes will be much lower and this will produce a better fit with predictive equations based on a cubic relationship between mean wind speed and transport rates. However, it should be noted that the high exponents were also obtained for conditions where there was continuous transport (c p=1). As we improve our ability to make high speed measurements of sediment transport in the field, the relationships between high frequency dynamics and the prediction of average transport rates over periods tens of minutes will need to be refined. There is considerable scatter in the data points relating transport rates to wind speed. Some of the scatter may be related to a tendency for a decrease
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in transport to lag slightly behind a decrease in wind speed (McKenna Neuman et al., 2000). Some of it may simply reflect the spatial and temporal variability of sand streamers, with higher transport rates associated with the streamers and lower rates between the streamers.
M. Christiansen, C. Houser, J. Nielsen and N. Vinther for their assistance in the field, and M. Finoro and M. Puddister for technical and cartographic assistance.
References 6. Conclusions The conclusions of the study can be summarized as follows: (1) Sand transport rates respond instantaneously to variations in wind speed at a range of frequencies from seconds to minutes for both intermittent and continuous sediment transport; (2) Surface moisture content on the beach greatly influences the threshold of movement at a point. However, the actual threshold is a dynamic one that is influenced by the rate of drying of the surface layer of grains. Moisture content influences both the fluid threshold and the impact threshold and entrainment of sediment from a point on the surface is controlled both by the conditions at that point and by events happening over the upwind surface; (3) Together with the intermittency threshold defined by Stout and Zobeck (1997) the minimum and maximum thresholds considered here provide different measures of the factors controlling sediment entrainment and transport; (4) The fetch effect influences the actual threshold at a point and, together with the availability of dry sand, it appears to influence the magnitude of the response of the transport rate to varying wind speed.
Acknowledgements The field study was supported by a research grant from the Danish Natural Sciences Research Council, Grant numbers 9701836 and 11-0925 (T. Aagaard Principal Investigator) and by a Natural Sciences and Engineering Research Council of Canada Research Grant to RD-A. We thank J. Dawson, B. Greenwood,
Aagaard, T., Nielsen, N., Nielsen, J., 1995. Skallingen—Origin and evolution of a barrier spit. Technical Memo No. 35, Institute of Geography, University of Copenhagen, 86 pp. Aagaard, T., Nielsen, J., Davidson-Arnott, R., Greenwood, B., Nielsen, N., 1998. Coastal morphodynamics at Skallingen, SW Denmark: high energy conditions. Geogr. Tidsskr. 98, 20 – 30. Aagaard, T., Davidson-Arnott, R., Greenwood, B., Nielsen, J., 2004. Sediment supply from shoreface to dunes: linking sediment transport measurements and long term morphological evolution. Geomorphology 60, 205 – 224. Anderson, R.S., Haff, P.K., 1991. Wind modification and bed response during saltation of sand in air. Acta Mech. (Suppl.) 1, 21 – 52. Arnold, S., 2002. Development of the saltation system under controlled environmental conditions. Earth Surf. Process. Landf. 27, 817 – 829. Bagnold, R.A., 1941. The Physics of Blown Sand and Desert Dunes. Methuen, London. 265 pp. Bauer, B.O., Davidson-Arnott, R.G.D., 2002. A general framework for modelling sediment supply to coastal dunes including wind angle, beach geometry, and fetch effects. Geomorphology 49, 89 – 108. Belly, P.-Y., 1964. Sand movement by wind. U.S. Army Corps of Engineers CERC, Tech. Memo. 1, 38 pp. Butterfield, G.R., 1991. Grain transport rates in steady and unsteady turbulent airflows. Acta Mech. (Suppl.) 1, 97 – 122. Butterfield, G.R., 1993. Sand transport response to fluctuating wind velocity. In: Clifford, N.J., French, J.R., Hardisty, J. (Eds.), Turbulence: Perspectives on Flow and Sediment Transport. John Wiley and Sons, Chichester, England, pp. 305 – 336. Chapman, D.M., 1990. Aeolian sand transport—an optimized model. Earth Surf. Process. Landf. 15, 751 – 760. Chepil, W.S., Milne, R.A., 1939. Comparative study of soil drifting in the field and in a wind tunnel. Sci. Agric., 249. Cornelis, W.M., Gabriels, D., 2003. The effect of surface moisture on the entrainment of dune sand by wind: an evaluation of selected models. Sedimentology 50, 771 – 790. Davidson-Arnott, R.G.D., Law, M.N., 1990. Seasonal patterns and controls on sediment supply to coastal foredunes, Long Point, Lake Erie. In: Nordstrom, K.F., Psuty, N.P., Carter, R.W.G. (Eds.), Coastal Dunes: Form and Process. John Wiley and Sons, pp. 177 – 200. Davidson-Arnott, R.G.D., Law, M.N., 1996. Measurement and prediction of long-term sediment supply to coastal foredunes. J. Coast. Res. 12, 654 – 663. Davidson-Arnott, R.G.D., Dawson, J.D., 2001. Moisture and fetch effects on rates of aeolian sediment transport, Skallingen,
R.G.D. Davidson-Arnott et al. / Geomorphology 68 (2005) 115–129 Denmark. Proceedings Canadian Coastal Conference, CCSEA. , pp. 309 – 321. Davidson-Arnott, R.G.D., Ollerhead, J., Hesp, P.A., Walker, I.J., 2003. Spatial and temporal variability in intensity of aeolian transport on a beach and foredune. Proc. Coastal Sediments ’03, ASCE. 11 pp. Dong, Z., Wang, H., Liu, X., Wang, X., 2004. The blown sand flux over a sandy surface: a wind tunnel investigation on the fetch effect. Geomorphology 57, 117–127. Fryberger, S.G., Dean, G., 1979. Dune forms and wind regime. In: McKee, E.D. (Ed.), Global Sand Seas, pp. 141 – 151. Gillette, D.A., Herbert, G., Stockton, P.H., Owen, P.R., 1996. Causes of the fetch effect in wind erosion. Earth Surf. Process. Landf. 21, 641 – 659. Greeley, R., Blumberg, D.G., Williams, S.H., 1996. Field measurements of the flux and speed of wind-blown sand. Sedimentology 43, 41 – 52. Jackson, N.L., Nordstrom, K.L., 1998. Aeolian transport of sediment on a beach during and after rainfall, Wildwood, NJ, USA. Geomorphology 22, 151 – 157. Kawamura, R., 1951. Study of sand movement by wind. University of Tokyo, Rept. Inst. Tech. 5, #314. Lee, J.A., 1987. A field experiment on the role of small scale wind gustiness in aeolian sand transport. Earth Surf. Process. Landf. 12, 331 – 335. Lettau, K., Lettau, H., 1977. Experimental and micrometeorological field studies of dune migration. In: Lettau, K., Lettau, H. (Eds.), Exploring the World’s Driest Climate, IES Report, vol. 101. University of Wisconsin Press, Madison, pp. 110 – 147. McKenna Neuman, C., Maljaars Scott, M., 1998. A wind tunnel study of the influence of pore water on aeolian sediment transport. J. Arid Environ. 39, 403 – 419. McKenna Neuman, C., Nickling, W.G., 1989. A theoretical and wind tunnel investigation of the effects of capillary water on the entrainment of sediment by wind. Can. J. Soil Sci. 69, 79 – 96. McKenna Neuman, C., Lancaster, N., Nickling, W.G., 2000. Effect of unsteady winds on sediment transport intermittency along the stoss slope of a reversing dune. Sedimentology 47, 211 – 226.
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Namikas, S.L., Sherman, D.J., 1995. A review of the effects of surface moisture content on aeolian sand transport. In: Tchakerian, V.P. (Ed.), Desert Aeolian Processes. Chapman and Hall, London, pp. 269 – 293. Namikas, S.L., Bauer, B.O., Sherman, D.J., 2003. Influence of averaging interval on shear velocity estimates for aeolian transport modelling. Geomorphology 53, 235 – 246. Nickling, W.G., Davidson-Arnott, R.G.D., 1990. Aeolian sediment transport on beaches and coastal sand dunes. In: DavidsonArnott, R.G.D. (Ed.), Proceedings Symposium on Coastal Sand Dunes. National Research Council of Canada, pp. 1 – 35. Nickling, W.G., McKenna Neuman, C., 1997. Wind tunnel evaluation of a wedge-shaped aeolian transport trap. Geomorphology 18, 333 – 345. Nordstrom, K.F., Jackson, N.L., 1992. Effect of source width and tidal elevation changes on aeolian transport on an estuarine beach. Sedimentology 39, 769 – 778. Owen, P.R., 1964. Saltation of uniform grains in air. J. Fluid Mech. 20, 225 – 242. Rasmussen, K., Sorensen, M., 1999. Aeolian mass transport near the saltation threshold. Earth Surf. Process. Landf. 24, 413 – 422. Sherman, D.J., Namikas, D.W.T., Wang, S.L., 1998. Wind blown sand on beaches: an evaluation of models. Geomorphology 22, 113 – 133. Stout, J.E., 1998. Effect of averaging time on the apparent threshold for aeolian transport. J. Arid Environ. 39, 395 – 401. Stout, J.E., Zobeck, T.M., 1997. Intermittent saltation. Sedimentology 44, 959 – 970. Wiggs, G.F.S., Baird, A.J., Atherton, R.J., 2004. The dynamic effect of moisture on the entrainment and transport of sand by wind. Geomorphology 59, 15 – 30. Yang, Y., 2003. The Effects of Surface Moisture Content on Aeolian Sediment Transport on a Beach. MSc thesis, University of Guelph, 105 pp.