Airflow Dynamics and Aeolian Sand Transport Across a Beach‐Climbing Dune‐Clifftop Dune System

This study presents an analysis of wind flow and sediment transport from the beach up a 50 m high, long (130 m), steep (mean slope 26°) climbing dune and across a 1.5 m high max, 85 m long and 17.5 m wide clifftop dune 30 km south of Dakhla in Morocco, NW Africa, during highly oblique incident wind conditions. Multiple 2D sonic and cup/vane anemometers and sand traps were utilized for measurements. Flow steering was significant on the upper climbing dune. Flow deceleration occurred near the dune toe, and topographic forcing of flow was considerable on the upper slopes of the climbing dune. Near‐surface flow steadiness (CVU1, CVU0.25) on the climbing dune straight slope segment was low and constant. The distance upslope over which the airflow reached a speed comparable to that on the beach increases as the incident wind speed increases. The greatest flow acceleration and speed‐up was observed at the cliff edge reaching 250% at 1 m height and 220% at 0.25 m height for the lowest incident wind speed class (4–5 m/s). The sand transport rate declined from the beach to the climbing dune toe and lower slope, but at the uppermost section of the climbing dune was 4 times higher than in the beach for the 7–8 m/s incident wind speed. Sand in aeolian transport was generally finer than surface sand, with the mean grain size increasing up the slope. A comparison of the sand transport data collected with sand transport models, and the effects of slope on Aeolian transport are also examined.

Modern active climbing dune-cliff-top dune systems have not been studied comprehensively.Tsoar et al. (1991) investigated the effect of 20-25 m high sea cliffs (with slopes higher than 40° at some portions) on airflow and inland encroachment of aeolian sand and concluded that sand could be transported inland only through gaps and depressions within the cliff edge.Tsoar et al. (1996) and White and Tsoar (1998) conducted research in the Negev Desert, where there are some examples of such systems, but they focused on wind flow and sand transport over the windward slope of a 20 m high climbing dune only.Some of the largest active cliff-top dunes, up to 40 m high, are found on the western coast of Jutland, Denmark, where 50-60 m high cliffs built from Weichselian sediments are present.However, these dunes have been studied in relation to their development in historical times (Christiansen et al., 1990) and the source of dune sand (Sadolin et al., 1997;Saye et al., 2006).The authors showed that cliff-top dunes have been developing since 1885 and are nourished with sand deflated from unconsolidated cliff deposits, so there is no climbing dune which acts as a transfer zone for beach sand.There are also some examples of such depositional systems in New Zealand, but studies focused on a single element of this system, either flow dynamics (Hesp, 2005), or dune sand textures (Dłużewski et al., 2021).Cliff-top dunes also develop on top of scarped foredunes (Carter et al., 1990;Davidson-Arnott et al., 2018;Hesp, 2002;Ollerhead et al., 2013) although they are not typically referred to as "cliff-top dunes" in this environment.The morphology of cliff-top dunes is variable and depends on the mode of their formation, source of sand and the way they are nourished with sand, the relief of the cliff face and the angle of the cliff edge relative to the dominant wind direction.
There are many issues in studying such systems, as modification of airflow, impact of slope inclination on sediment transport, relationship between sand transport rate and wind acceleration up the slope, changes in the mean grain size and sand sorting downwind and upslope, and differences in grain size parameters between surface and transported sand.Undoubtedly, climbing and cliff-top dunes present on rocky cliffs of the north-west African Atlantic coast are very good examples of such systems and because they are active today, they provide an opportunity for studying factors controlling their development.Some of these systems are found along 50-60 m high cliffs and feature significantly large climbing dune systems and variously small to large cliff-top dunes.

Sand Transport
Prediction of aeolian mass transport is usually based on one of the existing transport models such as those by Bagnold (1941), Zing (1953), Lettau andLettau (1978), andSorensen (2004) and many others (see Sherman et al., 1998Sherman et al., , 2013 for review) for review).All these models relate the sand transport rate to shear velocity, which, however, is difficult to measure directly in the field due to limitations of available measurement techniques (Sherman, 2020;Sherman & Hotta, 1990).For a flat and horizontal surface, sand transport can be calculated from a log-linear wind profile measured in the field.As the surface becomes inclined, the wind profile is no longer logarithmic, and the steeper the slope, the more it deviates from it (Frank & Kocurek, 1996a, 1996b).There have been some efforts to overcome this problem.Bagnold (1956) and Hardisty and Whitehouse (1988) developed slope-corrected transport formulae that recalculate the sand transport rate for horizontal surfaces against slope inclination.Sherman et al. (1998) evaluated many transport models and analyzed the validity of applying corrections for sand moisture and surface slope and suggested that a slope correction in Bagnold's model performed well, but contrary to them both, Howard (1977), Howard et al. (1978), andSabatier et al. (2002), who also evaluated this slope-corrected formulae, concluded that it did not significantly improve the predictions.On the other hand, results obtained from field studies in Saharan sand seas by Hardisty and Whitehouse (1988) showed that the bed slope strongly affected the transport rate which was related to the seventh power of bed slope.Therefore, the prediction of the sand transport rate over a long and steep slope is still a challenge.Some of the research on airflow modification along the stoss slope of different dunes was accompanied by measurements of sand transport rates and/or studies on sand texture and its change upslope on these bedforms.However, most of these studies were based on measurements made on windward slopes of transverse dunes, usually barchan, barchanoid, or reversing dunes, which are inclined at an angle of 12 or so degrees.They demonstrated that: (a) sand transport rate increases upslope; however, this increase is not always proportional to an increase in wind speed (e.g., Hesp et al., 1989;Lancaster, 1985;Lancaster et al., 1996;McKenna Neuman et al., 2000;Wang et al., 2002), (b) the lowermost part of the stoss slop experiences erosion, whereas at the crest-either deposition or erosion depending on dune shape (crest coincident with the brink or not; Baddock & Wiggs, 2011), wind speed and the intermittency of transport (McKenna Neuman et al., 2000), and, (c) the middle part of the dune is a by-passing zone (Walker et al., 2022).All this translates into a reduction in mean grain diameter up the slope with the coarsest mode of sand left as lag deposits in the lower part of the stoss slope due to the effect of winnowing of finer particles (Lancaster et al., 2002;White & Tsoar, 1998).
Much less studies were devoted to the differences between grain size and sorting of surface sand and sand transported by wind.White and Tsoar (1998), Wang et al. (2002), andYang et al. (2019) pointed to the great difference between surface and transported sand, but they have not found a simple relationship between these properties and wind speed.
While there have been many studies on lee-side flow expansion and deceleration (e.g., Bagnold, 1953;Frank & Kocurek, 1994, 1996b;Inman et al., 1966;Livingstone, 1986;Sweet & Kocurek, 1990;Tsoar, 1978Tsoar, , 1982Tsoar, , 1983Tsoar, , 1985;;Tsoar & Yaalon, 1983;Walker, 1999;Walker et al., 2000;see review in Walker et al., 2022) and related modes of transport (fallout from suspension and grain flow), there is relatively little quantitative data documenting the lee-side sand transport.There is some research trying to determine the rate of grainfall deposition with distance from the dune crest.Hunter (1985) suggested that this relationship may be described with a power function, whereas Anderson (1988) and Nickling et al. (2002) suggested an exponential function.They also showed that up to 99% of the total grainfall was deposited within 2 m beyond the dune crest.The exception is research conducted by Petersen et al. (2011), who documented sand transport at relatively significant distances (more than 100 m) past the foredune crest under conditions of high incident wind speeds, but in fact they mainly measured the rate of sand transport in suspension and modified saltation.To our knowledge, there is no research on sand transport rates on modern and active cliff-top dunes.
Therefore, the main objectives of this paper are to: (a) analyze airflow forcing and steering up a long (>130 m) and steep (effective slope up to 26°) stoss slope of a climbing dune where the effective slope is the inclination of 10.1029/2023JF007316 4 of 24 the climbing dune along the average flow direction, (b) determine the zone of flow expansion and deceleration beyond the cliff edge and the distance at which the airflow recovers, (c) determine sand transport rates on different parts of the climbing dune-clifftop dune system and relate it to flow speed-up and turbulence, and (d) examine changes in grain size and sand sorting of the surface sand and sand in transport along the transport path starting on the beach and extending to the most landward downwind tip of the cliff-top dune.

Study Site
A significant part of the Atlantic coast of Morocco is made up of rocky cliffs up to 70 m high, which face either direct impact from waves or are separated from the ocean by sandy beaches.In some places, sand from the beach is transferred by the wind over the cliff face toward the land, forming cliff-top dunes behind the cliff edge.These dunes occur atop cliffs east of Tarfaya and between Boujdour and south of Dakhla (Figure 1a).
The study area is located in southern Morocco, Río de Oro region (River of Gold), about 30 km south of Dakhla and south of Dakhla Bay, a spot known for its ideal conditions for kitesurfing.The flow experiments were carried out about 4 km south of the Tropic of Cancer, where the nearly straight cliff edge trending NNE-SSW bends toward the east, thus allowing for sand accumulation and beach formation (Figure 1b).The cliff is 50 m high (Figure 1c) and built of a sedimentary rock succession that consists of a thick sequence of white-beige marly siltstone interbedded with gray chert and black coprolite-supported conglomerates overlain by yellowish marly siltstones, sandstones, and muddy sandstone, sometimes with gypsum.The uppermost and the least thick part of the sequence consists of a massive sandy to bioclastic limestone with root traces (Adnet et al., 2010;Benammi et al., 2019).The rock succession exposed in this cliff represents a general marine shallowing-upward trend which ends with tidal/coastal deposits.The succession contains some horizons rich in fossils, which made it possible to estimate the age of the deposits as Upper Eocene-Lower Oligocene (Benammi et al., 2019).The succession outcropping in the cliff belongs to the Paleogene Samlat Formation formed in the Tarfaya-Laâyoune-Dakhla coastal basin developed in a stable passive margin and filled with Mesozoic and Cenozoic continental to shallow-marine sediments (Zouhri et al., 2018).
The coast is subject to semidiurnal meso-tides, with a tidal range up to 2.5 m (https://www.tide-forecast.com).The climate is extremely dry, with average precipitation equal to 40 mm/year (Dłużewski, 2013), but the air is relatively moist and the relative humidity is generally over 75%.The monthly average temperature in Dakhla, the nearest meteorological station, varies from 18°C in January to approximately 22-23°C from August to October.The effective wind regime is dominated by trade winds blowing from the north-northeast along the Atlantic coast of western Sahara and thus parallel to the coastline (Figure 2a).According to Fryberger and Dean (1979) indices the wind regime of the coast may be classified as narrow unimodal (RDP/DP 0.94) and high energy (DP 1076) (Figure 2a).The period of high sand drift potential includes summer months (June to August), when the monthly DP is significantly above the average with a maximum in August (DP is more than twice the average, Figures 2b  and 2c).The drift potential in autumn and winter months is less than half of the monthly average.Regardless of the period, the wind direction is relatively constant (RDD between 198° and 213°), resulting in a high monthly RDP/DP index value (>0.8) (Figures 2d and 2e).Due to the presence of a high cliff, onshore and oblique onshore, generally northerly winds are steered to alongshore ones that generate southward sand transport.However, as the orientation of the cliff edge changes southwards (Figure 1b), the protrusion in the cliff (Figure 1c) steers and forces the flow up the cliff, resulting in the formation of a climbing dune, which is a by-passing zone responsible for sand transfer from the beach to the top of the cliff and formation of a cliff-top dune.

Experimental Setup and Measurements
The main flow experiments were carried out on June 10th (12:15-18:40 UTC; Local time = UTC + 1 hr), 12th (12:20-18:20 UTC), 14th (11:30-18:20 UTC) and 16th (12:30-19:00 UTC), 2022 during relatively constant and moderate NNE winds.The wind direction in successive days ranged between 12° and 19° (±5°), and this direction reflects the dominant and typical conditions for the area (Figure 2e), particularly in late spring and summer seasons.The wind direction was nearly parallel to the shore with some onshore component.As the aim of the research was to determine both flow steering and forcing induced by the high cliff and sand transport rate generated in such conditions, sites with anemometers were distributed parallel to the path along which the wind flow was getting saturated with sand (Figures 3a-3c).At each site, a cup anemometer and vane were placed at 1 m elevation, and a 2D sonic anemometer at 0.25 m height.All direction sensors were aligned to the true north.Wind parameters were recorded every 1s.All instruments were oriented at 90° to the local slope.
We measured wind speed and direction at a height of 1 m at Site 1 on the lower beach as the reference station for the experiment.This site was close to the maximum wave run-up and 15 m away from the toe of the climbing dune and was used as a reference mast to analyze changes in wind speed and direction.Further sites downwind included site 2-at the foot of the climbing dune, sites 3-8-regularly spaced up the climbing dune, site 9-cliff edge, sites 10-15-the cliff-top dune with its top at sites 12-12A (Figure 3).
A preliminary experiment aiming at the reconstruction of flow patterns beyond the cliff edge was conducted on 18 October 2019 during similar wind conditions.Five 2D mini-sonic anemometers at heights of 4, 10, 15, 40, and 10.1029/2023JF007316 6 of 24 70 cm and a cup anemometer at heights of 0.1 and 1 m were placed 1.2 m from the cliff edge.Additionally, one cup anemometer was placed at 0.25 m at the cliff edge and a set of small vanes were distributed across the clifftop dune between the cliff edge and Site 10 (Figure 4a).Colored smoke bombs were used to visualize 3D flow via video, which was later analyzed frame by frame at 1 s intervals to determine flow patterns.
The total sand transport rate was measured by means of 0.5 m high passive sand traps composed of a steel casing and removable plexiglass catcher divided into 40 cells, each 1.27 cm high and 1 cm wide (Figure 4b; Rotnicka, 2013aRotnicka, , 2013b;;Rotnicka et al., 2023).The trap design allows for continuous accumulation of sand transported to a height of 0.5 m, and its efficiency has been estimated for medium sand at 82% regardless of wind speed.During each run, the sand traps were operated for 300-600 s depending on the wind strength.As some sand samples collected in sand traps were moist due to increased air humidity at the end of the day, the samples were first dried and then weighed.The total sand transport rate (Q, kg/m/s) was calculated by summing the weight of the sand collected in each cell and dividing by the time of measurement.
Due to the limited number of sand traps and the dimension of the climbing-cliff-top dune system, the sand transport was measured simultaneously at three consecutive sites, two sand traps in each site, starting from the beach Site 1, and repeated 3-4 times.Then, sand traps were left at Site 1 to be a reference site, and traps from two subsequent sites were moved to the next two sites, placed further upwind on the windward slope of the climbing dune (Figure 3a).The same procedure was continued on the cliff top-dunes; however, here the sand transport rate 10.1029/2023JF007316 7 of 24 was measured along the wind parallel dune central axis (∼N-S) as well as on both eastern and western slopes of the cliff-top dune, that is, on both sides of the dune axis (Figure 3b).In total, 100 sand transport measurements were made on the beach and climbing dunes and 162 on the cliff-top dune.
A TOPCON HiPer ® Pro real-time kinematic (RTK) differential global positioning system (DGPS) (precision of 1-2 cm in all dimensions) was used to develop a Digital Elevation Model (DEM) of the beach-dunes system, 2D topographic profile, and to determine wind sensors and sand trap positions.
As the beach and dune sand was macroscopically distinctly different, both surface sand samples and sand samples from sand traps were collected to analyze changes of sediment properties in the whole beach-dune system and properties of the sand transported by wind.All samples were dry sieved on a column of 1/4 phi sieves.Grain size parameters were calculated using the Folk and Ward (1957) graphical method by means of GRADISTAT v 9.1 (Blott & Pye, 2001).

Data Processing
All wind data were analyzed on the basis of 10-s averages.Flow acceleration was characterized by the speed-up factor (Mason & Sykes, 1979) calculated as the ratio between wind speed measured at a given elevation (0.25 and 1 m) at each site and the speed measured at the same elevation at the reference site on the beach (Site 1).To estimate wind steadiness, a proxy measure for turbulence, the coefficient of variance (CV V1 , CV V0.25 ), expressed as the standard deviation of wind speed to mean wind speed, was calculated (Piscioneri et al., 2019;Walker & Nickling, 2003;Walker et al., 2009).There was no significant heating or cooling during the day, temperature varied between 24°C (midday) and 21°C (dusk) and less than 1°C between the elevations of 0.25 and 1 m, so we assumed that the changes in airflow turbulence, as expressed by CV, were imposed only by topography.Directional steadiness was characterized using a standard deviation (SD).

Results
Air temperature ranged between 24°C around midday and 21°C around sunset.The decrease in temperature coincided with an increase in air humidity (from about 60% to 70% to more than 80%), which resulted in the moistening of both the surface sand layer and sand transported by the wind and caught in the sand traps.

Morphology of the Beach-Dune System
Based on a detailed DEM model of the beach-dunes system (Figure 3a), the beach was low gradient (up to 3.5°) with a steep 8° and long (>10 m) swash zone (Figure 5b).The lower part of the climbing dune was concave and its slope increased from 8° to 25° (Figures 3a and 5a).The surface of the upper slope was close to the angle of repose of dry sand, that is, a constant inclination of 33°.As a result, unlike most transverse dunes characterized by a concave-convex profile, the studied climbing dune exhibited a concave-straight profile (Figures 5a and 5b).The uppermost part of the cliff was mostly rocky, without aeolian deposition and inclined at an angle higher than 40° (Figures 3a and 5c).The effective slope, that is, the inclination of the climbing dune along the average flow direction, was 11-14° in its lower part and 22-26° in its middle and upper parts (Figure 3c).The effective flow distance on the climbing dune was 130 m, whereas the maximum fetch distance across the dry beach was more than 50 m.
The elevation of the cliff edge was 50 m above the MSL and the average cliff edge orientation within the study site was 40°-220°, that is, slightly oblique to the resultant drift direction (RDD = 202°).However, the cliff edge orientation within the notch that served as a sand transfer zone from the beach to the cliff (Figure 5b) was on average relatively perpendicular to the direction of flow approaching the cliff edge, steered by the steep >50° rocky slopes of the notch (Figures 3a, 5b, and 5c).
Landward of the cliff edge, the surface was flat and rocky to the horizon (Figures 3a, 3b, 5b, and 5c).A few dozen centimeters from the cliff edge, the cliff-top dune started to form (Figures 5c and 5d).It was 1.5 m high, 85 m long and 17.5 m wide.Its area was 1,037 m 2 and its volume 350 m 3 .The orientation of the dune central axis was 20°-200°, that is, parallel to the resultant drift direction (RDD).The slope inclination along the axis did not exceed 5° (Figure 3c), whereas the west and east slopes were inclined at an angle slightly above 10° (Figures 5c  and 5d).

Wind Steering
During the field measurements, the regional wind direction was relatively constant and at the Dakhla weather station it equaled 14° on average, which means that the wind approached the coastline at an angle of 26° (oblique onshore wind, Figure 6).On the beach and lower part of the climbing dune (up to Site 4), the wind direction was similar (16-19°, SD 4.5°) but further downwind, topographically forced flow steering was observed.It started at Site 5 (13°, SD 5.7°) and continued until Site 9 (359°, SD 3.9°) meaning that the wind direction got more perpendicular to the cliff edge in the notch which was aligned to ca. 90°.At the beginning of the cliff-top dune, it was still a more northerly wind but passing the top of the cliff-top dune (Site 12) it again aligned with the regional wind direction (Figure 6).

Wind Forcing
In 4 days of field campaign, between 12:00 and 18:00 UTC, during the sand transport measurement period, the regional wind speed at the Dakhla weather station was relatively constant with an average value of around 14 m/s with gusts of 17.5-19.0m/s.Only on June 14th was the wind speed slightly weaker, with an average value from 11.4 m/s at 12:00 UTC to 8.3 m/s at 18:00 UTC (with gusts of 14.4 m/s and 11.8 m/s, respectively).In the same periods, wind speed measured at 1 m above the beach surface (reference mast at Site 1) ranged between 4 and 12 m/s, but during most of the mass flux measurements, the 10-s-averages ranged from 8 to 9 m/s, well above threshold wind speed for sand movement.During all runs, sand transport within the studied beach-dune system was continuous.Across the entire beach-climbing dune system the presence of topographically induced wind forcing was clearly visible (Figure 7a), whereas on the cliff-top dune, wind speed reduction and then flow acceleration were observed.Comparing wind speed at the beach (Site 1) and at the cliff-top dune end (Site 14), flow recovery is quite visible (Figure 7b) and took place within a distance of 34 m.
The speed-up values calculated for 10 s wind speed averages (at 1 and 0.25 m elevations) in successive wind speed classes (Figure 8) resulted from topographic forcing of flow (acceleration and deceleration).For the wind speed class below 7-8 m/s (at reference Site 1), flow accelerated slightly up the lower part of the climbing dune (Sites 2-5) following the rule that the lower the speed, the greater the acceleration.For wind speed classes above 7-8 m/s, at the same part of the climbing dune, flow decelerated slightly up the slope and the greater the speed, the greater the deceleration.The distance upslope over which the airflow reached the speed comparable to that on the beach increases as the incident (Site 1) wind speed increases (Figure 8).The deceleration at the climbing dune toe is consistent with an increase in the pressure gradient and near surface streamline concavity that could be expected as a result of the concave topography (e.g., Wiggs et al., 1996).This resulted in an increase in flow steadiness (CV v1 , CV v0.25 ) (Figure 9).Past Site 5 until almost the cliff edge, that is, on the upper part of the climbing dune (Sites 5-8), a consistent flow acceleration was recorded regardless of the incident wind speed (Figure 8).The constant fractional flow speed-up for almost all analyzed wind speed-classes resulted from a constant slope inclination in this part of the dune.In contrast to the concave-convex slope, typical for transverse dunes and foredunes, where the stabilizing effect of streamline compression results in increasing steadiness of flow up the slope (inhibits turbulent motions; Walker & Nickling, 2003;Walker et al., 2009;Weaver & Wiggs, 2011;Wiggs et al., 1996), on the upper part of the climbing dune near-surface flow steadiness (CV v1 , CV v0.25 ) remained low and constant (Figure 9).The greatest flow acceleration was observed at the cliff edge (Site 9).At 1 m above the bed, it accelerated from 160% for the greatest incident wind speed class (11-12 m/s) to nearly 250% for the lowest incident wind speed class (4-5 m/s) (Figure 8a).At 0.25 m, the speed-up was less variable and flow acceleration ranged from 202% for the greatest wind speed class to nearly 220% for the lowest incident wind speed class (Figure 8b).These large speed-up values are related to the presence of a high topographic obstacle (the cliff) in the path of the flow, as the higher the hill, the greater the convergence of stream lines, resulting in increased speed-up (Jackson & Hunt, 1975;Parsons et al., 2004;Wiggs et al., 1996).Despite the high inclination of the climbing dune surface before the cliff edge, the near-surface factor/coefficient of flow steadiness was only slightly higher than that on a flat beach surface.Such flow conditions increased sand transport capacity but did not allow sand to be deposited just in front of the cliff edge.Based on wind data from the Dakhla meteorological station, the angle of the regional wind direction was on average 14° (with a standard deviation (SD) of 5.7°), that is, 26° in relation to the cliff edge orientation (40°-220°).Site numbers as in Figures 3a-3c, and standard deviations in the wind direction indicated for each site.Walker & Nickling, 2003).An earlier flow experiment performed at the same site on 18th October 2019 behind the cliff edge within the flow separation region, was intended to define flow directions and turbulence within this region.The smoke and the blue arrows (which indicate the direction the flow is coming from) show that pronounced flow separation occurred at the cliff top edge and extended a considerable distance downwind (Figure 10a).The approximate top of the separation envelope is shown.Figure 10b illustrates a typical 1 min average wind speed profile at 1.2 m downwind of the cliff edge.The flow is moving upwind (hence negative vales) in the 0-40 cm region and velocities are significant at up to −3.23 m/s.Above ∼40 cm+ height the flow is above the separation envelope and streams downwind following the incident wind.Flow at the cliff edge is 13.8 m/s at 25 cm above the bed, while it is 13.1 m/s at 100 cm height only 1.2 m downwind (Figure 10b).It is common to observe that the incident flow streamlines mimic (parallel) the steep, upwind slope topography (Davidson et al., 2022), so the 100 cm anemometer is reflecting this uppermost climbing dune slope streamline which is shearing upwards at a high angle from the cliff edge.This high angle shearing of the incident flow off the cliff-top and the concurrent formation of a flow separation envelope likely controls the sand deposition downwind, with minimal deposition in the first meters and increasing deposition downwind to produce the initial part of the cliff-top dune profile.
At the cliff-top upwind edge, flow directional variability (Figure 11) and CV values (Figure 9) were the highest and gradually decreased downwind to the dune crest highest point (Site 12), which together with flow acceleration (Figure 8) favored further downwind sand transport and gradual deposition.Such conditions resulted in a cliff-top dune formation in the form of an elongated dome-shaped dune.Flow acceleration on the cliff-top dune was recorded up to the highest point on the dune crest with flow approaching the speeds comparable with that recorded on the beach (Figure 8, Site 1).Thus, flow recovery took place up to this point.Further downwind, the flow velocity and steadiness remained constant, resulting in a reduction in the sand transport rate.However, flow unsteadiness was about two times greater than in the beach (Figure 9, Site 1).Therefore, between Sites 13 and 14, only a small amount of sand was deposited, and past Site 14 (end of the cliff-top dune) sand was transported downwind without being deposited.

Sand Transport Rate
The data set contains 262 measurements of sand transport rates made in different parts of the beach-dune system.During successive runs, the incident wind speed at 1 m height at the reference Site 1 on the beach ranged between 7.0 and 9.5 m/s.These speeds corresponded to speeds of 10.0-13.0m/s on the uppermost part of the climbing  The average sand transport rates across the beach-dune system calculated for two wind speed classes (8.0-8.5 m/s and 8.5-9.0 m/s) at the reference Site 1 (beach) generally followed changes in wind speed (black line in Figure 8), but was influenced by the changes of near surface flow turbulence.First, at the climbing dune toe and on its lower part, it slightly decreased to the lowest value at Site 4 (by 10% and 20% for a 8-8.5 m/s and 8.5-9 m/s incident wind speed class, respectively; Figure 12).Based on the whole set of sand transport data obtained for this part of the climbing dune, in the 7-9 m/s wind speed class it is observed that the higher the wind speed, the greater the decrease in sand transport rate toward the middle part of the climbing dune.Additionally, the lower the incident wind speed, the shorter the distance along which the sand transport rate reaches the values observed at reference Site 1 (beach).The lowest sand transport rate measured at Site 5 resulted from the presence of a small rock outcrop, which slightly disturbed the airflow at this site.Above this site, the sand transport rate rapidly increased up the climbing dune and at the uppermost part of the climbing dune it was 4 times higher than in the beach (Site 1) for the lower wind speed class (7-8 m/s at Site 1), and only twice as high for the greater wind speed class (9-10 m/s at Site 1).This is in line with the decrease in speed-up values as incident wind speed increases.Sand is regularly supplied to the climbing dune uppermost slope and crest from the beach, so surface lowering is minimal here.Given the steep slope, it is also likely that some sand grains will slide back downslope at times due to gravity.
Due to flow expansion and deceleration just over the cliff edge (Figure 8) a part of the transported sand is deposited which results in a drop of mass flux below values recorded at the beach (Figure 12).However, due to flow separation and development of a reversing vortice, some sand deposited in the initial part of the cliff-top dune is moved back by near-surface flow against the dominant wind direction, and then taken again by the incident flow downwind (Figure 10b).Further downwind, the separation envelope ceases to exist, and the near-surface airflow speeds up and reaches a speed comparable to that measured on the beach (Figure 8).Contrary to the trend of speed changes, flow turbulence decreased with distance from the cliff edge, but it was still much stronger than on the beach (Figure 9).This coupled with the flow acceleration resulted in an increase in the sand transport rate in this part of the cliff-top dune by about 100% (Figure 12).Downwind of the top or highest point of the cliff-top dune, wind speed and flow turbulence were relatively constant and the sand transport rate decreased and reached values similar to those on the beach (Figure 12).
The sand transport rate at each site was also combined with wind speed measured at this site and grouped into those representing beach (Site 1), climbing dune (Sites 2-8), and central longitudinal axis of the cliff-top dune  (Sites 10-13) (Figure 13a).At the wind velocity below 8.5 m/s, the sand transport rate analyzed for a given wind speed was similar to the beach and lower climbing dune, whereas on the cliff-top dune it was much higher.For a wind velocity above 8.5 m/s, the relatively lowest sand transport rate was observed on the upper part of the climbing dune, slightly higher on the beach and greatest on the cliff-top dune (Figure 13a).Relationships obtained for different parts of the beach-dune system show the impact of both flow saturation with sand, flow speed-up or deceleration, and inclination of the climbing dune surface on the sand transport rates (Figure 13a).However, this rule cannot be explained by differences in grain size as it will be shown in the next section, where the mean grain size decreased only by about 50 μm.
The high sand transport rate downwind of the cliff edge (Site 10, about 11 m from the cliff edge, Figure 13a) was unrelated to the flow velocity.It reflects rapid flow deceleration and development of a flow separation envelope characterized by a reversing vortice (compare Figure 10) and inertia-dominated mass flux (Figure 11a).Other sites, even though they already show good dependence of the mass flux rate on wind speed at a given site, generally recorded higher sand transport rates than those on the beach and climbing dune.It may, or probably results from higher flow turbulence on the cliff-top dunes (compare Figure 9) and thus a thicker saltation cloud than on the climbing dune.
There is also a strong asymmetry in the sand transport rates on both sides of the cliff-top dune (Figure 13b).As the flow at the cliff edge was deflected more toward the south (Figure 6), more sand was supplied on the eastern side of the cliff-top dune, transported a short distance along the cliff-top dune, and then as the flow direction recovered to the regional incident direction, the flow became slightly oblique to the dune axis.In consequence, it started to flow up the dune side slope and the sand was then deposited behind the dune axis, where the wind speed decreased.

Sand Bed and Transported Sand Properties
The beach and dunes were composed of well and very well sorted medium quartz sand with significant admixtures of shell debris on the beach and the toe of the climbing dune.The mean grain size was in the range of 276 and 436 μm depending on the site (Figure 14a).The coarsest sand extended from the beach up to the climbing dune toe and had the characteristics of a deflation surface depleted of the smaller quartz grains and enriched in coarser bioclasts.The mean grain size gradually decreased up the climbing dune, which was accompanied by an increase in sand sorting.The smallest mean grain size (276 μm) and the best sorting in the entire beach-dune system were recorded at the upper part of this dune (Sites 6-8).Within the cliff-top dune, the mean grain size varied between 280 and 326 μm with coarsest sand and poorest sorting just behind the cliff edge.Both parameters slightly decrease downwind (Figure 14a).Grain size distributions are, in the majority, fine or even very fine skewed with the exception of the beach surface (Sites 1 and 2) and upper part of the climbing dune (Sites 7 and 8) where they are symmetrical due to deposition in a high energy environment (wave action and significant airflow acceleration, respectively).
The mean grain size of sand transported by the wind (i.e., caught in the sand traps as opposed to being sampled from the bed) showed a very distinct trend, and it gradually increased downwind reaching the greatest values in the uppermost part of the climbing dune, where it even exceeded the mean grain size of the surface sand and decreased beyond the cliff edge (Figure 14b).Sorting of sand transported above the beach and climbing dune was better than sorting of sand transported on the cliff-top dune with the poorest sorting just downwind of the cliff edge.Sorting became better downwind along the cliff-top dune axis.All grain size distributions are symmetrical with some fluctuations toward fine skewed at the upper part of the climbing dune (Figure 14b).However, the characteristics of the sand transported by the wind were different from both sides of the cliff-top dune (Figure 15).The mean grain size was generally greater on the eastern side of the dune and smaller on the western side, which resulted from a wind direction that was slightly oblique to the dune axis and slowing down crossing that dune axis.

Discussion
The beach-climbing dune-cliff top dune system is an example of an active system in which the cliff-top dune is nourished exclusively by beach sand transferred atop a rocky cliff via a climbing dune.There are several factors that made the development of such a system possible.First, the supply of sediment to the beach by waves, and second, the presence of a long enough sandy beach fetch at the foot of the cliff, which can serve as an abundant source for aeolian sand transport.Third, the occurrence of alongshore or oblique onshore wind direction (which due to the presence of the cliff will be steered to higher oblique angles and alongshore) characterized by low directional variability which can assure sufficient flow saturation at the beach.Fourth, the presence of a notch in the cliff forces the flow to be more perpendicular to the cliff edge, allowing higher flow acceleration at the upper part of the cliff and thus sand transport from the beach up to the cliff edge and beyond.Fifth, the presence of a flat surface atop the cliff without any obstacle (boulders, trees), which can modify flow/impact on sand transport in the area beyond the cliff edge.

Wind Flow and Sand Transport Rates Over an Inclined Surface
The sand transport rate on a transverse dune stoss slope characterized by an average inclination of over 12° and with a concave-convex profile increases non-linearly up the slope (Hesp et al., 1989;Lancaster, 1985Lancaster, , 2023;;White & Tsoar, 1998) following flow acceleration and increasing surface shear stress (Jackson & Hunt, 1975;Mason & Sykes, 1979;Taylor & Gent, 1974).Both Lancaster (1985) andMcKenna Neuman et al. (1997) showed that sand transport intensity is highest at the dune crest (by 1-2 orders of magnitude) and the strongest effect was observed when wind velocity at the dune base fluctuated around the threshold value, such that as the wind speed increased, the difference became smaller.According to Lancaster (1985), this effect becomes more pronounced as the dune height increases and wind direction becomes more normal to the dune crest.During this study the wind speed was well above threshold, but even though the studied climbing dune was high, the increase in mass flux on its stoss slope was relatively small as this ratio varied between a value of 4 and 2 for the lower (7-8 m/s) and the higher (9-10 m/s) incident wind speed classes, respectively.The sand transport rate measured on the climbing dune correlates well with wind speed and the empirical relationship may be expressed by a power function with an exponent equal to 3.75 (Figure 16), which is slightly smaller than the one given by McKenna Neuman et al. (1997).
The only measurements on sand transport upslope on a steep slope (with an effective slope above 20°) were made by White and Tsoar (1998) on a 20 m high climbing dune.They suggested an exponential increase in sand flux with the height of the dune but it is questionable as their sand traps were left in the field for some days and they recorded a total sand transport in a given period rather than a transport rate in specific wind conditions.Later, Dong et al. ( 2017) studied airflow and sand transport over a slipface (25-28°) of a 6.9 m high barchan during reversing mode and found that the sand transport rate at the dune crest was several times greater than at a site located at roughly two thirds up the windward slipface.They also measured sand transport downwind from the dune crest and showed that it decreased with distance from the crest, and at distances of about 25 and 50 m from the crest, it was lower by 3.2 and 5.5 times from that measured at the crest, respectively.Most of this sand was transported in a suspension and saltation plume as the effect of highly accelerated crestal flow resulted in the development of an embedded jet, which made transport conditions similar to those met on the studied cliff-top dune.However, in our experiment, mass flux measured downwind from the cliff edge increased until Site 12 (34 m away from the cliff edge) (Figure 12).This was due to the fact that the flow reattachment which was formed on this part of the cliff-top dune occurred on the horizontal plane contrary to the conditions on the reversing barchan where it reappeared on the most downwind lee slope (Dong et al., 2017) and where the flow expansion occurred on a slope inclined downwind and thus covered a larger space than in the case of the cliff-top dune.Therefore, the effect of a highly accelerated flow was pronounced along a much longer distance.
The relationship between wind speed at a given site (or position on the climbing dune) and sand transport rate measured at the same site (Figure 16) shows that the sand transport rate on the upper part of the climbing dune is relatively lower and on the cliff-top dune is relatively higher than on the beach.For example, the sand transport rate at ca. 7 m/s on the cliff-top dune was the same as the sand transport recorded on the beach at a wind speed of more than 8 m/s, whereas the sand transport rate at ca. 11 m/s on the upper climbing dune was the same as that recorded on the beach at a wind speed of less than 10 m/s.These differences are independent of wind speed when comparing the sand transport rate on the cliff-top dune with that on any flat beach surface (as e.g., on the other beach 50 km south of Tarfaya shown in Figure 16; Rotnicka & Dłużewski, 2022), or increase significantly with wind speed when compared with that on a highly inclined surface (upper part of the climbing dune) (Figure 16).This suggests that past the cliff edge the transport capacity is lower due to abrupt flow deceleration and formation of reversing flow within the separation envelope.This, in fact, results in a significant drop in the sand transport rate and sand deposition.Therefore, the same amount of sand is transported here by a flow of velocity several m/s lower than on the climbing dune (Figure 13a, Site 10).This relatively low sand transport rate, as observed on the upper part of the climbing dune, usually favors erosion of the dune slope and results in lowering of its surface (McKenna Neuman et al., 1997).The question arises as to what wind conditions and time are required for the climbing dune to be eroded enough to prevent sand transport from the beach up to the cliff edge and thus inhibit the development of the cliff-top dune?During the short study period there was either no change or only a slight change in bed elevation as observed on the mast with anemometers and the undersaturation of mass flux on the upper part of the climbing dune did not necessarily translate into significant slope erosion.
The speed-up calculated for the upper part of the climbing, where flow is nearly normal to the cliff edge, is comparable with the speed-up recorded on the stoss slopes of different foredunes or transverse dunes (Hesp et al., 2005;Lancaster, 1985) and seems to be inversely proportional to wind speed.

Effects on Bed Slope on the Sand Transport Rate
The direct effect of surface slope on the sand transport rate is uncertain.Due to gravity, a sloping surface affects both the motion of grains saltating upslope and the threshold of motion.As a result, sand transport should be inhibited on windward slopes and enhanced by a downslope gradient (Howard, 1977).Excluding measurements of mass flux on windward slopes of different transverse dunes inclined at an angle of over 12°, there has been limited research that focused on steeper and longer unvegetated sandy slopes (Davidson et al., 2022;Tsoar et al., 1996;White & Tsoar, 1998;Whitehouse & Hardisty, 1988).Theoretical analyses also accounted mainly for the bed slope effect on the saltation threshold and its dependence on grain size (Dyer, 1986;Howard, 1977;Huang et al., 2008;Iversen & Rasmussen, 1994, 1999).During the present experiment, wind conditions and speed-up on the slope were well above the threshold conditions and the mass flux was not intermittent at any time.
The most common approach to account for the effect of slope follows that of Bagnold (1956, p. 294), where the slope adjusted rate of transport is Q slope = AQ horizontal .Q slope is the sand transport rate on the sloping bed, Q horizontal is the sand transport rate on a flat horizontal surface (predicted from Bagnold's (1941) or other formula) and factor A is defined as where α is the angle of internal friction of the sand (given as natural angle of repose 32-33°; Howard, 1977;Iversen & Rasmussen, 1994), and β is the effective bedslope (with negative values for upslope).Hardisty and Whitehouse (1988) emphasized that transport rate depends on the bedslope much stronger than it is predicted by Bagnold's (1956) theoretical Equation 1and based on field measurements made in Saharan dunes revealed that: The large discrepancy between sand transport upslope and over the horizontal bed was explained by Hardisty and Whitehouse (1988) by a process called the impact-induced gravity flow that led to downslope (against the wind) movement of grains under purely gravitational forces.This process becomes significant particularly over surfaces inclined at angles higher than 15°.
However, in the case of the studied climbing dune, none of the above formulae provided good results (Figure 17).The results of sand transport measurements made on the beach and climbing dune have been compared with sand transport rates predicted by Bagnold's model (1936Bagnold's model ( , 1941) ) for a flat surface (beaches) and inclined surface for which corrections of the model by both Equations 1 and 2 were used.Firstly, the comparison shows that sand transport rates predicted by the models for the two beaches (at the studied site and on a beach located 50 km south of Tarfaya, northern part of western Sahara Atlantic coast; Rotnicka & Dłużewski, 2022) are similar (Figure 17), which indicates the universality of the results obtained.Secondly, Bagnold's (1956) slope correction for sand transport rate prediction only slightly improves the results obtained, especially for greater values, noted mostly on the highly inclined upper part of the climbing dune where significant flow acceleration takes place.The divergence of the predicted values follows the rule that the greater the slope (the higher the sand transport rate), the greater the overestimation of the predicted values.On the other hand, the slope adjustment proposed by Hardisty and Whitehouse's (1988) (Equation 2) performs well for slope inclinations of 11° and 14°, whereas for lower slopes (<10°) and steeper slopes (22-26°) it either over-or underestimates mass flux, respectively (Figure 17), as compared with measured values, but the absolute difference between measured and predicted values are much lower than in the case of Formula 1.
According to Sherman et al. (1998Sherman et al. ( , 2013) ) and Strypsteen et al. (2021), who evaluated different theoretical transport models, all of them performed well under idealized transport conditions which include unlimited sand source, dry sand, steady wind, etc., otherwise they usually overestimate the transport rate, up to an order of magnitude.Thus, discrepancy between measured values and predicted slope-corrected values of transport is more of a problem of the basic transport model than of the slope correction itself.Contrary to it, the slope correction proposed by Hardisty and Whitehouse (1988) overestimates the impact of particularly steep slopes on the upslope mass flux and the share of the process of impact-induced gravity flow in the resultant transport.There may be several reasons for this, as they conducted research in an area of the Saharan dunes which were built of finer sand and whose windward slope had a concave-convex profile that probably influenced sand transport to a great extent.
The authors themselves also stressed that as the slopes got greater than +14°, their results become more divergent (Hardisty & Whitehouse, 1988).

Sand Properties
Some earlier studies on the textural characteristics of surface dune sand showed a gradual fining of sand toward the dune crest accompanied by improved sorting (Folk, 1971;Lancaster, 1981;Tsoar, 1990), which was attributed to low wind energy at the dune toe, insufficient to move coarse grains.
The climbing and cliff-top dunes in this study were examined in high energy wind conditions.Even though the sand source contained a significant admixture of coarse grains (>20% of grains in diameter >500 μm, Figure 14a), they were absent in the uppermost part of the climbing dune (above Site 5), which resulted from the large zone of airflow deceleration at the dune toe and lower part of the dune.Thus, the changes in surface sand texture follow those reported by Folk (1971), Lancaster (1981), and Dłużewski (2013) rather than by Lancaster et al. (2002).Field studies made on climbing dunes in the Negev Desert and numerical modeling by Tsoar et al. (1996) and White and Tsoar (1998) reported that particles in the range of 177-350 μm may be transported up to the lower half of the climbing dune and grains coarser than 250 μm are not able to reach the dune crest at a shear velocity of 0.3 m/s (about 9 m/s at 1 m elevation).These values are lower than those recorded during this study as the coarse sand (>500 μm) was present up to Site 5 and grains coarser than 355 μm were present at the uppermost part of the climbing dune (Figure 14a).
Sand in transport was generally finer than surface sand with mean grain size increasing up the slope (Figure 14b), which is consistent with previous findings by Lancaster et al. (2002), Wang et al. (2002), Tan et al. (2014), Cheng et al. (2015), Martin &Kok, 2017, andYang et al. (2019).This means, however, that the change in grain size does not follow that recorded in surface sands.On the other hand, sorting was poorer in the lower climbing dune and became better in its uppermost part, though the expected trend is opposite because as claimed by Lancaster et al. (2002), increasing wind speed and mass flux up the dune slope result in a greater size range of transported All grain size distributions of both surface and transported sand are unimodal (Figure 14) and contrary to data by Lancaster et al. (2002), in the case of surface sand, they progressively change from fine skewed at the lower climbing dune to symmetrical in the upper part.Sand in transport, even though symmetrical, is more negatively skewed than surface sand (Figure 14), which is consistent with findings by Lancaster et al. (2002).
To our knowledge, there is only one study devoted to this issue on a cliff-top dune on the mid-western Portuguese coastline (Jackson & Nevin, 1992), but the data are very scattered along shore normal profiles; therefore, only a few surface sand samples from cliff-top dunes and some from the cliff base were analyzed.The authors concluded that the sand in cliff-top dunes was better sorted than at the cliff base and beach, but there was no obvious trend in the change of grain size.

Conclusions
This study presents a relatively unique case of the first high resolution examination of flow and sediment transport from a beach over a 50 m high climbing dune and adjacent cliff-top dune system.
The principal results are as follows: 1. Flow steering was significant on the upper portion of the climbing dune.2. Speed-down occurred between the beach and lower climbing dune slope for winds higher than 8 m/s (but not for winds lower than this).Speed-up occurred on the mid-to upper slopes and was significant on the uppermost climbing dune.3. The greatest flow speed-up was observed at the clifftop edge, and the flow at 1 m above the bed accelerated from 160% (at 1 m height) and 202% (at 0.25 m height) for the greatest incident wind speed class (11-12 m/s), to nearly 250% (at 1 m height) and 220% (at 0.25 m height) for the lowest incident wind speed class (4-5 m/s).4. Flow separation occurred at the cliff-top edge and reversing flows within a separation envelope occurred near the bed. 5. Near-surface flow turbulence either decreased or was stable on the mid to upper climbing dune slopes likely due to high streamline compression, all resulting from the straight profile of the upper part of the climbing dune.6.At the cliff-top upwind edge, flow directional variability and CV values were the highest and gradually decreased downwind to the highest point of the cliff-top dune.7. The sand transport rate declined toward the climbing dune toe and lower slope in line with speed-down in this region.The transport rate rapidly increased up the climbing dune and at the uppermost part of the climbing dune, it was 4 times higher and 2 times higher than on the beach for the lower (7-8 m/s) and higher (9-10 m/s) incident wind speed classes respectively.8.The slope correction proposed by Hardisty and Whitehouse (1988) for sand transport on slopes overestimates the impact of particularly steep slopes on the upslope mass flux.9. Sand in transport was generally finer than surface sand with mean grain size increasing up the slope, while sorting was poorer on the lower climbing dune and got better in its uppermost part, 10.All grain size distributions of both surface and transported sand are unimodal.Aeolian sand in transport, even though symmetrical, is more negatively skewed than surface sand.
These findings allow for the formulation of certain symmetries regarding the development of the climbing-clifftop dunes.When the wind velocity is slightly above the threshold value, the sand transported from the beach is deposited within the lower part of the climbing dune due to flow deceleration in this part of the system.At the same time, strongly accelerated flow in the upper part of the climbing dune starts to saturate with sand and, thus, this part of the climbing dune is subject to erosion, but a relatively small amount of sand is delivered to the clifftop dune.Such a small supply of sand will not translate into significant cliff-top dune growth, and since the wind speed is above the threshold, the dune may decay.When the wind velocity is well above threshold, the sand from the beach is transported up the climbing dune and over the cliff edge, nourishing the cliff-top dune with a large amount of sand.Even though the flow speed-up across the climbing dune is lower than in the previous case, both the wind speed and sand transport rate are high.There is almost no erosion as the climbing dune acts as a transfer zone only, but the amount of sand deposited behind the cliff edge is large and favors cliff-top dune development.

Figure 1 .
Figure 1.Atlantic coast of Morocco with marked study site south of Dakhla (a), beach and cliff (Google Earth image, 7 January 2022) where flow experiments took place (b), and view of the study site facing south showing the 50 m high rocky cliff and climbing dune (c).

Figure 2 .
Figure 2. Wind regime of the study area in 2013-2022: (a) effective wind rose, (b-e) monthly values of Fryberger and Dean (1979) indices.Based on data from the Dakhla airport meteorological station (www.meteomanz.com).

Figure 3 .
Figure 3. Experimental setup: (a) DEM of the beach-dune system with (b) enlarged cliff-top dune and location of anemometer masts and sand traps, (c) beach-dune profile made along the flow saturation path and cliff-top dune axis, with effective slope indicated below the profile.

Figure 4 .
Figure 4. Equipment used in the experiments: (a) 18th October 2019 experiment showing 2D mini-sonics and cup anemometer and wind vanes located at the cliff edge and 1.2 m downwind from it, (b) sand traps (at the reference Site 1) during operation and removable catcher partially filled with sand.

Figure 5 .
Figure 5.View of the beach and climbing dune (a), surfzone, beach, climbing dune and cliff-top dune in the background (b), cliff-top dune from the cliff edge/seaward side (c) and from the landward side (d).
When flow passed over the sharp edge of a rocky cliff, that is, the abrupt change in the surface slope (from 33° to nearly horizontal), flow expansion and deceleration occurred, and a flow separation region or cell formed (cf.Bauer & Wakes, 2022;Bauer et al., 2012;Hesp & Smyth, 2019a;Parsons et al., 2004;Piscioneri et al., 2019;

Figure 6 .
Figure 6.Wind steering during the flow experiment.Based on wind data from the Dakhla meteorological station, the angle of the regional wind direction was on average 14° (with a standard deviation (SD) of 5.7°), that is, 26° in relation to the cliff edge orientation (40°-220°).Site numbers as in Figures3a-3c, and standard deviations in the wind direction indicated for each site.

Figure 7 .
Figure 7. One-minute averages of wind speed at a height of 1 m above the bed at chosen sites on (a) climbing dune (data collected on 10 June 2022) and (b) cliff-top dune (data collected on 16 June 2022).In both charts, wind speeds at the cliff edge and on the top of the cliff-top dune are shown.Note that the average wind speed at the highest point of the cliff-top dune is comparable with that on the beach.

Figure 8 .
Figure 8. Speed-up at a height of 1 m (a) and 0.25 m (b) in successive wind speed classes.Wind speed classes were defined at the reference site located on the beach (Site 1).Site numbers as in Figures 3a-3c.

Figure 9 .
Figure 9. Wind steadiness expressed by the wind speed coefficient of variation (CV) calculated for heights of 1 m (a) and 0.25 m (b) in successive wind speed classes.Wind speed classes were defined at the reference site on the beach (Site 1).Site numbers as in Figures 3a-3c.

Figure 10 .
Figure 10.Reversing flow within the separation envelope illuminated by the smoke: (a) approximate top of the separation envelope (red dots) and direction the flow is coming from (blue arrows) as shown by the wind vanes and smoke.The middle arrow facing into the photograph was spinning 360°, (b) typical 1 min averaged velocity profile utilizing the cup and sonic data from instruments located 1.2 m downwind of the cliff edge, and at the clifftop edge.

Figure 11 .
Figure 11.Wind roses for sites located between the cliff edge (Site 9) and the crest of the cliff-top dune (Site 12): (a) 1 m above the bed, (b) 0.25 m above the bed, and (c) 0.1 m above the bed (experiment from 18 October 2019).The 2019 site clearly portrays the spinning motion of the wind vane in the flow separation envelope.

Figure 12 .
Figure12.Changes in average sand transport rates across the beach-dune system corresponding to two incident wind speed ranges at the reference Site 1. Site numbers as in Figure3.

Figure 13 .
Figure 13.Relationship between wind speed and sand transport rate measured at co-located sites: (a) across the entire beach-dune system and (b) across the cliff-top dune (landward slope faces E and seaward slope faces W, see Figure3b).One data point equals one trap collection at one collection period (varying from 300 to 600 s).Cliff top axis data is the same in both plots.East and west slope data in (b) are not included in the regression curve.

Figure 14 .
Figure 14.Changes in grain size and statistical parameters of grain size distributions obtained for (a) surface sand samples, (b) sand samples from sand traps collected during measurements, which correspond to a wind speed class of 8-9 m/s at the reference Site 1. Black solid line reflects variation in sand transport rate caused by wind speed-up and speed-down.Both types of sand samples represent changes in parameters along the transect parallel to the wind direction.Site numbers as in Figure 3.

Figure 15 .
Figure 15.Changes in statistical parameters of grain size distributions obtained for sand samples collected in sand traps arranged in different cliff-top dune cross-profiles: (a) at Site 10A, (b) at Site 11, (c) at Site 11A, and (d) at Site 12.All measurements correspond to a wind speed class of 8-9 m/s at reference Site 1 (which corresponds with a speed of 7-8 m/s at the top of cliff-top dune, Site 12).Black boxes indicate results for sites located along the clifftop dune axis.Black solid line reflects variation in sand transport rate, which in most cases reflects a reduction in wind speed: from higher speed on the eastern slope to lower speed on the western slope.Site number as in Figure 3b.

Figure 16 .
Figure 16.Comparison of the relationship between wind speed (V 1m ) and sand transport rate (Q) measured on different parts of the beach-dune system with the Bagnold model (Bagnold, 1941) and another beach 50 km south of Tarfaya (source: Rotnicka & Dłużewski, 2022).

Figure 17 .
Figure 17.Comparison of sand transport rates measured on a horizontal beach surface (Site 1, this study and Tarfaya beach, Rotnicka & Dłużewski, 2022) and on the inclined stoss slope of the climbing dune (Sites 2-8) with values predicted for horizontal and inclined surfaces, respectively, and with a different approach for slope correction in the latter case.Bagnold's (1941) transport model was used as a basic model for the prediction of mass flux on a horizontal surface with the following data: constant C = 1.8 (for naturally graded dune sands), air density ρ a = 1.22 kg/m 3 , gravitational acceleration g = 9.81 m/s, mean grain diameter d = 310 μm (the average of sand grain in transport), reference grain diameter D = 0.25 mm.The shear wind velocity was calculated from the log-linear wind profile using the wind speed measured at a height of 1 m.
Part of the equipment used in this study was funded by a Grant from the National Science Centre, Poland, no.2018/31/B/ST10/03051.The GPS-RTK was supported by University of Warsaw, Excellence Initiative-Research University Programme (ID-UB action I.4.2,Priority Research Area II).JR thanks Faculty of Geographical and Geological Sciences of Adam Mickiewicz University in Poznan for the support of field work.PAH thanks Flinders University and the BEADS Lab for support.We thank Bashir and Hassan for the help in organizing the field work.We also thank Robin Davidson-Arnott and an anonymous reviewer for their excellent reviews.Open access publishing facilitated by Flinders University, as part of the Wiley-Flinders University agreement via the Council of Australian University Librarians.