Impact of coastline orientation on the dynamics of foredune growth (Łeba Barrier, south Baltic Sea coast, Poland)

Topographic profiles normal to the shoreline, extending from a point landward of the lee slope of the foredune, marked by a well-established benchmark, across the established and incipient foredunes, to the lower edge of the swash zone were established in November 2006 (Figure 1b). The length of the profiles ranged from 150 up to 250 m depending on sea level and wave run-up. The main criteria for the selection of foredune-beach profiles included: (i) difference in shoreline orientation, (ii) the presence of a wide beach with an incipient foredune, and (iii) similar heights of the incipient foredunes. The profiles were spaced 4.2 km apart.

The topographic surveys were undertaken bi-annually in autumn and spring, before and after storm periods, respectively, during 10+ years. The measurements were taken on average at 0.4 m intervals, at the beginning with an automatic level and subsequently by using a TOPCON HiPer® Pro real-time kinematic (RTK) differential global positioning system (DGPS) (precision of 1–2 cm in all dimensions). A set of permanent benchmarks were installed on an established foredune for the base station and for horizontal and vertical correction of the position which was performed each time at the beginning of the topographic surveys. For post processing verification of the horizontal and vertical accuracy of the measured profile, at least 2 benchmarks were established on each profile in the section where the foredune was established. During each survey point corresponding to limits of the following morphologic zones were recorded: i) boundary between established and incipient foredunes, ii) upper and lower limits of dune ramp, iii) maximum wave run-up, iv) lower edge of swash zone.

The sediment budget (the net volumetric change) was calculated for each of the studied periods only for those portions of the incipient foredunes where changes in surface morphology were related to wind action only and were not affected by waves. This method of sediment budget calculation allowed us to compare the amount of sand supplied to the foredune with the net aeolian deposition of sand within the foredune. The landward boundary of the incipient foredune was always well recognized and marked in the profile with an accuracy of a few centimeters. In contrast, the position of the limit of the dune toe was much more difficult to determine due to the highly dynamic nature of the aeolian ramp. Nevertheless its elevation on both profiles did not differ by more than 0.4 m in the studied period.

In order to calculate dune volumetric changes, data obtained during topographic surveys were interpolated onto a cross-shore grid (dx = 0.5 m). Grids of 2 successive profiles always corresponded to each other. For this procedure an R script was created. Total volume of sand deposited and eroded within 1 m wide belt normal to the foredune ridge was obtained for a given period as a sum of sand volumes calculated for each grid as an area between two successive profiles multiplied by 1 m.

Provided the foredune is not destroyed by storm waves, its sediment budget should reflect the amount of sand supplied by the wind from the beach. Therefore, potential sand transport (Q) for all periods between successive profile surveys were calculated based on hourly data of wind speed (resolution 1 m/s) and direction (resolution 10° until the end of 2010 and 1° later) from the Łeba weather station (Figure 1a). In fact these were 10-minute averages obtained from 1-s-measurements made during the last 10 minutes of every hour. The critical threshold velocity at which beach sand starts to move were determined to be 6.0 m/s at 10 m height (Rotnicka 2013a), a value used also in Fryberger & Dean's (1979) model. Therefore, winds of speed greater than or equal to 6 m/s (effective winds) was used for all calculations. The potential sand transport rate Q was predicted for alongshore and onshore winds separately for each part of the coast with different orientation. The alongshore and onshore wind directions included winds approaching the coastline at an angle of less than or equal to 20° and greater than 20°, respectively. The impact of offshore winds was not analyzed in this study, as previous research showed that it is negligible due to the presence of a set of established foredune ridges and a forest at the back of the dune (Rotnicka 2011a).

One of the most important factors controlling sand transport rate on the beach, and thus the amount of sand supplied to the foredune, is the available fetch distance (Bauer & Davidson-Arnott 2003; Davidson-Arnott, MacQuarrie & Aagaard 2005; Delgado-Fernandez 2010) which results from beach width and wind direction. According to the results of previous work by Rotnicka (2013a), which showed that on a beach narrower than 20 m, particularly during onshore winds, aeolian sand transport did not occur or was minimal (on average less than 0.001 kg/m/s), the potential sand transport rate was calculated only for the case of the wider beach.

The time when the beach was narrower than the critical value of 20 m, was determined on the basis of relationship between the swash zone simultaneous sea level data and elevation of the upper limit of the swash zone (Figure 3). The hourly sea level data came from the 2 nearest tide-gauges run under national IMGW-PIB, one located in Łeba, 18 km east from the study site, and the second in Ustka, 30 km west from the study site (Figure 1a); these data were recalculated taking into account the exact mounting height of each tide-gauge. The maximum landward limit of the swash zone was measured each time during profiling. The relationship between these data is significant (Figure 3) with average and maximum departures from the predicted value equal to ±9 cm and ±15 cm, respectively, and points out that wave parameters had no significant influence on the obtained relationship. Periods when the beach was narrower than 20 m during onshore winds did not exceed several percent.

Figure 3.

Others factors limiting aeolian sand transport under natural beach conditions include: sand moisture (e.g. Chepil 1956; Hotta et al. 1984; Davidson-Arnott & Dawson 2001; Cornelis, Gabriels & Hartmann 2004; Wiggs, Baird & Atherton 2004; Davidson-Arnott et al. 2008; Bauer et al. 2009), pebble coverage (e.g. Carter & Rihan 1978; Nickling & Davidson-Arnott 1990; Nickling & McKenna Neuman 1995; Davidson-Arnott, White & Ollerhead 1997; Rotnicka & Dłużewski 2022), and salt crusting (Nickling & Ecclestone 1981; Nickling 1984). Due to the climatic zone of the region, the studied beach remains moist for significant parts of the year (particularly during autumn and winter). However, previous measurements made on these beaches on moist sandy surfaces showed that sand moisture (up to 5%) as well as heavy rain did not prevent intense aeolian transport and what's more, its rate was even greater than on a dry sandy surface (Rotnicka 2013a,b, 2014). This was due to greater hardness and elasticity of the moist beach surface and splash erosion resulting from the impact of large rain drops on the beach surface. The pebbles coverage which occur periodically on some parts of a beach and may have a density up to 60 % also do not inhibit aeolian transport (Rotnicka & Dłużewski 2022). As the Baltic Sea is the world's largest inland brackish sea, the salinity of its water is much lower than the ocean water (near the study site the average salinity is around 7‰), so the salt crust, even if it is formed, is very thin and easily destroyed and removed by wind. Therefore, limitation of sand deflation and, thus, implication to sand transport was important only when wind was just above threshold (Rotnicka 2013b). Summing up, because such factors as: i) beach moisture ii) the pebble coverage and iii) salt crusting do not have a significant impact on the sand transport rate at the study site, they were not taken into account. Therefore, the potential sand transport rates (Q) were calculated taking into account only alongshore and onshore winds when fetch distance was greater than 20 m.

Previous sand transport measurements made on the beach of the Łeba Barrier (Rotnicka 2011b, 2013a,b, Rotnicka & Dłużewski 2022, Rotnicka et al. 2023) indicated that measured saturated sand flux was always significantly lower than the sand flux predicted on the basis of any theoretical models such as those by Bagnold (1941), Zing (1953), Lettau & Lettau (1978), Sørensen (2004) and many others (see Sherman et al. 1998, 2013 for review). Therefore, the potential sand transport rate (Q, kg/m/s) at given sites was calculated using empirical relationships between wind speed at 1 m elevation (v₁) and sand transport rate previously established by Rotnicka (2011b, 2013a) for dry (1) Q=1×10−8V16.30 {\rm{Q}} = 1 \times {10^{ - 8}}{{\rm{V}}_1}^{6.30} and moist beach surfaces: (2) Q=9×10−8V15.36 {\rm{Q}} = 9 \times {10^{ - 8}}{{\rm{V}}_1}^{5.36}

These relationships were obtained for saturated mass flux generated by alongshore winds when fetch distance was unlimited. However, during onshore winds and narrow beaches the fetch distance is limited and mass flux is not always fully saturated, thus the magnitude of landward sediment transport is reduced (Miot da Silva & Hesp 2010). According to Davidson-Arnott & Law (1996) and Bauer & Davidson-Arnott (2003) this effect may be overcome by applying the correction for the cosine effect: Qcos = Q cosα, where Qcos represents the potential transport into the foredune per unit alongshore distance, Q is saturated mass flux and α is the angle of wind attack, i.e. angle between shore normal and wind direction. This procedure of potential sand transport rate calculation was applied for all successive periods, separately for alongshore and onshore winds.

Many measurements of sand transport rate made on the beaches of the Łeba Barrier (Rotnicka 2011b, 2013a,b; Rotnicka & Dłużewski 2022; Rotnicka et. al. 2023) proved its great spatial and temporal variability depending on weather conditions and short-term sea level fluctuations. The factors having the greatest impact on the intensity of transport on these beaches include: directional variability of incident wind, topographic forcing and steering of windflow imposed by a foredune ridge, available fetch distance, and beach surface moisture and roughness. Results of these studies also showed that alongshore winds play an important role in the initial phase of the dune ridge formation as they are responsible for enlarging and lateral merging of the shadow dunes present in the upper part of the beach, while if the foredune ridge has already been formed, the main role in its supply with sand is played by onshore winds (Rotnicka 2013a).

Predictions of the potential sand transport rate in the analyzed periods, calculated for saturated onshore and alongshore effective winds for dry and moist beach surfaces (Figure 4), show that regardless of the method of sand transport rate calculation, landward sand transport at Site 1 (at an orientation more aligned to onshore winds; Figure 2) was on average 4 times greater than at Site 2 (at an orientation more aligned with alongshore winds), whereas the alongshore sand transport rate at Site 1 was on average 2 times smaller than at Site 2. However, it should be emphasized that there are many sources of discrepancy between the potential and real sand transport rate. First, the predicted transport may be underestimated for onshore winds and overestimated for alongshore winds which is due to the landward location of the weather station from which the wind data was utilized (see methods, Rotnicka & Dłużewski 2019).

Figure 4.

Second, due to wind forcing and steering, both airflow speed and direction are modified on a beach-dune system. Onshore winds favor the greatest sand transport rate in the middle part of the beach but, due to flow deceleration toward the foredune, especially during weak effective winds, sand is deposited near the dune foot resulting in formation of an aeolian ramp (Bauer & Wakes 2022; Tomczak, Dłużewski & Rotnicka-Dłużewska 2022). Only during strong onshore winds (> 9–10 m/s) sand is transported upslope the vegetated foredune stoss slope, provided that the vegetation is not so dense to slow down the flow near the surface (Miot da Silva et al. 2008; Hesp et al. 2009; Schwarz et al. 2021; Bauer et al. 2022; Walker, Hesp & Smyth 2021). During winds strong enough (>12 m/s), when skimming flow occurs, sand can be transported above marram grass inland, above the foredune crest and beyond (Petersen, Hilton & Wakes 2011; Hesp & Smyth, 2016; Li et al. 2022; Rotnicka et al. 2023). However, as the speed of onshore winds increases, the distance needed to attain the maximum sand transport rate also increases. On the other hand these winds often generate storm surges leading to significant beach narrowing (Ruessink et al. 2022) resulting in non-saturation of mass flux and overestimation of sand transport.

During alongshore winds and oblique winds approaching the coast at an angle less than 20°, which are steered by foredune topography to alongshore (Arens 1996), the sand transport rate near the dune foot is on an order of magnitude greater than that measured during any other onshore winds (Rotnicka 2013a). It is caused by unlimited fetch distance favouring maximum flow saturation (Delgado-Fernandez & Davidson-Arnott 2011). When vegetation is present on the upper beach, intensive growth of embryo dunes is observed, as even sparse vegetation traps blowing sand, otherwise, the upper beach acts as a transfer zone. Thus, such winds do not feed the dunes with sand and do not contribute to its growth. On the other hand, these winds favor the sand transport over unvegetated dune ramp, which often remains beyond the reach of storm waves and even during strong onshore winds, when the beach and fetch are reduced by storm waves, sand accumulated earlier on the dune ramp is the only source of sediment available for transport and may nourish the foredunes (Davidson-Arnott & Law 1990; Tomczak, Dłużewski & Rotnicka-Dłużewska 2022; Rotnicka et al. 2023).

Keeping in mind that the sediment budget was calculated only for part of the incipient foredune that during the whole study period remained beyond the range of marine impacts and was modelled only by aeolian processes, it has been found that at both test sites deposition outweighed erosion in all consecutive periods (Figure 5). During 10+-years of investigation at Site 1, where oblique onshore winds dominated, deposition within the foredune was on average 5 times greater than erosion, whereas at Site 2, where alongshore winds dominated, deposition was only 3 times greater than erosion (Figure 6). In consequence, during the study period, the average net deposition within the foredune was 2.5 time greater at Site 1 than at Site 2 (Figures 5 and 6). The results clearly show that oblique onshore winds are of high importance in nourishing the foredunes with sand. The calculated sand budget suggests that a coastline orientation (55°–235°) at Site 1 favors foredune development much stronger than at Site 2 where coastline orientation (75°–255°) favors alongshore transport of sand along the beach and not nourishment of the dunes.

Figure 5.

Figure 6.

The potential sand transport rate (Q) combined with the sediment budget calculated for the incipient foredunes (ΔV) in consecutive periods exhibits a strong correlation only at Site 1 (Figure 7). A very weak correlation obtained for Site 2 is related to the predominance of alongshore winds, and a much smaller share of onshore winds. Additionally, onshore winds at Site 2 are strongly oblique, and therefore a significant part of the airflow may be steered by the foredune to an alongshore direction resulting in sand transport parallel to the dune ridge. The relationship between Q and ΔV for Site 1 (Figure 7) indicates that the potential amount of sand transported from the beach by onshore winds and delivered to the foredune is underpredicted for weak winds and slightly overpredicted for strong winds, and these differences are even more pronounced in the case of the presence of a moist beach surface. This finding can be related to beach narrowing during extreme storm events, when an overestimation of the sand transport rate may result from non-saturation of the mass flux caused by shortening of the fetch distance significantly below the critical value.

Figure 7.

To eliminate the impact of mass flux non-saturation occurring during onshore winds, the potential sand transport rate was recalculated applying the correction for the cosine effect (Bauer & Davidson-Arnott 2003) (Q_cos, Figure 7). However, this correction has not improved the outcomes – regardless of wind regime, the predicted amount of sand potentially delivered to the foredune was underestimated regardless of wind speed. This underestimation may be related to: i) wind speed data were not representative and the real wind condition at the coast differed from those at the Łeba weather station that is sheltered from the onshore winds by forest (Rotnicka & Dłużewski 2019), ii) use of 10 minute averages data as representative for hourly wind speed data which results in a decrease in the frequency of weak but effective winds (Pearce & Walker 2005), i.e. wind speeds slightly above threshold which indeed have low capability to move sand grains but are frequent (in some periods they accounted for about 50% of the whole effective winds period).