Ängelholm Beach Study Site

Ängelholm Beach is located in the Skälderviken Bay in southwestern Sweden (Figure 1). The beach is microtidal, and the semidiurnal tide has an average amplitude of about 5 cm and a spring tide amplitude of up to 20 cm (SMHI, 2013). The wind climate is dominated by winds from SW to W (Figure 2). The beach has a sheltered location in the bay but is impacted almost yearly by storm surges and large waves from the NW, causing beach and dune erosion (Palalane et al., 2016). During onshore winds, a significant local wind setup can occur in the bay and the storm surges typically occur in combination with large waves. No wave measurements are available from the area, but the largest simulated wave at the bay mouth had a significant wave height of 5.3 m and a peak period of 9.2 m (Palalane et al., 2016).

Figure 1

The left panel shows the location of the study area and the Swedish Meteorological and Hydrological Institute (SMHI) measurement stations. The right panel shows Ängelholm Beach, where the longshore distance x is marked along the beach and is referred to throughout the paper.

Figure 2

Wind rose compiled with data from1976 to 2016, which is used for wave hindcasting. The wind climate is dominated by winds from SW to W.

The yearly maximum still water levels range between 0.8 and 1.8 m above normal (Figure 3). The water levels from station Viken (Figure 1), which is located outside Skälderviken Bay, have been corrected for wind setup according to the method outlined in Palalane et al. (2016). Because most storms occur during the winter season, the years in the analysis were defined fromJuly until June the next year. The storms in 2011, 2013, 2014, 2015, and 2016 all caused higher storm surges than observed in the previous two decades.

Figure 3

Yearly maximum still water levels (SWL) in 1976–2016 based on measurements from Viken (dashed grey line) and the yearly maximum corrected for local wind setup in Skälderviken Bay (solid black line). The current decade has seen several extreme events compared with the period 1990–2010.

The beach is situated between two rivers, the Rönne in the north and Vege River in the south, with average flows of 23.5 and 5.0 m³/s, respectively (SMHI, 2009). The amount of sediment supply from the rivers is largely unknown. At a measurement station upstream in the Rönne, where the average flow is about half the flow at the river mouth, the inorganic component of the suspended solids transport has been measured to be 1.8× 10⁶ kg/y on average (Brandt, 1996); however, the grain size of the material is unknown. Some erosion has been observed in the river catchments (Karlsson, 2014; Leth, 2014), and specific stretches of the rivers and their tributaries are regularly being dredged to maintain the water depth, which are indications of sediment transport and deposition in the rivers. Even though sandy floodplain deposits are found in some areas near the rivers, the main part of the catchments consists of clay and clayey till. Therefore, most of the sediment transported by the rivers is expected to be finer than the beach sediment and not contribute significantly to the sediment budget of the beach.

Sand deposits are mainly found in shallow water along the coast and a few kilometres inland (Daniel, 1977). The sandy deposits originate from reworked till in the area below the highest Pleistocene coastline, which is about 55–60 m above present mean sea level (MSL). Several kilometres inland from the coast are aeolian deposits that were active until the 19th century when the dunes were stabilized with sand fences and vegetation.

The beach can be divided into five sections by dune shape and crest height (Figure 4); section A: longshore distance x = 0–850 m; section B: x = 850–2050 m; section C: x = 2,050–3400 m; section D: x = 3400–4700 m; and section E: x = 4700–6500 m (Figure 1). Figure 5 shows photos from the different sections together with typical profiles of the dune and dry beach, extracted from the Swedish National Elevation Model from 2010 (Lantmäteriet, 2019).

Figure 4

Variation of foredune crest elevation from north to south. The grey line indicates the crest elevation every 2malongshore, and the black line is a running average over 400 m. The dunes within the first 850 m are constructed with a gabion core. South of the constructed dunes, the crest elevation increases and is about 6–7 m between x = 1000 and 3000 m. Then, the crest elevation decreases in the southward direction down to about 2min the south, where no dunes are present.

Figure 5

Characteristic subaerial beach and dune profiles in sections A–E. The dune profiles in the right panels are extracted from the national digital elevation model; the distance on the x axis is relative to the intersection with MSL. The colour of the beach is changing from more red in the north (section A), where the sand has a larger content of feldspar, toward more white in the south (section E), where quartz is dominant. The photos are taken in the north–south direction.

In the northern part of the beach, section A, the Rönne outlet is fixed with 380-m-long piers. The Rönne has breached the narrow dune row at several occasions, of which 1868, 1902, and 1967 were particularly severe (Almström and Fredriksson, 2011). After the storm in 1967, the dunes were reconstructed with a gabion core. The dune height, defined from the dune foot to the foredune crest, is about 2–4 m. The beach and dunes were nourished with 53,000 m³ of sand taken from the north side of the harbour piers at the Rönne outlet in the year 2000 (Almström and Fredriksson, 2011). Further south in section B, the dunes are higher, 5–6.5 m high, and have been eroding as a result of multiple storms during the last decade. The area behind the dunes is developed, and the dunes function as flood protection for the low-lying hinterland (Palalane et al., 2016). After the storms in 2011, 2013, 2014, 2015, and 2016, the dunes were replenished with sediment from the surf zone the following spring. At some of these occasions also the dunes in section A were supplied with sand. In section C, the dune erosion has not been as severe and the dunes have to a larger extent recovered after storm events by aeolian processes (Palalane et al., 2016). The dunes here are about 4–5 m high. Further south, in section D, the dune system consists of multiple relict foredune ridges about 2–4 m high. In section E, the dunes are only about 1–1.5 m high, and the beach is wide, low-lying, and moist most of the time.

A previous study at Ängelholm Beach investigated the crossshore grain-size distribution at three profiles in sections B, C, and D at four occasions (Fredriksson, Larson, and Hanson, 2017). Samples were collected in seven cross-shore distributed sampling points in the subaerial part of the beach, from the water line to the dune crest. In all profiles, the median grain size of aeolian-transported sediment found up in the dunes was about 0.2–0.3 mm. In the eroding section B, where the aeolian transport has not been sufficient to recover the storm erosion, the grain sizes found across the beach were in general coarser than the grain size found in the dune. In sections C and D, where dune recovery from aeolian transport was observed, grain sizes in the dune-building fractions were available at all sampling occasions.

The main portion of the bottom sediment in the deeper parts of Skälderviken Bay consists of clay. For this study, the Swedish Geological Survey provided a bathymetric survey from October 2012 (the material cannot be published because of military security restrictions). In this bathymetry, no bars are observed. However, from aerial photos, parallel bars can be detected in section E, and along the entire beach, temporary crescentic subaqueous deposits are visible within 70 m of the shoreline.

Shoreline Change Analysis

The shoreline change analysis was performed with DSAS version 4.4 (Digital Shoreline Analysis System; Thieler et al., 2017), an extension to Esri's ArcGIS with the capability to calculate shoreline change statistics. In this study, shorelines and vegetation lines were digitized from aerial photos (Table 1). To avoid differences in the result related to the coverage from different years, only aerial photos with a complete coverage of the study area were selected (i.e. 1940, 1947, 1960, 2012, 2014, and 2016). The aerial photos from the 1940s are an exception, where the photo covering x = 0–3250mis dated to 1947, and the photo covering x = 3250–6500 m is dated to 1940.

Table 1

Aerial photos used in the DSAS analysis.

The vegetation line was based on the most nearshore vegetation that could be identified in the aerial photos. The shoreline was defined as the water line, which was distinct on this microtidal beach. The beach width was computed as the difference between the shoreline and vegetation line for each year.

The rates of change of shorelines and vegetation lines were estimated with the linear regression method LRR. DSAS computes LRR by fitting a least squares regression line to all shoreline points for each shore-perpendicular transect. An alternative computation method is the weighted linear regression WLR, where the estimated error of shoreline position in the observations also is taken into account so that increased weight is given to the more precise observations. In this study, the uncertainty related to seasonal variations, temporary water level changes, resolution, and georeferencing was estimated to 10 m for the aerial photos from the 1940s and 1960s, and 5 m for those from the 2010s. The estimated uncertainties were higher for the older photos because of lower resolution and quality. The LRR method was selected to avoid an unproportionally large effect of recent extreme storms—coinciding with the more precise observations—on the analysis.

The shoreline change was analysed at shore-perpendicular transects with 50-m spacing, and the results were linearly interpolated to the grain size sampling locations.

Wave Model

Energy-based significant wave height, spectral peak period, and wave direction were calculated at the outer bay using the Sverdrup–Munk–Bretschneider (SMB) formulations for wave hindcasting (USACE, 1984). The formulations were modified with a memory function, as used by Hanson and Larson (2008), so that antecedent wave conditions were taken into account, both for wave growth and decay. The method applied was identical to that described in Palalane et al. (2016).

A SWANmodel (Booij, Ris, and Holthuijsen, 1999) was set up for Skälderviken Bay (Figure 6). The calculated offshore waves were used as input in the SWAN model to simulate the wave climate for the period 1976–2016. A nested modelling approach was used to simulate the nearshore wave propagation, using a 500-m grid size for the bay model and 100 m for the nearshore model (<10 m depth). Because no wave measurements were available for calibration, default model parameter settings were applied.

Figure 6

Extent of the bay and nearshore wave model together with the bathymetry of Skälderviken.

Longshore Sediment Transport

The potential longshore sediment transport rates were calculated with the Coastal Engineering Research Center (CERC) formula (USACE, 1984) at 59 positions with 110-m spacing alongshore so that the sampling points were located halfway between the computation points.

Wave heights were extracted every hour from the SWAN model at 5 m depth and transformed to breaking depth using an explicit formula (Larson, Hoan, and Hanson, 2010). The explicit formula computes wave height H _sb and wave angle α_b at incipient breaking based on a simplified solution of the wave energy flux conservation equation combined with Snell's law.

The longshore sediment transport rate was calculated using the CERC formula (USACE, 1984):

where, Q _ls is the potential sediment transport rate integrated across the surf zone, s the relative density of the sediment (typically 2.65), P is the sediment porosity (typically 40%), c _gb is the wave group celerity at breaking, and K is an empirical coefficient equal to 0.39. Here, it is assumed that c _gb = (gh _b)^1/2, where g is the acceleration due to gravity, and h _b is the breaker depth, where h _b = H _sb/0.8. The orientation of the coastline was taken from the 2-mdepth contour, which was slightly smoother than the shoreline and assumed to represent the average coastline orientation of the area where longshore sediment transport occurs.

Sediment transport is defined as positive in the southward direction, Q _south, and negative in the northward direction, Q _north. The gross sediment transport rate Q _gross is defined as Q _net = Q _south+|Q _north|, and the net sediment transport rateQ _net as Q _net = Q _south+Q _north.

Gradients in net longshore transport rates are computed as the difference in the transport between two consecutive computation points with index i, divided by the longshore distance:

Assuming an equilibrium profile, the potential shoreline change rate, dy/dt (m/y), is computed through:

where, h is the height of the active profile from the depth of closure to an upper reference, taken as both the dune foot h _df and dune crest position h_dc to estimate the shoreline and vegetation line changes. The depth of closure has been estimated to 5 m and the dune foot height to 2 m (Palalane et al., 2016) and are considered constant for all computation points. The dune crest level is varying and was determined from the digital elevation model (Figure 4).

Observed longshore transport gradients are derived from the shoreline and vegetation line changes, dy_b/dt and dy_d/dt, through:

where, V_nour/dt is the nourished volume per meter of beach length divided by the length of the analysis period.

Sampling and Grain Size Analysis

Samples were collected on 28 March 2018. In total, 58 sand samples were collected at an alongshore spacing of 110 m. The samples were taken from the Bascom reference point located at the mid–beach face position, halfway between the swash zone and wrack line or berm crest (Bascom, 1951).

Samples of 200 g were obtained with a plastic beaker measuring 6 cm in diameter and 4 cm depth. The samples were sieved in a Retsch AS 200 basic shaker for 20 min with half-phi sieve sizes of 2, 1.4, 1, 0.71, 0.5, 0.355, 0.25, 0.18, 0.125, 0.09, and 0.063 mm.

Grain-size statistics were analysed with the computer program GRADISTAT (Blott and Pye, 2001). For the application of the McLaren model, the Folk and Ward (1957) graphical method was used to compute mean M, sorting σ, and skewness Sk, in phi units (Φ = –log₂d), where d is the grain size (mm), according to:

where, the subscript of the phi units indicates the percentile of the cumulative distribution.

McLaren Method

The McLaren model builds on the assumption that lighter grains have a higher probability of being transported than heavier grains and that the deposition of sediment is a selective process that changes the grain size distribution compared with the source sediment (McLaren, 1981).

Transport direction is analysed by comparing all possible pairs of sediment samples in one transport direction with respect to changes in mean grain size, sorting, and skewness. Eight possible combinations of these three parameters exist. Transport in one dominant direction is assumed if a downdrift sample compared with an updrift sample is becoming: (A) finer, better sorted, and more negatively skewed or (B) coarser, better sorted, and more positively skewed. The McLaren model assumes that all possible combinations of changes to statistical distribution parameters have the same probability of occurrence, 1/8, which should be significantly exceeded for cases (A) or (B) above to indicate transport.

For each transport indicator (A and B), a Z test (Equation [8]) is applied to determine whether the number of occurrences n out of the total number of pairs N exceeds the random probability p. The null hypothesis H₀ is that there is no preferred transport direction: p ≥ 1/8. The tested hypothesis H₁ is that transport is occurring in the analysed direction, p > 1/8:

The H₁ hypothesis is accepted at the 5% significance level if Z > 1.645 and at the 1% significance level if Z > 2.33.

Analysis of Aerial Photos

The rate of shoreline change was calculated based on five aerial photos from1940 to 2016 by the linear regression method in DSAS (Thieler et al., 2017). The left panel in Figure 7 displays the yearly rate of change for the shoreline and vegetation line. Positive rates indicate accretion and negative rates erosion. In general, the shoreline shows a more positive rate of change than the vegetation line, both in the eroding and accreting parts of the beach. As a consequence, the beach is becoming wider, which is shown in the right panel of Figure 7. This is probably because of the severe storms during the last decade, which caused large dune erosion that has not fully recovered because of limited aeolian transport. South from x = 5300m, the rates of change of the shoreline and vegetation line are almost equal; thus, in this part, beach width has been nearly constant over the study period. The widest beach in the observations from 1940 and 1960 was found at x = 5300 m. However, in later years, the widest point has progressively moved north and is found in the last observation from 2016 at x = 4300 km.

The shoreline evolution is positive except at x = 800–2500 m and x = 6300–6400 m, whereas the vegetation line is only positive at x = 3500–6000 m. Thus, the shoreline evolution is explained both by supply from the eroding dunes and gradients in longshore transport. The coastal evolution due only to gradients in longshore sediment transport is probably somewhere between the rate of change of the shoreline and the vegetation line.

At x = 0–500 m, the shoreline has advanced, which is explained by a nourishment carried out in 2000. In the southernmost part of the beach at x = 6200–6400 m, the beach erosion is probably caused by the interaction between the flow from the Vege River and the longshore current. Figure 8 shows the coastal evolution in the southernmost part of the study area from photos from 1940, 1960, and 2014. In 1940, the river mouth was at x = 6500mand further north; at x = 6300–6400m, the beach was protruding from the coastline. In 1960, this protrusion had been flattened out, and an island had formed on the SW side of the river outlet. In 2014, the island had grown further, and the beach on the updrift side of the river had advanced to the SW.

Figure 8

Evolution of the coastline around the Vege River mouth in the southern end of the study area. The red line shows the shoreline in 1940, the magenta line in 1960, and the green line in 2014. The protruding coastline in 1940 has been flattened out, and an island has formed SW of the beach.

Altogether, the shoreline change analysis indicates a net sediment transport from north to south and that the northern part of the beach at x = 0–3000 m is eroding and the southern part at x = 3000–6500m is accreting because of gradients in the longshore sediment transport.

Wave Climate

The wave climate at the entrance of the bay was computed with a modified version of the SMB formula for wave hindcasting and propagated to the nearshore in SWAN. Figure 9 displays wave roses at the outer bay and at three locations in the nearshore zone at 5 m depth: in the northern x = 1500 m, central x = 3300 m, and southern x = 5000m parts of the beach. The dominant wave direction in the outer bay is W to SW. Along the studied coastline, the waves refract toward the south. The wave climate is more energetic in the northern part of the beach than in the southern part.

Figure 9

Hindcasted significant wave height during 1976–2016 at the mouth of Skälderviken Bay and at 5 m depth for three locations along the beach. Because of wave sheltering and refraction in the bay, the wave climate is much less energetic and the directional spectrum more narrow. The beach mainly receives waves from NW to NNW.

The wave climate was simulated for three stationary cases, in which 2-m waves with 5-s periods enter the bay from three different directions: parallel to the bay normal, α = 0°, and oblique, α = ±22.5° (Figure 10). A positive value means that the waves are entering the bay from a direction south of the bay normal and vice versa. The incoming wave direction at the bay mouth has a large effect on the wave height nearshore, but only a minor effect on the wave direction, which is quite similar for all three cases. The largest waves relative to incoming waves occur at α = –22.5° because of the bathymetry and geometric shape of the Skälderviken Bay.

Figure 10

Nearshore wave climate for three stationary SWAN model runs with input of waves with H_s = 2 m, T = 5 s, and wind speed = 10 m/s in the wave direction from α = 0°, –22.5°, and 22.5°, respectively (H_s is significant wave height). The results show that the nearshore wave height is significantly affected by the incoming wave direction, where waves coming from north of the bay normal (α = –22.5°) give the largest wave heights because of the geometric shape of Skälderviken Bay. For all cases, the waves refract toward the south before reaching the beach, indicating that the incoming offshore wave direction does not markedly affect the general wave direction in the nearshore.

Computed Longshore Transport Rates

The simulated waves at 5 m depth were transformed to breaking depth with the explicit formula, and the longshore sediment transport rate was computed with the CERC formula. The computed potential yearly average transport rates were about 70,000–100,000 m³/y (left panel in Figure 11). At about x = 4000 m, sediment transport decreases because of the presence of a subdued salient. The net transport is almost equal to the gross transport, implying that only a small ratio of the gross sediment is transported against the dominant transport direction from north to south.

The right panel in Figure 11 shows the computed shoreline change based on the potential longshore transport gradients, together with the observed changes of the shoreline and vegetation line. The computed values are about six to seven times larger than the observed, which is not unusual when employing the CERC formula with default values on the empirical coefficient (Smith, Zhang, and Wang, 2003).

The shape of the computed shoreline change deviates from the observations specifically in three parts of the beach. First, at x = 0–800 m (section A), the model predicts erosion, whereas accretion is observed, probably because of the nourishment in this area, which is not included in the shoreline change computations. Second, at x = 6000–6500 m, the model predicts accretion, whereas erosion is observed. The observed erosion is probably from shoreline changes created by the interaction between the longshore current and the river flow, which is not accounted for in the shoreline change computations. Third, the model predicts erosion at x = 4300–5100 m, whereas accretion is observed. There is a similar signal in the change of vegetation line; however, the model appears to overpredict the influence of the small salient in the coastline at this location, which coincides with the widest point of the beach.

Overall, the computed sediment transport rates indicate that wave refraction in the bay causes an almost unidirectional sediment transport from north to south, in agreement with the observations from the aerial photos.

Longshore Grain Size Variations

The mean and median grain sizes are becoming significantly finer in the transport direction from north to south (Figure 12). The sediment is also less well sorted and more negatively skewed moving south; however, these trends are not significant (5% level). The results suggest that the mean and median grain sizes are the most relevant parameters to study in relation to longshore sediment transport. However, in engineering applications of today, the median grain size D₅₀ in metric units are more commonly used to describe grain size than the phi units (Blott and Pye, 2001); therefore, only D₅₀ is further analysed.

The upper left panel of Figure 13 shows the distribution of D₅₀ for all samples. The two peaks in this distribution, one at 0.15 mm and another one at 0.30–0.35 mm, could be explained by wind erosion at the sampling points, because grain sizes ranging from 0.15 to 0.30 mm are most easily entrained and transported by the wind (Bagnold, 1941). In the other panels of Figure 13, D₅₀ is plotted against longshore distance, average wave height at the 5-m depth, observed changes of the vegetation line and shoreline, and the computed gradients in longshore sediment transport. The strongest correlation is found with the longshore distance, yielding a coefficient of determination, R² = 0.69, for a linear fit. There are also marked correlations between D₅₀ and the observed changes in the shoreline and vegetation lines; however, linear fits yield a weaker agreement, R² = 0.32 and R² = 0.51, respectively. These correlations indicate a relationship between gradients in longshore sediment transport and grain size, as well. However, the result suggests that on this beach, sediment grain size has a stronger correlation to transport direction than the size of transport gradients.

Figure 13

Histogram over median grain size (D₅₀) sampled alongshore and linear regression between D₅₀ and longshore distance, average significant wave height, observed shoreline change, observed vegetation line change, and computed gradients in longshore transport (dQ/dx).

The McLaren Model

The alongshore variation in grain-size distribution was analysed with the McLaren model to see whether the dominant transport direction could be determined by this method. The result indicates two significant transport directions, from north to south by type A sorting and from south to north by type B sorting (Table 2). The transport from south to north was most significant: 500 out of a total 1653 sample pairs indicate northward-directed transport as the sediment becomes coarser, better sorted, and more positively skewed in this direction, which is opposite to the result of the analysis of aerial photos and the transport computations. On the basis of the analysis of the statistical grain-size distribution parameters in the McLaren model (Figure 12), the mean grain size is found to be the only parameter that can be correlated with longshore sediment transport.

Dune Morphology

Results in the previous sections have shown that the vegetation line has advanced in the accreting areas of the beach and that the reference grain size there is within the range of dune-building sediment on this beach, about 0.2–0.3 mm (Figures 7 and 13). The dune height was correlated with the observed gradients in longshore transport according to Equation (3) (Figure 14). Although the data exhibit a lot of scatter, there is a weak correlation between sediment budget and dune height. In eroding or more or less stable stretches of the beach, the dunes are high, with crest elevations of about 6–7 m. In the accreting areas where dQ/dx < –1.5 m³/m per year, the dunes are lower, with dune heights of about 3–5.5 m.