Dynamics of Barred Coast at Different Temporal Scales (by the Example of Vistula Spit in the Baltic Sea)

Abstract

According to fundamental concepts, the morphodynamic system of an accumulative sandy coast with underwater bars exhibits cyclic behavior across various time scales. This raises the question: which factor is more significant for the dynamics of a given coast—individual storms or seasonal changes in wave activity? While observations and studies addressing this issue have primarily been conducted on oceanic coasts, there is a lack of comparable data for fetch-limited areas. Monitoring of the bottom topography along the west coast of Vistula Spit (Baltic Sea) revealed a cyclic behavior in morphology, transitioning from a straightened external bar to its connection with the shore. Analysis of field measurement results indicated that seasonal variations in wave intensity do not significantly impact coastal relief. Furthermore, it was found that the complete cycle of underwater bar evolution lasts approximately two years, during which the coast profile maintains a stable shape at the stage of the straightened external bar. The identification of the primary factor influencing coastal evolution can be characterized by the Dean number (Ω), which combines wave parameters (wave height and period) with sediment fall velocity. Utilizing ERA5 wave reanalysis data, we compared the variability of Ω values on both annual and monthly scales. The analysis revealed that for the section of the coast under consideration, there is no clearly dominant evolutionary factor; rather, the coast is influenced approximately equally by individual storm events and seasonal fluctuations in wave energy. Modeling storm-induced bed profile deformations using the CROSS-PB model demonstrated that the position of the external underwater bar remains nearly constant even during intense and prolonged storms. It is concluded that under specific conditions—determined by a combination of sediment size, coastal slope, and wave regime characteristics—the coast can remain stable, exhibiting minimal response to relatively strong storms and seasonal variations in wave energy. Such coasts are characterized by an absence of a dominant evolutionary factor as indicated by fluctuations in the Dean parameter, allowing their morphodynamic cycles to span several seasons. This type of morphodynamics in coastal accumulative relief appears to be typical for conditions found in fetch-limited areas, such as regional and semi-closed seas.

1. Introduction

The morphodynamic system of an accumulative sandy coast may include one or more underwater bars. The presence, number, and evolution of these bars depend on several factors: the coastal sediment budget, the initial slope of the coast, and the intensity of wave action. According to [1], bars do not form when the coastal slope is steep and when small waves break close to the shore. This situation often occurs where the slope is influenced by underlying bedrock and in areas with limited fetch for waves. When the coastal profile consists of sand, and the waves are sufficiently large, the formation and shape of bars are influenced by the wave climate and the size of sediments.

From a morphological perspective, we can identify different types of bars on open sea non-tidal coasts [2]:

• Two-dimensional straightened bars (parallel to the coastline);
• Three-dimensional bars (varying along the coast by 100–1000 m);
• Crescentic bars (located at relatively equal distances from the shore).

Bars can exist as single formations or as part of multiple bar systems. The average slopes of coastal profiles that can support underwater bars range from 0.005 to 0.03. During high-energy events, bars form at the outer edge of the surf zone and gradually move toward the shore due to relatively low waves. This movement results in shoreward sediment transport caused by differences in wave velocities [3,4]. Fundamental concepts suggest that the morphodynamic system of an accumulative sandy coast with underwater bars exhibits cyclic behavior over various time scales [2,5,6,7].

Traditionally, the morphodynamics of coasts with underwater bars are linked to seasonal changes in wave intensity or to a series of storm events, as noted in [8,9,10,11]. This type of morphodynamics is common along open ocean coasts, where prolonged exposure to swell waves during non-storm seasons causes underwater bars to shift toward the shore [1]. It was on these coasts that the seasonal deformation of the coastal sand profile was first described [5,6,12].

Additionally, some coastal areas are characterized by resistance to fluctuations in wave energy on a seasonal scale but remain sensitive to individual storm events [13,14]. This type of morphodynamics is more typical in fetch-limited regions, where high-energy events are driven by wind waves and the influence of swell waves is minimal [15]. In such areas, underwater bars formed during extreme storm conditions are expected to be less active during non-storm seasons.

It is important to record the evolutionary cycles of underwater bars in natural conditions and to establish criteria for specific types of morphodynamics using accessible methods and quantitative indicators recognized in coastal science.

This paper discusses the morphodynamics of the Vistula Spit located in the southeastern Baltic. In the northeastern part of the spit, a nearshore topography survey has been conducted over several years. The data collected provide a foundation for identifying certain stages of accumulative coast evolution and the behavior of sand bars.

In the following sections of this article, we will describe the observation area and research methodology. We will then discuss the results obtained and present the main conclusions.

2. Study Site

The Vistula Spit stretches 65 km from the mainland of Poland (17 km east of the mouth of the Vistula River) to the southwestern part of the Sambian (Kaliningrad) peninsula (Figure 1). The northeastern part of the Vistula Spit, which is 35 km long, is Russian territory (Baltic Spit), while the southwestern part, measuring 30 km, belongs to Poland. The Vistula Spit separates the Vistula Lagoon from the Baltic Sea, which connects to the sea through the Baltic Strait in the northeast and through the navigable channel of Nowy Świat in the southwest (since 2022). The width of the spit varies from 0.7 km to 1.9 km.

The Vistula Spit is an accumulative landform located in the southeastern Baltic. The shore consists of a foredune and a beach. The above-water Holocene dune ridges are made up of wind-blown marine sands [16,17]. The shallow marine nearshore and surf zone feature accumulative landforms such as shoals and longshore bars.

The formation of the Vistula Spit began about 8000 years ago and was linked to the Littorina transgression in the Baltic Sea basin. During this time, transgressive bars formed in the southern part of the Gulf of Gdańsk due to the reworking of deltaic deposits from the proto-rivers Vistula and Pregolya. This process led to the creation of a large accumulative barrier and a bay where the flooded delta plain once existed. The further development of the barrier occurred alongside fluctuations in sea level, with accumulation during regressive periods and erosion, which caused some material to move landward during transgressions [18,19,20]. Today, the beaches are nourished by material supplied from the bottom of the Gulf of Gdańsk, from the erosion of the foredune and dune ridge, as well as from alluvium from the Vistula River and abrasion material from the western coast of the Sambian Peninsula [18,21].

The above-water part of the Vistula Spit includes several dune ridges, a beach with a berm ridge, and a lagoon that occurs in some areas. The nearshore zone of the spit features a system of two or three longshore bars. The bottom of the nearshore zone, located behind the most seaward longshore bar, is flat and slightly inclined [22].

The nearshore sediments consist of fine-grained, well-sorted sands. In the northeastern direction, there is an increase in the median diameter of the sediments, which becomes medium-grained [18,22].

Tides in the Baltic Sea do not significantly affect coastal morphodynamics because their amplitude does not exceed 0.2 m.

The study site is located on the open sea coast of the Vistula Spit, 3500 m southwest of the Baltic Strait (Figure 1). The research area was established in May 2019 to observe the dynamics of the coastal accumulative relief, and it was codenamed “Baltiysk-2019”. The length of the study site along the coast is 600 m. It includes the above-water part of the coastal zone up to the surface of the dune adjacent to the coastal cliff, as well as the underwater coastal slope down to depths of 7–8 m.

The coastal relief within the study area features a sandy beach that is 30–35 m wide, with a coastal cliff at the back of the beach (Figure 2). The connection between the beach and the coastal cliff is covered by aeolian deposits. The coastal cliff has a gentle slope and is stabilized by grass above these deposits. In some areas, it has two sections separated by a gently sloping terrace. The upper edge of the cliff is rounded and not clearly defined. The land surface adjacent to the edge of the cliff is covered with grass and various woody and shrubby vegetation.

The beach on the outer side can be either straight or marked by beach cusps during certain periods (Figure 3). The distance between the beach cusps, based on an analysis of available satellite images, can vary from 80 to 400 m. The relief of the underwater coastal slope is shaped by a large outer underwater bar, which is generally straight or slightly curved in plan (Figure 4). Less frequently, the outer bar takes on a crescent shape. The inner slope of the outer bar is relatively steep, with a slope of about 0.06, while the seaward slope is gentler, with a slope of about 0.027. The top of the bar is located at a depth of approximately 2.6 m, and the depth of the trough on its inner side is about 4.5 m.

In front of the outer bar, on the land side, there is an inner bar that almost always has a crescent shape. The ends of the crescent-shaped sections of the inner bar typically connect to the shore in the form of terraces that align with the beach cusps.

3. Materials and Methods

3.1. Field Measurements

Monitoring observations of the relief dynamics on the open sea section of the accumulative coast at the “Baltiysk-2019” study site were conducted from May 2019 to August 2023. The work area covered a 600 m stretch of the coast. Relief measurements were taken from the upper part of the coastal cliff down to depths of 7–8 m. During this period, a total of 11 series of measurements were completed: 4 series in 2019, 4 series in 2020, and 1 series each in 2021, 2022, and 2023.

Coastal relief measurements were conducted from a boat using a Garmin GPSMAP 585 Plus echo sounder (Figure 5a) and two Emlid (Budapest, Hungary) Reach RS+ GPS receivers (Figure 5b). Depending on the equipment used and the frequency of surveys, the coastal zone was divided into three sectors (Figure 6). The survey of the underwater coastal slope deeper than 1 m was carried out from a boat. Measurements of the beach and surf zone, up to a depth of 1.5 m, as well as the surface above the edge of the coastal cliff, were taken using GPS receivers. The area above the edge of the coastal cliff was surveyed only during certain stages. The average distance between survey tracks and profiles on the beach was about 30 m.

A detailed description of the measurement methodology, including all primary data obtained, is available in the project of Figshare (https://figshare.com/projects/Monitoring_observations_of_section_of_the_sandy_coast_of_the_Baltic_Spit_dynamics/132524 (accessed on 25 October 2024)).

3.2. Wave Data

To characterize the wave regime, we used ERA5 wave reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF) [23].

The reanalysis data were validated using wave measurements taken in the water area. These measurements were conducted with a Spotter buoy designed by Spoondrift from 11 July to 27 July 2019, at a depth of 20 m, located 5.3 km from the Vistula Spit in the Kaliningrad Region of Russia (54.63 N, 19.77 E; see Figure 7).

From the measurement results, we selected the data point with the highest correlation coefficient (0.94) between the measured data and the reanalysis data based on the two closest available points. More details on the verification of the ERA5 reanalysis data are provided in [24]. The location of the reanalysis data point used is shown in Figure 7.

The following wave regime characteristics were extracted: Hs, m (significant wave height), Tm, s (average wave period), and mean wave direction. The values that are not wave-hazardous for the studied coastal section were removed from the available wave data series. Such values include wave parameters with a wave approach direction in the range from 30° to 210°, which corresponds to the orientation of the coastline of the studied coastal section.

3.3. Calculation and Using Dean Number

A classical concept of sandy shore morphodynamics describes the evolution of underwater bars, which was proposed by Australian researchers [25]. This concept helps identify the main stages in the evolution of underwater bars. According to this framework, two limiting states are defined for a sandy shore, where wave energy dissipation and reflection dominate, respectively. The dissipative profile is characterized by a low slope and may have one or more bars. In contrast, the reflective profile is relatively steep and features an accumulative terrace adjacent to the shore. Between these two limiting states, four intermediate stages are identified. These stages transition from the dissipative profile to the reflective profile and are represented by straightened, three-dimensional, and crescentic adjacent bars. A key quantitative indicator in this concept is the Gourlay parameter [26], also known as the Dean number [27]:

$$\mathsf{\Omega }={\displaystyle \frac{H_b}{w_{s}T}}$$

(1)

where $H_b$ is the height of breaking waves, $T$ is the average wave period, and $w_s$ is the fall velocity of sediments. The significance of this parameter in relation to the concept is that different stages of sand profile evolution correspond to specific values of this parameter—ranging from $\mathsf{\Omega }$ < 1 for reflective profiles to $\mathsf{\Omega }$ > 6 for dissipative profiles.

The relationship between $\mathsf{\Omega }$ values and the stages of profile evolution is conditional. This is because morphodynamics typically lags behind hydrodynamics, meaning the beach requires time to reach equilibrium [28,29]. The intensity of profile changes is directly proportional to the difference between the current wave regime, indicated by $\mathsf{\Omega }$, and the previous regime, where the profile reached its equilibrium state ${\mathsf{\Omega }}_{\mathrm{e}\mathrm{q}}$ [30]:

$$\mathsf{\Delta } \mathsf{\Omega }=\mathsf{\Omega }-{\mathsf{\Omega }}_{\mathrm{e}\mathrm{q}}$$

(2)

where accumulation will occur at $\mathsf{\Delta } \mathsf{\Omega }<0$, and erosion will occur at $\mathsf{\Delta }\mathsf{\Omega }>0$. In accumulation mode, larger differences between $\mathsf{\Omega }$ and ${\mathsf{\Omega }}_{\mathrm{e}\mathrm{q}}$ indicate a lower intensity of the process. Conversely, in erosion mode, larger values of $\mathsf{\Delta }\mathsf{\Omega }$ correspond to a higher intensity.

The typical timescale of coastal relief dynamics in the study area can be estimated by examining the variability of the $\mathsf{\Omega }$ parameter. This is performed using the ratio ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}/{\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ [13], where ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$ is the average standard deviation of $\mathsf{\Omega }$ per year, and ${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ is the average value of $\mathsf{\Omega }$ for each month. The parameter ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$ characterizes annual wave climate variability while ${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ reflects variability in wave action during individual storms. If the ratio ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}/{\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ is close to one, it indicates that the dynamics of this coastal section are largely influenced by individual storms. If the ratio ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}/{\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ is greater than one, then coastal dynamics are associated with seasonal cycles of wave activity.

To calculate the parameter $\mathsf{\Omega }$, Equation (1) was used: $\mathsf{\Omega }=H_b/w_s{T}_p$. The breaker height $H_b$ was calculated based on the following equation [31]:

$${\displaystyle \frac{H_b}{H_{\infty }}}=0.53{\left({\displaystyle \frac{H_{\infty }}{L_{\infty }}}\right)}^{-0.24}$$

(3)

where $H_{\infty }$ represents the deep water wave height, which corresponds to the significant wave height $Hs$ based on ERA5 reanalysis data, $L_{\infty }$ refers to the deep water wavelength defined by the equation $L=g{T}^2/2\pi$. In this case, the mean wave period $Tm$ from ERA5 reanalysis data is used as the value for the wave period $T$. The wave direction is not considered when calculating the breaker height.

Using Equation (3) to calculate $H_b$ is appropriate because the depths in the wave transformation zone decrease gradually, and the isobaths are oriented parallel to each other. Equation (3) proposed by the authors [31] based on a large number of laboratory experiments that used a wide range of bottom slopes. The regression analysis shows that using deep water wave steepness to define breaker height is valid in 80% of the cases studied. It supports the methodological justification for using Equation (3) for calculating parameter $\mathsf{\Omega }$.

The sediment fall velocity $w_s$ was calculated using the following equation [32]:

$$w_s=0.155d_s-0.0075$$

(4)

where $d_s$ is sediment size, mm.

According to references [18,22], the median diameter of sediments ($Md$) in the above-water part of the beach is 0.35 mm. However, since the sediment size decreases with depth in the beach zone, a value of $Md$ = 0.25 mm was used for calculations. To define this sediment size, we compared this section of the coast with the Dean equilibrium profile, as described in [33,34,35]:

$$h=A{x}^{2/3};A=2.25{\left({\displaystyle \frac{{w_s}^2}{g}}\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$$

(5)

In this equation, $h$ represents the water depth, and $x$ is the distance from the coastline. The following points support the validity of using the Dean equilibrium profile to determine the sediment size at depth:

• The Dean model represents the average slope of the coastal profile and is based on extensive empirical data;
• The coastal area under consideration does not experience a deficit of sediments.

The peak period $T_p$ was calculated using the relationship for deep water according to the following [36]:

$$T_p=1.25Tm$$

(6)

3.4. Mathematical Modeling

To study the transformation of the underwater bar during strong storms, we conducted mathematical modeling using the CROSS-PB model [37]. The previous version, CROSS-P [38,39], demonstrated good results, particularly in predicting the erosion of sandy coastal profiles under extreme storm conditions. The updated CROSS-PB model incorporates key mechanisms that control sediment transport in the shoaling and surf zones. These mechanisms include the horizontal and vertical asymmetry of wave velocities, undertow, and infragravity oscillations associated with wave groups. The sediment transport rate is calculated using the Bailard formula [40], which is based on R. Bagnold’s concept of energetics [41].

The initial data for running the model include the median sediment size, the coastal profile, and the time variation of wave parameters such as significant wave height, mean wave period, and wave direction. We used a median grain size of 0.25 mm, which is typical for the underwater slope in this coastal area (see Section 3.3). For our calculations, we utilized chronograms of individual storm events that provided wave data with a time interval of 3 h. Within each 3 h interval, the time step for calculations was set to 5 wave periods. The length of the calculation area was 600 m, with a spatial step of 2 m.

4. Results

4.1. Observations of the Morphodynamics of the Coastal Zone Results

At the start of monitoring in May 2019, a straightened outer underwater bar was observed on the Vistula Spit. Over time, this bar gradually moved closer to the shore (Figure 8) without significant changes in its shape. By March 2020, the bar began to deform, and by the end of the year, it had broken into several crescent-shaped bars, with their ends connecting to the shore as terraces (November 2020). In the fall of 2021, measurements showed that the underwater bar had fully reached the shore and transformed into an accumulative terrace adjacent to the beach. Thus, the measurements indicated that the bar’s movement towards the shore takes about two years.

In March 2022, the formation of a new straightened outer bar was recorded in the same position as the previous one. The next measurement cycle, conducted in August 2023, revealed that the bar had remained stable for over a year.

This cycle of underwater bar evolution aligns closely with the main stages described in the sandy coast morphodynamics model [25] (Figure 9 and Figure 10). In the observations at the Vistula Spit, the coastal relief did not reach extreme states, such as the dissipative or reflective profile, but instead passed through the key intermediate stages, including the following:

• An outer straightened bar (LBT—Longshore Bar-Through);
• The appearance of crescent-shaped outlines in plan view (RBB—Rhythmic Bar and Beach);
• The connection of the crescent-shaped bar ends to the shore, forming transverse bars and rip current channels (TBR—Transverse Bar and Rip);
• The bar’s transformation into an accumulative terrace adjacent to the shore (LTT—Ridge-Runnel or Low Tide Terrace).

The measurements allow us to evaluate the presence of seasonal changes in the coastal profile, which are reflected in shifts between accumulation and erosion processes. As shown in Figure 8, seasonal deformations of the profile were observed only between September 2021 and March 2022. During this time, the straightened profile without a bar transformed into a profile with a clearly defined underwater bar. This change suggests that material was moved to the lower part of the underwater coastal profile following the storm season.

4.2. Determination of the Predominant Factor Influencing the Morphodynamics of the Coast

The studied coastal section can be classified using the $\mathsf{\Omega }$ parameter [25], specifically its average value. The average $\mathsf{\Omega }$ ($\overline{\mathsf{\Omega }}$) for the monitoring period at the study site is 6.87, which classifies this coast as an intermediate type, with the most typical relief corresponding to the Longshore Bar-Through (LBT) stage.

To assess the intra-annual variability of the wave climate at the “Baltiysk-2019” site, hourly ERA5 wave reanalysis data were used for the full years that correspond to the measurement period (2020, 2021, 2022). The results of the calculated values for ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$ and ${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ are presented in

Table 1. Annual variability of wave intensity of study site.

Year	2020	2021	2022
${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$	2.9	2.59	2.91

and

Table 2. Intra-month variability of wave intensity of study site.

Month	Jan	Feb	March	Apr	May	June
${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$	2.91	2.74	2.83	2.59	2.21	1.56
Month	July	Aug	Sep	Oct	Nov	Dec
${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$	2.25	2.42	2.65	2.38	2.79	2.43

.

The dynamics of the ${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ indicator show that wave activity decreases throughout the year, reaching a minimum in June. The average values of ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$ and ${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ are 2.79 and 2.48, respectively. Thus, the ratio of ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$ to ${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ for the study area is 1.125. This value indicates that the site experiences some fluctuations in wave height and steepness throughout the year. However, there is no significant seasonal pattern, and individual storm events have a major impact on coastal behavior.

4.3. Modeling of Storm Dynamics of the Coastal Profile Results

The seasonal and annual evolution of underwater bars, based on natural measurements, has been discussed above. However, the behavior of these bars during individual storms is also of interest. Unfortunately, we were unable to measure the seabed profile during storms or immediately after their end. To analyze the transformation of the bar during strong storms, we used mathematical modeling based on the CROSS-PB model [23,24,25]. This model simulates the behavior of underwater bars during storm events. A full storm cycle typically involves erosion of the coastal profile during periods of high wave activity, followed by partial recovery during the calmer phase, influenced by lower swell waves.

It is important to note that we do not aim to directly compare the model results with observational data. In this case, the modeling serves as an illustration of the potential changes in the underwater bar during typical storm conditions for the studied region.

Data from four storm events were analyzed based on ERA5 reanalysis data for the area adjacent to the study site. The most intense events, occurring between 21 May and 7 November 2019, were selected (Figure 11). Storms were chosen using an approximate criterion, where the significant wave height (Hs) was no less than 1 m. Priority was given to the strongest storms with varying durations and structures. The start and end dates of this period align with the coastal relief surveys, during which the coast was in the Longshore Bar-Through (LBT) stage, meaning the underwater bar had a straightened shape relative to the coastline. A similar profile was recorded on an intermediate date, 30 July 2019. This allows for the consideration of two-dimensional morphology and modeling based on the profile approach.

To compare the selected storm events, several key parameters are proposed:

• Storm duration ($T_{\sum }$, hr.);
• Maximum wave height during the storm (${Hs}_{max}$, m);
• Average $\mathsf{\Omega }$ value ($\overline{\mathsf{\Omega }}$).

These parameters—$T_{\sum }$, ${Hs}_{max}$ and $\overline{\mathsf{\Omega }}$ —characterize the intensity of the waves during each storm. The values for all studied storm events are shown in

Table 3. Parameters of studied storm events.

	${\mathit{T}}_{\sum }$, hr.	${\mathit{H}\mathit{s}}_{\mathit{m}\mathit{a}\mathit{x}}$, m	$\overline{\mathsf{\Omega }}$
storm 1	144	4.08	10.05
storm 2	364	4.32	8.73
storm 3	51	3.85	9.16
storm 4	141	3.31	8.69

.

As shown in Table 1, the selected storm events vary widely in duration (from 51 to 364 h) but are generally similar in terms of ${Hs}_{max}$, and $\overline{\mathsf{\Omega }}$. Storm 1 is somewhat of an outlier, with an average $\mathsf{\Omega }$ value of 10.05, while the $\overline{\mathsf{\Omega }}$ for the other three storms does not exceed 9.5. Although this storm is not the longest and does not have the highest ${Hs}_{max}$, its higher $\overline{\mathsf{\Omega }}$ indicates that it produced the steepest waves.

The coastal profile measured in May 2019 was used as the initial condition for the modeling. The results of the simulated storm impacts on the coastal profile are shown in Figure 12 and Figure 13.

The modeling results show that all storms lead to a lowering of the bar’s crest and its apparent shift towards the sea. This change reflects not so much the movement of the bar itself but rather a transformation in its shape. The trough on the front slope of the bar deepens slightly, but its position remains stable.

The extent of this transformation increases with the storm’s duration and the rise of its maximum wave height (${Hs}_{max}$). This type of change is typical during both the storm’s intensification and its weakening phases. It is important to note that during these phases, sediment transport occurs in opposite directions—towards the coast and towards the sea—resulting from the bar’s reshaped profile (Figure 12 and Figure 13—insets A, C) and increased sediment accumulation near the shore (Figure 12 and Figure 13—insets B, D).

Since the relief measurements during field surveys were conducted only during calm sea conditions long after the storms, direct verification of the CROSS-PB model’s results was not possible. A comparison of the model’s outputs with empirical data is provided in [37].

5. Discussion of the Results

The complete evolution cycle of the accumulative relief was documented during field observations on the Vistula Spit coast. Initially, a straightened external underwater bar was observed (LBT stage, see Section 3.1). This bar later transformed into several crescent bars (RBB stage) that connected to the shore at their ends (TBR stage). Eventually, the bar fully joined the shore, forming an accumulative terrace (LTT stage). The movement of the bar towards the shore took about two years. After the storm season, a new bar formed in the same location as the previously observed one (LBT stage).

Throughout the observed cycle, a consistent displacement of the underwater bar towards the shore was noted. This trend is typical for the morphodynamics of accumulative coasts with underwater bars. Similar examples can be found on the west coast of Denmark, particularly in the Skallingen area [42], and on the east coast of Australia, specifically in the Narrabeen area [43]. In both cases, like in our observations, the bar formed at depth after storm impacts and gradually shifted landward, ultimately connecting to the shore as a terrace.

Another type of underwater bar behavior is also known. Off the coast of the Netherlands in the Egmond region, a bar forms near the shore (at depths of 1–2 m), moves seaward while increasing in size, and then degrades and disappears at depths greater than 7 m [44,45]. The differences in bar migration directions are likely due to variations in bottom slopes, which affect sediment transport differently due to gravity. In Egmond, the underwater slope is steeper than in the Skallingen region and the Vistula Spit region we studied. The displacement of the bar seaward will be discussed further.

The morphodynamics of the studied section of the accumulative coast can be analyzed using quantitative indicators, particularly the mean value of the Dean parameter $\mathsf{\Omega }$. This parameter characterizes the amount of wave energy responsible for the transformation of the relief. The calculated average $\overline{\mathsf{\Omega }}$ for the monitoring period is 6.87, allowing us to classify the coast as an intermediate type, closer to dissipative. This classification corresponds to the Longshore Bar-Through (LBT) stage, according to [25]. According to this conceptual framework, this type of profile is characterized by relatively low variability. It is important to identify the factor that most significantly influences the morphodynamics of this coast—whether it is seasonal fluctuations in wave energy or individual storms.

According to the methodology described in [13], the indicator reflecting the influence of different factors on the morphodynamics of the Vistula Spit coast is ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$⁄${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ = 1.125. The authors of [13] analyze these indicators using examples from accumulative ocean coasts. A similar coast, the Gold Coast in Narrowneck, Australia, has parameters of $\overline{\mathsf{\Omega }}$ = 6.17 and ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$⁄${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ = 1.13. With these parameters, the morphodynamics of the Gold Coast are characterized by straightened underwater bars during high-energy events and crescent-shaped bars during low-energy wave conditions.

In contrast, for the Vistula Spit, the same parameters indicate that the coast does not respond significantly to seasonal fluctuations in wave energy based on field observations. Coasts that show a greater response to individual storms typically have ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$⁄${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ values close to one, as noted in [13]. Therefore, the section of the Vistula Spit coast we studied, based on observational data and the calculated ${\overline{\sigma }}_{{\mathsf{\Omega }}_{360}}$⁄${\overline{\sigma }}_{{\mathsf{\Omega }}_{30}}$ = 1.125, cannot be clearly linked to either seasonal fluctuations in wave energy or individual storms. Since we are unable to record the morphodynamic effects of individual storms directly, we can analyze these effects through mathematical modeling results.

First, it is important to note that, according to the concept presented in [25], the LBT stage corresponds to $\mathsf{\Omega }$ values of about 5–6. In contrast, the $\overline{\mathsf{\Omega }}$ values for the storms we studied range from approximately 8.73 to 10.05 (see Table 3). Therefore, based on condition (2), for all the storm events considered, $\mathsf{\Delta }\mathsf{\Omega }>0$, indicating that erosion predominates.

The results from the CROSS-PB model showed that after the storms, the crest of the underwater bar shifts slightly seaward. However, this type of deformation is difficult to interpret as erosion since erosion typically involves the entire bar moving seaward. Instead, the deformations observed from the modeling results can be described as changes in the shape of the bar. This interpretation is supported by the stable position of the bar trough at the base of the bar’s front slope (Figure 12 and Figure 13). Thus, during high-energy events, we should consider not a shift of the bar but a change in its shape, which results in a lowering of the bar.

This idea is further supported by physical modeling of the bar’s response to high-energy events conducted in a wave flume [29]. In this case, the bar does not shift seaward; rather, after prolonged exposure to relatively high waves, it moves toward the shore and only then shifts seaward in response to the wave regime parameters.

Measurements taken several days after the severe storm on the Vistula Spit also showed that there was no bar shift toward the sea. Between the two measurement series conducted on 7 March and 23 March 2020, a significant storm occurred, lasting about 4.5 days with a maximum wave height ($Hs$) reaching 6 m (Figure 14). The repeated measurements on 23 March 2020 revealed that the bar had shifted slightly shoreward. This shift may be a result of lower wave intensity following the storm’s attenuation. This observation, along with the results of mathematical modeling, largely confirms that during high-energy events, the underwater bar in the studied conditions maintains its position.

This study marks the first time that regular observations of coastal relief have been conducted over several years on the Vistula Spit, allowing us to apply approaches that have primarily been used for ocean coasts. These observations helped identify patterns in the morphodynamics of the accumulative coast across different time scales for a given combination of conditions.

We found that the trend of the bar moving toward the shore, revealed by field observations, is not interrupted by short-term erosion stages during strong storms. Furthermore, the relief of the studied section of the coast does not respond to seasonal fluctuations in wave energy. Coastal development occurs systematically in stages. Under the conditions defined by the slope of the coastal profile, sediment size, and wave regime, only the bar displacement toward the shore and changes in its shape occur. Significant deformations, characterized as erosion of the profile and the formation of a new underwater bar, take place only after the bar has completely joined the coast.

6. Conclusions

Using the example of the Vistula Spit coast, we demonstrate that seasonal deformations may not be typical for high-energy accumulative coasts in regional and semi-closed seas. This sets them apart from similar oceanic coasts, where gentle swell waves play a significant role during non-storm periods.

A combination of factors, including coastal slope, sediment size, and wave regime characteristics, lead to the formation of large external underwater bars. These bars maintain their position and effectively dissipate wave energy during strong storms.

The long-term behavior of the studied coast is characterized by the shoreward movement of nearshore bars, which supply sediment to the subaerial beach and the adjacent foredune. The displacement of the bars is likely controlled by an imbalance between two opposing dynamic factors: wave-driven transport toward the shore and the downslope pull of gravity.

Furthermore, it would be interesting to trace the evolution of this coast over a longer timescale, as this may reveal additional cycles of coastal development.