This research includes the analysis of hydrological and meteorological data related to the development of the storm surges under discussion. The meteorological data on wind direction and velocity were obtained from the Institute of Meteorology and Water Management (IMGW, https://hydro.imgw.pl/, Institute of Meteorology and Water Management and National Research Institute, 2022). Hydrological data on the sea level and duration of the storm were obtained from the Polish Harbor Offices and publications of the IMGW (https://hydro.imgw.pl/). Presented sea level (SL) is related to the Amsterdam sea level since 2012. The names of storm surges originate from the names of cyclones that are recorded and published on the website of the Institute of Meteorology of the Freie Universität Berlin (Institut für Meteorologie, Freie Universität Berlin, https://www.wetterpate.de). Additional remarks on meteorological conditions during both storm surges were obtained from the Meteorological Service in Germany (wetterzentrale.de). Wind maps (Figure 3) were obtained from a model presented for each hour from the meteorological web page (windy.com). Significant wave heights (Hws) for the open coast located closest to the gauge stations were obtained from WAM wave model for the Baltic Sea. Data was obtained during surges from an online ICM model held by the University of Warsaw (Numerical Weather Forecast ICM, https://old.meteo.pl/).

These materials were the basis for the determination of the velocity and direction of the wind during storm surges (Figure 2C) and the course of the changes in sea level, including the characteristic values (resultant or maximum). The analyses presented below take into consideration the changes in sea level on the western coast from the data from the sea level meter in Świnoujście (SW code, used on figs) and on the eastern coast from Władysławowo (WA code). The analyzed sea level data for the central part of the coast were collected from the data from Kołobrzeg (KG code) and Ustka (US code). The analyses also considered the changes in sea level during all significant storm surges that were recorded in the harbors on the Polish coast in the Autumn-Winter period 2021/22 (Table 1). Those were studied to exclude additional dune retreat before Marie&Nadine surges (M&N). The data in this material only explains the coast retreat after significant SL during both surges.

The volume of dune erosion was analyzed based on field measurements. All measures were done between former small surges and ongoing M&N surges. The measurement date was between January 22 and 28, just after surges named Gerhild and Ida (Table 1). The measurements were repeated in February and then in June 2022. This method allows for obtaining changes of the coast directly after each selected surge, including the main one studied in this paper. The materials included topographic measurements of coastal dunes and beaches conducted in the field and on sandbar shores with dune sections of the coastline. The work was conducted based on a predefined and systematically completed network of measurement points located at distances of 1–2 km along the sandbars (Figure 2D). Topographic measurements were taken along the transverse profiles from benchmark points to the waterline with elevation accuracy to 1 cm. Measurements on profiles were taken with the use of a leveller or the GPS RTK device Topcon HiPer SR (Figures 4C, D). Moreover, in some areas, mapping was conducted between the measurement points, along with recording changes in beach width and locating erosion formations, including washover fans and debris accumulations as a result of water flowing onto the shore or coast, so-called run-up. The height of run-up on the shore or coast was determined based on debris and wreck material and compared to the sea level elevation at the nearest measurement station. In total 304 cross-shore profiles from 320 km of dune coast were used in further analyses. The maximum value of water run-up on the coast, shore or waterfront is defined as the maximum wave uprush measured from the water level (Stockdon et al., 2006; Melby et al., 2012).

The storm characteristics data were compared with the results of measurements that were conducted before and after both storms Marie&Nadine in January 2022 in selected areas. For each cross-shore profile, several indicators were analyzed (Figure 4). The main index of the dune erosion is the value of the toe retreat (ΔPfr) (Łabuz, 2016; 2022). Beach height (Hbe) indicates the places that will be subject to erosion due to a specific sea level with run-up. The influence of these variables on the size of the erosion and the retreat of dunes concerning the sea level was analyzed. The parameters of the relief were calculated based on the juxtaposition of the transverse profiles before the storms (before B) and after the storms (after A). Calculations were performed with the use of Grapher Golden Software and Excel Office software, with the additional tool for volume measurement between two profile lines (Grabit)!. The results were then compared to specific values of storm surges in the harbors that were nearest to the analyzed areas. The following parameters of the coastline morphology were analyzed:

The variable (x) associated with morphological forms parameters (fe and be) was a variable that reflected the pre-storm (B-before) and post-storm (A-after) values change (Δ) as value x difference (Equation 1):

Those changes were expressed as a sum of each meter (i) of the form distance (d) by equations as presented for foredune toe retreat P fr (Equation 2) and volume change Q fr (Equation 3):

The analysis and interpretation of relief changes (Δ) took into consideration the following hydrological and meteorological factors: maximum sea level (HSL), run-up of the water on the coast (HSLr), presenting highest range of the sea level (HSL) and significant wave height (Hsw), duration of the surge (t), wind velocity (Vw), and the coast azimuth (Azw). The morphological changes were presented on selected transverse profiles and marked in the form of summary histograms for the sandbars and for the whole analyzed coast. For the specific independent and dependent variables, Pearson’s correlation was tested. Basic statistical analyses of the dependencies of variables were carried out. Statistical significance, dependence and normal distribution were analyzed. Main statistical parameters of dune retreat were conducted, including mean, median, 25 and 75% percentiles and maximum value for separate sandbars or their longer sections.

On the 27-31.01.2022, two cyclones: Marie and Nadine passed over the Baltic Sea (Figure 1). During the passage, there was high-velocity wind blowing from the W and NW directions (Figure 2D). This caused an increase in sea undulating and in the sea level up to + 1.2 m above average (Tables 1, 2).

The cyclone named Marie formed on the 25^th of January 2022 above the Northern Atlantic (Figure 1A). On the 26^th of January, the cyclone passed over central Scandinavia. This resulted in the development of strong wind on the western coast of the Baltic Sea. The wind was blowing from the south-western direction to the center of the cyclone. In the initial phase of the storm, on the 27^th of January, the dominant winds on the Polish sea coast blew from the SSW-W direction with a velocity of 11–13 m/s. The wind blew from the coast to the north-east, causing a short-term decrease in the sea level (Figure 3A). The direction and velocity of wind during both storm surges on the Polish coast of the southern Baltic Sea are presented in Figure 2D.

The decrease of sea level in the western part of the coast (Świnoujście, Kołobrzeg, see Figure 2A) was higher than in the eastern part (Władysławowo). This resulted from the fact that the water level in the eastern part of the Baltic Sea remained high after the previous storms (Table 1). At the same time, the cyclone Marie was moving from Estonia to Belarus (Figure 1B). As a result, the wind direction changed to W and WNW during the night of the 28^th of January (Figure 3B). On the Polish coast, the impact of that wind led to undulation and another surge of the water. An increase in the sea level by 0.6 to 0.8 m above average was noted in harbors (Table 2). The highest sea level was noted in the central part of the coast, in Koszalin Bay, where the coast was exposed to the strongest wind from the WNW direction. There, the sea level reached 0.89 m AMSL (Table 2). As the cyclone was moving into the continent (Figure 1C), wind velocity over the Baltic Sea decreased, and its direction changed to South. The strong wind from the sea lasted for a short time; therefore, the sea level also decreased rapidly.

The decreasing wind velocity towards the end of the Marie cyclone was accompanied by an almost immediate increase in wind velocity from the SW direction to 14 m/s. This signaled the start of another storm, caused by the Nadine cyclone (Figures 1B–D). On the 28^th of January, Nadine was over Iceland, while on the next day, the 29^th, it had already moved to central Scandinavia. Early on the 29^th of January, the wind on the Polish coast was blowing from the SW direction towards the center of the cyclone, which was located over Scandinavia (Figure 3A). The sea level decreased to +0.2-0.4 m below average (Figure 5A). Higher decreases were noted in the western part of the coast, where stronger winds from the land were blowing for a longer time. This was caused by the fact that the velocity of the wind blowing from land was higher, and the levels remained lower after the passing of the Marie cyclone. During several subsequent hours, the sea level increased 1 m above the average (Figure 5A), because of the change in the wind direction from SW to W, and the wind velocity up to 20 m/s (Figures 3B, 5B). As a result of the log-term influence of the wind blowing from the W and NW direction, on the 30^th of January, the sea level on the central and eastern part of the coast exceeded + 1.1 m AMSL, while in the western part, the maximum sea level was only up to 1 m above the average (SW - Świnoujście).

The increase in the sea level was similar throughout the coast, but the maximum increase was lower in the western part because of the larger decrease between the Marie and Nadine storms. A large surge in the sea level, up to 1.2 m above average, occurred between the western and central parts of the coast (KG - Kołobrzeg and DA - Darłowo). In the eastern part, where the sea level remained high after the previous storm (Marie), high-velocity wind caused the sea level to increase even further, to + 1.28 m above average (WA - Władysławowo). On the 31^st of January, the Nadine cyclone moved to Latvia and further on to the south-east (Figures 1D, 3D). The wind direction changed from NNW to NNE, and the velocity decreased. As a result, the sea level decreased to approximately + 0.5 m AMSL on the 1^st of February. Such analysis is important to understand the relation of the highest SL level versus the start position of the water table, which could be much lower than average, due to air-pressure changes or the impact of previous weather action (wind).

The Marie&Nadine cyclone system, which occurred in January 2022, produced a sequence of two combined storm surges. The effects of dune erosion discussed in this study refer to the cumulative impact of both events. The resulting erosion was extensive and observed along the entire investigated stretch of the southern Baltic coastline (Figure 2D).

In the western part of the coast, the sea level rise did not exceed 1.0 m AMSL, qualifying as a medium-intensity surge. Consequently, dune erosion was relatively minor on the Świna Gate Sandbar, the Dziwna Sandbar, and the Rega River Sandbar (Figure 2D). In contrast, more substantial erosion occurred on the eastern coast, where sea levels reached up to 1.2 m AMSL, indicating a high-intensity storm surge.

Dune erosion varied significantly across sandbars, with the most severe retreat ranging from 5 to 8 meters, recorded on shoreline capes (Figures 6, 7B). These dynamic coastal segments, where the coastline orientation shifts every 1–2 km (typically NW to N), are particularly vulnerable due to their exposure to prevailing storm wave directions. In areas where beach elevation exceeded the storm wave run-up, no dune erosion was observed (Figures 2D, green line; 7A). Figure 7 presents examples of cross-shore profiles showing morphological changes under varying sea levels (HSL), run-up heights (HSLr), and beach heights (Hbe). The value of dune retreat was directly correlated with these parameters and is summarized as average values for each of the studied sandbar (Figure 8).

On the Świna Gate Sandbar, dune erosion was confined to its eastern portion (km 412–416), which is exposed to NW wave action, as during the investigated surges. Here, the maximum retreat reached only 0.5–2 meters (Figure 8). More extensive erosion was recorded further east, where sea levels were higher. In Kołobrzeg (KG) and Władysławowo (WA), water levels exceeded 1.2 m AMSL. In Kołobrzeg, dune retreat ranged between 2 and 5 meters. Variations in erosion intensity were influenced by both beach height and the historical development trends of the coastline. Sections already experiencing long-term erosion, typically with beach elevations not exceeding 1.0-1.5 m AMSL underwent more severe retreat, averaging 5–7 m (Figure 7B). Nearly all locations with pre-storm beach elevations below 2 m AMSL experienced significant erosion. Previous storm events in 2021/22 primarily affected sections with similarly low beach profiles.

Even greater erosion occurred on the sandbars of the Koszalin Bay (sandbars no. 5-7), which are exposed to NW wind and wave directions (Figures 2D, 8). In this region, average dune toe retreat reached 3 meters, with maximum values of 5–6 m.

Considerable erosion was also noted along the eastern coast, from Rowy to Karwia (Figure 2D) where SL was the highest +1.28 m. The most pronounced erosion was observed on low-elevation beach sections, especially those previously affected by minor surges. Erosion was particularly severe on the western flanks of small capes, where the coastline projects northward. On the Gardno and Łeba Sandbars (approx. 36 km total length), erosion varied, with more exposed NW-facing sections suffering the greatest impacts (Figures 7, 8). On the Gardno Sandbar, average dune retreat reached 3.8 meters, with maximum values up to 13 meters, largely due to the highest sea levels recorded during the Nadine storm. On the Łeba Sandbar, erosion was more variable, ranging from 0.2 to 10 m, depending primarily on local beach elevation, where the coast with lower beaches suffered more significant retreat.

Along the 47 km section encompassing the Sarbsko, Kashubian, and Karwia sandbars, average dune retreat ranged from 3 to 4.5 m (Figure 8). The most severe erosion occurred on capes where the shoreline orientation shifted northward. These capes, particularly on their western sides, were fully exposed to NW wave activity. In the eastern Sarbsko Sandbar, dune retreat reached up to 5–9 meters on a 1 km section (km 173–174.5). Similar erosion patterns were observed at other capes on the Kashubian and Karwia sandbars (km 163, 168, 155, 150, and 144). On capes, usually on 100–200 m long sections, the beaches are significantly narrowed and lowered to a height of 0.5 m, and the base of the dunes is subject to stronger erosion. The lowering of beaches in these locations was caused by the previous, smaller storm surges. These areas were intensely eroded during the Marie&Nadine surges.

On the Hel Spit, dune erosion was highly variable. It was most severe where the orientation of the coastline changed and minimal in areas where the beach elevation exceeded wave run-up (Figures 7C, 8). Although the Hel Spit is predominantly oriented NE, opposite the NW storm wave direction, strong erosion occurred. During NW storms, resultant currents and wave energy were directed obliquely along the coast, particularly affecting narrow beaches preceding small capes. In these zones, the coastline bends southward, and the narrow, low-lying beaches are exposed to consistent NW erosion. Conversely, the southeastern shores, exposed to E-SE directions, had wider and higher beaches, and thus remained stable (Figure 2D, section no. 14). This created an alternating pattern of eroded and stable zones along the southern part of the Hel Spit. The northern part of the spit, comprising approximately 20 km of artificially nourished beach, was not included in this analysis.

On the Vistula Sandbar, significant dune erosion occurred in the eastern sector, particularly along coastlines exposed to NW directions (east of the new canal and Krynica Morska). The central and western parts, protected by the Hel Peninsula, typically experience lower erosion intensity. Maximum dune retreat on the Vistula Sandbar reached up to 4.0 m. In the eastern part, average retreat was 3.7 m, while in the central section it was up to 2.0 m (Figure 8). The average and maximum erosion were lower on the Vistula Sandbar due to higher beaches before surges.

The previous analyses revealed that each increase in the sea level is linked to a proportionate height of run-up of water on the shore. It is the sum of the sea level and the height of waves that result from wind velocity. The height of run-up is determined by the maximum reach of water on the shore (Nielsen and Hanslow, 1991; Stockdon et al., 2006; Łabuz, 2022). The stronger the storm, the higher the sea level and wave height. Both are causing the observed run-up on the shore. The significant wave height from the ICM model was between 2.6-3.3 m. These values are not strictly related to the water range on the shore but can make the prognosis of storm strength on the coast (Sallenger, 2000). The height of the run-up determines the height of the coast where the dune (or cliff) waterfront will be eroded. Based on that, one may determine the locations where the strongest erosion may occur or has occurred due to high water run-up. The comparison of SL and separately SLr to foredune retreat presented a significant relation (Tab. 3). Dune erosion, expressed as the retreat of the dune toe, was most strongly correlated with the measured wave run-up height. While high sea levels (SL), including those exceeding 1.0 or 1.2 m AMSL, and their duration (t, in hours), contributed to the erosional process, their influence was less significant in statistical analyses. This trend was also confirmed by observations at individual field profiles. A crucial additional factor influencing erosion was the pre-storm beach height (Hbe), particularly its relative elevation compared to the sea level and run-up parameters.

At sea level up to 0.6 m above average, the run-up of water during the lower storms in Autumn-Winter 2021/22 ranged from 0.9 to 1.1 m AMSL. During these surges, only beaches up to 1.2 m high were eroded. During M&N surges sea level of + 1.2 m AMSL was related to 2.8 – 3.3. m high run-up. The run-up resulted in erosion of the beaches lower than the run-up range 3.3 m. In areas with SL + 1 m AMSL coast was safe up to 2 m height. Dune erosion was observed where the beach was lower than this elevation above run-up related to sea level and wave uprush to the shore. The main remark is that SL is not a valuable variable for determining probable coastal erosion without analyzing run-up height (SLr) and shore (beach) height before SL rise. The value of significant wave height from the achieved model did not prove a relation to shore or coast change.

The erosion of dunes in the given section depended on the height of the beach related to SL and SLr. An example might be the large difference in beach height and dune erosion that results from maximum run-up, as presented in Figure 7. Dune erosion was low or not observed in areas where the beach (Hbe) was higher than the sea run-up (HSLr) (Figure 7A). Sections with lower beach height were influenced by higher erosion (Figure 7B). Dune toe retreat (erosion) occurred in places where the beaches were significantly lower than the run-up of water on the shore. Dune retreat was higher on sections with measured higher SL plus SLr. The correlation of these variables was significant (Table 3). Dune volume erosion did not show a strong correlation with other independent storm-related variables. In contrast, beach volume erosion was primarily influenced by the initial height and width of the beach prior to the surge. Wider and higher beaches experienced greater sediment loss, whereas narrower and lower beaches, already lacking in sediment, exhibited minimal volume change regardless of storm parameters.

During the Marie&Nadine storm events, the average dune toe retreat reached 3.0-4.5 m, with maximum values of up to 8–13 m in areas where the coastline orientation shifted significantly. The most intense erosion was recorded in sections of the coast that were fully exposed to dominant wind and wave action from the W to NW direction, such as Koszalin Bay, Ustka Bay, and the eastern parts of both the Vistula Sandbar and the Świna Gate Sandbar (Figure 2D). Changes in dune volume were primarily dependent on dune height and, to a lesser extent, on the magnitude of toe retreat. As a result, using volume change alone, especially when expressed solely through elevation differences is not a reliable indicator of erosion risk.

Sections where SL was higher than beach height were affected by larger dune retreats, including those with high beaches. Sections with beaches up to 2 m AMSL were eroded differently depending on shore orientation. The comparison of SL and beach dune changes presented a low correlation but was statistically significant (p > 0.05). The highest similarity was between max. HSL, time of high SL and beach height change. The HSLr variable presented a better correlation to dune retreat than sea level parameters or wave height. As was expected, there was no relation between wind velocity and wave height in sections with observed erosion.

On sections with beaches of the height of 3-3.5 m a.s.l., erosion was not observed. There, after a surge was observed even wider beach, which was related to sediment accumulation. It was not observed, either, on the western coast of Poland on a low beach shore, where the sea level was lower than 1 m AMSL (Figures 2D, 7). Because the height of most of the beaches ranges from 1.5 and 2.5 m, most coasts are eroded by a run-up of 2.8-3.4 m AMSL. Figure 9 presents the relationship between beach height before surges to dune toe retreat during different SL. The variables are divided into sections with three different SL related to the analyzed coast sections. The aggregate data shows that dune retreat grows with beach height decrease in relation of SL. This trend is similar for all SL heights. A beach’s height rather than its width is more important as protection against coastal erosion.

The greatest erosion occurs in periods when a large storm is preceded by smaller ones that cause a lowering of the beaches. In erosion-prone sections with low beaches, smaller surges also lead to the erosion of dunes. The size of the dune retreat depends on:

In general, as a rule, the higher the sea level is, the stronger the erosion of dunes (toe retreat). The erosion of dune volume is not the key factor. It is related to the dune height, not its retreat value. The likelihood of dune (cliff) erosion during storm phenomena increases on coastal sections with low beaches. They are usually eroded even during smaller storm surges. The consequence is a permanent dune retreat. Therefore, the erosion along the coastline is highly differentiated, as the height of beaches varies even in adjacent sections.