4.1.3. Influence of Storms and Wave Incidence Angle on Bar Dynamics

The analysis was based on hourly time series (SWAN model output transformed to 4.4 m depth) of parameters Hs, Tp and Hs/Lp for November 2008–August 2010, which were chronologically collated with bar crest positions. It was obvious that discrepancies in the temporal resolution of modeled and measured data introduce difficulties in definition of direct causal connection between particular wave events and monthly measurements of the bar profiles with pre- or post-storm identity. Therefore, we applied the thresholds for scenarios with strong non-linearity (Hs > 1 m, Tp > 6 s and Hs/Lp > 0.03) to the time series in order to identify individual storms or sequences of storms that might be claimed responsible for the cross-shore bar migration.

Application of the thresholds showed that in summer months of 2009–2010 waves corresponded to scenarios S1 and S3 and wave conditions caused minor changes to bar height at its farthermost position at ≈ 220 m (Figure 3). However, influenced by the first autumn storms in September 2009 having characteristics valid for scenarios S2&S4 (Hs ≈ 1.5 m, Tp ≈ 6.5 s, Hs/Lp ≈ 0.04), the sand bar began to move towards the shore reaching its reference location of 196 m in November 2009. The following storm events (Hs ≈ 1.5–2 m, Tp ≈ 7–9 s, Hs/Lp > 0.04) caused minor back-and-forth bar crest shifts of 10–15 m. This state retained up to mid-storm season (January–February), when a storm occurred causing the bar crest initial shoreward displacement. For 2009, such a storm was in January, while for 2010 in February (Figure 3b). The subsequent heavy storm: in February for 2009 (Hs > 2 m, Tp ≈ 8 s, Hs/Lp ≈ 0.04) and in March for 2010 (Hs ≈ 2.2 m, Tp ≈ 9 s, Hs/Lp ≈ 0.045) caused the maximum bar crest offshore shift to its spring-summer location increasing significantly the depth above the crest (Figure 3a,b; Table 1).

Such approach contributed to the definition of individual storms that were deemed responsible for the shoreward/seaward shifts of the bar (Table 2). The hourly time series for each storm or sequence of storms were additionally processed, keeping for analysis only the data fulfilling the thresholds for non-linear scenarios, i.e., Hs > 1 m, Tp > 6 s and Hs/Lp > 0.03. Afterwards, wave parameters of each storm were averaged to a single value in order to make a comparison between wave steepness values, significant wave heights and peak periods for each storm group (Table 2).

**Table 2.** Average wave parameters fulfilling the thresholds for scenarios S2&S4 for storms responsible for outer bar displacements.


It appeared that in 2009–2010 storm conditions for each group were rather similar, although waves in SG2 are slightly higher, steeper and with longer periods. The importance of wave height and period for shore profile changes at the site were studied by means of numerical modeling in [66,67]. They revealed that the typical scenario of wave action on the beach profile regardless of the season is characterized by erosion near the shoreline and accumulation of sediments seaward. The general trend is that the higher the storm waves and longer the periods the larger the shoreline erosion and the further the seaward accumulation of sediments. For same storm waves with shorter periods, the sediments move closer to the shore. However, a significant difference was noticed concerning the time duration of wave conditions for which Hs/Lp exceeded 0.04 (Table 2). For storms causing bar's seaward shift (SG2) these conditions lasted as twice longer (121 h) as those moving the bar closer to the coast (66 h). This suggests that not only steepness and wave period should be taken under consideration in analysis of bar behavior but the duration of these conditions as well.

To examine the role of wave incidence angle on bar migration hourly time series of mean direction of wave propagation Dm (depth 17 m) for November 2008–August 2010 were used. As previously, the time series were subjected to the threefold criterion for scenarios S2&S4 to analyze only the data fulfilling these conditions on three time scales:

• Storm season, November 2008–April 2009 and September 2009–April 2010;


Results are presented in Figure 6 using rose charts for each time scale.

**Figure 6.** Rose charts of mean direction of wave propagation for: (**a**) storm seasons; (**b**) storm groups SG1&SG2; (**c**) strongest storms moving the outer bar seaward; (**d**) strongest storms moving the outer bar shoreward.

During season 2008–2009 (Figure 6a), waves predominantly were approaching in normal to the shore (E-ENE), while in 2009–2010 oblique incidence dominated (NE-ENE). So, for the present case an assumption was made that waves coming at an angle to the coast contribute to bar being moved shoreward due to the presence of long-shore currents, while those approaching in the normal move the bar seaward, mainly governed by non-linear transformation of waves, when they propagate to the coast. Confirmation was found in results concerning the other two time scales. For Storm groups (Figure 6b) waves displacing the bar shoreward have a more oblique approach (NE-ENE) than those moving it seaward. The assumption was verified at the time scale Monthly storms (Figure 6c,d) because storms causing bar shoreward displacement have a distinct NE approach as opposed to storms moving it seaward (ENE to ESE).

Another factor affecting the outer bar movements is the duration of storms. For both time scales Storm groups and Monthly storms (Figure 6b–d) the storms coming from NE-ENE and moving the bar shoreward have shorter durations than the storms approaching from E-ENE and shifting the bar offshore. These duration differences do not exceed 20–30%, which means that the impact of storms balance the bar's cross-shore migration during the

winter season, causing the bar crest to move back-and-forth with respect to the reference distance of 196 m (Figure 3a). As for the time scale Storm seasons results show (Figure 6a) that for season 2009–2010, when the dominant direction of wave approach was NE-ENE the duration is 17.7% longer than the duration in season 2008–2009. These findings were also considered with regard to displacements of the bar crest (Figure 3a). To this end, we determined the maximum cross-shore offsets of the crest from its reference distance. The analysis showed that for storm season 2008–2009 bar's seaward offset is larger (19.87 m) than its offset to the shore (8.24 m). An opposite situation was detected for storm season 2009–2010, when bar's seaward offset equals 11.93 m, while its shoreward displacement is 26.17 m. Therefore, the predominance of oblique wave approach and the longer storm duration in 2009–2010 may have caused the shift of the bar's evolution pattern toward the shore in 2010 (Figure 4d).

Thus far, it may be concluded that intra-annual outer bar evolution follows a seasonal pattern of cross-shore migration, which is mainly governed by scenarios of transformation of highly non-linear waves, and the direction of its off/onshore displacement depends on wave period, duration of wave conditions with steepness >0.04, angle of wave approach and total duration of storms. Annual bar evolution, on the other hand, depends on wave height and storm's parameters as angle of approach and duration.
