*3.1. Field Data: Cross-Shore Profiles*

The morphodynamics of the outer bar was analyzed using discrete measurements of beach profile depths collected along the pier. In the last decades, such measurements were made during a number of international field experiments 'Shkorpilovtsi 2007, 2016, 2018' and within the MICORE project in 2008–2010. Each survey extended from a base point marked as zero at the shore-end of the pier out to typical depths of 4–5 m. The base point was a reference marker in the determination of the offshore distance and it does not coincide with elevation zero of the beach profiles. The data were collected with either a metal pole or a rope lot, as both devices have markings at every 10 cm. The accuracy of both measuring methods is approximately commensurable, as reported accuracy for the metal pole is about 10 cm [51]. The measurements were made at points of known coordinates distanced at every 2 m by lowering the metal pole (rope lot) from the pier deck. In 2008–2010 measurements were acquired only with the metal pole. In 2007, 2016 and 2018 cross-shore profiles were surveyed on a daily basis for about a month, usually in October [50]. In 2008–2010 measurements were done predominantly once a month [32].

The dataset collected in 2008–2010 was used to study the intra-annual morphodynamics of the outer bar. During these monthly measurements, the summer surveys were less frequent, while in winter the regularity depended primarily on meteorological forecasts, giving preference to calm seas or very weak swell. In total, 33 cross-shore profiles were measured: one profile in November 2008, 25 profiles in January-December 2009, six profiles in January–April 2010, and one profile in August 2010. For this period, the average shoreline position was approx. 29 m away from the pier base point. The profiles were subjected to additional processing. The mean slope of each profile was determined as tanβ [52] taking into account only its submerged part, i.e., from elevation zero down to the last measured depth. Thus, for 2008 tanβ = 0.034, while the average tanβ for 2009 and 2010 is 0.039 and 0.045, respectively. Preliminary analysis of the transects revealed that in 2008–2010 the outer bar was localized at distances 130–220 m off the shore at depths 3.5–4.5 m. Having this in mind, profile depths from elevation zero down to a 100 m-offshore distance were

removed in order to ease the determination of bar characteristics. The remaining data were subjected to smoothing by Moving Average method with factor 5 for correction of potential errors due to applied measuring technique. The smoothed data series were used to define the deepest shoreward point (fore-bar depth) and the shallowest shoreward value (bar crest) in order to isolate its entire form. It should be preliminary commented that offshore distance available for performing cross-shore measurements was limited by the pier's length. Thereby, in some cases, the last measured profile points with the smallest depths were considered as bar crests, e.g., data for March–July 2009. Outer bar characteristics used for analysis of its intra-annual dynamics were bar profile, bar crest offshore distance, depth above the bar crest (bar location depth) and bar height, determined by subtraction of fore-bar depth from the depth above the crest.
