*3.2. Modeled Data: Wave Parameters*

Wave fields at the study site were simulated by the SWAN (Simulating Waves Nearshore) Cycle III spectral numerical wave model, which is based on wave action balance equation [53]. The regional wave climate was reconstructed by means of hindcasting for a period of 62 years. More specifically, the available hindcast data for 1948–2006, obtained using wind fields from the regional climate model REMO (Regional Atmosphere Model) [54] were complemented by simulations for 2007–2010 making use of the Global Forecast System's (GFS) analysis winds [55] to encompass the study period. Both sources of wind forcing are based on atmospheric reanalysis of the National Centers for Environmental Prediction (NCEP) having horizontal resolution of 0.5◦. The model was run in a non-stationary mode as numerical simulations had 32 frequencies and 36 directional bands. Two nested SWAN regular grids were set to compute the wave fields in the Western Black Sea shelf and nearshore domain off Kamchia-Shkorpilovtsi beach with horizontal resolution of 1/30◦ and 400 m, respectively. Boundary condition for the SWAN runs were provided by the WAM (Wave Model) output. More details on both models set-up and validation can be found in [46,56]. Thus, long-term numerical simulations secured availability of multi-annual time series of various wave parameters with temporal resolution of one hour.

To analyze the role of regional wave climate on the inter-annual outer bar dynamics the annual 99th Quantiles (Q99) of significant wave height Hs and peak period Tp were calculated from 1948–2010 hindcast data for deep water location (depth 52 m) in front of the study site. For intra-annual analysis, two data sets were needed. First set served to establish how 2009–2010 wave conditions related to the regional wave climate. Therefore, multi-annual monthly Q99 of Hs and Tp were evaluated based on the full time span of the hindcast, while monthly Q99 of the same parameters were determined only for 2009 and 2010. In both cases the source data for quantiles estimation were extracted for location offshore the pier in a zone of weak transformation of waves at 17 m depth (Figure 1). Hourly time series of Hs, Tp and mean direction of wave propagation Dm in November 2008–August 2010 were made available to support detailed analysis. The second set of wave data aided assessment of 2009–2010 bar's dynamics in close vicinity to its location. To this end, initial sea states (wave parameters' time series and monthly Q99 values) were transformed from 17 to 4.4 m depth—a position located at the end of pier (Figure 1). The transformation was performed using the XBeach (eXtreme Beach) model [57] on a cross-shore profile located along the pier on a grid with variable cell sizes and resolution increasing from 7.3 m at the offshore boundary up to 1 m at shore. The input boundary conditions were provided from the SWAM modeling and the XBeach model was run in stationary mode without calculation of sediment transport and morphology update. Model output was post-processed to extract significant wave heights Hs, spectral peak wavelengths Lp and wave steepness Hs/Lp. According to recent studies [58] the efficiency of the SWAN model is very high in deep and transitional waters, and it should not be used for shallow water applications. The XBeach, on the other hand, is used for computation of nearshore hydrodynamics, as in stationary mode it resolves physical processes as wave propagation, directional spreading, shoaling, refraction, wave breaking, etc. [57]. The

preference to work with the 99th quantile of wave parameters was based on the concept that the position of the nearshore bars is closely related to the position of the breaker line(s), which in turn depends on the severity of wave conditions [4]. Thus, when considering the outer bar, it is only expected to be in the breaker zone during severe storms [10], and as pointed out in [59] large offshore waves are required to induce the outer bar into activity and cause significant morphological change.
