*4.2. Possible Periods of Inter-Annual Outer Bar Evolution due to Variations of Wave Climate*

According to analysis in Section 4.1, the location of the outer sand bar predominantly depends on variations of 99th Quantile of the significant wave heights (Q99Hs). As presented in Figure 4 for different years (2009 and 2010) annual variations of bar location depend on the annual variations of Q99Hs, i.e., whether maximum waves were higher or smaller throughout a given year. The fluctuations in wave heights and wave climate depend on wind conditions (wind climate), the variations of which depend on teleconnection patterns determined through the values of the corresponding climatic indices.

Based on long-term data for the Black Sea it was revealed in [68,69] that on a large time scale the indices the Atlantic Multi-decadal Oscillation (AMO), the North Atlantic Oscillation (NAO) and the East Atlantic-Western Russia (EA/WR) have significant influence on the fluctuations of maximum annual wave heights. On a decadal time scale and less, variations of maximum annual wave heights might depend on the NAO, the Arctic Oscillation (AO), the EA/WR, the East Atlantic Oscillation (EA) and the Scandinavian (SCAND) patterns [68,70–72].

In order to determine any periodicity in variations of the maximum annual wave height analysis was conducted to reveal a connection between temporal fluctuations of the Q99Hs and variations of the main climatic indices for the Black Sea study region. The following indices were considered: the NAO, the AMO, the EA, the AO, the EA/WR and the SCAND. Their dimensionless values were taken from the National Oceanic and Atmospheric Administration (NOAA) of the USA [73]. Variations of the Q99Hs for a deep-water point (depth 55 m, Figure 1) offshore the study site and selected climatic indices are shown in Figure 7.

Results show that the maximum annual wave height fluctuates in time around a mean value of 3.04 m. The analysis did not reveal any significant linear trend toward decrease or increase of wave height in time. Minimum wave height was found to be 2.04 m, while the maximum was equal to 4.28 m.

Wavelet analysis by the Morlet wavelet function, representing the temporal evolution of frequency spectrum shows that fluctuations of the maximum annual waves have nonstationary nature (Figure 8, upper panel). Frequency interval 0.08–0.2 [1/year] is of a particular interest, since trends for both increase and decrease were observed therein. Additionally, fluctuations of amplitudes (Figure 8, lower panel) vary in time, as well. Most stable are the temporal variations in frequency interval 0.05–0.03 [1/year] corresponding to periods of 20–30 years. However, there is an insignificant trend toward decrease of fluctuation frequency in time.

**Figure 7.** Variations of (**a**) 99th quantile of the significant wave height and (**b**) the North Atlantic Oscillation (NAO), (**c**) the Atlantic Multi-decadal Oscillation (AMO), (**d**) the East Atlantic Oscillation (EA), (**e**) the Arctic Oscillation (AO), (**f**) the East Atlantic-Western Russia (EA/WR) and (**g**) Scandinavian (SCAND) patterns for 1950–2010.

**Figure 8.** Fluctuations of normalized maximum annual wave time series (mean multi-annual was removed) (upper panel) and wavelet transformation (lower panel).

A previous study by [68] has shown that fluctuations of climate indices are also nonstationary, which makes it impossible to apply the classic correlation analysis to determine the relation between them and the wave height variations. However, a methodology to correlate two non-stationary process based on wavelet analysis was developed in [68,72]. According to this method, mutual correlation functions were calculated between the same frequency scales of two wavelet decompositions, which gives the advantage of having both correlation coefficients and frequencies, where these coefficients have the largest values.

Wavelet correlation coefficients (with time lag = 0) of the maximum wave height variations for selected climate indices are presented in Figure 9. If one considers that correlation coefficient >0.4 represents good correlation between geophysical processes, then for large (multi-decadal) time spans of 20–30 years variations of wave heights depend on indices the EA and the SCAND, respectively. Fluctuations corresponding to 10–15 years depend on the EA/WR (9–13 years), the EA (10–11 years), the AMO (13 years), the NAO (15 years) and the AO (15–16 years). There are also fluctuations of the order of few years that depend on the EA (4–5 years), the EA/WR (4 years), the AMO/AO (3 years), the SCAND and the EA/WR (2 years).

According to the presented analysis, it may be suggested that the Q99 of the wave climate in the coastal region under study at all time spans would be influenced the strongest by the EA and the EA/WR climate indices. Additionally, strong influence might be expected due to variations of indices the AMO, the AO and the SCAND. Significant correlation was established for the NAO index (0.5), but only for variations with time span of 15 years.

**Figure 9.** Wavelet correlation coefficients for fluctuations of maximum annual wave height and climate indices: the North Atlantic Oscillation (NAO), the Atlantic Multi-decadal Oscillation (AMO), the East Atlantic Oscillation (EA), the Arctic Oscillation (AO), the East Atlantic-Western Russia (EA/WR) and Scandinavian (SCAND).

Thus, it could be expected that mean inter-annual location of the outer bar crest may vary depending on periods of maximum annual wave fluctuations, which in turn predominantly depend on climate indices the EA and the EA/WR. For example, 9 years periodicity of autumn bar location possibly connected with EA/WR can be seen in Figure 2 for years 2007 and 2016.
