Mechanism of generation and propagation characteristics of coastal trapped waves in the Black Sea

. Costal trapped waves (CTW) are a major mechanism to distribute the energy from the atmosphere in the ocean and play a significant role in large scale, low frequency sea level, and current variability on the continental shelf and slope areas. Despite their significance in the coastal dynamics, observational evidences on the influence of the CTWs on the large-scale 10 circulation are rather limited. In this study, mode-1 coastal trapped waves that was captured on Coastal trapped waves (CTW) were investigated in the Black Sea during 2012–2016 using observations from the sea level stations at five locations along the southern coast of the Black Sea is examined together with the sea surface height model reanalysis from Copernicus Marine Service to reveal their generation mechanisms and their role on the coastal dynamics. It is found that CTWs were formed when water accumulated on the western shelf after gale force alongshore winds blowing in the western Black Sea. Excited 15 wavesSpectral and wavelet analysis of sea level data shows that CTWs exist in the Black Sea with a period of 12–13 days and 15 days duration. These waves propagate along the Black Sea coast from west to east with a speed of 2.3-2.6 m s -1 and cause 10-20 cm variability in sea level transport the atmospherically induced energy all over the Black Sea. The coastal current generated on the order of 1 m s -1 magnitude by CTWs and the main Black Sea current merge and flow eastward as a single structure resulting in intensification in Black Sea circulation during winter. To investigate formation mechanisms of CTWs, 20 sea surface height and surface velocities from Copernicus Marine Service, wind measurements from sea level stations and atmospheric model results from Copernicus Marine Service are jointly analyzed. These analyses showed that CTWs were formed when water accumulated on the western shelf after gale force alongshore winds blowing in the western Black Sea. Our results provide clear observational evidence on process of the excitement of CTWs by wind stress. CTWs generate a coastal current reaching up to 0.5 m s -1 . This coastal current joins the to large-scale cyclonic inertial current flowing over the 25 continental slope and accelerates it. Hence, we present evidence on the influence of the CTWs on the large-scale circulation.


Introduction
The existence of trapped modes in certain cases was first discovered by Stokes (1846), who obtained a trapped wave solution on for fundamental mode edge waves on a sloping beach; these waves propagate in the longshore direction and their amplitude 30 decays exponentially in the offshore direction. This theory was extended a century later by Ursell (1951) to include the whole spectrum of possible modes. These initial studies were mainly concerned with edge waves without rotation whose typical 2 frequencies are above the inertial frequency. Reid (1958) studied the effect of the rotation on shallow water edge waves and showed that unidirectionally propagating waves with the coast to the right (left) in the northern (southern) hemisphere at subinertial frequencies arise. 35 Coastal trapped waves (CTWs) were first observed by Shoji (1961) as the coastal sea level disturbances of several days period moving southward along the east Japanese coast, and as low frequency long waves propagating clockwise along the Australian coast by Hamon (1962). Hamon analyzed mean sea level and atmospheric pressure fluctuations at some stations along the east Australian coast and noticed that at very low frequencies the daily sea level on the shelf did not respond as an inverse barometer as would be expected. Hanon found that the sea level was depressed only about half the expected response. He also found that 40 the spectra of the adjusted sea level were peaked at six and nine days, corresponding to peaks in the atmospheric pressure spectrum. The results suggested the presence of a low frequency nondispersive left bounded wave which travelled along the continental shelf. Robinson (1964) developed a model based on the linearized shallow water equations with rotation and variable topography to explain the phenomenon observed by Hamon (1962). Robinson (1964) has suggested that low frequency waves are generated as a response of sea level to atmospheric pressure on the Australian coasts. Robinson called these waves 45 as Continental Shelf Waves and shelf wave theory was proposed. Adams and Buchwald (1969) have shown that wind stress is the driving mechanism for the low frequency response of the sea surface rather than the pressure changes due to the largescale moving weather system. Later, it was shown that the alongshore component of the wind stress was a dominant factor for the generation of continental shelf waves (Gill and Schumann, 1974). The model has been extended with offshore stratification, variable bottom, and longshore current by Mysak (1967) and Gill and Clarke (1974). It is shown that stratification and 50 topography with a coastal boundary support the existence of both shelf waves and internal Kelvin waves. The free coastal modes are a hybrid between the two and Gill and Clarke (1974) proposed to call them as coastal trapped waves. Coastal trapped waves were investigated in depth after these initial theoretical and experimental developments. An extensive review of these earlier studies and developments can be found in Mysak (1980). Following these pioneering studies, further theoretical and observational efforts have been rapidly pursued leading to the deeper characterization of coastal trapped waves (Brink, 1991;55 Huthnance, 1995).
It is now well known that the margins of the ocean act as an efficient waveguide for the propagation of CTWs from the region of their excitation. Typically mode-1 CTWs have the maximum amplitude on the shore and their amplitude decays exponentially offshore with the scale of the Rossby radius of deformation. They can freely propagate very long distances from the formation area with the coast on the right (left) in the Northern (Southern) Hemisphere, with periods ranging from a few 60 days to weeks, without changing their character. Hence, CTWs are a major mechanism to distribute the energy from the atmosphere in the ocean. It was shown theoretically and observationally that Coastal trapped waves (CTWs ) play a significant role in large scale, low frequency sea level, and current variability on the continental shelf and slope areas (Huthnance, 1995). Although CTWs are produced by different mechanisms, those in Kelvin mode are formed by winds blowing parallel to the coast by accumulating water to the shore through Ekman transport (Adams and Buchwald, 1969;Gill and Schumann, 1974).

3
Observational evidence of CTWs forced by the longshore wind has been documented all around the margins of the ocean since it was first observed in the 1960s (Shoji, 1961;Hamon, 1962) . Examples of observations of CTWs at sub-inertial frequencies induced by storms include along the west coast of South America (Zamudio, 2002;Romea and Smith, 1982), the west coast of North America (Beckenbach and Washburn, 2004), the coast of South Africa (Schumann and Brink, 1990), along the Japanese coasts (Kitade, 2000;Igeta et al., 2007), around Australia and New Zealand (Maiwa et al., 2010;Stanton, 1990), 70 along the west coast of India (Amol et al., 2012), in the East China Sea (Yin et al., 2014) and so on. It has been shown by these observations that CTWs have typically 8-16 days period with 2-4 m s -1 phase speeds and have O (10 cm) amplitudes on the coast.
Despite the significant role of low frequency CTWs in the coastal dynamics, observational studies on CTWsthe coastal trapped waves in the Black Sea are limited, being confined to the northern coast ( Fig. 1). Besides, these studies were based on short-75 duration measurements carried out during spring-summer periods (Ivanov et al., 2015). To our knowledge, the generation mechanism of mode-1 Coastal Trapped Waves (CTWs) propagating along the coast of the Black Sea and their roles on in the dynamics of the large scale circulation have not been studied.
In their study based on analysis of current measurements made on the Crimean shelf, Ivanov and Yankovsky (1993) found that 11-12 day oscillations in coastal currents have the largest amplitude, leading to a 15-20 cm s -1 increase in the alongshore 80 component of the velocity. As a result of the analysis, it was postulated that these oscillations were produced by distant winds on a spatial scale comparable to the length of the Black Sea and were trapped on the shore with a phase velocity of 2 m s -1 . Ivanov and Bagaiev (2014) used a 3-d regional model in this area to investigate a wide range of oscillations in sea level and temperature. Ivanov and Bagaiev (2014) noted that oscillations at 120, 260, and 360 h5, 10.8 and 15 days periods in the sea level at the coast have statistically significant spectral energy. They explained these oscillations as Kelvin waves or a response 85 of the shelf water to synoptic winds. CTWs propagating westward in this area scatter at the southernmost tip of the Crimea Peninsula due to the coastline and topographic variations and anticyclonic eddies could be developed downstream Chapman, 1995, 1997).
In basin-scale modelling studies on the Black Sea current system, the presence of coastal trapped waves and their possible effects on the current was also stated. Rachev and Stanev (1997) performed numerical experiments using the a 90 primitive equation model, which and found that a general cyclonic circulation in the Black Sea can be formed even in conditions of weak cyclonic wind vorticity, due to the propagation of coastal trapped waves. Stanev and Beckers (1999)  The large scale circulation of the Black Sea is cyclonic with a strong inertial current over the continental slope around the basin (Fig. 1). The well-defined Black Sea cyclonic boundary current (rim current) flows over the continental slope with a mean velocity of 30 cm s -1 (Oğuz and Beşiktepe, 1995). Black Sea boundary current intensify during winter due to strong atmospheric forcing (Korotaev, et al., 2003;Stanev, 2005). Classically, cyclonic wind patterns (positive wind stress curl) and the inflows of freshwater that originate from the large rivers on the nNorthwestern part of the Black Sea are postulated as 105 the main forces for cyclonic surface circulation. The presence of the rim current flowing cyclonically is expected to be modified by long waves propagating along the same direction. On the other hand, CTWs are expected to play an important role in the stability of the black sea rim current and the formation of mesoscale variability.
The objective of this study is firstly to provide observational evidence for CTWs in the Black Sea using a series of sea level data along the southern coast and then to identify their generation mechanism and demonstrate their impact on the rim current. 110 The paper is structured as follows: observed data sets and CMEMS numerical model resultsreanalysis protucts used in this study are described in section 2. Section 3 introduces the identification of CTW from sea level records along the Turkish coast. In section 4, generation mechanisms of the observed CTWs are identified, and in Section 5 impacts of the CTWs on the coastal current will be evaluated using model resultsCMEMS reanalysis protucts.

Data
In situ sea level data were obtained from the Turkish National Sea Level Monitoring System (TUDES) operated by the Turkish General Directorate of Mapping along the Black Sea coast of Turkey. There are five stations (İğneada, Şile, Amasra, Sinop, and Trabzon) along the Black Sea coast of Turkey from west to east, respectively (Fig. 1). The data were collected at 15 min.
intervals at local datum. The raw data is processed to remove outliers and then cleaned data are binned into hourly sea levels. 120 Afterwards data smoothed with robust linear regression method using MATLAB smoothdata fuction with rlowess option. Hourly wind data is obtained from the Turkish State Meteorological Service in proximity to sea level stations. Wind fields are also provided by the Copernicus Marine Environment Monitoring Services. They are estimated from ASCAT and OSCAT 130 scatterometers retrievals and from ECMWF operational wind analysis with a spatial resolution of 0.25 ° and 6 h in time, and available at synoptic time 00h:00; 06h:00; 12h:00; 18h:00. (Bentamy and Fillon, 2012).

Identification of CTWs in the southern southern Black Sea
Because the amplitude of mode-1 CTWs is greatest on the coast, these waves can be inferred from coastal sea level 135 measurements. The sea level obtained between January 2012 and January 2017 from the stations of the TUDES network in the Black Sea is shown in Fig. 2 after the mean and trend are removed. Sea levels at all stations synchronously vary on different time scales ranging from from a few days (meteorological scale) to seasonal and annual due to different physical processes acting on different timescales. Changes in sea level in the Black Sea show an obvious seasonal cycle; the highest sea level occurs between spring and summer, while the lowest is seen in fall. This seasonal cycle is in accordance with the seasonal 140 change in freshwater entering the Black Sea. Increasing river inflows increase the sea level of the Black Sea in the spring and the lowest sea level is in autumn when river flows are the minimum. The outflow from the Black Sea is controlled by the flow through the Turkish Straits, and changes in river influxes could be felt in sea level. Moreover, interannual variability of sea levels is also evident and can be attributed to the decadal nonseasonal changes in freshwater influxes (Volkov and Landerer, 2015). from rivers. In addition to these variations in long time scales, energetic variations at sea level, which occur at shorter 145 than monthly timescales, are visible. These energetic events, which are of interest in this study, can be attributed to atmospheric forcing as will be demonstrated in Section 4.
To detect the dominant frequencies of variability in the sea level time series to qualitatively examine the changes in sea level, the variance-preserving spectra of sea level are calculated at all stations (Fig. 3). Spectral analysis using the Welch method was conducted on the hourly binned sea level data. 150 Although tidal amplitudes are small in the Black Sea, diurnal and semidiurnal (not shown in this figure) tidal frequencies we re found to be evident in sea level spectra at all stations. As we move to lower frequencies, i.e., longer periods, clear peaks in the low frequency region (0.07 -0.16 cpd or 5-14 day period) of the spectrum are visible. A sharp peak in low frequency spectra occurs at a occurs at 14.2 days (0.07 cpd), followed by 5-6 days (0.15 to 0.19 cpd). The peaks in the spectra at periods of 5-15 days correspond to the weather band, indicating atmospheric forcing. These values are in good agreement with the numerical 155 calculations of wave properties in the Black Sea (Stanev and Beckers, 1999;Ivanov and Bagaiev, 2014;Ivanov et al., 2015).
The spectral analysis results given above reveal that periods of 5-15 days were predominant in the sea level time series at all stations in the southern Black Sea. The spectral analysis assumes that processes are stationary in time and hence does not give information on the nonstationary parts of the signal. However, due to the seasonal variation in atmospheric forcing, nonstationarity in sea level changes should be expected, particularly in the weather band. Wavelet analysis expands time series 6 into time-frequency space and then is convenient to identify the time dependent signal characteristics of sea level oscillations. In this study, the Continuous Wavelet Transform (CWT) is based on the Morlet wavelet function applied to the sea level using the wavelet toolbox (MATLAB) developed by (Grinsted et al., 2004). The results are presented in Fig. 4.
Power is seen to reach a maximum at low frequencies with 10 to 15 days periods between the autumn-winter months at all sites. These periods are well matched with the results obtained from the spectral analysis presented above. The years 2015 to 165 2016 in Sinop and 2012 in Amasra are exceptions, due to missing data (see Fig. 2). However, this portion of the missing data does not prevent us from seeing the overall structure.
The wavelet analysis presented above allowed us to detect the low frequency variations in on specific time periods. At least three identical events identified through visual inspection in those periods, and their characteristics are documented (Aydın, 2019). One of these low frequency sea level variations was formed during October-November 2014 period and we selected 170 this period as a case to perform a detailed analysis to reveal characteristics of low frequency waves and their impact on the Black Sea circulation.  (Hughes et al., 2019) and are comparable with the phase velocities of 11-12 days oscillations in the Black Sea estimated by Ivanov and Yankovsky (1993).

4 Mechanism of Generation of the Observed CTWs in the Black Sea
To understand the mechanisms of generation of the observed CTWs as described above, wind data coinciding with the same period were examined. The temporal variation of hourly wind at the westernmost station (İğneada), from 15 October to 15 November 2014 is shown in Fig. 7.
The wWind speed varied periodically on 3-4 days time scales, changing direction 180 degrees after each relaxation. The region 195 is mainly dominated by the recurrence of the north wind blowing, alternating with weak wind periods. The frequent change in direction indicates the passage of fronts over the area. A strong wind with a speed of more than 8 m s -1 often occurred and wind speed attained its maximum (>18 m s -1 ) on October 25 from the north-eastern direction. Spatial distribution of this storm for the period of 24-27 October 24-27, 2014 presented in Fig. 7 spans the duration of southerly winds that change direction to strong north-easterly and reach 18 m s -1 . This gale force wind parallel to the coastline from the northeast is favourable to 200 downwelling and piles up the water to the shore. Before and after this gale force wind from the northeast, two wind patterns are visible; before, the wind over the area fluctuated few times from downwelling favourable (north-easterly) to upwelling favourable (south-easterly), each lasting approx. 2 days. After the storm, the wind changes direction to north-westerly. This peak in wind speed corresponds to the peak in the sea level at İğneada.
The wind stress, as resulting from the meteorological model is presented in Fig. 8. The wind field obtained from CMEMS is 205 in good agreement with the corresponding time series recorded at the coastal station. It should be noted that the coastal station is located at the southern end of the core of the storms.  winter is well known through the modelling and altimeter data analysis in the Black Sea (Korotaev, et al., 2003;Stanev, 2005) Stanev at al (2003)  During the October-March period, eastward-travelling depressions produce gale force winds from the north (Özsoy and 250 Ünlüata, 1997). These gale force winds trigger a persistent downwelling along the western boundary of the Black Sea and the accumulation of water at the coast. Following the relaxation of the wind, coastal trapped waves at sub-inertial frequencies Formatted: Superscript 9 propagated eastward along the southern boundary, keeping the coast on the right. These waves are produced in the western part of the basin during the winter when the wind speeds exceed 12 m s -1 . This phenomenon was occurring a few times a year.
The internal Rossby radius of deformation (20-30 km) is larger than the width of the continental shelf (20-25 km) along the 255 southern and eastern boundary of the Black Sea. When the shelf scale is comparable with the internal Rossby radius, as, in the southern and eastern Black Sea, the margins of the Black Sea act as a vertical wall and become an efficient waveguide for the propagation of internal Kelvin waves. The waves formed have maximum amplitude on the shore and decay exponentially offshore with the scale of the Rossby radius of deformation.
The coastal trapped waves produce currents up to 0.5 m s -1 in magnitude along the western and southern boundary of the Black 260 Sea. Black Sea rim current flowing over the continental slope comes closer to the coast because of the narrowing shelf along the southern boundary. Hence, the transient strong currents generated by CTWs interact with this rim current. Since both are cyclonic, the rim current is intensified. This suggests that the intensification of the Black Sea mean circulation during winter is associated with the coastal trapped waves generated by the alongshore winds on the western boundary.
In their study based on analysis of current measurements made on the Crimean shelf, Ivanov and Yankovsky (1993) found 265 that 11-12 day oscillations in coastal currents have the largest amplitude, leading to a 15-20 cm s -1 increase in the alongshore component of the velocity. As a result of the analysis, it was postulated that these oscillations were produced by distant winds on a spatial scale comparable to the length of the Black Sea and were trapped on the shore with a phase velocity of greater than 2 m s -1 . Although we do not have data during their observations period, comparing characteristics of waves they found and our results, Observations of the CTWs observed on the northern boundary of the Black Sea reported in Ivanov and 270 Yankovsky (1993) were possibly generated on the western boundary of the Black Sea. Furthermode considering the shelf width and the wind direction, the only favourable location for generation of mode-1 CTWs is western boundary of the Black Sea and can propagate only cyclonically.

Data availability 275
In situ sea level data used in this study can be obtained from https://tudes.harita.gov.tr. The CMEMS data can be obtained from https://marine.copernicus.eu/.

Author contribution
MA conducted the research as a part of his master thesis supervised by STB. STB wrote the paper with input from MA.