Coastal trapped waves (CTW) are a major mechanism to
distribute energy from the atmosphere in the ocean and play a significant
role in large-scale, low-frequency sea-level and current variability in
continental shelf and slope areas. Despite their significance for coastal
dynamics, observational evidence of the influence of CTWs on the large-scale
circulation is rather limited. In this study, mode-1 coastal trapped waves
that were captured at sea-level stations at five locations along the
southern coast of the Black Sea are examined together with sea surface
height reanalysis from the Copernicus Marine Service to reveal their generation
mechanisms and role in the coastal dynamics. It is found that the CTWs were
formed when water accumulated on the western shelf after gale-force
alongshore winds in the western Black Sea. Excited waves propagate
along the Black Sea coast from west to east with a speed of 2.3–2.6 m s
It is 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 their 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 their
formation area with the coast on their right (left) in the Northern (Southern)
Hemisphere, doing so with periods ranging from a few days to weeks and without changing
their character. Hence, CTWs are a major mechanism to distribute energy from
the atmosphere in the ocean. It was shown theoretically and observationally
that CTWs play a significant role in large-scale, low-frequency sea-level
and current variability in continental shelf and slope areas (Brink,
1991; Huthnance, 1995). Although CTWs are produced by different mechanisms,
those that are in Kelvin mode are formed by winds blowing parallel to the coast, which
cause the accumulation of water at the shore through Ekman transport (Adams and Buchwald,
1969; Gill and Schumann, 1974). Observational evidence of CTWs forced by
longshore wind has been documented all around the margins of the ocean since
they were first observed in the 1960s (Shoji, 1961; Hamon, 1962). Examples
of observations of CTWs at sub-inertial frequencies induced by storms
include those from the west coast of South America (Zamudio, 2002; Romea and
Smith, 1983), the west coast of North America (Beckenbach and Washburn,
2004), the coast of South Africa (Schumann and Brink, 1990), the
Japanese coast (Kitade, 2000; Igeta et al., 2007), around Australia and New
Zealand (Maiwa et al., 2010; Stanton, 1995), the west coast of India
(Amol et al., 2012), the East China Sea (Yin et al., 2014), and so on. It
has been shown using these observations that CTWs typically have 8–16 d
periods, 2–4 m s
Despite the significant role of low-frequency CTWs in coastal dynamics, observational studies on CTWs in the Black Sea are limited in that they are confined to the northern coast (Fig. 1). Besides, those studies were based on short-duration measurements carried out during spring–summer periods (Ivanov et al., 2015). To our knowledge, the generation mechanism of mode-1 CTWs propagating along the coast of the Black Sea and their role in the dynamics of the large-scale circulation have not been studied.
Locations of tide gauge stations and the bathymetry (m) of the Black Sea with an overlaid schematic of the circulation (after Korotaev et al., 2003).
Ivanov and Bagaiev (2014) used a 3-D regional model of this area to investigate a wide range of oscillations in sea level and temperature. Ivanov and Bagaiev (2014) noted that oscillations with 5, 10.8, and 15 d periods in the sea level at the coast have statistically significant spectral energy. They explained these oscillations as Kelvin waves or a response of the shelf water to synoptic winds. Yankovsky and Chapman (1995, 1997) studied the scattering of these Kelvin waves into higher wave modes at the southernmost tip of the Crimean Peninsula using numerical models.
Basin-scale modelling studies of the Black Sea current system have also shown the presence of coastal trapped waves and their possible effects on the current. Rachev and Stanev (1997) performed numerical experiments using a primitive equation model 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) studied basin-wide barotropic and baroclinic oscillations in the Black Sea using a three-dimensional primitive equation model. At low frequencies, they found energetic oscillations in temperature with periods of 11.7 and 14.7 d in the southeastern part. Staneva et al. (2001) detected eastward-propagating CTWs along the southern boundary in modelling results.
The Black Sea is a deep basin shaped like a bent ellipse. Its major axis extends 1180 km in the east–west direction and
its minor axis extends 264 km north–south. The shelf in the western part of
the sea constitutes approximately 20 % of the whole sea. The width of
the shelf gradually narrows toward the southwestern corner of the basin and
terminates to the east at 31
The large-scale circulation of the Black Sea is cyclonic, with a strong
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
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.
The paper is structured as follows: the observational data set and Copernicus Marine Environment Monitoring Services (CMEMS) reanalysis products used in this study are described in Sect. 2. Section 3 introduces the identification of CTWs from sea level records along the Turkish coast. In Sect. 4, generation mechanisms of the observed CTWs are identified, and impacts of the CTWs on the coastal current are evaluated in Sect. 5 using CMEMS reanalysis products.
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 along the Black Sea coast of Turkey: İğneada, Şile, Amasra, Sinop, and Trabzon, respectively, from west to east (Fig. 1). The data were collected at 15 min intervals at local datum. The raw data were processed to remove outliers, and then cleaned data were binned into hourly sea levels. Afterwards, the data were smoothed by robust linear regression using the MATLAB smoothdata function with the rlowess option.
Sea-level and surface currents from the Black Sea Reanalysis of Physical
Fields (BS-Currents) from the Copernicus Marine Environment Monitoring Service
(
Hourly wind data were obtained from the Turkish State Meteorological Service
in proximity to sea level stations. Wind fields were also provided by the
Copernicus Marine Environment Monitoring Services. They were estimated from
ASCAT and OSCAT scatterometer retrievals and from ECMWF operational wind
analysis with a spatial resolution of 0.25
Because the amplitude of mode-1 CTWs is greatest at the coast, these waves can be inferred from coastal sea level measurements. The sea levels obtained between January 2012 and January 2017 from the stations of the TUDES network in the Black Sea after the mean and trend have been removed are shown in Fig. 2. Sea levels at all stations synchronously vary over different timescales ranging from a few days (meteorological scale) to seasonally and annually 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 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 occurs in autumn, when river flows are at their minima. The outflow from the Black Sea is controlled by the flow through the Turkish Straits, and changes in river influxes can be seen in the sea level. Moreover, interannual variability of the sea level is also evident, which can be attributed to nonseasonal changes in freshwater influxes (Volkov and Landerer, 2015). In addition to these variations on long time scales, energetic variations in sea level at shorter 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 Sect. 4.
Time series of hourly sea level in meters from İğneada, Şile, Amasra, Sinop, and Trabzon from 2012 to 2017. The data have been smoothed using the robust linear regression method of the MATLAB smoothdata function with the rlowess option.
To detect the dominant frequencies of the variability in the sea-level time series, variance-preserving spectra of sea levels were calculated for all stations (Fig. 3). Spectral analysis using the Welch method was conducted on the hourly binned sea-level data.
Variance-preserving spectra of the sea levels for İğneada, Şile, Amasra, Sinop, and Trabzon; frequency is in cycles per day (cpd).
Although tidal amplitudes are small in the Black Sea, diurnal and semidiurnal (not shown in this figure) tidal frequencies were 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 periods of 5–14 d) of the spectrum are visible. A sharp peak occurs in low-frequency spectra at 14.2 d (0.07 cpd), followed by 5–6 d (0.15 to 0.19 cpd). These values are in good agreement with numerical calculations of wave properties in the Black Sea (Stanev and Beckers, 1999; Ivanov and Bagaiev, 2014; Ivanov et al., 2015). These numerical modelling studies have shown that oscillations with a period of 14.7 d have the maximum energy and can occurr as a response of the basin to synoptic wind forcing. It has also been shown that these oscillations have properties of coastal trapped waves in mode 1.
The spectral analysis results given above reveal that periods of 5–15 d 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. To identify the time-dependent characteristics of sea level oscillations, we employed wavelet analysis which expands time series into time-frequency space. In this study, the continuous wavelet transform 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.
Wavelet power spectra of the sea levels for İğneada,
Şile, Amasra, Sinop, and Trabzon, obtained using the Morlet wavelet. Time is
indicated on the
Power is seen to reach a maximum at low frequencies with 10 to 15 d 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 and 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 at specific time periods. At least three very similar events were identified through visual inspection of those periods, and their characteristics are documented (Aydın, 2019). One of these low-frequency sea level variations occurred during October–November 2014, and we selected this period as a representative example to reveal the characteristics of low-frequency waves and their impact on the Black Sea circulation.
Figure 5 shows variations of the sea level with time during 1 month between 15 October and 15 November 2014. Due to problems with the measurements, data from İğneada station are not shown. At all stations, the sea level first evidently decreased and then attained a maximum of 20 cm. Characteristically, the sea level reached its peak level 2 d after the minimum sea level. This 2 d lag is the same for all stations. The wave crest observed in Şile on 26 October 2014 emerged in Amasra on 28 October, in Sinop on 30 October, and in Trabzon on 1 November. This visual inspection of the time series of sea levels shows that the sea level fluctuation propagates eastward, and the sea level signal is not modified during this propagation. There are clear time lags between the sea level responses at each station. In this case, we can say that a wave has progressed from west to east and reached Trabzon from Şile in about 5–6 d.
Time series of the sea level variations from 15 October to 15 November 2014. The data were subsampled from Fig. 2. The data have been smoothed using the robust linear regression method of the MATLAB smoothdata function with the rlowess option.
Lagged cross-correlation of the sea levels between the first station in the west
(Sile) and stations towards the east demonstrate the propagating nature of
the observed oscillations (Fig. 6). The maximum lagged correlations between the
westernmost station (Şile) and the other stations towards the east
(Amasra, Sinop, Trabzon) occur at days 1.4, 2.5, and 5.2, respectively.
The Şile–Amasra, Şile–Sinop, and Şile–Trabzon distances are 280,
510, and 1010 km, respectively. By using time-delayed correlations and
inter-station distances, the phase velocity of the wave was calculated as
approximately 2.3 m s
Time-lagged correlations between the sea level at the westernmost station (Sile) and those at other stations towards the east for October–November 2014.
To understand the mechanisms for generating the observed CTWs as described above, wind data coinciding with the same period were examined. The temporal variation of the hourly wind at the westernmost station (İğneada) from 15 October to 15 November 2014 is shown in Fig. 7.
Wind speeds and directions at İğneada for the October 2014 event. Shaded area highlights the CTW excitation period.
The wind speed varied periodically on timescales of 3–4 d, changing
direction 180
Spatial distributions of the wind field in the Black Sea obtained from CMEMS
for the period of 24 October to 1 November 2014 are presented in Fig. 8. These
span the duration of southerly winds that change direction to strong
northeasterly winds that reach 18 m s
Sequence of wind stress (colour scale) and direction (wind barbs) distributions from 24 October to 1 November 2014 at 00:00 UTC.
The winds were rather weak and directed E–S across the whole Black Sea basin on 24 October 2014. On 25 October 2014, the wind suddenly changed direction and increased in intensity, blowing at gale force from the northeast in the western part of the basin. The intensity of the wind increased on 26 October, showing an intensity maximum in the northwestern and central parts of the Black Sea. On 27 October 2014, the intensity of the wind gradually decreased while keeping its direction. Note that the wind direction was oriented along the coastline during the storm.
Figure 9 shows the evolution of the sea surface height (SSH) during the event
presented above. The strongest storm occurred on 25 October, and the sea
level responded quickly. On 25 October, surface waters started to accumulate
along the western boundary of the Black Sea with strong northeasterly
winds, resulting in Ekman transport toward the coast. On the following day,
this layer became wider and extended toward the southwestern boundary. Joint
analysis of the winds (see Figs. 7 and 8) and sea level data showed
that the accumulation of water at the coast began when the wind speed
exceeded 8 m s
Sequence of daily mean sea surface height (SSH) distributions from 24 October to 1 November 2014, obtained from the Black Sea reanalysis product of CMEMS.
The event was preceded by moderate wind conditions. The coastal sea level reached an anomaly of 0.3 m due to Ekman transport. The accumulated waters consistently propagated south through 27 October after the winds had weakened and changed direction toward the NW.
Sequence of daily mean horizontal velocity distributions at 2.5 m from 24 October to 1 November 2014, obtained from the Black Sea reanalysis product of CMEMS. For clarity of presentation, only 1 of every 10 vectors is plotted.
Figure 10 shows horizontal distributions of the current vector at the
surface from CMEMS, coinciding with Figs. 8 and 9. On 24 October, the surface current
in the Black Sea was weak except in some parts near the northern boundary.
On 25 October, surface currents in the western Black Sea started to increase
and southwestward velocities of about 0.5 m s
In their study based on an analysis of current measurements made on the Crimean
shelf, Ivanov and Yankovsky (1993) found that 11–12 d oscillations of
coastal currents have the largest amplitude and lead to a 15–20 cm s
Sea level measurements from five coastal stations situated in the southern
Black Sea revealed low-frequency oscillations in the basin. The generation
of coastal trapped waves along the western coast of the Black Sea and their
propagation along the southern boundary were demonstrated using CMEMS
reanalysis products. The sea level oscillations had a 10–20 cm range in the
frequency band along with 14 d periodicity. These waves propagated from west to
east with a speed of 2.3–2.6 m s
During the October to March period, eastward-travelling depressions produce
gale-force winds from the north (Özsoy and 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
propagated eastward along the southern boundary, keeping the coast on their
right. These waves are produced in the western part of the basin during the
winter, when the wind speeds exceed 12 m s
The internal Rossby radius of deformation (20–30 km) is larger than the width of the continental shelf (20–25 km) along the southern and eastern boundaries of the Black Sea. When the shelf scale is comparable with the internal Rossby radius, as it is 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 coastal trapped waves in mode 1.
The coastal trapped waves produce currents of up to 1 m s
In situ sea level data used in this study are available upon request from Turkish General Directorate of Mapping (
MA conducted the research as a part of his master's thesis, supervised by STB. STB wrote the paper with input from MA.
The contact author has declared that none of the authors has any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank the editor, John M. Huthnance, for his comments and suggestions which helped us to clarify some important aspects of the paper. We would also like to thank our reviewers, Emil Stanev and an anonymous reviewer, for their constructive comments on our paper.
This research has been supported by the European Union's Horizon 2020 DOORS project (grant no. 101000518).
This paper was edited by John M. Huthnance and reviewed by Emil Stanev and one anonymous referee.