The present study examines the seasonal and decadal changes of the variance of the synoptic (periods from 2 days to 30 days) and mesoscale (periods from 2 h to 2 days) sea level oscillations in the Baltic Sea. Long-term hourly sea level records were used at 12 tide gauges located in different parts of the sea. We used spectral analysis to estimate the variance for different time scales. The spectral density of sea level oscillations in the Baltic Sea has maximum values in winter when the cyclonic activity in the atmosphere is more intensive. The maximum variances of synoptic

The Baltic Sea is a semi-enclosed shelf basin connected to the open ocean through the narrow shallow Danish straits. As a result, in the inland water basin, the sea level variability totally differs from the open ocean. The tides make a dominating contribution to the sea level variance in the marginal seas (up to 85–90%), but they are negligibly small in the Baltic Sea. The amplitude of the main diurnal and semidiurnal constituents is 2–3 cm, and the maximum tidal range is 20–23 cm [

Medvedev [

Medvedev [

Samuelsson and Stigebrandt [

Synoptic and mesoscale sea level variations in the Baltic Sea level are mainly influenced by meteorological factors, primarily the zonal wind [

Medvedev [

Long-term hourly sea level records at 12 coastal tide gauges located in different parts of the Baltic Sea were used to analyze synoptic and mesoscale sea level variability: Kalix, Furuogrund, Ratan, Stockholm, Kungsholmsfort, Klagshamn, Gedser, Warnemünde, Ristna, Pärnu, Narva, and the Gorny Institute (

Monthly data sets of wind at 10 m and atmospheric pressure at sea level were obtained from the 20th Century Reanalysis from 1871 to 2012 [

Medvedev [

We used the fast Fourier transform (Welch’s method) for each year to calculate the sea-level spectra for each tide gauge. The linear trend was previously removed from the hourly series of observations. The variance of synoptic and mesoscale sea level variability was estimated as the sum of the spectral density values within the frequency band

The wavelet coherence method was used to identify frequency bands in which time series of sea level and atmospheric processes are covarying [

We calculated spectra at nine tide gauges for four seasons (

The difference between the spectra at various seasons decreases with increasing frequency. Therefore, for the Gorny Institute, Pärnu, and Warnemünde, these spectra for four seasons merge. These tide gauges are located at the head of the bays, where the maximum amplitudes of seiches and the maximum of the variance of the mesoscale sea level oscillations in the Baltic Sea are observed [

The spectral peaks with periods of 4, 5, 6, 7, and 8 cpd are observed at the summer spectrum of Narva. These peaks are less in the spectra of other seasons. This confirms the assumption of [

In general, the results of the spectral analysis showed a significant seasonal modification of the Baltic sea level spectrum. This seasonal variability is caused by seasonal changes of the driving forces, primarily, of the wind and atmospheric pressure fields and the cyclones trajectories.

We calculated the variance of the synoptic

The seasonal variation of

The

For each month we estimated trends in interannual changes in

Wind stress is one of the main factors determining sea level oscillations in the Baltic Sea [

The pairs

The pairs

For the pairs

For the pairs

Long-term changes in wind stress over the Baltic Sea are closely related to large-scale atmospheric circulation over the North Atlantic and numerically partially displayed in the North Atlantic Oscillation (NAO) index [

In the current study, we examined the dependences of interannual changes in the

The AO is a large-scale mode of climate variability. It is also known as the Northern Hemisphere annular mode [

The Scandinavia pattern SCAND consists of a primary circulation center over Scandinavia, with weaker centers of an opposite sign over Western Europe and eastern Russia [

We estimated the correlation coefficients between

The largest values of the modulus of the correlation coefficient are observed in the period from November to March (

At the Gorny Institute, Narva, and Kungsholmsfort, the correlation coefficient between the variance

The seasonal variations of the correlation coefficient calculated for pairs of time series of

The variance of synoptic (^{2}/year at Ratan to 0.14 cm^{2}/year at Kungsholmsfort. In the current study, we investigated the temporal changes of

We estimated ^{2} at Stockholm to 50 cm^{2} at Gedser, which is 16–19% of the long-term average values. A pronounced negative trend of −0.66 cm^{2}/year was detected at Gedser, i.e., ^{2}/year is observed, as a result of which the average value of

In general, interannual changes in

The variance of mesoscale sea level oscillations ^{2}, and at Ratan from 6 to 22 cm^{2}. General periods of increase in ^{2}/year, and these trends have significant values in relative units (for example, in percent). The trend at Gedser is 0.08 cm^{2}/year, i.e., over 100 years, ^{2}, which is about 9–10% of the average value of ^{2}). For Klagshamn, 0.17 cm^{2}/year is about 32% of the average ^{2}), for Ratan up to 36% (average ^{2}), and for Kungsholmsfort up to 60% (average ^{2}).

We paid special attention to the change in the values of ^{2}/year at the Gorny Institute to −0.71 cm^{2}/year at Pärnu. At most stations, ^{2}, which is 13% of the average value. A local minimum

The rate of ^{2}/year at Kungsholmsfort to −1.02 cm^{2}/year at Gorny Institute. At Ratan, Furuogrund, and Stockholm, the trend was −0.02–0.03 cm^{2}/year, which ranges from 6% of the average

In the current study, using cross-wavelet analysis, we estimated the coherence of changes in

The high coherence area moved from the annual cycle to a period of 1.5–3 years on the diagrams of the SCAND index and the values of

We estimated the wavelet coherence for pairs of monthly mean values of the zonal and meridional wind over the Baltic Sea and the values of

The main period of storm surges (floods) in the Gulf of Finland and the Gulf of Riga is about 24–30 h. Storm surges contribute a lot to the variance of mesoscale sea level oscillations in the Baltic Sea. Storm surges are separate extreme events, and it is difficult to obtain an integral estimate of their energy in individual years. The approach presented in the current study allowed us to obtain these estimates of the energy of storm surges, to study their seasonal and interannual variability, and also to discover their connection with atmospheric processes at various time-frequency scales. In [

At Stockholm and Kungsholmsfort, the absolute maximum of ^{3} of the Baltic Sea volume change. They detected 74 LVCs in filtering Landsort sea surface elevation anomalies daily time series for 1948–2013. LVC leads to high values of

In general, the same consistent pattern is observed in the seasonal variations of

The atmospheric circulation is the main factor determining the seasonal and interannual changes of

The seasonal changes of the correlation coefficient in

Bednorz and Tomczyk [

Suursaar and Sooäär [

One of the most pressing challenges of science today is global climate change. Much attention is paid to climatic changes in the mean sea level of the World Ocean and changes in the return period and height of storm surges on the seacoast. In [^{2}/year (

The results of our study are in good agreement with the results of the earlier research of the other authors [

The spectral density of the sea level oscillations in the Baltic Sea has maximum values in winter when the cyclonic activity in the atmosphere is more intensive. However, in the head of the Gulf of Finland (Gorny Institute), the autumn spectrum is even higher than winter, which can be explained by the influence of the ice cover, which can reduce the sea level oscillations of wind origin.

The maximum variance of synoptic

The values of

The diagrams of wavelet coherence of the meridional/zonal wind, atmospheric indices, and

The

The obtained results contribute to the knowledge of the sea level oscillations in the Baltic Sea and its climate changes.

I.M. jointly developed the concept of the study. I.M. performed the analysis, visualization, and manuscript writing. A.M. performed the analysis and visualization. All authors have read and agreed to the published version of the manuscript.

This research was partially supported by the Russian Science Foundation (Grant 20-77-00099) and the Russian State Assignment of IO RAS #0128-2021-0004.

Not applicable.

Not applicable.

The data presented in this study are available on the websites of the European Marine Observation and Data Network (

The authors declare no conflict of interest.

Locations of the tide gauges (circles) and reanalysis grid point (square) with the wind and pressure data.

Seasonal spectra of the sea level oscillations at nine Baltic Sea stations: (

Seasonal changes of the variance of synoptic oscillations (

Seasonal changes of the variance of the mesoscale sea level oscillations (

Correlation coefficient (R) of the variance of (

Correlation coefficient (R) of the variance of (

Interannual changes of the synoptic Baltic Sea level oscillation variance at stations (1) Gedser, (2) Klagshamn, (3) Kungsholmsfort, (4) Furuogrund, (5) Ratan, and (6) Stockholm. The dashed line shows the long-term linear trends with 95% confidence intervals (the lighter shaded area); the bold solid line shows the 13-year moving average for the corresponding stations.

Interannual changes of the mesoscale Baltic Sea level oscillation variance at stations (1) Gedser, (2) Klagshamn, (3) Kungsholmsfort, (4) Furuogrund, (5) Ratan, and (6) Stockholm. The dashed line shows the long-term linear trends with 95% confidence intervals (the lighter shaded area); the bold solid line shows the 13-year moving average for the corresponding stations.

Interannual variability of the synoptic (left) and mesoscale (right) Baltic Sea level oscillation variance for the period from 1977 (1978) to 2013 (2007, 2009) at stations (1) Gorny Institute, (2) Pärnu, (3) Ratan, (4) Furuogrund, (5) Klagshamn, (6) Kungsholmsfort, and (7) Stockholm. The dashed line shows multiyear linear trends with 95% confidence intervals (the lighter shaded area).

Wavelet coherence of (

Wavelet coherence of wind speed from the 20th Century Reanalysis mean monthly values of (

The tide gauges which data were used in the study. Numbers in column 1 correspond to stations in

No. | Tide Gauge | Longitude (° E) | Latitude (° N) | Observation Period |
---|---|---|---|---|

1 | Gorny Institute | 30.3 | 59.9 | 1977–2007 |

2 | Narva | 28.1 | 59.5 | 1978–2009 |

3 | Pärnu | 24.5 | 58.4 | 1978–2009 |

4 | Ristna | 22.1 | 58.9 | 1978–2009 |

5 | Kalix | 23.1 | 65.7 | 1974–2013 |

6 | Furuogrund | 21.2 | 64.9 | 1916–2013 |

7 | Ratan | 20.9 | 64.0 | 1892–2013 |

8 | Stockholm | 18.1 | 59.3 | 1889–2013 |

9 | Kungsholmsfort | 15.6 | 56.1 | 1887–2013 |

10 | Warnemünde | 12.1 | 54.2 | 1956–2006 |

11 | Gedser | 11.9 | 54.6 | 1891–2005 |

12 | Klagshamn | 12.9 | 55.5 | 1930–2013 |