# Seasonal and Decadal Variations of the Variance of the Synoptic and Mesoscale Sea Level Variability in the Baltic Sea

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. The Seasonal Variability of the Baltic Sea Level Spectra

#### 3.2. Seasonal Changes of the Sea Level Variance

#### 3.3. The Link between the Atmospheric Circulation, Wind, and Air Pressure in Different Seasons

#### 3.4. Interannual Changes in Sea Level Oscillations Variance

^{2}/year at Ratan to 0.14 cm

^{2}/year at Kungsholmsfort. In the current study, we investigated the temporal changes of ${\sigma}_{syn}^{2}$and ${\sigma}_{mes}^{2}$ in more detail.

^{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., ${\sigma}_{syn}^{2}$decreased by 19% over 90 years. At Ratan, an increase in ${\sigma}_{syn}^{2}$with a rate of 0.27 cm

^{2}/year is observed, as a result of which the average value of ${\sigma}_{syn}^{2}$over 90 years increased by 17%.

^{2}, and at Ratan from 6 to 22 cm

^{2}. General periods of increase in ${\sigma}_{mes}^{2}$, typical for most stations, were observed in 1936–1946, 1970–1979, and 1986–1995. Local minima of ${\sigma}_{mes}^{2}$ occurred in 1925–1933, 1953–1966, and 1980–1985. After 1996, a negative trend in ${\sigma}_{mes}^{2}$ is typical for most tide gauges. For the entire observation period (XX–XXI centuries), the absolute estimates of the rate of change of ${\sigma}_{mes}^{2}$ differ from 0 to 0.17 cm

^{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, ${\sigma}_{mes}^{2}$ increased by 8 cm

^{2}, which is about 9–10% of the average value of ${\sigma}_{mes}^{2}$ for this station (85 cm

^{2}). For Klagshamn, 0.17 cm

^{2}/year is about 32% of the average ${\sigma}_{mes}^{2}$ (53 cm

^{2}), for Ratan up to 36% (average ${\sigma}_{mes}^{2}$ = 11 cm

^{2}), and for Kungsholmsfort up to 60% (average ${\sigma}_{mes}^{2}$ = 23 cm

^{2}).

^{2}/year at the Gorny Institute to −0.71 cm

^{2}/year at Pärnu. At most stations, ${\sigma}_{syn}^{2}$ from 1977 to 2013 decreased by 4–7% from the average for this period. A significant trend was found at Pärnu, where the ${\sigma}_{syn}^{2}$ decreased from 184 in 1978 to 161 in 2009, i.e., by 23 cm

^{2}, which is 13% of the average value. A local minimum ${\sigma}_{syn}^{2}$ was observed at all stations from 1985 to 1991.

^{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 ${\sigma}_{mes}^{2}$ at Ratan and up to 14% at Stockholm. The most intense decrease in ${\sigma}_{mes}^{2}$ in 1977–2009 was found at Pärnu, 19% of the average value of ${\sigma}_{mes}^{2}$, and for the Gorny Institute, 26%. However, these trends of ${\sigma}_{syn}^{2}$ and ${\sigma}_{mes}^{2}$ have low statistical significance (see confidence limits in Figure 9). This is caused by the short period of time series and the large year-to-year variability of these values.

#### 3.5. Relationship with Atmospheric Circulation, Wind, and Air Pressure Variations

## 4. Discussion

^{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 ${\sigma}_{syn}^{2}$ in February at Stockholm and Kungsholmsfort.

^{2}/year (Figure 8).

## 5. Conclusions

- 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 ${\sigma}_{syn}^{2}$ and mesoscale ${\sigma}_{mes}^{2}$ sea level oscillations is observed in winter, except the heads of the Gulf of Finland (Gorny Institute) and Gulf of Riga (Pärnu), where the absolute maximum of ${\sigma}_{syn}^{2}$ is reached in November. The variances ${\sigma}_{syn}^{2}$ and ${\sigma}_{mes}^{2}$ from November to February are 2–3 and 5 times higher than in the summer.
- The values of ${\sigma}_{syn}^{2}$ and ${\sigma}_{mes}^{2}$ are characterized by high correlation (up to 0.70–0.75) with wind variations and atmospheric indices in winter and low correlation in summer.
- The diagrams of wavelet coherence of the meridional/zonal wind, atmospheric indices, and ${\sigma}_{syn}^{2}$ and ${\sigma}_{mes}^{2}$ are characterized by high values at the annual frequency. The zonal wind and ${\sigma}_{mes}^{2}$ at the Gorny Institute are characterized by wide areas of high coherence for periods of 0.7–4 years.
- The ${\sigma}_{syn}^{2}$and ${\sigma}_{mes}^{2}$ values change greatly from year to year. At Gedser, ${\sigma}_{syn}^{2}$decreased by 19%, and at Ratan it increased by 17% over 90 years. The values of ${\sigma}_{mes}^{2}$ for 90 years increased by 32% at Klagshamn, 36% at Ratan, and up to 60% at Kungsholmsfort.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Medvedev, I.P.; Rabinovich, A.B.; Kulikov, E.A. Tidal oscillations in the Baltic Sea. Oceanology
**2013**, 53, 526–538. [Google Scholar] [CrossRef] - Medvedev, I.P.; Rabinovich, A.B.; Kulikov, E.A. Tides in three enclosed basins: The Baltic, Black, and Caspian seas. Front. Mar. Sci.
**2016**, 3, 46. [Google Scholar] [CrossRef][Green Version] - Medvedev, I.P. Formation of the Baltic Sea level spectrum. Dokl. Earth Sci.
**2015**, 463, 760–764. [Google Scholar] [CrossRef] - Kulikov, E.A.; Medvedev, I.P.; Koltermann, K.P. Baltic sea level low-frequency variability. Dyn. Meteorol. Oceanogr.
**2015**, 67, 25642. [Google Scholar] [CrossRef] - Medvedev, I.P. Spatial and temporal features of synoptic and mesoscale variability of the Baltic Sea level. Russ. Meteorol. Hydrol.
**2018**, 43, 815–826. [Google Scholar] [CrossRef] - Samuelsson, M.; Stigebrandt, A. Main characteristics of the long-term sea level variability in the Baltic Sea. Dyn. Meteorol. Oceanogr.
**1996**, 48, 672–683. [Google Scholar] [CrossRef][Green Version] - Suursaar, Ü.; Sooäär, J. Decadal variations in mean and extreme sea level values along the Estonian coast of the Baltic Sea. Dyn. Meteorol. Oceanogr.
**2007**, 59, 249–260. [Google Scholar] [CrossRef] - Johansson, M.; Boman, H.; Kahma, K.K.; Launiainen, J. Trends in sea level variability in the Baltic Sea. Boreal Environ. Res.
**2001**, 6, 159–180. [Google Scholar] - Hünicke, B.; Zorita, E.; Soomere, T.; Madsen, K.S.; Johansson, M.; Suursaar, Ü. Recent change—Sea level and wind waves. In Second Assessment of Climate Change for the Baltic Sea Basin, Regional Climate Studies; The BACC II Author Team, Ed.; Springer International Publishing: Cham, Switzerland, 2015; pp. 155–185. [Google Scholar]
- Andersson, H.C. Influence of long-term regional and large-scale atmospheric circulation on the Baltic sea level. Dyn. Meteorol. Oceanogr.
**2002**, 54A, 76–88. [Google Scholar] [CrossRef] - Dailidienė, I.; Davulienė, L.; Tilickis, B.; Stankevičius, A.; Myrberg, K. Sea level variability at the Lithuanian coast of the Baltic Sea. Boreal Environ. Res.
**2006**, 11, 109–121. [Google Scholar] - Hünicke, B.; Zorita, E. Influence of temperature and precipitation on decadal Baltic Sea level variations in the 20th century. Dyn. Meteorol. Oceanogr.
**2006**, 58, 141–153. [Google Scholar] [CrossRef][Green Version] - Johansson, M.M.; Kahma, K.K.; Boman, H.; Launiainen, J. Scenarios for sea level on the Finnish coast. Boreal Environ. Res.
**2004**, 9, 153–166. [Google Scholar] - Suursaar, U.; Jaagus, J.; Kullas, T. Past and future changes in sea level near the Estonian coast in relation to changes in wind climate. Boreal Environ. Res.
**2006**, 11, 123. [Google Scholar] - Jevrejeva, S.; Moore, J.C.; Woodworth, P.L.; Grinsted, A. Influence of large-scale atmospheric circulation on European sea level: Results based on the wavelet transform method. Dyn. Meteorol. Oceanogr.
**2005**, 57A, 183–193. [Google Scholar] [CrossRef] - Compo, G.P.; Whitaker, J.S.; Sardeshmukh, P.D.; Matsui, N.; Allan, R.J.; Yin, X.; Gleason, B.E.; Vose, R.S.; Rutledge, G.; Bessemoulin, P.; et al. The twentieth century reanalysis project. Q. J. R. Meteorol. Soc.
**2011**, 137, 1–28. [Google Scholar] [CrossRef] - Li, J.; Wang, J.X.L. A new North Atlantic Oscillation index and its variability. Adv. Atmos. Sci.
**2003**, 20, 661–676. [Google Scholar] [CrossRef] - Monin, A.S.; Kamenkovich, V.M.; Kort, V.G. Variability of the Oceans; Wiley: Hoboken, NJ, USA, 1977. [Google Scholar]
- Kamenkovich, V.M.; Koshlyakov, M.N.; Monin, A.S. Synoptic Eddies in the Ocean; Springer Science & Business Media: Berlin, Germany, 1986; Volume 5. [Google Scholar]
- Kulikov, E.A.; Medvedev, I.P. Variability of the Baltic Sea level and floods in the Gulf of Finland. Oceanology
**2013**, 53, 145–151. [Google Scholar] [CrossRef] - Wubber, C.; Krauss, W. The two-dimensional seiches of the Baltic Sea. Oceanol. Acta
**1979**, 2, 435–446. [Google Scholar] - Grinsted, A.; Moore, J.C.; Jevrejeva, S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process. Geophys.
**2004**, 11, 561–566. [Google Scholar] [CrossRef] - Thompson, D.W.; Wallace, J.M. The Arctic Oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett.
**1998**, 25, 1297–1300. [Google Scholar] [CrossRef][Green Version] - Barnston, A.G.; Livezey, R.E. Classification, seasonality and persistence of low-frequency atmospheric circulation patterns. Mon. Weather Rev.
**1987**, 115, 1083–1126. [Google Scholar] [CrossRef] - Bueh, C.; Nakamura, H. Scandinavian pattern and its climatic impact. Q. J. R. Meteorol. Soc.
**2007**, 133, 2117–2131. [Google Scholar] [CrossRef] - Lehmann, A.; Post, P. Variability of atmospheric circulation patterns associated with large volume changes of the Baltic Sea. Adv. Sci. Res.
**2015**, 12, 219–225. [Google Scholar] [CrossRef][Green Version] - Heyen, H.; Zorita, E.; von Storch, H. Statistical downscaling of monthly mean North Atlantic air-pressure to sea level anomalies in the Baltic Sea. Dyn. Meteorol. Oceanogr.
**1996**, 48A, 312–323. [Google Scholar] [CrossRef][Green Version] - Bastos, A.; Trigo, R.; Barbosa, S.M. Discrete wavelet analysis of the influence of the North Atlantic Oscillation on Baltic Sea level. Dyn. Meteorol. Oceanogr.
**2013**, 65A, 20077. [Google Scholar] [CrossRef][Green Version] - Hünicke, B.; Zorita, E. Trends in the amplitude of Baltic Sea level annual cycle. Dyn. Meteorol. Oceanogr.
**2008**, 60A, 154–164. [Google Scholar] [CrossRef][Green Version] - Johansson, M.M.; Pellikka, H.; Kahma, K.K.; Ruosteenoja, K. Global sea level rise scenarios adapted to the Finnish coast. J. Mar. Syst.
**2014**, 129, 35–46. [Google Scholar] [CrossRef] - Karabil, S.; Zorita, E.; Baehr, J. Mechanisms of variability in decadal sea-level trends in the Baltic Sea over the 20th century. Earth Syst. Dyn.
**2017**, 8, 1031–1046. [Google Scholar] [CrossRef][Green Version] - Medvedev, I.P.; Rabinovich, A.B.; Kulikov, E.A. The pole tide/14-month oscillations in the Baltic Sea during the 19th and 20th centuries: Spatial and temporal variations. Cont. Shelf Res.
**2017**, 137, 117–130. [Google Scholar] [CrossRef] - Medvedev, I.; Kulikov, E. Low-frequency Baltic sea level spectrum. Front. Earth Sci.
**2019**, 7, 284. [Google Scholar] [CrossRef] - Bednorz, E.; Tomczyk, A.M. Influence of macroscale and regional circulation patterns on low-and high-frequency sea level variability in the Baltic Sea. Theor. Appl. Climatol.
**2021**, 144, 115–125. [Google Scholar] [CrossRef]

**Figure 1.**Locations of the tide gauges (circles) and reanalysis grid point (square) with the wind and pressure data.

**Figure 2.**Seasonal spectra of the sea level oscillations at nine Baltic Sea stations: (

**a**) Gorny Institute, (

**b**) Narva, (

**c**) Pärnu, (

**d**) Ristna, (

**e**) Furuogrund, (

**f**) Kalix, (

**g**) Stockholm, (

**h**) Kungsholmsfort, (

**i**) Warnemünde.

**Figure 3.**Seasonal changes of the variance of synoptic oscillations (${\sigma}_{syn}^{2}$) for stations at (

**a**) the Gorny Institute, (

**b**) Ratan, (

**c**) Narva, (

**d**) Stockholm, (

**e**) Pärnu, and (

**f**) Kungsholmsfort. The light blue color is ± standard deviations of interannual changes of ${\sigma}_{syn}^{2}$, blue vectors are trends of its value: up is positive, down is negative, right is no trend.

**Figure 4.**Seasonal changes of the variance of the mesoscale sea level oscillations (${\sigma}_{mes}^{2}$) for stations at (

**a**) the Gorny Institute, (

**b**) Ratan, (

**c**) Narva, (

**d**) Stockholm, (

**e**) Pärnu, and (

**f**) Kungsholmsfort. The light blue color is ± standard deviations of interannual changes of ${\sigma}_{mes}^{2}$, blue vectors are trends of its value: up is positive, down is negative, right is no trend.

**Figure 5.**Correlation coefficient (R) of the variance of (

**a**,

**c**,

**e**) synoptic and (

**b**,

**d**,

**f**) mesoscale sea level oscillations and monthly mean values of (

**a**,

**b**) surface atmospheric pressure, (

**c**,

**d**) zonal, and (

**e**,

**f**) meridional winds in different months.

**Figure 6.**Correlation coefficient (R) of the variance of (

**a**,

**c**,

**e**) synoptic and (

**b**,

**d**,

**f**) mesoscale sea level oscillations and (

**a**,

**b**) NAO, (

**c**,

**d**) AO, and (

**e**,

**f**) SCAND indices.

**Figure 7.**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.

**Figure 8.**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.

**Figure 9.**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).

**Figure 10.**Wavelet coherence of (

**a**–

**d**) NAO and (

**e**–

**h**) SCAND monthly values with (

**a**,

**c**,

**e**,

**g**) ${\sigma}_{syn}^{2}$ and (

**b**,

**d**,

**f**,

**h**) ${\sigma}_{mes}^{2}$ at (

**a**,

**b**,

**e**,

**f**) Kungsholmsfort and (

**c**,

**d**,

**g**,

**h**) the Gorny Institute. Contours are wavelet squared coherencies. In all panels, the black thin line and the lighter shaded picture show the cone of influence of the edge effects that might distort the coherence.

**Figure 11.**Wavelet coherence of wind speed from the 20th Century Reanalysis mean monthly values of (

**a**,

**b**,

**e**,

**f**) zonal and (

**c**,

**d**,

**g**,

**h**) meridional components of with (

**a**,

**c**,

**e**,

**g**) ${\sigma}_{syn}^{2}$, (

**b**,

**d**,

**f**,

**h**) ${\sigma}_{mes}^{2}$ at (

**a**–

**d**) Kungsholmsfort and (

**e**–

**h**) the Gorny Institute. Contours are wavelet squared coherencies. In all panels, the black thin line and the lighter shaded picture shown the cone of influence of the edge effects where might distort the coherence.

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

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 |

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Medvedev, I.; Medvedeva, A. Seasonal and Decadal Variations of the Variance of the Synoptic and Mesoscale Sea Level Variability in the Baltic Sea. *Water* **2021**, *13*, 1785.
https://doi.org/10.3390/w13131785

**AMA Style**

Medvedev I, Medvedeva A. Seasonal and Decadal Variations of the Variance of the Synoptic and Mesoscale Sea Level Variability in the Baltic Sea. *Water*. 2021; 13(13):1785.
https://doi.org/10.3390/w13131785

**Chicago/Turabian Style**

Medvedev, Igor, and Alisa Medvedeva. 2021. "Seasonal and Decadal Variations of the Variance of the Synoptic and Mesoscale Sea Level Variability in the Baltic Sea" *Water* 13, no. 13: 1785.
https://doi.org/10.3390/w13131785