Long-Term Dynamics of the Annual Average Wave Heights in the Baltic Sea

A. N. Sokolov1, 2, ✉, B. V. Chubarenko1

1 Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russian Federation

2 Immanuel Kant Baltic Federal University, Kaliningrad, Russian Federation

✉ e-mail: tengritag@gmail.com

Abstract

Purpose. The paper is purposed at revealing the time periods since the mid-20th century when the annual average wave heights in the Baltic Sea tended to increase or decrease, assessing the statistical significance of potential time trends, as well as analyzing the statistical relationship between annual average wave heights in the Baltic Sea and the North Atlantic Oscillation.

Methods and Results. The analysis is based on several points located in different parts of the Baltic Sea, in which the data on annual average wave heights cover the time intervals of several decades and are obtained by instrumental methods (one point), from field observations (two points) and modeling results (six points). The time series of annual average wave heights at these points are divided into the time segments of conditional monotony with predominant tendencies towards increase or decrease. The rates of change in wave heights at each segment and statistical significance of potential time trends are assessed using the non-parametric techniques. In the majority of cases, the trends within the segments under consideration are found to be statistically significant at the 90% level or more and the rates of change in the trend can range from 5 to 20 mm per year. The statistical relationship between annual average wave heights and the North Atlantic Oscillation is evaluated using the Pearson and Spearman correlation analysis. The correlation coefficients between the North Atlantic Oscillation indices and the annual average wave heights are statistically significant at the 90% level or more. Their numerical values within the interannual variability range constitute 0.3–0.6 and those between the five-year moving averages – 0.4–0.8.

Conclusions. The increasing and decreasing phases in wave heights in the Baltic Sea alternate, at that each phase lasts ~ 20 years. The time trends for each phase are statistically significant at least at some points in the sea. The correlation between the North Atlantic Oscillation index and the annual average wave heights is statistically significant but not high. Such correlation can account for ~ 30–65% of the variations in wave characteristics.

Keywords

Baltic Sea, significant wave height, NAO index, time trend, statistical significance, correlation coefficient

Acknowledgements

The work was carried out within the framework of state assignment of IO RAS (theme FMWE-2024-0025).

Original russian text

Original Russian Text © A. N. Sokolov, B. V. Chubarenk, 2025, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 41, Iss. 2, pp. 171–184 (2025)

For citation

Sokolov, A.N. and Chubarenko, B.V., 2025. Long-Term Dynamics of the Annual Average Wave Heights in the Baltic Sea. Physical Oceanography, 32(2), pp. 197-210.

References

  1. Broman, B., Hammarklint, T., Rannat, K., Soomere, T. and Valdmann, A., 2006. Trends and Extremes of Wave Fields in the North-Eastern Part of the Baltic Proper. Oceanologia, 48(S), pp. 165-184.
  2. Nesterov, E.S., ed., 2013. Regime, Diagnosis and Forecast of Wind Waves in the Oceans and Seas. Moscow: Hydrometeorological Research Center of Russian Federation, 292 p. (in Russian).
  3. Tuomi, L., Kahma, K.K. and Pettersson, H., 2011. Wave Hindcast Statistics in the Seasonally Ice-Covered Baltic Sea. Boreal Environment Research, 16(6), pp. 451-472.
  4. Soomere, T., 2023. Numerical Simulations of Wave Climate in the Baltic Sea: A Review. Oceanologia, 65(1), pp. 117-140. https://doi.org/10.1016/j.oceano.2022.01.004
  5. Suursaar, Ü. and Kullas, T., 2009. Decadal Variations in Wave Heights near The Cape Kelba, Saaremaa Island, and Their Relationships with Changes in Wind Climate. Oceanologia, 51(1), pp. 39-61. https://doi.org/10.5697/oc.51-1.039
  6. Soomere, T., 2013. Extending the Observed Baltic Sea Wave Climate back to the 1940s. Journal of Coastal Research, 65(sp. 2), pp. 1969-1974. https://doi.org/10.2112/SI65-333.1
  7. Cieślikiewicz, W., Paplińska-Swerpel, B. and Soares, C.G., 2005. Multi-Decadal Wind Wave Modelling over the Baltic Sea. In: National Civil Engineering Laboratory, 2005. Coastal Engineering 2004: Proceedings of the 29th International Conference. Lisbon, Portugal: World Scientific Publishing Company, pp. 778-790. https://doi.org/10.1142/9789812701916_0062
  8. Sokolov, A.N. and Chubarenko, B.V., 2020. Temporal Variability of the Wind Wave Parameters in the Baltic Sea in 1979–2018 Based on the Numerical Modeling Results. Physical Oceanography, 27(4), pp. 352-363. https://doi.org/10.22449/1573-160X-2020-4-352-363
  9. Sokolov, A. and Chubarenko, B., 2024. Baltic Sea Wave Climate in 1979–2018: Numerical Modelling Results. Ocean Engineering, 297, 117088. https://doi.org/10.1016/j.oceaneng.2024.117088
  10. Nesterov, E.S., 2013. [The North Atlantic Oscillation: Atmosphere and Ocean]. Moscow: Triada Ltd, 127 p. (in Russian).
  11. Bacon, S. and Carter, D.J.T., 1993. A Connection between Mean Wave Height and Atmospheric Pressure Gradient in the North Atlantic. International Journal of Climatology, 13(4), pp. 423-436. https://doi.org/10.1002/joc.3370130406
  12. Bauer, E., 2001. Interannual Changes of the Ocean Wave Variability in the North Atlantic and in the North Sea. Climate Research, 18(1-2), pp. 63-69. https://doi.org/10.3354/cr018063
  13. Woolf, D.K., Challenor, P.G. and Cotton, P.D., 2002. Variability and Predictability of the North Atlantic Wave Climate. Journal of Geophysical Research: Oceans, 107(C10), 3145. https://doi.org/10.1029/2001JC001124
  14. Dodet, G., Bertin, X. and Taborda, R., 2010. Wave Climate Variability in the North-East Atlantic Ocean over the Last Six Decades. Ocean Modelling, 31(3-4), pp. 120-131. https://doi.org/10.1016/j.ocemod.2009.10.010
  15. Różyński, G., 2010. Long-Term Evolution of Baltic Sea Wave Climate near a Coastal Segment in Poland; Its Drivers and Impacts. Ocean Engineering, 37(2-3), pp. 186-199. https://doi.org/10.1016/j.oceaneng.2009.11.008
  16. Surkova, G.V., Arkhipkin, V.S. and Kislov, A.V., 2015. Atmospheric Circulation and Storm Events in the Baltic Sea. Open Geosciences, 7(1), 20150030. https://doi.org/10.1515/geo-2015-0030
  17. Myslenkov, S., Medvedeva, A., Arkhipkin, V., Markina, M., Surkova, G., Krylov, A., Dobrolyubov, S., Zilitinkevich, S. and Koltermann, P., 2018. Long-Term Statistics of Storms in the Baltic, Barents and White Seas and Their Future Climate Projections. Geography, Environment, Sustainability, 11(1), pp. 93-112. https://doi.org/10.24057/2071-9388-2018-11-1-93-112
  18. Adell, A., Almström, B., Kroon, A., Larson, M., Uvo, C.B. and Hallin, C., 2023. Spatial and Temporal Wave Climate Variability along the South Coast of Sweden during 1959–2021. Regional Studies in Marine Science, 63, 103011. https://doi.org/10.1016/j.rsma.2023.103011
  19. Sen, P.K., 1968. Estimates of the Regression Coefficient Based on Kendall’s Tau. Journal of the American Statistical Association, 63(324), pp. 1379-1389. https://doi.org/10.1080/01621459.1968.10480934
  20. Mann, H.B., 1945. Nonparametric Tests against Trend. Econometrica, 13(3), pp. 245-259. https://doi.org/10.2307/1907187
  21. Kendall, M.G., 1975. Rank Correlation Methods. London: Charles Griffin, 202 p.
  22. Jones, P.D., Jonsson, T. and Wheeler, D., 1997. Extension to the North Atlantic Oscillation Using Early Instrumental Pressure Observations from Gibraltar and South-West Iceland. International Journal of Climatology, 17(13), pp. 1433-1450. https://doi.org/10.1002/(SICI)1097-0088(19971115)17:13%3C1433::AID-JOC203%3E3.0.CO;2-P
  23. Hurrell, J.W., 1995. Decadal Trends in the North Atlantic Oscillation: Regional Temperatures and Precipitation. Science, 269(5224), pp. 676-679. https://doi.org/10.1126/science.269.5224.676
  24. Rodwell, M.J., Rowell, D.P. and Folland, C.K., 1999. Oceanic Forcing of the Wintertime North Atlantic Oscillation and European Climate. Nature, 398, pp. 320-323. https://doi.org/10.1038/18648
  25. Post, E. and Stenseth, N.C., 1999. Climatic Variability, Plant Phenology, and Northern Ungulates. Ecology, 80(4), pp. 1322-1339. https://doi.org/10.1890/0012-9658(1999)080[1322:CVPPAN]2.0.CO;2
  26. D'Odorico, P., Yoo, J.C. and Jaeger, S., 2002. Changing Seasons: An Effect of the North Atlantic Oscillation. Journal of Climate, 15(4), pp. 435-445. https://doi.org/10.1175/1520-0442(2002)015%3C0435:CSAEOT%3E2.0.CO;2
  27. Kolstad, E.W. and O’Reilly, C.H., 2024. Causal Oceanic Feedbacks onto the Winter NAO. Climate Dynamics, 62(5), pp. 4223-4236. https://doi.org/10.1007s00382-024-07128-y
  28. Zhang, W. and Jiang, F., 2023. Subseasonal Variation in the Winter ENSO-NAO Relationship and the Modulation of Tropical North Atlantic SST Variability. Climate, 11(2), 47. https://doi.org/10.3390/cli11020047

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