ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
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Estonian Journal of Engineering
Spatial variations of wave loads and closure depths along the coast of the eastern Baltic Sea; pp. 93–109
PDF | doi: 10.3176/eng.2013.2.01

Authors
Tarmo Soomere, Maija Viška, Maris Eelsalu
Abstract

The closure depth is a key parameter in coastal processes as it characterizes the overall wave intensity in the nearshore and indicates the water depth down to which storm waves are able to maintain a universal shape of equilibrium coastal profiles. The properties and alongshore variations of the closure depth for the eastern Baltic Sea coast are evaluated at a coarse resolution (5.5 km) and for the vicinity of Tallinn Bay at a higher resolution (0.5 km). The study is based on numerical simulations of wind-generated wave fields. It is shown that, due to the small contribution of remote swell in the Baltic Sea, the typical ratio of wave heights in strongest storms and average wave heights is about 5.5, which departs considerably from that of open ocean coasts. A modification of the formula for the approximate calculation of the closure depth from the average wave height is derived. The estimates are based on four methods: from the wave heights of the strongest storms, from average wave heights based on a linear approximation, and using two versions of a second-order approximation. The greatest closure depth of up to 7.25 m was found to occur along the coast of the Baltic Proper near Hiiumaa, Saaremaa and the Kurzeme Peninsula. These areas also experience the largest wave intensities. Along other parts of the Baltic Proper coast the closure depth is typically 5–6 m, whereas in the Gulf of Riga and along the southern coast of the Gulf of Finland it is usually in the range of 3–4 m.

References

 1. Dean, R. G. and Dalrymple, R. A. Coastal Processes with Engineering Applications. Cambridge University Press, Cambridge, 2002.

 2. Dean, R. G. Equilibrium beach profiles: characteristics and applications. J. Coast. Res., 1991, 7, 53–84.

 3. Bruun, P. Sea level rise as a cause of erosion. J. Waterw. Harb. Div. – ASCE, Vancouver, 1962, 88, 117–133.

 4. Edelman, T. Dune erosion during storm conditions. In Proc. 13th International Conference on Coastal Engineering. ASCE, Vancouver, 1972, 1305–1312.

 5. Dean, R. G. and Maurmeyer, E. M. Models for beach profile response. In CRC Handbook of Coastal Processes and Erosion (Komar, P. D., ed.). CRC Press, Boca Raton, 1983, 151–166.

 6. Dean, R. G., Healy, T. R. and Dommerholt, A. A “blind-folded” test of equilibrium beach profile concepts with New Zealand data. Marine Geol., 1993, 109, 253–266.
http://dx.doi.org/10.1016/0025-3227(93)90064-3

 7. Steetzel, H. J. Cross-shore Transport During Storm Surges. Delft Hydraulics, Delft, The Netherlands, Publ. No. 476, 1993.

 8. Kit, E. and Pelinovsky, E. Dynamical models for cross-shore transport and equilibrium bottom profiles. J. Waterw. Port Coast. Ocean Eng., 1998, 124, 138–146.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1998)124:3(138)

 9. Didenkulova, I. and Soomere, T. Formation of two-section cross-shore profile under joint influence of random short waves and groups of long waves. Marine Geol., 2011, 289, 29–33.
http://dx.doi.org/10.1016/j.margeo.2011.09.011

10. Hallermeier, R. J. Uses for a calculated limit depth to beach erosion. In Proc. 16th International Conference on Coastal Engineering. ASCE, Hamburg, 1978, 1493–1512.

11. Hallermeier, R. J. A profile zonation for seasonal sand beaches from wave climate. Coast. Eng., 1981, 4, 253–277.
http://dx.doi.org/10.1016/0378-3839(80)90022-8

12. Coastal Engineering Manual. Manual No. 1110-2-1100. US Army Corps of Engineers, Washington, DC, Chapter III-3-2, 2002 (CD).

13. Kask, A., Soomere, T., Healy, T. R. and Delpeche, N. Rapid estimates of sediment loss for “almost equilibrium” beaches. J. Coast. Res., 2009, Special Issue 56, 971–975.

14. Kartau, K., Soomere, T. and Tõnisson, H. Quantification of sediment loss from semi-sheltered beaches: a case study for Valgerand Beach, Pärnu Bay, the Baltic Sea. J. Coast. Res., 2011, Special Issue 64, 100–104.

15. Kraus, N. C. Engineering approaches to cross-shore sediment processes. In (Proc. Short Course On) Design and Reliability of Coastal Structures (Lamberti, A., ed.), attached to 23rd International Conference on Coastal Engineering, Venice, 1992, 175–209.

16. Birkemeier, W. A. Field data on seaward limit of profile change. J. Waterw. Port. Coast. Ocean Eng., 1985, 111, 598–602.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1985)111:3(598)

17. Are, F. and Reimnitz, E. The A and m coefficients in the Bruun/Dean Equilibrium Profile equation seen from the Arctic. J. Coast. Res., 2008, 24, 243–249.
http://dx.doi.org/10.2112/05-0572.1

18. Nicholls, R. J., Birkemeier, W. A. and Hallermeier, R. J. Application of the depth of closure concept. In Proc. 25th International Conference on Coastal Engineering. ASCE, Orlando, 1996, 3874–3887.

19. Houston, J. R. Simplified Dean’s method for beach-fill design. J. Waterw. Port. Coast. Ocean Eng., 1996, 122, 143–146.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1996)122:3(143)

20. Soomere, T. Wind wave statistics in Tallinn Bay. Boreal Environ. Res., 2005, 10, 103–118.

21. Broman, B., Hammarklint, T., Rannat, K., Soomere, T. and Valdmann, A. Trends and extremes of wave fields in the north–eastern part of the Baltic Proper. Oceanologia, 2006, 48(S), 165–184.

22. Soomere, T., Weisse, R. and Behrens, A. Wave climate in the Arkona Basin, the Baltic Sea. Ocean Sci., 2012, 8, 287–300.
http://dx.doi.org/10.5194/os-8-287-2012

23. Soomere, T. Extreme wind speeds and spatially uniform wind events in the Baltic Proper. Proc. Estonian Acad. Sci. Eng., 2001, 7, 195–211.

24. Soomere, T. and Keevallik, S. Directional and extreme wind properties in the Gulf of Finland. Proc. Estonian Acad. Sci. Eng., 2003, 9, 73–90.

25. Soomere, T., Kask, A., Kask, J. and Healy, H. Modelling of wave climate and sediment transport patterns at a tideless embayed beach, Pirita Beach, Estonia. J. Mar. Syst., 2008, 74, Suppl., S133–S146.
http://dx.doi.org/10.1016/j.jmarsys.2008.03.024

26. Soomere, T., Viška, M., Lapinskis, J. and Räämet, A. Linking wave loads with the intensity of coastal processes along the eastern Baltic Sea coasts. Estonian J. Eng., 2011, 17, 359–374.
http://dx.doi.org/10.3176/eng.2011.4.06

27. Raukas, A. and Hyvärinen, H. (eds). Geology of the Gulf of Finland. Valgus, Tallinn, 1992 (in Russian).

28. Komen, G. J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, S. and Jans­sen, P. A. E. M. Dynamics and Modelling of Ocean Waves. Cambridge University Press, Cambridge, 1994.
http://dx.doi.org/10.1017/CBO9780511628955

29. Räämet, A. and Soomere, T. The wave climate and its seasonal variability in the northeastern Baltic Sea. Estonian J. Earth Sci., 2010, 59, 100–113.
http://dx.doi.org/10.3176/earth.2010.1.08

30. Seifert, T., Tauber, F. and Kayser, B. A high resolution spherical grid topography of the Baltic Sea, 2nd ed. Baltic Sea Science Congress, Stockholm, 2001, Poster #147. www.io-warnemuende.de/iowtopo

31. Soomere, T. and Räämet, A. Spatial patterns of the wave climate in the Baltic Proper and the Gulf of Finland. Oceanologia, 2011, 53(1-TI), 335–371.
http://dx.doi.org/10.5697/oc.53-1-TI.335

32. Myrberg, K., Ryabchenko, V., Isaev, A., Vankevich, R., Andrejev, O., Bendtsen, J., Erich­sen, A., Funkquist, L., Inkala, A., Neelov, I. et al. Validation of three-dimensional hydro­dynamic models in the Gulf of Finland based on a statistical analysis of a six-model ensemble. Boreal Environ. Res., 2010, 15, 453–479.

33. Räämet, A., Suursaar, Ü., Kullas, T. and Soomere, T. Reconsidering uncertainties of wave con­ditions in the coastal areas of the northern Baltic Sea. J. Coast. Res., 2009, Special Issue 56, 257–261.

34. Launiainen, J. and Laurila, T. Marine wind characteristics in the northern Baltic Sea, Finnish Mar. Res., 1984, 250, 5–86.

35. Soomere, T., Behrens, A., Tuomi, L. and Nielsen, J. W. Wave conditions in the Baltic Proper and in the Gulf of Finland during windstorm Gudrun. Nat. Hazard. Earth Syst. Sci., 2008, 8, 37–46.
http://dx.doi.org/10.5194/nhess-8-37-2008

36. Tuomi, L., Kahma, K. K. and Pettersson, H. Wave hindcast statistics in the seasonally ice-covered Baltic Sea. Boreal Environ. Res., 2011, 16, 451–472.

37. Soomere, T. Anisotropy of wind and wave regimes in the Baltic Proper. J. Sea Res., 2003, 49, 305–316.
http://dx.doi.org/10.1016/S1385-1101(03)00034-0

38. Babanin, A. V., Hsu, T.-W., Roland, A., Ou, S.-H., Doong, D.-J. and Kao, C. C. Spectral wave modelling of Typhoon Krosa. Nat. Hazard. Earth Syst. Sci., 2011, 11, 501–511.
http://dx.doi.org/10.5194/nhess-11-501-2011

39. Arinaga, R. A. and Cheung, K. F. Atlas of global wave energy from 10 years of reanalysis and hindcast data. Renew. Energy, 2013, 39, 49–64.
http://dx.doi.org/10.1016/j.renene.2011.06.039

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