# Methods for calculating the speed of sound distribution by water temperature: case study for the Black Sea

### Abstract

The article presents the results of the research aimed at calculating the vertical speed of sound distribution in the active layer of the Black Sea based on water temperature readings. The research was carried out in the active layer of the deep-water section of the Black Sea at the depth range of 0 – 50 meters. The water temperature values taken at the hydrological stations or the shipboard measurements (OSD: Ocean Station Data) taken with the help of floats (PFL: Profiling Float Data) were used as initial data. The calculations were based on the identification of correlation relationships between the water temperature values at standard horizons of the Black Sea as per OSD data and the speed of sound calculated using the UNESCO equation. The calculation accuracy was estimated after comparing the speed of sound calculated by the established regression equations and by the UNESCO equation based on PFL data.

The research allowed establishing the regression equations for calculating the vertical speed of sound distribution in the Black Sea up to the depth of 50 meters over the spring-autumn period. The possibility of calculating the vertical speed of sound distribution using the developed regression equations was also estimated.

The calculations indicated statistically significant results over the spring-autumn period. Multiple correlation coefficients appeared to be significant and amounted to 0.99. The developed regression equations were efficient and reliable. Verification of effectiveness and reliability of the regression equations showed that the standard error was within ± 1 m s^{-1}.

In order to visualize the results the calculation of the vertical speed of sound distribution in the Black Sea using the regression equations was carried out for 6 hydrological sections (1 section for each of the months) introduced in 2018. The research showed that the isolines of the vertical speed of sound distribution calculated using the regression equations and the UNESCO equation are practically coherent.

The studied equations can be used for calculating the vertical speed of sound profile distribution in the Black Sea up to the depth of 50 meters over the May-October period based on the measured or modeled data of water temperature variability. This calculation can be used for the purposes of scientific research and applied purposes in the field of hydrography, hydroacoustics, oceanology, marine ecology, navigation etc.

### References

2. Yaroshenko, A.A. et al. (2007). O vliyanii profilya skorosti zvuka i techeniy na rasprostranenie akusticheskikh voln v more [About the influence of velocity profile of sound and currents on the propagation of acoustic waves in the sea]. Vіsnik SumDU. Serіya Fіzika, matematika, mekhanіka [J. Herald SumDU], 1, pp. 178-186. (in Russ)

3. Yaroshenko, A.A. (2012). Vychislenie skorosti zvuka v morskoy vode. Ot Kolladona i Shturma do nashikh dney [The calculation of sound velocity is in the sea water. From Colladon and Sturm to our days]. Vodnyy transport [Water Transport], 3, pp. 8-12. (in Russ)

4. Arkhipkin, V.S., & Deev, M.G. (2008). Osobennosti polya skorosti zvuka v Chernom more [Characteristic features of the acoustic velocity field in the Black Sea]. Vestnik Moskovskogo Universiteta. Seria 5, Geografia [Moscow University Bulletin. Series 5, Geography], 6, pp. 30-33. (in Russ)

5. Magnitsky, V.A. (1995). Obshchaya geofizika [General geophysics]. Moscow: MSU. (in Russ)

6. Lisiutin, V.A., & Yaroshenko, A.A. (2003). Vertikal'noe raspredelenie skorosti zvuka v okeane [The vertical distribution of sound velocity in the ocean]. Bulletin of Sumy State University. Technical Sciences Series, 12(58), pp. 61-65. (in Russ)

7. Vadov, R.A. (2007). Otkrytie podvodnogo zvukovogo kanala, eksperimental'nye issledovaniya, regional'nye razlichiya [The Discovery of the Underwater Sound Channel, the Experimental Studies, the Regional Differences]. Akusticheskiy Zhurnal [Acoustic Journal], 53(3), pp. 313-328. (in Russ)

8. Vadov, R.A. (2011). Poverkhnostnaya predreverberatsiya pri dal'nem rasprostranenii vzryvnykh signalov v podvodnom zvukovom kanale [Surface Prereverberation in Long-Range Propagation of Explosion-Generated Signals in Underwater Sound Channel]. Akusticheskiy Zhurnal [Acoustic Journal], 57(2), pp. 169-178. (in Russ)

9. Vadov, R.A. (2011). Osobennosti formirovaniya struktury zvukovogo polya tochechnogo istochnika v chernomorskom podvodnom zvukovom kanale [Peculiarities in the Formation of the Sound Field Structure of a Point Source in the Black Sea Underwater Sound Channel]. Akusticheskiy Zhurnal [Acoustic Journal], 57(5), pp. 623-632. (in Russ)

10. Lisiutin, V.A., Lastovenko, O.R., & Yaroshenko, A.A. (2018). Sravnitel'naya otsenka vklada luchevykh i volnovykh komponent pri rasprostranenii impul'snykh signalov v podvodnom zvukovom kanale Chernogo morya [The comparative evaluation of the ray and wave components contribution to the impulse signals propagation of the Black Sea underwater sound channel]. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2, pp. 74-85 (in Russ). https://doi.org/10.31429/vestnik-15-2-74-85

11. Zamarenova, L.N., & Skipa, M.I. (2009). Akusticheskaya model' kvazistatsionarnykh trass. Chast' 1. Kontseptsiya issledovaniy [The quasi-stationary lines acoustic model. Part 1. Research Concept]. Hydroacoustical Journal (Problems, Methods and Means for Researches of World Oceans), 6, pp. 10-23. (in Russ)

12. Andrianova, O.R., Skipa, M.I., Sryberko, A.V. et. al. (2015). Otsenka vozmozhnosti rascheta vertikalnogo raspredeleniya temperatury vody v Chernom more po sputnikovym dannym [Estimation of ability of vertical temperature distribution’s calculation for the Black sea’s water by satellite data]. Odessa National University Herald. Series: Geography & Geology, 20(4), pp. 9-21. (in Russ)

13. Miladinova, S., Stips, A., Garcia-Gorriz, E. et al. (2017). Black Sea thermohaline properties: Long-term trends and variations. Journal of Geophysical Research: Oceans, 122(7), pp. 5624-5644. https://doi.org/10.1002/ 2016JC012644

14. Fofonoff, N.P. & Millard, Jr. R. C. (1983). Algorithms for computation of fundamental properties of seawater. UNESCO Technical Papers in Marine Sciences. Paris, France, UNESCO, vol. 4. Available at: http://hdl.handle.net/11329/109 (Accessed 19 September 2019)

15. Kudryavaya, K.I., Seryakov, E.I. & Skriptunova, L.I. (1974). Morskie gidrologicheskie prognozy [Marine hydrological forecasts]. Leningrad: Gidrometeoizdat. (in Russ)

16. Abuzyarov, Z.K., Kudryavaya, K.I., Seryakov, E.I. et. al. (1988). Morskie prognozy [Marine forecasts]. Leningrad: Gidrometeoizdat. (in Russ)

17. Kobzar, A.I. (2006). Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov [Applied Mathematical Statistics. For Engineers and Scientists]. Moscow: Fizmatlit. (in Russ)

18. Eliseeva, I.I., Kurysheva, S.V., Kosteeva, T.V. et. al. (2007). Ekonometrika [Econometrics]. 2nd ed. Edited by I. I. Eliseeva. Moscow: Finance and Statistics. (in Russ)

19. Hogg Robert, V., Tanis Elliot, A. & Zimmerman, D. (2015). Probability and Statistical Inference. 9th ed. Pearson Education, Inc., USA.

20. Ahn, H. (2018). Probability and Statistics for Science and Engineering with Examples in R Second Edition. California, Cognella Inc. & University Readers.

21. NOAA World Ocean Database. Available at: http://www.nodc.noaa.gov (Accessed 27 May 2019).

22. Schlitzer, R. (2018). Ocean Data View. Available at: https://odv.awi.de (Accessed 19 September 2019).

*Ukrainian Hydrometeorological Journal*, (24), 83-91. https://doi.org/10.31481/uhmj.24.2019.08

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