# 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.

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