Development of an empirical model of pH long-term changes in the surface waters of the deep-water part of the Black Sea

E.A. Grebneva

 Institute of Natural and Technical Systems, RF, Sevastopol, Lenin St., 28


DOI: 10.33075/2220-5861-2021-4-22-30

UDC 551.464.6/465.7(262.5) 


   The paper analyzes the interannual variability of the pH value in the surface layer of the deep-water part of the Black Sea for the period from 1957 to 1996. It is shown that the time series is divided into two different time periods in terms of sign and quality of data: from 1957 to 1976 and from 1977 to 1996. Due to the lower measurement accuracy of the first-time interval, further data from 1977 are used in the work. For the period from 1977 to 1996. an empirical model of the time series was developed and a retrospective forecast is calculated with an assessment of its quality based on the data of field studies carried out from 2019 to 2021. The choice of a time series model was carried out on the basis of an analysis of the structure of seasonal fluctuations. The calculation of the values ​​of the seasonal component show that the amplitude of fluctuations is approximately constant. Therefore, when developing a model, each term of the time series is presented in an additive form. Extrapolation from 1996 to 2021 is calculated on the basis of a simple regression model using the performed series decomposition. Based on the results of the developed empirical model of the long-term change in the pH value, it is obtained that in the interannual pH variations, two quasi-periodic components of variability are distinguished. Their periods are about 6.7 and 2.5 years. The trend of changes in pH values ​​in the surface layer of the deep-water part of the Black Sea is close to the trends observed in other regions of the open parts of the World Ocean. The pH values ​​decreased from 1977 to 2021. with an average rate of about 0.01 units pH/10 years. Expeditionary data obtained in 2019–2021, on the whole, confirm the identified trends and fully correspond to the presented retrospective forecast.

Keywords: Black Sea, deep-water part, surface layer, pH value, time series, additive model, extrapolation.

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  1. Gattuso J.-P. and Hansson L. Ocean acidification: background and history, Ocean Acidification. Oxford University Press, Oxford, 2011, pp. 1–20.
  2. Polonsky A.B. pH variability in the Black Sea waters in the 20th century: is the acidity of sea water increasing? Reports of the National Academy of sciences of Ukraine, 2012, No. 2, pp. 146–149.
  3. IPCC5 Assessment (Chapter 3). 2013, pp. 255–266.
  4. Andersson A.J., Mackenzie F.T., and Bates N.R. Life on the margin: implications of ocean acidification on Mg-calcite, high latitude and cold-water marine calcifiers. Marine Ecology
    Progress Series, 2008, Vol. 373, pp. 265–273.
  5. Ries J.B. Skeletal mineralogy in a high-CO2 world. Journal of Experimental Marine Biology and Ecology, 2011, Vol. 403, pp. 54–64.
  6. Schulz K.G., Barcelos e Ramos J., Zeebe R.E., and Riebesell U. CO2 perturbation experiments: similarities and differences between dissolved inorganic carbon and total alkalinity manipulations. Biogeosciences, 2009, No. 6, pp. 2145–2153. doi:10.5194/bg-6-2145-2009
  7. Leseurre C., Monaco Cl., Reverdin G., Metzl N., Fin J., Olafsdottir S., and Racapé V. Ocean carbonate system variability in the North Atlantic Subpolar surface water (1993–2017). Biogeosciences, 2020, No. 17, pp. 2553–2577.
  8. Simonova A.I., Ryabinin A.I., and Gershanovich D.Ye. Gidrometeorologiya i gidrokhimiya morey SSSR. Chernoye more. Gidrokhimicheskiye usloviya i okeanologicheskiye osnovy
    formirovaniya biologicheskoy produktivnosti (Hydrometeorology and Hydrochemistry of the USSR Seas. Black Sea. Hydrochemical conditions and oceanological foundations for the formation of biological productivity), Saint-Petersburg: Gidrometeoizdat, 1992, Vol. 4, No. 2, pp. 31–35.
  9. Polonskiy A.B. and Grebneva E.A. Prostranstvenno-vremennaya izmenchivost’ vodorodnogo pokazatelya vod Chernogo moray (Spatio-temporal variability of the pH of the Black Sea
    waters). Doklady Akademii nauk, 2019, Vol. 486, No. 4, pp. 494–499.
  10. Mel’nikov V.V., Polonskiy A.B. Kotolupova A.A., Grebneva E.A., Mel’nik L.A., and Biryukova M.A.GIS Instituta prirodno-tekhnicheskikh system (GIS of the Institute of Natural and
    Technical Systems). Sistemy kontrolya okruzhayushchey sredy, 2016, No. 4 (24), pp. 49–55.
  11. Berezin I.S. and Zhidkov N.P. Metody vychisleniy (Calculation methods), Moscow: GIFML, 1962, Vol. 1, 464 p.
  12. Mal’tsev K.A. and Mukharamova S.S. Postroyeniye modeley prostranstvennykh chisel (s ispol’zovaniyem paketa Surfer) (Building models of spatial variables (using the Surfer package), Kazan’: Kazanskiy universitet, 2014, 103 p.
  13. Grebneva E.A. and Polonsky A.B. Dekompozitsiya vremennogo ryada velichiny pH poverkhnostnykh vod glubokovodnoy chasti Chernogo morya po arkhivnym dannym vtoroy
    poloviny XX veka (Decomposition of the time series of the pH value of the surface waters of the deep-water part of the Black Sea according to the archival data of the second half of the XX century). Sistemy kontrolya okruzhayushchey sredy, 2021, No. 2 (44), pp. 29–38.
  14. Afanas’yev V.N. and YUzbashev M.M. Analiz vremennykh ryadov i prognozirovaniye (Time series analysis and forecasting), Moscow: INFRA-M “Finansy i statistika”, 2010, 320 p.
  15. Zorich V.A. Matematicheskiy analiz (Mathematical analysis), Moscow: Fizmatlit, 1984, 544 p.
  16. Babeshko L.O. Osnovy ekonometricheskogo modelirovaniya (Fundamentals of Econometric Modeling), Moscow: KomKniga, 2013, 428 p.
  17. Zeebe R.E. and Wolf-Gladrow D. CO2 in seawater: equilibrium, kinetics, isotopes. Elsevier Oceanogr, 2001, 346 p.