Ocean Dynamics

, Volume 64, Issue 3, pp 315–324 | Cite as

Untangling spatial and temporal trends in the variability of the Black Sea Cold Intermediate Layer and mixed Layer Depth using the DIVA detrending procedure

  • A. Capet
  • C. Troupin
  • J. Carstensen
  • M. Grégoire
  • J.-M. Beckers


Current spatial interpolation products may be biased by uneven distribution of measurements in time. This manuscript presents a detrending method that recognizes and eliminates this bias. The method estimates temporal trend components in addition to the spatial structure and has been implemented within the Data Interpolating Variational Analysis (DIVA) analysis tool. The assets of this new detrending method are illustrated by producing monthly and annual climatologies of two vertical properties of the Black Sea while recognizing their seasonal and interannual variabilities : the mixed layer depth and the cold content of its cold intermediate layer (CIL). The temporal trends, given as by-products of the method, are used to analyze the seasonal and interannual variability of these variables over the past decades (1955–2011). In particular, the CIL interannual variability is related to the cumulated winter air temperature anomalies, explaining 88 % of its variation.


Black Sea Data interpolation Detrending Inverse method 40°N–48°N 27°E–42°E Cold intermediate layer Mixed layer depth Climatologies 



The authors thank the European Center for Medium-Range Weather for providing the reanalysis and the US National Oceanographic Data Center for providing access to in situ data through the World Ocean Database. DIVA has received funding from the European Union Seventh Framework Program (FP7/2007–2013) under grant agreement no. 283607, SeaDataNet 2, and from project EMODNET (MARE/2008/03 - Lot 3 Chemistry - SI2.531432) from the Directorate-General for Maritime Affairs and Fisheries. This research was supported by the SESAME Project (EC contract no. GOCE036949) and the PERSEUS Project (EC grant agreement no. 287600). This is a MARE publication.

Supplementary material

10236_2013_683_MOESM1_ESM.pdf (10.9 mb)
(PDF 10.8 MB)


  1. Blatov A, Bulgakov N, Ivanov V, Kosarev A, Tujilkin V (1984) Variability of hydrophysical fields in the Black Sea. Gidrometeoizdat, LeningradGoogle Scholar
  2. Boyer TP, Antonov JI, Baranova OK, Garcia HE, Johnson DR, Locarnini RA, Mishonov AV, O’Brien TD, Seidov D, Smolyar IV, Zweng MM (2009) World ocean database 2009, chapter 1: introduction. Tech. rep.US Government Printing Office, Washington. p 216Google Scholar
  3. Brankart JM, Brasseur P (1996) Optimal analysis of in situ data in the Western Mediterranean using statistics and cross-validation. J Atmos Ocean Tech 13:477–491CrossRefGoogle Scholar
  4. Brasseur P, Beckers JM, Brankart JM, Schoenauen R (1996) Seasonal temperature and salinity fields in the Mediterranean Sea: climatological analyses of a historical data set. Deep-Sea Res I43:159–192. doi: 10.1016/0967-0637(96)00012-X CrossRefGoogle Scholar
  5. Capet A, Barth A, Beckers JM, Grégoire M (2012) Interannual variability of Black Sea’s hydrodynamics and connection to atmospheric patterns. Deep-Sea Res II 77–80:128–142. doi: 10.1016/j.dsr2.2012.04.010. CrossRefGoogle Scholar
  6. Duchon J (1977) Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Schempp W, Zeller K (eds) Constructive theory of functions of several variables. Springer, Berlin, pp 85–100CrossRefGoogle Scholar
  7. Kara AB, Helber RW, Boyer TP, Elsner JB (2009) Mixed layer depth in the Aegean, Marmara, Black and Azov Seas: part 1: general features. J Mar Syst 78:S169–S180CrossRefGoogle Scholar
  8. Korotaev G, Oguz T, Nikiforov A, Koblinsky C (2003) Seasonal, interannual, and mesoscale variability of the Black Sea upper layer circulation derived from altimeter data. J Geophys Res 108(C4):3122. doi: 10.1029/2002JC001508. CrossRefGoogle Scholar
  9. Oguz T, Dippner JW, Kaymaz Z (2006) Climatic regulation of the Black Sea hydro-meteorological and ecological properties at interannual-to-decadal time scales. J Mar Syst 60(3–4):235–254. doi: 10.1016/j.jmarsys.2005.11.011. CrossRefGoogle Scholar
  10. Piotukh VB, Zatsepin AG, Kazmin AS, Yakubenko VG (2011) Impact of the Winter Cooling on the Variability of the Thermohaline Characteristics of the Active Layer in the Black Sea. Oceanology 51(2):221–230CrossRefGoogle Scholar
  11. Stanev E, Bowman M, Peneva E, Staneva J (2003) Control of Black Sea intermediate water mass formation by dynamics and topography: comparison of numerical simulations, surveys and satellite data. J Mar Res 61(1):59–99. doi: 10.1357/002224003321586417 CrossRefGoogle Scholar
  12. Stanev E, He Y, Grayek S, Boetius A (2013) Oxygen dynamics in the black sea as seen by argo profiling floats. Geophys Res Lett 40(12):3085–3090CrossRefGoogle Scholar
  13. Troupin C, Sirjacobs D, Rixen M, Brasseur P, Brankart JM, Barth A, Alvera-Azcárate A, Capet A, Ouberdous M, Lenartz F, Toussaint ME, Beckers JM (2012) Generation of analysis and consistent error fields using the Data Interpolating Variational Analysis (DIVA). Ocean Model 52–53:90–101. doi: 10.1016/j.ocemod.2012.05.002. CrossRefGoogle Scholar
  14. Troupin C, Ouberdous M, Sirjacobs D, Alvera-Azcárate A, Barth A, Toussaint ME, Beckers JM (2013) DIVA user’s guide. GeoHydrodynamics and Environment Research, March edn. Accessed March 2013
  15. Wahba G (1975) Smoothing noisy data with spline functions. Numer Math 24:383–393CrossRefGoogle Scholar
  16. Wahba G, Wendelberger J (1980) Some new mathematical methods for variational objective analysis using splines and cross validation. Mon Weather Rev 108:1122–1143CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • A. Capet
    • 1
  • C. Troupin
    • 2
  • J. Carstensen
    • 3
  • M. Grégoire
    • 4
  • J.-M. Beckers
    • 1
  1. 1.Department of Astrophysics, Geophysics and Oceanography (AGO), GeoHydrodynamics and Environment Research (GHER)Université de LiègeLiègeBelgium
  2. 2.TMOOS DepartmentIMEDEA (CSIC-UIB)EsporlesSpain
  3. 3.Department of BioscienceAarhus UniversityRoskildeDenmark
  4. 4.Department of Biology, Ecology and Evolution, Oceanology LaboratoryUniversité de LiègeLiègeBelgium

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