Environmental and Ecological Statistics

, Volume 21, Issue 4, pp 697–714 | Cite as

Investigating the complex relationship between in situ Southern Ocean \(pCO_{2}\) and its ocean physics and biogeochemical drivers using a nonparametric regression approach

  • Wesley Byron Pretorius
  • Sonali Das
  • Pedro M. S. Monteiro


The objective in this paper is to investigate the use of a non-parametric approach to model the relationship between oceanic carbon dioxide \((pCO_2)\) and a range of ocean physics and biogeochemical in situ variables in the Southern Ocean, which influence its in situ variability. The need for this stems from the need to obtain reliable estimates of carbon dioxide concentrations in the Southern Ocean which plays an important role in the global carbon flux cycle. The main challenge involved in this objective is the spatial limitation and seasonal bias of the in situ data. Moreover, studies have also reported that the relationship between \(pCO_2\) and its drivers is complex. As such, in this paper, we use the non-parametric kernel regression approach since it is able to accurately capture the complex relationships between the response and predictor variables. In this analysis we use the in situ data obtained from the SANAE49 return leg journey between Antarctic to Cape Town. To the best of our knowledge, this is the first time this data set has been subjected to such analysis. The model variants were developed on a training data subset, and the ‘goodness’ of the models were assessed on an “unseen” test data subset. Results indicate that the nonparametric approach consistently captures the relationship more accurately in terms of mean square error, root mean square error and mean absolute error, over a standard parametric approach (multiple linear regression). These results provide a platform for using the developed nonparametric regression model based on in situ measurements to predict \(pCO_2\) for a larger spatial region in the Southern Ocean based on satellite biogeochemical measurements of predictor variables, given that satellites do not measure \(pCO_2\).


Carbon dioxide Carbon flux Non-parametric kernel regression Prediction SANAE Southern Ocean 



This work was partially supported by the CSIR Parliamentary and the Strategic Research Panel Grants [TA_2010_035] in the ambit of the Southern Ocean Carbon Climate Observatory (SOCCO) programme. We would also like to thank Dr Nicolas Fauchereau for data facilitation. The authors declare that they have no conflict of interest.


  1. Fox J (2005) Introduction to nonparametric regression. Accessed 14 Nov 2011, Economic and Social Research Council
  2. Goyet C, Davis D (1997) Estimation of total CO\(_{2}\) concentration throughout the water column. Deep Sea Res I 44(5):859–877CrossRefGoogle Scholar
  3. Jamet C, Moulin C, Lefévre N (2007) Estimation og the oceanic pCO\(_{2}\) in the North Atlantic from VOS lines in situ measurements: parameters needed to generate seasonally mean maps. Ann. Geophys. 25:2247–2257CrossRefGoogle Scholar
  4. Le Quéré C, Rodenbeck C, Buitenhuis E, Conway T, Langenfelds R, Gomez A, Labuschagne C, Ramonet M, Nakazawa T, Metzl N, Gillett N, Heimann M (2007) Saturation of the Southern Ocean \(CO_{2}\) sink due to recent climate change. Science (New York, NY) 316(5832):1735–1738CrossRefGoogle Scholar
  5. Lefévre N, Watson A, Watson A (2005) A comparison of multiple regression and neural network techniques for mapping in situ pCO\(_{2}\) data. Tellus 57B:375–384CrossRefGoogle Scholar
  6. Lenton T, Livina V, Dakos V, Scheffer M (2012) Climate bifurcation during the last deglaciation. Clim Past 8:321–348CrossRefGoogle Scholar
  7. Li Q, Racine J (2004) Cross-validated local linear nonparametric regression. Stat Sin 14:485–512Google Scholar
  8. Lüger H, Wallace D, Körtzinger A (2004) The pCO\(_{2}\) variability in the midlatitude North Atlantic Ocean during a full annual cycle. Global Biogeochem Cycles 18(3). doi: 10.1029/2003GB002200
  9. McNeil B, Metzl N, Key R, Matear R, Corbiere A (2007) An empirical estimate of the Southern Ocean air-sea CO\(_{2}\) flux. Global Biogeochem Cycles 21(3). doi: 10.1029/2007GB002991
  10. Monteiro P, Schuster U, Hood M, Lenton A, Metzl N, Olsen A, Rogers K, Sabine C, Takahashi T, Tilbrook B, Yoder J, Wanninkhof R, Watson A (2010) A global sea surface carbon observing system: assessment of changing sea surface CO\(_{2}\) and air-sea CO\(_{2}\) fluxes. In: Hall J, Harrison D, Stammer D (eds) OceanObs09: sustained ocean observations and information for society, vol 2. ESA Publication WPP-306, Venice. doi:  10.5270/OceanObs09.cwp.64 Google Scholar
  11. Pretorius W, Das S, Mostert P (2011) Application of a nonparametric approach to analyze \(\varDelta \) pCO\(_{2}\) data from the southern ocean. In: Sharp G, Hugo J, Brettenny W (eds) 53rd annual conference of the South African Statistical Association for 2011 (SASA 2011), pp 76–87Google Scholar
  12. R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. ISBN 3-900051-07-0,
  13. Racine J, Li Q (2004) Nonparametric estimation of regression functions with both categorical and continuous data. J Econ 119(1):99–130CrossRefGoogle Scholar
  14. Rangama Y (2005) Variability of the net air-sea CO\(_{2}\) flux inferred from shipboard and satellite measurements in the Southern Ocean south of Tasmania and New Zealand. J. Geophys. Res. 110(C9):1–17. doi:  10.1029/2004JC002619 Google Scholar
  15. Sarmiento J, Gruber N (2002) Sinks for anthropogenic carbon. Phys. Today 55(8):30CrossRefGoogle Scholar
  16. Schlitzer R (2002) Carbon export fluxes in the Southern Ocean: results from inverse modeling and comparison with satellite-based estimates. Deep Sea Res II 49:1623–1644CrossRefGoogle Scholar
  17. Takahashi T, Broecker W, Bainbridge A (1981) The alkalinity and total carbon dioxide concentration in the world oceans, chap 16. Wiley, New York, pp 271–286Google Scholar
  18. Takahashi T, Sutherland S, Sweeney C, Poisson A, Metzl N, Tilbrook B, Bates N, Wanninkhof R, Feely R, Sabine C (2002) Global sea-air CO\(_{2}\) flux based on climatological surface ocean pCO\(_{2}\), and seasonal biological and temperature effects. Deep Sea Res Part II 49(9–10):1601–1622CrossRefGoogle Scholar
  19. Takahashi T, Sutherland S, Kozyr A (2009) Global ocean surface water partial pressure of CO\(_{2}\) database: measurements performed during 1957–2009 (version 2009). ORNL/CDIAC-152, NDP-088(V2009). Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, US Department of Energy, Oak Ridge, Tennessee. doi: 10.3334/CDIAC/otg.ndp088(V2009)
  20. Takahashi T, Sweeney C, Hales B, Chipman D, Newberger T, Goddard J, Iannuzzi R, Sutherland S (2012) The changing carbon cycle in the southern ocean. Oceanography 25(3):26–37. doi: 10.5670/oceanog.2012.71 CrossRefGoogle Scholar
  21. Telszewski M, Chazottes A, Schuster U, Watson A, Moulin C, Bakker D, González-Dávila M, Johannessen T, K ortzinger A, L uger H, Olsen A, Omar A, Padin X, Ríos A, Steinhoff T, Santana-Casiano M, Wallace D, Wanninkhof R (2009) Estimating the monthly pCO\(_{2}\) distribution in the North Atlantic using a self-organizing neural network. Biogeosciences 6:1405–1421CrossRefGoogle Scholar
  22. Tréguer P, Jacques G (1992) Dynamics of nutrients and phytoplankton, and fluxes of carbon, nitrogen and silicon in the Antarctic Ocean. Polar Biol 12(2):149–162CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Wesley Byron Pretorius
    • 1
    • 2
  • Sonali Das
    • 3
  • Pedro M. S. Monteiro
    • 4
  1. 1.Department of Statistics and Actuarial SciencesStellenbosch UniversityStellenbosch South Africa
  2. 2.Credit DepartmentOld Mutual Finance (PTY) Ltd (RF)Pinelands, Cape Town South Africa
  3. 3.Spatial Planning and SystemsCSIR Built EnvironmentPretoria South Africa
  4. 4.Ocean Systems and Climate GroupCSIR-CHPCRosebank, Cape Town South Africa

Personalised recommendations