Journal of Oceanology and Limnology

, Volume 37, Issue 2, pp 410–422 | Cite as

Quantifying the non-conservative production of potential temperature over the past 22 000 years

  • Cunjie Zhang
  • Xueshuang HanEmail author
  • Xiaopei Lin


The energy budgets of the ocean play a crucial role in the analysis of climate change. Potential temperature is traditionally used as a conservative quantity to express variations associated with “heat” in oceanography, such as the heat content and heat transport. However, potential temperature is usually not conserved during turbulent mixing, so the use of conservative temperature is more accurate. Based on climatological simulations under the modern and Last Glacial Maximum (LGM; ~21 ka; ka=thousand years ago), as well as a transient climate simulation of the past 22 000 years, we quantify the errors induced by the neglect of the non-conservation of potential temperature in paleo-climate research for the first time. The temperature error reaches 0.9°C near the coasts affected by river discharges but is much smaller in the open oceans, typically 0.03°C above the main thermocline and less than 0.01°C elsewhere. The error of the ocean heat content (OHC) is roughly 3×1022 J and is relatively steady over the past 22 000 years. However, the OHC increases to six times the original value during the last glacial termination from 20 ka to 7 ka. As a result, the relative OHC error decreases from 1.2% in the LGM climate to 0.14% in the modern climate. The error of the ocean meridional heat transport (OMHT) is generally smaller than 0.005 PW (1 PW=1015 W), with very small temporal variations (typically 0.000 4 PW), and induces a relative OMHT error of typically 0.3% over the past 22 000 years. Therefore, the neglect of the non-conservation of potential temperature induces a relative error of generally less than 1% in the analyses of basin-scale climate variations.


conservative temperature potential temperature ocean heat content ocean heat transport paleoclimate 


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We thank the National Center for Atmospheric Research (NCAR), the Earth System Grid Federation (ESGF) and University of Wisconsin-Madison for sharing the data with the public. We thank YANG Haijun, LI Qing and WANG Kun from Beijing University for assistance in the calculations of heat transport. All the calculations involving potential enthalpy and conservative temperature are calculated using Gibbs-SeaWater (GSW) Oceanographic Toolbox Version 3.05.5 in Matlab, and we thank Trevor J. McDougall and Paul M. Barker for their efforts. We also thank two anonymous reviewers, GUO Yongqing, ZHANG Cong and DUAN Juan for their efforts to improve the quality of the article. We thank Richard Foreman, PhD, from Liwen Bianji, Edanz Editing China (, for editing the English text of a draft of this manuscript.


  1. Batchelor G K. 1967. An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge. 615 p.Google Scholar
  2. Bryan K. 1962. Measurements of meridional heat transport by ocean currents. Journal of Geophysical Research, 67(9): 3 403–3 414.CrossRefGoogle Scholar
  3. Bryden H L, Imawaki S. 2001. Ocean heat transport. In: Siedler G, Church J, Gould J eds. Ocean circulation and climate: Observing and Modelling the Global Ocean. Academic Press, San Fransisco CA, USA. p. 455–474.Google Scholar
  4. Chen X, Tung K K. 2014. Climate. Varying planetary heat sink led to global-warming slowdown and acceleration. Science, 345(6199): 897–903.CrossRefGoogle Scholar
  5. Denton G H, Anderson R F, Toggweiler J R, Edwards R L, Schaefer J M, Putnam A E. 2010. The last glacial termination. Science, 328(5986): 1 652–1 656.CrossRefGoogle Scholar
  6. Dyke A S, Prest V K. 1987. Late Wisconsinan and Holocene history of the Laurentide ice sheet. Géographie Physique et Quaternaire, 41(2): 237–263.CrossRefGoogle Scholar
  7. Ferrari R, Ferreira D. 2011. What processes drive the ocean heat transport? Ocean Modelling, 38(3-4): 171–186.CrossRefGoogle Scholar
  8. Fischer N, Jungclaus J H. 2010. Effects of orbital forcing on atmosphere and ocean heat transports in Holocene and Eemian climate simulations with a comprehensive Earth system model. Climate of the Past, 6(2): 155–168.CrossRefGoogle Scholar
  9. Fofonoff N. 1962. Physical properties of sea-water. The Sea, 1: 3–30.Google Scholar
  10. Gill A E. 1982. Atmosphere-Ocean Dynamics. Academic Press, New York. 662 p.Google Scholar
  11. Graham F S, McDougall T J. 2013. Quantifying the nonconservative production of conservative temperature, potential temperature, and entropy. J. Phys. Oceanogr., 43(5): 838–862.CrossRefGoogle Scholar
  12. Gu D F, Philander S G H. 1997. Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics. Science, 275(5301): 805–807.CrossRefGoogle Scholar
  13. Hatzianastassiou N, Matsoukas C, Hatzidimitriou D, Pavlakis C, Drakakis M, Vardavas I. 2004. Ten year radiation budget of the Earth: 1984–93. International Journal of Climatology, 24(14): 1 785–1 802.CrossRefGoogle Scholar
  14. He F. 2011. Simulating Transient Climate Evolution of the Last Deglaciation with CCSM3. University of Wisconsin-Madison, Wisconsin. 171 p.Google Scholar
  15. IOC, SCOR, IAPSO. 2010. The international thermodynamic equation of seawater–2010: calculation and use of thermodynamic properties. In: Intergovern-mental Oceanographic Commission, Manuals and Guides No. 56. Paris: IOC, SCOR, IAPSO, 196.Google Scholar
  16. IPCC. 2007. Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Intergovernmental Panel on Climate Change, Cambridge. 104 p.Google Scholar
  17. Jackson L C, Kahana R, Graham T, Ringer M A, Woollings T, Mecking J V, Wood R A. 2015. Global and European climate impacts of a slowdown of the AMOC in a high resolution GCM. Climate Dynamics, 45(11-12): 3 299–3 316.CrossRefGoogle Scholar
  18. Kleman J, Jansson K, De Angelis H, Stroeven A P, Hättestrand C, Alm G, Glasser N. 2010. North American Ice Sheet build-up during the last glacial cycle, 115–21 kyr. Quaternary Science Reviews, 29(17-18): 2 036–2 051.CrossRefGoogle Scholar
  19. Macdonald A M, Baringer M O. 2013. Ocean heat transport. International Geophysics, 103: 759–785.CrossRefGoogle Scholar
  20. Marschall J, Plumb R A. 2008. Atmosphere, Ocean, and Climate Dynamics. Elsevier Academic Press, Burlington. 344 p.Google Scholar
  21. Marson J M, Wainer I, Mata M M, Liu Z. 2014. The impacts of deglacial meltwater forcing on the South Atlantic Ocean deep circulation since the Last Glacial Maximum. Climate of the Past, 10(5): 1 723–1 734.CrossRefGoogle Scholar
  22. McCreary Jr J P, Lu P. 1994. Interaction between the subtropical and equatorial ocean circulations: the subtropical cell. J. Phys. Oceanogr., 24(2): 466–497.CrossRefGoogle Scholar
  23. McDougall T J, Barker P M. 2011. Getting started with TEOS-10 and the Gibbs Seawater (GSW) oceanographic toolbox. SCOR / IAPSO WG, 127: 1–28.Google Scholar
  24. McDougall T J. 2003. Potential enthalpy: a conservative oceanic variable for evaluating heat content and heat fluxes. J Phys Oceanogr, 33: 945–963.CrossRefGoogle Scholar
  25. Olbers D, Willebrand J, Eden C. 2012. Ocean dynamics. Springer, Heidelberg. 704 p.CrossRefGoogle Scholar
  26. Otto-Bliesner B L, Brady E C, Clauzet G, Tomas R, Levis S, Kothavala Z. 2006. Last glacial maximum and Holocene climate in CCSM3. Journal of Climate, 19(11): 2 526–2 544.CrossRefGoogle Scholar
  27. Peltier W R. 2004. Global glacial isostasy and the surface of the ice-age earth: the ICE-5G (VM2) model and GRACE. Annual Review of Earth and Planetary Sciences, 32(1): 111–149.CrossRefGoogle Scholar
  28. Stouffer R J, Yin J, Gregory J M, Dixon K W, Spelman M J, Hurlin W, Weaver A J, Eby M, Flato G M, Hasumi H, Hu A, Jungclaus J H, Kamenkovich I V, Levermann A, Montoya M, Murakami S, Nawrath S, Oka A, Peltier W R, Robitaille D Y, Sokolov A, Vettoretti G, Weber S L. 2006. Investigating the causes of the response of the thermohaline circulation to past and future climate changes. Journal of Climate, 19(8): 1 365–1 387.CrossRefGoogle Scholar
  29. Tailleux R. 2015. Observational and energetics constraints on the non-conservation of potential/conservative temperature and implications for ocean modelling. Ocean Modelling, 88: 26–37.CrossRefGoogle Scholar
  30. Toucanne S, Zaragosi S, Bourillet J F, Cremer M, Eynaud F, Van Vliet-Lanoë B, Penaud A, Fontanier C, Turon J L, Cortijo E. 2009. Timing of massive ‘Fleuve Manche’ discharges over the last 350 kyr: insights into the European ice-sheet oscillations and the European drainage network from MIS 10 to 2. Quaternary Science Reviews, 28(13-14): 1 238–1 256.CrossRefGoogle Scholar
  31. Trenberth K E, Fasullo J T. 2013. An apparent hiatus in global warming? Earth’s Future, 1(1): 19–32.CrossRefGoogle Scholar
  32. Warren B A. 1999. Approximating the energy transport across oceanic sections. Journal of Geophysical Research: Oceans, 104(C4): 7 915–7 919.CrossRefGoogle Scholar
  33. Yang H J, Li Q, Wang K, Sun Y, Sun D. 2015a. Decomposing the meridional heat transport in the climate system. Climate Dynamics, 44(9-10): 2 751–2 768.CrossRefGoogle Scholar
  34. Yang H J, Zhao Y Y, Liu Z Y, Li Q, He F, Zhang Q. 2015b. Heat transport compensation in atmosphere and ocean over the past 22,000 years. Sci. Rep., 5: 16661.CrossRefGoogle Scholar
  35. Zhang R, Delworth T L. 2005. Simulated tropical response to a substantial weakening of the Atlantic thermohaline circulation. Journal of Climate, 18(12): 1 853–1 860CrossRefGoogle Scholar

Copyright information

© Chinese Society for Oceanology and Limnology, Science Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Physical Oceanography Laboratory/CIMSTOcean University of China and Qingdao National Laboratory for Marine Science and TechnologyQingdaoChina
  2. 2.Research Vessel CenterOcean University of ChinaQingdaoChina

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