Acta Oceanologica Sinica

, Volume 33, Issue 5, pp 28–36 | Cite as

Estimation of vertical diffusion coefficient based on a one-dimensional temperature diffusion equation with an inverse method

  • Hui Liang
  • Wei Zhao
  • Dejun DaiEmail author
  • Jun Zhang


Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography. It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.

Key words

inverse method temperature diffusivity one-dimensional vertical diffusion equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alford M H. 2001. Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer nearinertial motions. J Phys Oceanogr, 31: 2359–2368, doi: 10.1175/1520-0485(2001)031〈2359:ISGTSD〉2.0.CO;2CrossRefGoogle Scholar
  2. Cisewski B, Strass V H, Prandke H. 2005. Upper-ocean vertical mixing in the Antarctic Polar Front Zone. Deep-Sea Res: Part II, 52: 1087–1108CrossRefGoogle Scholar
  3. Dai Dejun, Qiao Fangli, Xia Changshui, et al. 2006. A numerical study on dynamic mechanisms of seasonal temperature variability in the Yellow Sea. J Geophys Res, 111: C11S05, doi: 10.1029/2005JC003253Google Scholar
  4. Decloedt T, Luther D S. 2010. On a simple empirical parameterization of topography-catalyzed diapycnal mixing in the abyssal ocean. J Phys Oceanogr, 40: 487–508CrossRefGoogle Scholar
  5. Egbert G D, Ray R D. 2001. Estimates of M2 tidal energy dissipation from TOPEX/Poseidon altimeter data. J Geophys Res, 106: 22475–22502, doi: 10.1029/2000JC000699CrossRefGoogle Scholar
  6. Finnigan T D, Luther D S, Lukas R. 2002. Observations of Enhanced Diapycnal Mixing near the Hawaiian Ridge. J Phys Oceanogr, 32: 2988–3002CrossRefGoogle Scholar
  7. Ganachaud A, Wunsch C. 2000. Improved estimates of global ocean circulation, heat transport and mixing from hydrographic data. Nature, 408: 453–457CrossRefGoogle Scholar
  8. Gill A E, Green J S A, Simmons A J. 1974. Energy partition in the largescale ocean circulation and the production of mid-ocean eddies. Deep-Sea Res, 21: 499–528Google Scholar
  9. Gregg M C. 1989. Scaling turbulent dissipation in the thermocline. J Geophys Res, 94: 9686–9698CrossRefGoogle Scholar
  10. Gregg M C, Sanford T B, Winkel D P. 2003. Reduced mixing from the breaking of internal waves in equatorial waters. Nature, 422(6931): 513–515CrossRefGoogle Scholar
  11. Hasumi H, Suginohara N. 1999. Effects of locally enhanced vertical diffusivity over rough bathymetry on the world ocean circulation. J Geophys Res, 104(C10): 23367–23374CrossRefGoogle Scholar
  12. Jayne S R. 2009. The impact of abyssal mixing parameterization in an ocean general circulation model. J Phys Oceanogr, 39: 1756–1775CrossRefGoogle Scholar
  13. Jing Zhao, Wu Lixin. 2010. Seasonal variation of turbulent diapycnal mixing in the northwestern Pacific stirred by wind stress. Geophys Res Lett, 37: L23604, doi: 10.1029/2010GL045418Google Scholar
  14. Kunze E, Firing E, Hummon J M, et al. 2006. Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J Phys Oceanogr, 36(8): 1553–1576CrossRefGoogle Scholar
  15. Ledwell J R, Montgomery E T, Polzin K L, et al. 2000. Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature, 403(13): 179–182CrossRefGoogle Scholar
  16. Ledwell J R, Watson A J, Law C S. 1993. Evidence for slow mixing across the pysnocline from an open ocean tracer release experiment. Nature, 364: 701–703CrossRefGoogle Scholar
  17. Lumpkin R, Speer K. 2007. Global ocean meridional overturning. J Phys Oceanogr, 37: 2550–2562CrossRefGoogle Scholar
  18. Munk W, Wunsch C. 1998. Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res, 45: 1977–2010CrossRefGoogle Scholar
  19. Naveira Garabato A C, Polzin K L, King B A, et al. 2004. Widespread intense turbulent mixing in the Southern Ocean. Science, 303: 210–213CrossRefGoogle Scholar
  20. Osborn T R. 1980. Estimates of the local-rate of vertical diffusion from dissipation measurements. J Phys Oceanogr, 10: 83–89CrossRefGoogle Scholar
  21. Osborn T R, Cox C S. 1972. Oceanic fine structure. Geophysical Fluid Dynamics, 3: 321–345CrossRefGoogle Scholar
  22. Polzin K L, Toole J M, Ledwell J R, et al. 1997. Spatial Variability of Turbulent Mixing in the Abyssal Ocean. Science, 276: 93–96CrossRefGoogle Scholar
  23. Quay P D, Broecker W S, Hesslein R H, et al. 1980. Vertical diffusion rates determined by tritium tracer experiments in the thermocline and hypolimnion of two lakes. Limnol Oceanogr, 25(2): 201–218CrossRefGoogle Scholar
  24. Rudnick D L, Boyd T J, Brainard R E, et al. 2003. From Tides to Mixing Along the Hawaiian Ridge. Science, 301: 355–357CrossRefGoogle Scholar
  25. Saenko O A, Merryfield W J. 2005. On the effect of topographically enhanced mixing on the global ocean circulation. J Phys Oceanogr, 35: 826–834CrossRefGoogle Scholar
  26. Simmons H L, Jayne S R, Laurent Louis C S, et al. 2004. Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modell, 6: 245–263CrossRefGoogle Scholar
  27. Thompson A F, Gille S T, Mackinnon J A, et al. 2007. Spatial and temporal patterns of small-scale mixing in Drake Passage. J Phys Oceanogr, 37: 572–592CrossRefGoogle Scholar
  28. Thorpe S A. 1977. Turbulence and mixing in a Scottish Loch. Philosophical Transactions of the Royal Society of London: Series A, 286: 125–181CrossRefGoogle Scholar
  29. Wunsch C, Ferrari R. 2004. Vertical mixing, energy, and the general circulation of the oceans. Annual Review of Fluid Mechanics, 36: 281–314CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Physical Oceanography LaboratoryOcean University of ChinaQingdaoChina
  2. 2.The First Institute of OceanographyState Oceanic AdministrationQingdaoChina
  3. 3.Key Laboratory of Marine Science and Numerical ModelingState Oceanic AdministrationQingdaoChina
  4. 4.The Third Institute of OceanographyState Oceanic AdministrationXiamenChina

Personalised recommendations