Surveys in Geophysics

, Volume 35, Issue 6, pp 1507–1525 | Cite as

A Tailored Computation of the Mean Dynamic Topography for a Consistent Integration into Ocean Circulation Models

  • S. BeckerEmail author
  • M. Losch
  • J. M. Brockmann
  • G. Freiwald
  • W.-D. Schuh


Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography—the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99–110, 2012; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie 2012). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.


Mean dynamic topography Ocean circulation Altimetry Gravity field Consistent combination 



This work was funded within the DFG priority program SPP 1257 “Mass transport and mass distribution in the system Earth.” Since 2013, the first author is co-financed by ESA within ESA’s Support To Science Element program. The computations were performed on the JUROPA supercomputer at FZ Jülich. The computing time was granted by John von Neumann Institute for Computing (Project HBN15). We thank Dmitry Sidorenko for indispensible help with IFEOM.


  1. Andersen O, Knudsen P (2009) DNSC08 mean sea surface and mean dynamic topography models. J Geophys Res 114:C11,001. doi: 10.1029/2008JC005179 CrossRefGoogle Scholar
  2. AVISO (2008) AVISO and PODAAC user handbook, IGDR and GDR Jason products.
  3. Becker S (2012) Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie. PhD thesis, Universität Bonn.
  4. Becker S, Freiwald G, Losch M, Schuh WD (2012) Rigorous fusion of gravity field, altimetry and stationary ocean models. J Geodyn 59−60:99–110. doi: 10.1016/j.jog.2011.07.0069 CrossRefGoogle Scholar
  5. Becker S, Brockmann J, Schuh WD (2013) Consistent combination of gravity field, altimetry and hydrographic data. In: Willis P (ed) Proceedings of the international symposium on gravity, geoid and height systems (GGHS2012), IAG symposia, Springer, Berlin, Heidelberg (accepted)Google Scholar
  6. Bingham RJ, Haines K, Hughes CW (2008) Calculating the ocean’s mean dynamic topography from a mean sea surface and a geoid. J Atmos Ocean Technol 25. doi: 10.1175/2008JTECHO568.1
  7. Bosch W, Savcenko R (2010) On estimating the dynamic ocean topography a profile approach. Int Assoc Geodesy Symp 135:263–269. doi: 10.1007/978-3-642-10634-7_34 CrossRefGoogle Scholar
  8. Brockmann JM, Schuh WD (2010) Fast variance component estimation in GOCE data processing. In: Mertikas S (ed) Gravity, Geoid and Earth Observation, IAG Symposia, Springer Berlin, Heidelberg doi: 10.1007/978-3-642-10634-7_25
  9. Freiwald G (2012) Combining stationary ocean models and mean dynamic topography data. PhD thesis, Universität Bremen, Bremen.
  10. Gouretski VV, Koltermann KK (2004) WOCE global hydrographic climatology. Berichte des Bundesamtes für Seeschifffahrt und Hydrographie, no. 35.
  11. Hernandez F, Schaeffer P (2001) The CLS01 mean sea surface: a validation with the GSFC00.1 surface. Report, 14 pp, CLS, Ramonville, St Agne, FranceGoogle Scholar
  12. Kaula WM (1966) Theory of satellite geodesy. Blaisdell Publishing Company, MassachusettsGoogle Scholar
  13. Klein B, Molinari R, Müller T, Siedler G (1995) A transatlantic section at 14.5°N: meridional volume and heat fluxes. J Mar Syst 53:929–957Google Scholar
  14. Knudsen P, Bingham R, Andersen O, Rio MH (2011) A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model. Journal of Geodesy doi: 10.1007/s00190-011-0485-8
  15. Koch KR (1999) Parameter Estimation and hypothesis testing in linear models, 2 edn. Springer, BerlinCrossRefGoogle Scholar
  16. Koch KR, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geodesy 76:259–268. doi: 10.1007/s00190-002-0245-x CrossRefGoogle Scholar
  17. Lavín A, Bryden HL, Parrilla G (2003) Mechanisms of heat, freshwater, oxygen and nutrient transports and budgets at 24°N in the subtropical North Atlantic. Deep-Sea Res I 50:1099–1128CrossRefGoogle Scholar
  18. Lorbacher K, Koltermann P (2000) Subinertial variability of transport estimates across 48°N in the North Atlantic. Int WOCE Newsl 40:3–5Google Scholar
  19. Losch M, Sloyan B, Schröter J, Sneeuw N (2002) Box inverse models, altimetry and the geoid: problems with the omission error. J Geophys Res 107(C7). doi: 10.1029/2001JC000855
  20. Lumpkin R, Speer KG (2007) Global ocean meridional overturning. J Phys Oceanogr 37(10):2550–2562. doi: 10.1175/JPO3130.1 CrossRefGoogle Scholar
  21. Macdonald AM, Wunsch C (1996) An estimate of the global ocean circulation and heat flux. Nature 382:436–439CrossRefGoogle Scholar
  22. Maximenko N, Niiler P, Rio MH, Melnichenko O, Centurioni L, Chambers D, Zlotnicki V, Galperin B (2009) Mean dynamic topography of the ocean derived from satellite and drifting buoy data using three different techniques. Atmos Oceanic Technol 26:1910–1918. doi: 10.1175/2009JTECHO672.1 CrossRefGoogle Scholar
  23. Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010 gravity field model.
  24. MSS_CNES_CLS10 (2010) MSS_CNES_CLS10 was produced by CLS space oceanography division and distributed by Aviso, with support from Cnes (
  25. Pail R, Bruinsma S, Miggliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann J, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansó F, Tscherning C (2011) First GOCE gravity field models derived by three different approaches. J Geodesy 85(11):819–843. doi: 10.1007/s00190-011-0467-x CrossRefGoogle Scholar
  26. Pavlis N, Holmes S, Kenyon S, Factor J (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Rese 117. doi: 10.1029/2011JB008916
  27. Richter F (2010) Nutzung von Argo-Driftern und Satellitenaltimetriedaten zur Ableitung der Zirkulation im Nordatlantik. PhD thesis, Universität BremenGoogle Scholar
  28. Rio MH, Guinehut S, Larnicol G (2011) New CNES-CLS09 global mean dynamic topography computed from the combination of grace data, altimetry, and in situ measurements. J Geophys Res 116:C07,018. doi: 10.1029/2010JC006505 Google Scholar
  29. Sato OT, Rossby T (2000) Seasonal and low-frequency variability of the meridional heat flux at 36°N in the North Atlantic. J Phys Oceanogr 30(3):606–621CrossRefGoogle Scholar
  30. Schuh WD, Becker S (2010) Potential field and smoothness conditions. In: Contadakis M, Kaltsikis C, Spatalas S, Tokmakidis K, Tziavos I (eds) The apple of knowledge—inn honour of Prof. N. Arabelos, University of Thessaloniki, AUTH—Faculty of rural and surveying engineering, pp 237–250Google Scholar
  31. Schuh WD, Becker S, Brockmann J (2013) Completion of band-limited data sets on the sphere. In: Kutterer H, Seitz F, Alkhatib H, Schmidt M (eds) Proceedings of the 1st international workshop on the quality of geodetic observations and monitoring systems (QuGOMS’11), IAG symposia, Springer, Berlin, Heidelberg (accepted)Google Scholar
  32. Sidorenko D (2004) The North Atlantic circulation derived from inverse models. PhD thesis, Universität BremenGoogle Scholar
  33. Wunsch C (2005) The total meridional heat flux and its oceanic and atmospheric partition. J Clim 18(21):4374–4380. doi: 10.1175/JCLI3539.1 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • S. Becker
    • 1
    Email author
  • M. Losch
    • 2
  • J. M. Brockmann
    • 1
  • G. Freiwald
    • 2
  • W.-D. Schuh
    • 1
  1. 1.Department of Theoretical Geodesy, Institute of Geodesy and GeoinformationUniversity of BonnBonnGermany
  2. 2.Alfred Wegener InstituteHelmholtz Centre for Polar and Marine ResearchBremerhavenGermany

Personalised recommendations