Journal of Geodesy

, Volume 91, Issue 2, pp 195–206 | Cite as

Mass evolution of Mediterranean, Black, Red, and Caspian Seas from GRACE and altimetry: accuracy assessment and solution calibration

  • B. D. LoomisEmail author
  • S. B. Luthcke
Original Article


We present new measurements of mass evolution for the Mediterranean, Black, Red, and Caspian Seas as determined by the NASA Goddard Space Flight Center (GSFC) GRACE time-variable global gravity mascon solutions. These new solutions are compared to sea surface altimetry measurements of sea level anomalies with steric corrections applied. To assess their accuracy, the GRACE- and altimetry-derived solutions are applied to the set of forward models used by GSFC for processing the GRACE Level-1B datasets, with the resulting inter-satellite range-acceleration residuals providing a useful metric for analyzing solution quality. We also present a differential correction strategy to calibrate the time series of mass change for each of the seas by establishing the strong linear relationship between differences in the forward modeled mass and the corresponding range-acceleration residuals between the two solutions. These calibrated time series of mass change are directly determined from the range-acceleration residuals, effectively providing regionally-tuned GRACE solutions without the need to form and invert normal equations. Finally, the calibrated GRACE time series are discussed and combined with the steric-corrected sea level anomalies to provide new measurements of the unmodeled steric variability for each of the seas over the span of the GRACE observation record. We apply ensemble empirical mode decomposition (EEMD) to adaptively sort the mass and steric components of sea level anomalies into seasonal, non-seasonal, and long-term temporal scales.


GRACE Sea surface altimetry Steric sea level Inter-satellite range-acceleration EEMD 



Support for this work was provided by the NASA GRACE and GRACE Follow-On Science Team Grants NNH10ZDA001N and NNH15ZDA001N. We gratefully acknowledge the quality of the GRACE Level-1B products produced by our colleagues at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena. We thank J.P. Boy and R.D. Ray for contributions to the forward models applied in our GRACE data reduction and analysis. We especially acknowledge the numerous contributions of D.D. Rowlands and T.J. Sabaka in developing the foundation of algorithms and software necessary to carry out this research. We also thank the reviewers who provided valuable feedback towards improving this manuscript. The GRACE Level-1B products are available at the Physical Oceanography Distributed Active Archive Center (PO.DAAC) at The sea level anomaly grids are produced by the Sea Level Thematic Assembly Centre (SL-TAC) and hosted by Copernicus Marine Environment Monitoring Service at The Gibbs Seawater Oceanographic Toolbox for implementing TEOS-10 is available at MERRA-2 data is available at


  1. Bettadpur S (2012) GRACE level-2 gravity field product user handbook. GRACE 327-734 (CSR-GR-03-01). Center for Space Research, The University of Texas at AustinGoogle Scholar
  2. Carrère L, Lyard F (2003) Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing—comparisons with observations. Geophys Res Lett 30(6):1275–1278. doi: 10.1029/2002G016473 CrossRefGoogle Scholar
  3. Chambers D, Willis JK (2008) Analysis of large-scale ocean bottom pressure variability in the North Pacific. J Geophys Res 113:C11003. doi: 10.1029/2008JC004930 CrossRefGoogle Scholar
  4. Cheng MK, Tapley BD, Ries JC (2013) Deceleration in the Earth’s oblateness. J Geophys Res 118:1–8. doi: 10.1002/jgrb.50058 Google Scholar
  5. Feistel R (2003) A new extended Gibbs thermodynamic potential of seawater. Progr Oceanogr 58:43–114CrossRefGoogle Scholar
  6. Feistel R (2008) A Gibbs function for seawater thermodynamics for -6\(^{\circ }\) to 80\(^{\circ }\) C and salinity up to 120 g kg\(^{-1}\). Deep-Sea Res I 55:1639–1671CrossRefGoogle Scholar
  7. Feng W, Lemoine J-M, Zhong M, Hsu HT (2015) Mass-induced sea level variations in the Red Sea from GRACE, steric-corrected altimetry, in situ bottom pressure records, and hydrographic observations. J Geodyn 78:1–7. doi: 10.1016/j.jog.2014.04.008 CrossRefGoogle Scholar
  8. Fenoglio-Marc L, Kusche J, Becker M (2006) Mass variation in the Mediterranean Sea from GRACE and its validation by altimetry, steric and hydrologic fields. Geophys Res Lett 33:L19606. doi: 10.1029/2006GL026851 CrossRefGoogle Scholar
  9. Fenoglio-Marc L, Rietbroek R, Grayek S, Becker M, Kusche J, Stanev E (2012) Water mass variation in the Mediterranean and Black Seas. J Geodyn 59–60:168–182. doi: 10.1016/j.jog.2012.04.001 CrossRefGoogle Scholar
  10. Flechtner F, Dobslaw H, Fagiolini E (2014) Gravity recovery and climate experiment AOD1B product description document for product release 05. GRACE 327-750Google Scholar
  11. Han S-C, Riva R, Sauber J, Okal E (2013) Source parameter inversion for recent great earthquakes from a decade-long observation of global gravity fields. J Geophys Res Solid Earth 118:1240–1267. doi: 10.1002/jgrb.50116 CrossRefGoogle Scholar
  12. Harig C, Simons FJ (2012) Mapping Greenland’s mass loss in space and time. Proc Natl Acad Sci 109(49):19934–19937. doi: 10.1073/pnas.1206785109 CrossRefGoogle Scholar
  13. Huang NE et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond A 454:903–995CrossRefGoogle Scholar
  14. Jacob T, Wahr J, Pfeffer T, Swenson S (2012) Recent contributions of glaciers and ice caps to sea level rise. Nature 482(7386):514–518. doi: 10.1038/nature10847 CrossRefGoogle Scholar
  15. Kusche J (2007) Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. J Geod 81:733. doi: 10.1007/s00190-007-0143-3 CrossRefGoogle Scholar
  16. Landerer FW, Volkov DL (2013) The anatomy of recent large sea level fluctuations in the Mediterranean Sea. Geophys Res Lett 40:553–557. doi: 10.1002/grl.50140 CrossRefGoogle Scholar
  17. Loomis BD, Luthcke SB (2014) Optimized signal denoising and adaptive estimation of seasonal timing and mass balance from simulated GRACE-like regional mass variations. Adv Adapt Data Anal 06:1450003. doi: 10.1142/S1793536914500034 CrossRefGoogle Scholar
  18. Luthcke SB, Zwally HJ, Abdalati W, Rowlands DD, Ray RD, Nerem RS, Lemoine FG, McCarthy JJ, Chinn DS (2006) Recent Greenland ice mass loss by drainage system from satellite gravity observations. Science 314(5803):1286–1289. doi: 10.1126/science.1130776 CrossRefGoogle Scholar
  19. Luthcke SB, Arendt AA, Rowlands DD, McCarthy JJ, Larsen CF (2008) Recent glacier mass changes in the Gulf of Alaska region from GRACE mascon solutions. J Glaciol 54(188):767–777CrossRefGoogle Scholar
  20. Luthcke SB, Sabaka TJ, Loomis BD, Arendt AA, McCarthy JJ, Camp J (2013) Antarctica, Greenland and Gulf of Alaska land ice evolution from an iterated GRACE global mascon solution. J Glaciol 59(216):613–631. doi: 10.3189/2013JoG12J147 CrossRefGoogle Scholar
  21. McDougall TJ, Barker PM (2011) Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox. SCOR/IAPSO WG127 ISBN 978-0-646-55621-5Google Scholar
  22. Peltier WR, Argus DF, Drummond R (2015) Space geodesy constrains ice-age terminal deglaciation: the global ICE-6G_C (VM5a) model. J Geophys Res Solid Earth 120:450–487. doi: 10.1002/2014JB011176 CrossRefGoogle Scholar
  23. Rodell M et al (2004) The global land data assimilation system. Bull Am Meteorol Soc 85(3):381–394. doi: 10.1175/BAMS-85-3-381
  24. Rowlands DD, Luthcke SB, Klosko S, Lemoine FG, Chinn DS, McCarthy JJ, Cox CM, Anderson OB (2005) Resolving mass flux at high spatial and temporal resolution using GRACE intersatellite measurements. Geophys Res Lett 32:L04310. doi: 10.1029/2004GL021908 CrossRefGoogle Scholar
  25. Sabaka TJ, Rowlands DD, Luthcke SB, Boy J-P (2010) Improving global mass flux solutions from gravity recovery and climate experiment (GRACE) through forward modeling and continuous time correlation. J Geophys Res 115:B11403. doi: 10.1029/2010JB007533 CrossRefGoogle Scholar
  26. Schroeder K et al (2016) Abrupt climate shift in the Western Mediterranean Sea. Sci Rep 6:23009. doi: 10.1038/srep23009 CrossRefGoogle Scholar
  27. Swenson S, Wahr J (2002) Methods for inferring regional surface-mass anomalies from gravity recovery and climate experiment (GRACE) measurements of time-variable gravity. J Geophys Res 107(B9):2193. doi: 10.1029/2001JB000576 Google Scholar
  28. Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33:L08402. doi: 10.1029/2005GL025285 Google Scholar
  29. Swenson S, Wahr J (2007) Multi-sensor analysis of water storage variations of the Caspian Sea. Geophys Res Lett 34:L16401. doi: 10.1029/2007GL030733 CrossRefGoogle Scholar
  30. Swenson S, Chambers D, Wahr J (2008) Estimating geocenter variations from a combination of GRACE and ocean model output. J Geophys Res 113:B08410. doi: 10.1029/2007JB005338 CrossRefGoogle Scholar
  31. Torres ME, Colominas MA, Schlotthaur G, Flandrin P (2011) A complete ensemble empirical mode decomposition with adaptive noise. IEEE Ann Int Conf on Acoustics, Speech and Signal Processing ICASSP11, Prague, p 4144–4147Google Scholar
  32. Volkov DL, Landerer FW (2015) Internal and external forcing of sea level variability in the Black Sea. Clim Dyn 45(9):2633–2646. doi: 10.1007/s00382-015-2498-0 CrossRefGoogle Scholar
  33. Wahr J, Molenaar M (1998) Time variability of the Earth’s gravity field: hydrological and oceanic effects and their possible detection using GRACE. J Geophys Res 103(B12):30205–30229CrossRefGoogle Scholar
  34. Wahr J, Smeed DA, Leuliette E, Swenson S (2014) Seasonal variability of the Red Sea, from satellite gravity, radar altimetry, and in situ observations. J Geophys Res Oceans 119:5091–5104. doi: 10.1002/2014JC010161
  35. Wahr J, Nerem RS, Bettadpur SV (2015) The pole tide and its effect on GRACE time-variable gravity measurements: implications for estimates of surface mass variations. J Geophys Res Solid Earth 120:4597–4615. doi: 10.1002/2015JB011986 CrossRefGoogle Scholar
  36. Watkins MM, Wiese DN, Yuan D-N, Boening C, Landerer FW (2015) Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons. J Geophys Res Solid Earth 120(4):2648–2671. doi: 10.1002/2014JB011547 CrossRefGoogle Scholar
  37. Wu Z, Huan NE, Long SR, Peng C-K (2007) On the trend, detrending, and variability of nonlinear and nonstationary time series. PNAS 104(38):14889–14894. doi: 10.1073/pnas.0701020104 CrossRefGoogle Scholar
  38. Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adap Data Anal 01:1–41CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg (outside the USA) 2016

Authors and Affiliations

  1. 1.SGT Inc. at NASA Goddard Space Flight CenterGreenbeltUSA
  2. 2.NASA Goddard Space Flight CenterGreenbeltUSA

Personalised recommendations