Abstract
Greenland ice mass loss is one of the most serious phenomena of present-day global climate change. In this context, both the quantification of overall deglaciation rates and its spatial localization are highly significant. We have thoroughly investigated the technique of point-mass modeling in order to derive mass-balance patterns from GRACE (Gravity Recovery And Climate Experiment) gravimetry. The method infers mass variations on the Earth’s surface from gravitational signals at satellite altitude. In order to solve for point-mass changes, we applied least-squares adjustment. Due to downward continuation, numerical stabilization of the inversion process gains particular significance. We stabilized the ill-posed problem by Tikhonov regularization. Our simulation and real data experiments show that point-mass modeling provides both rational deglaciation rates and high-resolution spatial mass variation patterns.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bamber JL, Riva REM, Vermeersen BLA, LeBrocq AM (2009) Reassessment of the potential sea-level rise from a collapse of the West Antarctic ice sheet. Science 324: 901–903. doi:10.1126/science.1169335
Baur O, Kuhn M, Featherstone WE (2009) GRACE-derived ice-mass variations over Greenland by accounting for leakage effects. J Geophys Res 114: B06407. doi:10.1029/2008JB006239
Baur O, Kuhn M, Featherstone WE (2011) Linear and non-linear secular mass variations from GRACE. In: Proc VII Hotine-Marussi symposium Rome. Springer, New York (in press)
Chen JL, Wilson CR, Tapley BD (2006) Satellite gravity measurements confirm accelerated melting of Greenland ice sheet. Science 313: 1958–1960. doi:10.1126/science.1129007
Farrell WE, Clark JA (1976) On postglacial sea level. Geophys J R Astron Soc 46: 647–667
Forsberg R, Reeh N (2007) Mass change of the Greenland ice sheet from GRACE. In: Proceedings of the 1st international symposium of IGFS, Harita Dergisi, vol 18, pp 454–458. ftp://ftp.spacecenter.dk/pub/igfs2006-proceedings/IGFS_2006_Proceedings.pdf
Golub GH, Heath M, Wahba G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21: 215–223
Haagmans RHN, van Gelderen M (1991) Error variances-covariances of GEM-T1: their characteristics and implications in geoid computation. J Geophys Res 96(B12): 20011–20022
Hanke M, Hansen PC (1993) Regularization methods for large-scale problems. Surv Math Ind 3: 253–315
Hansen PC (1992) Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev 34: 561–580
Hansen PC, Jensen TK, Rodriguez G (2007) An adaptive pruning algorithm for the discrete L-curve criterion. J Comput Appl Math 198: 483–492
Heiskanen WA, Moritz H (1967) Physical geodesy. WH Freeman and Company, San Francisco
Hobson EW (1931) The theory of spherical and ellipsoidal harmonics. University Press, Cambridge
Koch K-R (1999) Parameter estimation and hypothesis testing in linear models. Springer, Berlin
Koch K-R, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geod 76: 259–268
Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J Geod 76: 359–368
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: 1286–1289. doi:10.1126/science.1130776
Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind. J ACM 9: 54–97
Ramillien G, Lombart A, Cazenave A, Ivins ER, Llubes M, Remy F, Biancale R (2006) Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE. Glob Planet Change 53: 198–208. doi:10.1016/j.gloplacha.2006.06.003
Tikhonov AN (1963) Regularization of incorrectly posed problems. Sov Mat Dokl 4: 1035–1038
van den Broeke M, Bamber J, Ettema J, Rignot E, Schrama E, van de Berg WJ, van Erik M, Velicogna I, Wouters B (2009) Partitioning recent Greenland mass loss. Science 326: 984–986. doi:10.1126/science.1178176
Velicogna I, Wahr J (2005) Greenland mass balance from GRACE. Geophys Res Lett 32: L18505. doi:10.1029/2005GL023955
Velicogna I, Wahr J (2006) Acceleration of Greenland ice mass loss in spring 2004. Nature 443: 329–331. doi:10.1038/nature05168
Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earths gravity field: hydrological and oceanic effects and their possible detection using GRACE. J Geophys Res 103: 30205–30229. doi:10.1029/98JB02844
Wouters B, Chambers D, Schrama EJO (2008) GRACE observes small-scale mass loss in Greenland. Geophys Res Lett 35: L20501. doi:10.1029/2008GL034816
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baur, O., Sneeuw, N. Assessing Greenland ice mass loss by means of point-mass modeling: a viable methodology. J Geod 85, 607–615 (2011). https://doi.org/10.1007/s00190-011-0463-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-011-0463-1