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GRACE-derived surface water mass anomalies by energy integral approach: application to continental hydrology

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Abstract

We propose an unconstrained approach to recover regional time-variations of surface mass anomalies using Level-1 Gravity Recovery and Climate Experiment (GRACE) orbit observations, for reaching spatial resolutions of a few hundreds of kilometers. Potential differences between the twin GRACE vehicles are determined along short satellite tracks using the energy integral method (i.e., integration of orbit parameters vs. time) in a quasi-inertial terrestrial reference frame. Potential differences residuals corresponding mainly to changes in continental hydrology are then obtained after removing the gravitational effects of the known geophysical phenomena that are mainly the static part of the Earth’s gravity field and time-varying contributions to gravity (Sun, Moon, planets, atmosphere, ocean, tides, variations of Earth’s rotation axis) through ad hoc models. Regional surface mass anomalies are restored from potential difference anomalies of 10 to 30-day orbits onto 1 continental grids by regularization techniques based on singular value decomposition. Error budget analysis has been made by considering the important effects of spectrum truncation, the time length of observation (or spatial coverage of the data to invert) and for different levels of noise.

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References

  • Awange JL, Sharifi MA, Baur O, Keller W, Featherstone WE, Kuhn M (2009) GRACE hydrological monitoring of Australia: current limitations and future prospects. J Spat Sci 54(1): 23–36

    Article  Google Scholar 

  • Bruinsma S, Lemoine J-M, Biancale R, Valès N (2010) CNES/GRGS 10-day gravity models (release 2) and their evaluation. Adv Space Res 45(4): 587–601. doi:10.1016/j.asr.2009.10.012

    Article  Google Scholar 

  • Carrère L, Lyard F (2003) Modeling the barotropic response of the global ocean to atmosphere wind and pressure forcing—comparisons with observations. Geophys Res Lett 30: 1275. doi:10.1029/2002GL016473

    Article  Google Scholar 

  • Desai SD (2002) Observing the pole tide with satellite altimetry. J Geophys Res 107(C11): 3186. doi:10.1029/2001JC001224

    Article  Google Scholar 

  • Dickey J et al (1997) Satellite gravity and the geosphere: contribution to the study of the solid earth and its fluid envelope. National Research Council (NRC), National Academy Press, Washington DC. ISBN: 0-309-05792-2.10.1126/science.1130776

  • Döll P, Kaspar F, Lehner B (2003) A global hydrological model for deriving water availability indicators: model tuning and validation. J Hydrol 270(1–2): 105–134

    Article  Google Scholar 

  • Eicker A, Mayer-Gürr T, Ilk KH (2007) Improved resolution of GRACE gravity field model by regional refinements. In: Proceedings IUGG general assembly, Peruggia

  • Eicker A (2008) Gravity field refinement by radial basis function from in situ satellite data. Institut für Geodäsie und Geoinformation der Universität Bonn, thesis manuscript, D98

  • Fengler MJ, Freeden W, Kohlhaas A, Michel V, Peter T (2007) Wavelet modelling of regional and temporal variations of the Earth’s gravitational potential observed by GRACE. J Geod 81: 5–15. doi:10.1007/s00190-006-0040-1

    Article  Google Scholar 

  • Földvàry L, Svehla D, Gerlach C, Wermuth M, Gruber T, Rummel R, Rothacher M, Frommknecht B, Peters T, Steigenberger P (2003) Gravity model TUM-2Sp based on the energy balance approach and kenatic CHAMP orbits. In: Earth observation with CHAMP—results from three years in orbit. Springer, Berlin, pp 13–18

  • Földvàry L (2007) Determination of satellite velocity and acceleration from kinematic LEO orbits. Acta Geod Geophys Hung 42(4): 399–419. doi:10.1556/AGeod.42.2007.4.3

    Article  Google Scholar 

  • Földvàry L (2007) Analysis of numerical differentiation methods applied for determination of kinematic velocities for LEOs. Period Polytech Civ Eng 51(1): 17–24. doi:10.3311/pp.ci.2007-1.03

    Article  Google Scholar 

  • Forsythe GE, Malcolm MA, Moler CB (1977) Computer methods for mathematical computations. Prentice-Hall, Englewood Cliffs, 259 pp. ISBN: 0131653326

  • Freeden W, Schreiner M (2008) Spherical functions of mathematical geosciences, a scalar, vectorial and tensorial setup. Advances in geophysical and environmental mechanics and mathematics. Springer, Berlin, 602 pp. ISBN: 978-3-540-85111-0

  • Garcia R (2002) Local geoid determination from GRACE mission, Department of Civil and Environmental Engineering and Geodetic Sciences, The Ohio State University, Columbus, Report 460

  • Han S-C, Jekeli C, Shum CK (2003) Static and temporal gravity field recovery using GRACE potential difference observables. Adv Geosci 1: 19–26

    Article  Google Scholar 

  • Han S-C (2004) Efficient determination of global gravity field from satellite-to-satellite tracking mission GRACE. Celest Mech Dyn Astron 88: 69–102

    Article  Google Scholar 

  • Han S-C, Shum CK, Jekeli J, Alsdorf D (2005) Improved estimation of terrestrial water storage changes from GRACE. GRL 32: L07302. doi:10.1029/2005GL02238

    Article  Google Scholar 

  • Han S-C, Shum CK, Bevis M, Ji C, Kuo C-Y (2006) Crustal dilatation observed by GRACE after the 2004 Sumatra-Adaman earthquake. Science 313(5787): 658–662. doi:10.1126/science.1128661

    Article  Google Scholar 

  • Han S-C, Rowlands DD, Luthcke SB, Lemoine FG (2008) Localized analysis of satellite tracking data for studying time variable Earth’s gravity fields. JGR 113:B06401. doi:10.1029/2007JB005218

  • Han S-C, Sauber J, Luthcke SB, Ji C, Pollitz FF (2008) Implications of postseismic gravity change following the great 2004 Sumatra-Andaman earthquake from the regional harmonic analysis of GRACE intersatellite tracking data. JGR 113:B11413. doi:10.1029/2008JB005705

  • Hansen PC (1997) Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. SIAM monographs on mathematical modeling and computation, vol 4, 247 pp. ISBN-13: 978-0-898714-03-6

  • Hansen PC, O’Leary DP (1993) The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput 14(6): 1487–1503

    Article  Google Scholar 

  • Howe E, Stenseng L, Tscherning CC (2003) Analysis of one month of CHAMP state vector and accelerometer data for the recovery of the gravity potential. Adv Geosci 1: 1–4

    Article  Google Scholar 

  • Ilk KH, Löcher A (2003) The use of energy balance relations for validation of gravity field models and orbit determination results. In: A window on the future of geodesy, IUGG general assembly 2003, Sapporo, Japan, IAG symposia, vol 128. Springer, Berlin, 494–499

  • Jekeli C (1999) The determination of gravitational potential differences from satellite-to-satellite tracking. Celest Mech Dyn Astron 7582: 85–101

    Article  Google Scholar 

  • Keller W (2004) Wavelets in geodesy and geodynamics. Walter de Gruyter, Berlin. ISBN: 3-11-017546-0

  • Kusche J, van Loon J (2003) Statistical assessment of CHAMP data and models using energy balance approach. In: Earth observation with CHAMP—results from three years in orbit. Springer, Berlin, pp 133–138

  • Lambeck K (1988) Geophysical geodesy. Oxford Science Publications, New York, 718 pp. ISBN: 0-19-854438-3

  • Lemoine FG et al (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-206861, July 1998

  • Lemoine J-M, Bruinsma S, Loyer S, Biancale R, Marty J-C, Perosanz F, Balmino G (2007a) Temporal gravity field models inferred from GRACE data. Adv Space Res. doi:10.1016/j.asr.2007.03.062

  • Lemoine FG, Luthcke SB, Rowlands DD, Chinn DS, Klosko SM, Cox CM (2007b) The use of mascons to resolve time-variable gravity from GRACE. In: Dynamic planet: monitoring and understanding a dynamic planet with geodetic and oceanographic tools, chap 35, IAG symposium, Cairns, Australia, 22–26 August 2005. Springer, Berlin, 130 pp. doi:10.1007/978-3-540-49349-5

  • Le Provost C, Genco ML, Lyard F, Vincent P, Canceil P (1994) Spectroscopy of the world ocean tides from a finite element hydrodynamic model. J Geophys Res 99(C12): 24777–24797. doi:10.1029/94JC01381

    Article  Google Scholar 

  • Löcher A, Ilk KH (2005) Energy balance relations for validation of gravity field models and orbit determination applied to the results of the CHAMP. In: Earth observation with CHAMP—results from three years in orbit. Springer, Berlin, pp 53–58

  • Löcher A, Ilk KH (2007) A validation procedure for satellite orbits and force function models based on a new balance equation approach. In: Dynamic planet: monitoring and understanding a dynamic planet with geodetic and oceanographic tools, chap. 42, IAG symposium, Cairns, Australia, 22–26 August 2005. Springer, Berlin, 130 pp

  • 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

    Article  Google Scholar 

  • McCarthy DD, Petit G (2003) IERS conventions. IERS Technical Notes, 32. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie

  • Muller PM, Sjogren WL (1968) Mascons: lunar mass concentrations. Science 161(3842): 680–684. doi:10.1126/science.161.3842.680

    Article  Google Scholar 

  • Pail R (2000) Synthetic global gravity model for planetary bodies and applications in staellite gravity gradiometry. Dissertation manuscript, Mitteilungen der Geodätischen Institute der Technischen Universität, Graz

  • Panet I, Mikhailov V, Diament M, Pollitz F, King G, de Viron O, Holschneider M, Biancale R, Lemoine JM (2007) Co-seismic and post-seismic signatures of the Sumatra December 2004 and March 2005 earthquakes in GRACE satellite gravity. Geophys J Int. doi:10.1111/j.1365-246X.2007.03525.x

  • Ramillien G, Cazenave A, Brunau O (2004) Global time variations of hydrological signals from GRACE satellite gravimetry. GJI 158(3): 813–826. doi:10.1111/j.1365-246X.2004.02328.x

    Google Scholar 

  • Ramillien G, Lombard A, Cazenave A, Ivins E, 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

    Article  Google Scholar 

  • Ramillien G, Frappart F, Güntner A, Ngo-Duc T, Cazenave A (2006) Mapping time variations of evaporation rate from GRACE satellite gravimetry. WRR 42: W10403. doi:10.1029/2005WR004331

    Article  Google Scholar 

  • Ramillien G, Famiglietti J, Wahr J (2008) Detection of continental hydrology and glaciology signals from GRACE: a review. Surveys in geophysics. Special issue: hydrology from space. doi:10.1007/s10712-008-9048-9

  • Reubelt T (2009) Harmonische Gravitationsfeldanalyse aus GPS-vermessenen kinematischen Bahnen niedrig fliegender Satelliten vom Typ CHAMP, GRACE und GOCE mit einem hoch auflösenden Beschleunigungsansatz. Dissertation, Geodätisches Institut der Universität Stuttgart (in German)

  • Reuter R (1982) Über Integralformeln der Einheitssphäre und harmonische Splinefunktionen, In: Veröffentlichungen des Geodätischen Instituts, RWTH Aachen, Report 33

  • Rodell M, Famiglietti J (1999) Detectability of variations in continental water storage from satellite observations of the time dependent gravity field. WRR 35(9): 2705–2723

    Article  Google Scholar 

  • Rodell M, Famiglietti J (2001) An analysis of terrestrial water storage variations in Illinois with implications for the gravity and climate experiment (GRACE). WRR 37(5): 1327–1339

    Article  Google Scholar 

  • Rodell M, Famiglietti J, Chen J, Seneviratne SI, Viterbo P, Holl S, Wilson CR (2004) Basin scale estimates of evapotranspiration using GRACE and other observations. GRL 31: L20504. doi:10.1029/2004GL020873

    Article  Google Scholar 

  • Rowlands DD, Ray RD, Chinn DS, Lemoine FG (2002) Short-arc analysis of intersatellite tracking data in a mapping mission. J Geod 76: 307–316. doi:10.1007/s.00190-002-0255-8

    Article  Google Scholar 

  • Rowlands DD, Luthcke SB, Klosko SM, Lemoine FG, Chinn DS, McCarthy JJ, Cox CM, Anderson OB (2005) Resolving mass flux at high spatial and temporal resolution using GRACE intersatellite measurements. GRL 32: L04310. doi:10.1029/2004GL022386

    Article  Google Scholar 

  • Rowlands DD, Luthcke SB, McCarthy JJ, Klosko SM, Chinn DS, Lemoine FG, Boy J-P, Sabaka TJ (2010) Global mass flux solutions from GRACE: a comparison of parameter estimation strategies—mass concentrations versus Stokes coefficients. J Geophys Res 115: B01403. doi:10.1029/2009JB006546

    Article  Google Scholar 

  • Schmidt R, Schwintzer P, Flechtner F, Reigber C, Güntner A, Döll P, Ramillien G, Cazenave A, Petrovic S, Jochmann H, Wunsch J (2006) GRACE observations of changes in continental water storage. Glob Planet Change 50(1–2): 112–126. doi:10.1016/j.gloplacha.2004.11.018

    Article  Google Scholar 

  • Schmidt R, Flechtner F, Meyer U, Neumayer K-H, Dahle Ch, Koenig R, Kusche J (2008) Hydrological signals observed by GRACE satellites. Surv Geophys 29: 319–334. doi:10.1007/s107/12-008-9033-3

    Article  Google Scholar 

  • Standish EM, Newhall XX, Williams JG, Folkner WF (1995) JPL Planetary and Lunar Ephemerides, DE403/LE403, JPL IOM 314.10-127

  • Swenson S, Wahr J (2006) Estimating large scale precipitation minus evapotranspiration from GRACE satellite gravimetry measurements. J Meteorol 7(2): 252–270. doi:10.1175/JHM478.1

    Google Scholar 

  • Syed T, Famiglietti J, Chen J, Rodell M, Seneviratne S, Viterbo P, Wilson CR (2005) Total basin discharge for the Amazon and the Mississippi river basins from GRACE and a land-atmosphere water balance. GRL 32(24): L24404. doi:10.1029/2005GL024851

    Article  Google Scholar 

  • Tapley B, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. GRL 31: L09607. doi:10.1029/2004GL019920

    Article  Google Scholar 

  • Tapley B, Bettadpur S, Ries J, Thompson P, Watkins M (2004) GRACE measurements of mass variability in the Earth system. Science 305(5683): 503–505. doi:10.1126/science.1099192

    Article  Google Scholar 

  • Velicogna I, Wahr J (2005) Ice mass balance in Greenland from GRACE. GRL 32(18): L18505. doi:10.1029/2005GL023955

    Article  Google Scholar 

  • Velicogna I, Wahr J (2006) Measurements of time-variable gravity show mass loss in Antarctica. Science 311(5768): 1754–1756. doi:10.1126/science.1123785

    Article  Google Scholar 

  • Velicogna I, Wahr J (2006) Acceleration of Greenland ice mass loss in Spring 2004. Nature 443: 329–331. doi:10.1038/nature.05168

    Article  Google Scholar 

  • Visser PNAM, Sneeuw N, Gerlach C (2003) Energy integral method for gravity field determination from satellite orbit coordinates. J Geod 77: 207–216. doi:10.1007/s00190-003-0315-8

    Article  Google Scholar 

  • Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth gravity field: hydrological and oceanic effects and their possible detection using GRACE. JGR Solid Earth 103(B12): 30205–30229

    Article  Google Scholar 

  • Wahr J, Swenson S, Zlotnicki V, Velicogna I (2004) Time-variable gravity from GRACE: first results. GRL 31(11): L11501. doi:10.1029/2004GL019779

    Article  Google Scholar 

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Correspondence to Guillaume Ramillien.

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Ramillien, G., Biancale, R., Gratton, S. et al. GRACE-derived surface water mass anomalies by energy integral approach: application to continental hydrology. J Geod 85, 313–328 (2011). https://doi.org/10.1007/s00190-010-0438-7

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