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Regularization and error characterization of GRACE mascons

  • B. D. LoomisEmail author
  • S. B. Luthcke
  • T. J. Sabaka
Original Article
  • 93 Downloads

Abstract

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

Keywords

GRACE Time-variable gravity Mascons Range-acceleration Regularization Model resolution Estimator bias 

Notes

Acknowledgements

Support for this work was provided by the NASA GRACE and GRACE Follow-On Science Team Grant NNH15ZDA001N. We acknowledge the quality of the GRACE Level-1B products produced by our colleagues at the Jet Propulsion Laboratory. We also acknowledge the numerous contributions of D.D. Rowlands, K.E. Rachlin, and J.B. Nicholas in developing the algorithms and software necessary to carry out this research, and we thank the three anonymous reviewers and the editors who provided valuable feedback toward improving this manuscript. The MEI is provided at https://www.esrl.noaa.gov/psd/enso/mei/.

References

  1. AG WJ, Zhong S (2013) Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada. Geophys J Int 192(2):557–572.  https://doi.org/10.1093/gji/ggs030 CrossRefGoogle 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.  https://doi.org/10.1029/2002G016473 CrossRefGoogle Scholar
  3. Cazenave A, Henry O, Munier S et al (2012) Estimating ENSO Influence on the Global Mean Sea Level, 1993–2010. Mar Geodesy 35:82–97.  https://doi.org/10.1080/01490419.2012.718209 CrossRefGoogle Scholar
  4. Cheng MK, Tapley BD, Ries JC (2013) Deceleration in the Earth’s oblateness. J Geophys Res 118:1–8.  https://doi.org/10.1002/jgrb.50058 Google Scholar
  5. Donoho DL, Johnstone IM (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3):425–455.  https://doi.org/10.1093/biomet/81.3.425 CrossRefGoogle Scholar
  6. Foster M (1961) An application of the Wiener–Kolmogorov smoothing theory to matrix inversion. J Soc Ind Appl Math 9(3):387–392.  https://doi.org/10.1137/0109031 CrossRefGoogle Scholar
  7. Hoerl A, Kennard R (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1):55–67.  https://doi.org/10.2307/1267351 CrossRefGoogle Scholar
  8. Ivins ER, James TS, Wahr J, Schrama EJO, Landerer FW, Simon KM (2013) Antarctic contribution to sea level rise observed by GRACE with improved GIA correction. J Geophys Res Solid Earth 118:3126–3141.  https://doi.org/10.1002/jgrb.50208 CrossRefGoogle Scholar
  9. Kim JR (2000) Simulation study of a low-low satellite-to-satellite tracking mission. Ph.D. thesis, University of Texas at AustinGoogle Scholar
  10. Kusche J (2003) Noise variance estimation and optimal weight determination for GOCE gravity recovery. Adv Geosci 1:81–85.  https://doi.org/10.5194/adgeo-1-81-2003 CrossRefGoogle Scholar
  11. Kusche J, Springer A (2017) Parameter estimation for satellite gravity field modeling. In: Naeimi M, Flury J (eds) Global gravity field modeling from satellite-to-satellite tracking data. Lecture notes in Earth system sciences. Springer, Berlin, pp 127–160.  https://doi.org/10.1007/978-3-319-49941-3_4 Google Scholar
  12. Lee J, Lund R (2004) Revisiting simple linear regression with autocorrelated errors. Biometrika 91(1):240–245.  https://doi.org/10.1093/biomet/91.1.240 CrossRefGoogle Scholar
  13. Lemoine FG, Goosens S, Sabaka TJ et al (2013) High–degree gravity models from GRAIL primary mission data. J Geophys Res Planets 118:1676?1698.  https://doi.org/10.1002/jgre.20118 CrossRefGoogle Scholar
  14. Leuliette E, Willis J (2011) Balancing the sea level budget. Oceanography 24(2):122–129.  https://doi.org/10.5670/oceanog.2011.32 CrossRefGoogle Scholar
  15. 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.  https://doi.org/10.1142/S1793536914500034 CrossRefGoogle Scholar
  16. Loomis BD, Luthcke SB (2017) Mass evolution of Mediterranean, Black, Red, and Caspian Seas from GRACE and altimetry: accuracy assessment and solution calibration. J Geod 91(2):195–206.  https://doi.org/10.1007/s00190-016-0952-3 CrossRefGoogle Scholar
  17. 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.  https://doi.org/10.1126/science.1130776 CrossRefGoogle Scholar
  18. 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):767–777.  https://doi.org/10.3189/002214308787779933 CrossRefGoogle Scholar
  19. 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.  https://doi.org/10.3189/2013JoG12J147 CrossRefGoogle Scholar
  20. Menke W (2015) Review of the generalized least squares method. Surv Geophys 36:1–25.  https://doi.org/10.1007/s10712-014-9303-1 CrossRefGoogle Scholar
  21. Nerem RS, Chambers DP, Choe C, Mitchum GT (2010) Estimating mean sea level change from the TOPEX and Jason altimeter missions. Mar Geodesy 33(1):435–446.  https://doi.org/10.1080/01490419.2010.491031 CrossRefGoogle Scholar
  22. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Res 117:B04406.  https://doi.org/10.1029/2011JB008916 CrossRefGoogle Scholar
  23. 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.  https://doi.org/10.1002/2014JB011176 CrossRefGoogle Scholar
  24. Phillips T, Nerem RS, Fox-Kemper B, Famiglietti JS, Rajagopala B (2012) The influence of ENSO on global terrestrial water storage using GRACE. Geophys Res Lett 39:L16705.  https://doi.org/10.1029/2012GL052495 Google Scholar
  25. Reager JT, Gardner AS, Famiglietti JS, Wiese DN, Eicker A, Lo MH (2016) A decade of sea level rise slowed by climate-driven hydrology. Science 351:699–703.  https://doi.org/10.1126/science.aad8386 CrossRefGoogle Scholar
  26. Rodell M, Famiglietti JS, Wiese DN, Reager JT, Beaudoing HK, Landerer FW, Lo MH (2018) Emerging trends in global freshwater availability. Nature 557(7707):651–659.  https://doi.org/10.1038/s41586-018-0123-1 CrossRefGoogle Scholar
  27. Rowlands DD, Ray RD, Chinn DS, Lemoine FG (2002) Short-arc analysis of intersatellite tracking data in a gravity mapping mission. J Geod 76:307.  https://doi.org/10.1007/s00190-002-0255-8 CrossRefGoogle Scholar
  28. 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.  https://doi.org/10.1029/2004GL021908 CrossRefGoogle Scholar
  29. 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.  https://doi.org/10.1029/2009JB006546 CrossRefGoogle Scholar
  30. 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.  https://doi.org/10.1029/2010JB007533 CrossRefGoogle Scholar
  31. Save H, Bettadpur S, Tapley BD (2016) High resolution CSR GRACE RL05 mascons. J Geophys Res Solid Earth 121:7547–7569.  https://doi.org/10.1002/2016JB013007 CrossRefGoogle Scholar
  32. Savitzky A, Golay MJE (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal Chem 36(8):1627–39.  https://doi.org/10.1021/ac60214a047 CrossRefGoogle Scholar
  33. Scanlon BR, Zhang Z, Save H et al (2018) Global models underestimate large decadal declining and rising water storage trends relative to GRACE satellite data. PNAS.  https://doi.org/10.1073/pnas.1704665115 Google Scholar
  34. Shepherd A, Ivins ER et al (2012) A reconciled estimate of ice-sheet mass balance. Science 338(6111):1183–1189.  https://doi.org/10.1126/science.1228102 CrossRefGoogle Scholar
  35. Shepherd A et al (2018) Mass balance of the Antarctic Ice Sheet from 1992 to 2017. Nature 558(7709):219–222.  https://doi.org/10.1038/s41586-018-0179-y CrossRefGoogle Scholar
  36. Swenson S, Chambers D, Wahr J (2008) Estimating geocenter variations from a combination of GRACE and ocean model output. J Geophys Res 113:B08410.  https://doi.org/10.1029/2007JB005338 CrossRefGoogle Scholar
  37. Tikhonov AN (1963) Solution of incorrectly formulated problems and the regularization method. Sov Math Dokl 4:1035–1038Google Scholar
  38. Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. J Geophys Res Solid Earth 103(B12):30,205–30,229.  https://doi.org/10.1029/98JB02844 CrossRefGoogle Scholar
  39. Wahr J, Swenson S, Velicogna I (2006) Accuracy of GRACE mass estimates. Geophys Res Lett 33:L06401.  https://doi.org/10.1029/2005GL025305 CrossRefGoogle Scholar
  40. 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.  https://doi.org/10.1002/2015JB011986 CrossRefGoogle Scholar
  41. 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.  https://doi.org/10.1002/2014JB011547 Google Scholar
  42. WCRP Global Sea Level Budget Group (2018) Global sea level budget 1993-present. Earth Syst Sci Data 10:1551–1590.  https://doi.org/10.5194/essd-10-1551-2018 CrossRefGoogle Scholar
  43. Weigelt M (2017) The acceleration approach. In: Naeimi M, Flury J (eds) Global gravity field modeling from satellite-to-satellite tracking data. Lecture notes in Earth system sciences. Springer, Berlin, pp 127–160.  https://doi.org/10.1007/978-3-319-49941-3_4 Google Scholar
  44. Wiese DN, Landerer FW, Watkins MM (2016) Quantifying and reducing leakage errors in the JPL RL05M GRACE mascon solution. Water Resour Res 52:7490–7502.  https://doi.org/10.1002/2016WR019344 CrossRefGoogle Scholar

Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  1. 1.Geodesy and Geophysics LaboratoryNASA Goddard Space Flight CenterGreenbeltUSA

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