Alternative Gravity Field Representations: Solutions, Characteristics, and Issues

1. Alternative Gravity Field Representations: Solutions, Characteristics, and Issues Michael M. Watkins, Dah-Ning Yuan, Gerhard Kruizinga Jet Propulsion Laboratory California Institute of Technology GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

2. Overview • GRACE gravity validation solutions • Mascon modeling for surface mass variations • Characterisics • Issues • Mascon solution from GRACE KBRR data • Mascon solution from “filtered” GRACE KBRR residual • Summary GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

3. JPL GRACE Gravity Validation Solution • KBR1B, GPS1B, ACC1B, and SCA1B from GRACE L1B • AOD RL04 • FLINN GPS ephemeris and clock solution • Release 4 harmonic solutions from April 2002 to July 2007 • Stochastic GPS transmitter clock & GPS phase biases • Daily ACC biases, KBRR empirical biases every orbital revolution • Global 120x120 harmonic partials from KBRR data • Global 90x90 harmonic partials from GPS data GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

4. Mascon Modeling for Surface Mass Variation • Mascon models in MIRAGE software • Point mass, flat disk, spherical cap and spherical ring • Equal area or variable area (with latitude) • Compute direct gravity acceleration from mascons, no truncation from any conversion to harmonics • Same dynamic models, local parameterization, and reference orbit for GRACE as our harmonic solution. • Simultaneous solution for all mascon regions • Use both GPS and KBR data for solution GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

5. Advantages of Mascon Basis vs. Spherical Harmonic Basis Functions • The mass concentration solution is localized in both time and space. • Weakens correlations between regional solutions • Less “leakage” and propagation of long period errors • The application of spatial constraints are easier to implement than with spherical harmonics • Potentially higher temporal and spatial resolution than harmonic solution GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

6. Distribution of 4 Equal Area Spherical Caps GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

7. Monthly Smoothed Surface Mass Variation Mapfrom KBRR Mascon Solution

8. RA-Resid. Filter RR-Resid. RR-Obs. MIRAGE Gravity Solution Gravity Solution from Filtered KBRA Residual GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

9. Monthly Stacked Residual Map vsSmoothed Surface Mass Variation Map from Mascon SolutionUsing CRN filtered KBRA Residual

10. Issues on the Estimate of Mascon • Loading effect not included in the computation of perturbing force on a spacecraft • Optimal time and spatial correlation between the mascons • Apriori constraint for the mascons GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

11. Summary - I • JPL RL04 harmonic solutions are available from Apr. 2002 through Jul. 2007 (except Jun/03, Jul-Oct/04). • Mascon solutions computed for entire globe of Earth with KBRR are availabe from Jan. 2003 through Dec. 2007. • Surface mass variation map from mascons generally consistent with harmonics for large features but appear able to resolve and localize smaller features more cleanly. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

12. Summary - II • Stacked CRN filtered KBRA residual map provides the most detail RA anomaly in a geographical map. Thanks to the near realistic nominal mean gravity model. • Mascon solution using CRN filtered KBRA residual provides the cleanest surface mass variation map compared to KBRR solutions. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

13. Background Material GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

14. Harmonic Solution • FLINN GPS ephemeris and clock solution • Parameterization for GRACE orbit determination • Daily ACC biases • KBR empirical biases every orbital revolution • Stochastic GPS transmitter clock & GPS phase biases • Estimated gravity harmonics • 120x120 harmonic partials from KBRR data • 90x90 harmonic partials from GPS data. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

15. Background Model Improvement • Nominal gravity model - GIF22A to degree 180 • IERS 2003 • J2-dot, J3-dot, J4-dot, C21/S21-dot • solid earth tide • solid earth pole tide • Ocean tide using convolution formalism with weights derived from FES04 model to degree 90 (Desai) • Ocean pole tide SCEQ (Desai) model to 30x30 GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

16. Mascon Solution • Estimated globally distributed 4 equal-area spherical cap mascons • Optionally apply a spatial correlation of the form: • dijisthe angular distance between mascon i and j; • D is the correlation distance GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

17. Post-processing of Harmonic and Mascon Solutions in Surface Water Variations • Gaussian spectral smoothing with a spherical cap applied to harmonic solutions (Swenson and Wahr, 2002). • Gaussian discrete smoothing with a spherical cap applied to mascon solutions (Jekeli, 1981). GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

18. = Gaussian smoothing factor (Swenson and Wahr, 2002) = Load Love number = Normalized Legendre Function = Mean density of Earth = Density of water Post-processing of Harmonic Solution in Surface Water Variations GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

19. Monthly Surface Mass Variation Mapfrom KBRR Harmonics Solution

20. Gravity Solution from Filtered KBRA Residual • KBRR residual • CRN filter • KBRA residual • Monthly stacked residual map • Gravity solution (harmonics and mascon) • Monthly smoothed surface mass variation map GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

21. Future Works • Comparisons with hydrology models & in-situ data will be used for selection of solution strategy in general. • Mascon solution strategies • Submonthly intervals • Correlation between regional mascon solutions • Sensitivity to the modeling errors GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

22. Monthly Surface Mass Variation Map from L1B KBRA Mascon Solution

23. Monthly Surface Mass Variation Map from CRN filtered KBRA-only Mascon Solution