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

2. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

3. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

4. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

5. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

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

7. Monthly Smoothed Surface Mass Variation Map from KBRR Mascon Solution

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

9. Monthly Stacked Residual Map vs Smoothed Surface Mass Variation Map from Mascon Solution Using CRN filtered KBRA Residual

10. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

11. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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.

12. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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.

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

14. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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.

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

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

17. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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). Post-processing of Harmonic and Mascon Solutions in Surface Water Variations

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

19. Monthly Surface Mass Variation Map from KBRR Harmonics Solution

20. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

21. GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany 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

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

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