1. Assessing the GIA Contribution to SNARF Mark Tamisiea and Jim Davis Harvard-Smithsonian Center for Astrophysics

2. Outline Review (background) of GIA field in SNARF 1.0 Inclusion of GRACE data Radial (and geoid) only solutions Discussion –How the product will be used –How to assign/use/interpret rotational and translational terms

3. GIA Predictions: Requirements A model for the Earth’s viscoelastic structure A history of the time-dependent ice load Theory and code to convolve the time- dependent load with the viscoelastic Green’s functions, while simultaneously solving for effects due to the redistribution of the surface load (ice  water)

4. GIA Predictions: Practical Issues Uncertainties in viscosity structure and ice history Ice & Earth models are generally not independent (inversions nonunique) Generally, Earth models used to generate GIA predictions are spherically symmetric, but lateral variations are important

5. New Approach Treat model predictions as statistical quantities (Bayesian approach) Combine data and models using assimilation techniques (Kalman filter) How do we get model “uncertainties”? Calculate field mean, covariance over suite of reasonable Earth, ice models

6. Model Covariances Example: covariance of east component of deformation at point 1 with radial component of deformation at point 2: Covariance matrix has “physics” of GIA

7. Prior Correlation wrt ALGO

8. Given a geodetic solution with site velocities V GPS at locations (  ), we can describe the solution using The velocity rotation and translation parameters are unknown and must be estimated as part of the SNARF definition Definitions and Assumptions

9. GPS Data Assimilation We simultaneously estimate six rotation and translation para- meters, and GIA velocities at n grid locations and at m GPS sites At right, the parameter vector (u = east velocity, v = north, w = radial) The observations consist of (u,v,w) for GPS sites The GIA values at the grid locations are adjusted through the covariances calculated from the suite of model predictions

10. Assimilation (SNARF 1.0) Ice model: Ice-1 [Peltier & Andrews, 1976] Earth models: Spherically symmetric three- layer, range of elastic lithospheric thicknesses, upper and lower mantle viscosities (see Milne et al., 2001) Elastic parameters: PREM GPS data set: Velocities from “good” GPS sites, NAREF solution from Mike Craymer Placed in approximate NA frame by Tom Herring (unnecessary step but simpler)

11. SNARF 1.0 GIA Field Prefit statistics: WRMS (hor): 1.22 mm/yr WRMS (rad): 3.81 mm/yr WRMS (all): 1.74 mm/yr Postfit statistics: WRMS (hor): 0.71 mm/yr WRMS (rad): 1.30 mm/yr WRMS (all): 0.80 mm/yr

13. Changes, Recent Work Utilize ICE-5G [Peltier, 2004] Incorporate GRACE data –GRACE is insensitive to geocenter motion –Better spatial coverage Consider the extent to which horizontal velocities help (due to added info) or hurt (due to errors in the NA field or inaccuracies in the GIA predictions/correlations)

14. Complementary Data Set: GRACE GRACE time series now sufficiently long to extract rates Solution from CSR RL01 fields with GLDAS/Noah hydrological model removed

15. GRACE Only Geoid Prior (ICE-5G) Postfit

16. Deformations: GRACE Only vs. GRACE+GPS

17. GPS Only vs. GRACE+GPS

18. GRACE and … Radial Only vs. Radial + Horizontals

19. Conclusions The GRACE data set can significantly contribute to the GIA field used in SNARF Observed horizontal velocities don’t significantly alter the derived vertical GIA estimates When considering only the RMS reduction on of the GPS data, not much difference between ICE1 and ICE-5G. However, ICE- 5G does better with the geoid data.

20. Discussion How will the product be used? To that end, how do we define/use/interpret the estimated rotation and translation terms?