1. Assessing the GIA Contribution to SNARF Mark Tamisiea, James Davis, and Emma Hill Proudman Oceanographic Laboratory Harvard-Smithsonian Center for Astrophysics

2. GIA Predictions 1)Ice history (both spatial and temporal) 2)Earth model a)mantle viscosity b)lithospheric thickness c)elastic parameters d)spherical symmetry 3)Theory, code

3. GIA Predictions 1)Ice history (both spatial and temporal) 2)Earth model a)mantle viscosity b)lithospheric thickness c)elastic parameters d)spherical symmetry 3)Theory, code Data generally used to constrain 1, 2a, and 2b.

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

5. Prior Correlation wrt ALGO

6. 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 Frame Parameters

7. Assimilation (SNARF 1.0) Parameters: –3-D GIA deformations –GPS reference frame parameters Data –GPS solution (T. Herring, E. Calais, M. Craymer) Locations: 2°  2° grid plus GPS sites GIA models –Milne et al. [2001] Earth models –ICE1 [Peltier & Andrews, 1976] Approach –sequential least-squares, “inside-out” algorithm

8. 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 SNARF 1.0 GIA Field

10. Changes, Recent Work ICE-5G [Peltier, 2004] Denser GPS solution [Sella et al., 2007] Tests exploring –Impact of starting model –Ability to recover motions caused by 3D Earth structure –Assimilating GRACE data –Contribution of horizontal velocity observations to vertical velocity solution

11. GIA Field Using ICE-5G Prefit statistics: WRMS (hor): 1.27 mm/yr WRMS (rad): 5.95 mm/yr WRMS (all): 2.36 mm/yr Postfit statistics: WRMS (hor): 0.69 mm/yr WRMS (rad): 1.27 mm/yr WRMS (all): 0.78 mm/yr

12. Impact of Different GPS Solution SNARF 1.0Sella et al., 2007

13. Difference

14. Frame Parameters

15. Impact of Background Model

16. Ability to Recover Differences Caused by 3D Structure

18. 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

19. 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

20. 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)