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Assessing the GIA Contribution to SNARF. Mark Tamisiea, James Davis, and Emma Hill Proudman Oceanographic Laboratory Harvard-Smithsonian Center for Astrophysics. GIA Predictions. Ice history (both spatial and temporal) Earth model mantle viscosity lithospheric thickness
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Assessing the GIA Contribution to SNARF Mark Tamisiea, James Davis, and Emma Hill Proudman Oceanographic Laboratory Harvard-Smithsonian Center for Astrophysics
GIA Predictions • Ice history (both spatial and temporal) • Earth model • mantle viscosity • lithospheric thickness • elastic parameters • spherical symmetry • Theory, code
GIA Predictions • Ice history (both spatial and temporal) • Earth model • mantle viscosity • lithospheric thickness • elastic parameters • spherical symmetry • Theory, code Data generally used to constrain 1, 2a, and 2b.
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
Frame Parameters • Given a geodetic solution with site velocities VGPS at locations (l,f), we can describe the solution using • The velocity rotation and translation parameters are unknown and must be estimated as part of the SNARF definition
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
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
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
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
Impact of Different GPS Solution SNARF 1.0 Sella et al., 2007
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
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
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)