Assessing the GIA Contribution to SNARF

Mark Tamisiea, James Davis, and Emma Hill

Proudman Oceanographic LaboratoryHarvard-Smithsonian Center for Astrophysics

GIA Predictions

1) Ice history (both spatial and temporal)2) Earth model

a) mantle viscosityb) lithospheric thicknessc) elastic parametersd) spherical symmetry

3) Theory, code

GIA Predictions

1) Ice history (both spatial and temporal)2) Earth model

a) mantle viscosityb) lithospheric thicknessc) elastic parametersd) spherical symmetry

3) 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

Prior Correlation wrt ALGO

• Given a geodetic solution with site velocities VGPS 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

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

Prefit statistics:

WRMS (hor): 1.22 mm/yrWRMS (rad): 3.81 mm/yrWRMS (all): 1.74 mm/yr

Postfit statistics:

WRMS (hor): 0.71 mm/yrWRMS (rad): 1.30 mm/yrWRMS (all): 0.80 mm/yr

SNARF 1.0 GIA Field

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/yrWRMS (rad): 5.95 mm/yrWRMS (all): 2.36 mm/yr

Postfit statistics:

WRMS (hor): 0.69 mm/yrWRMS (rad): 1.27 mm/yrWRMS (all): 0.78 mm/yr

Impact of Different GPS Solution

SNARF 1.0 Sella et al., 2007

Difference

Frame Parameters

Impact of Background Model

Ability to Recover Differences Caused by 3D Structure

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)