Geophysical Institute, University of Alaska Fairbanks How well do we know the North American frame today?: Differences between recent realizations and implications Jeff Freymueller Julie Elliott Geophysical Institute, University of Alaska Fairbanks

Topics You can fit velocities to a fraction of a mm/yr, but what is the real uncertainty in the NOAM frame? Uncertainty in underlying frame (ITRF) How precise is ITRF, really? Differences between NOAM angular velocities Sella et al. (2007) Initial SNARF pole

Uncertainty in ITRF Uncertainty in ITRF commonly ignored. The TZ rate difference (1.8 mm/yr) between ITRF2005 and ITRF2000 has gotten a lot of attention. There may actually be a similar (or larger) difference between ITRF2000 and ITRF97 If so, uncertainty in frame (geocenter origin) may be much larger than precision of GPS baseline rates.

ITRF2000 Velocities – Sella pole

ITRF2000 Velocities – other poles Black – Sella 2007 White – REVEL Yellow – SNARF Note systematic residual in REVEL, 2-3 mm/yr

NOAM Poles With past studies, it is common that NOAM poles do not lie within 95% confidence ellipses of other studies Systematic errors or missing uncertainty Difference between SNARF and Sella is a rotation about a pole in the SE United States.

This is Expected The least certain component of the plate’s angular velocity vector is a rotation about an axis through the centroid of the network. Consider the angular velocity vector of the plate expressed in the local east-north-up coordinates at a particular site:

The site’s velocity is Two components of the plate angular velocity are directly determined by the site’s velocity, while the third (local vertical component) is completely undetermined. When sites span a small area, their local vertical directions will be similar, and this component of the angular velocity will be the least well determined.

More About Angular Velocity We could resolve the undetermined component by taking a minimum norm solution: In this case the pole is located 90° away from the site. The pole could also be located anywhere on the great circle that lies between this minimum-norm solution and the site itself. The component of the angular velocity in the average radial direction will naturally be the least constrained.

Strategy for Augmented Covariance Sella and SNARF differ by almost 1 mm/yr in Alaska, significant relative to CGPS site velocities, and we really can’t tell which is “right” We thus augment the covariance in two ways: Add an uncertainty corresponding to the difference in angular velocity between Sella and SNARF Add an uncertainty in Zdot of 1.8 mm/yr as a conservative uncertainty in the ITRF.

Additional Uncertainty Rotation Only

Additional Uncertainty Rotation + Zdot

Augmented Covariance

Conclusions May be ~2 mm/yr frame differences between all past ITRFs, not just ITRF2000 to ITRF2005. 1.8 mm/yr in Tzdot between ITRF2000, ITRF2005 Probably 2-3 mm/yr between ITRF97, ITRF2000 Latest NOAM poles in ITRF2000 agree to with 0.3 mm/yr over the actual stable part of NOAM Difference is a rotation about a pole located on Gulf Coast Difference is ~ 0.5 mm/yr on west coast, almost 1 mm/yr in Alaska We propose an augmented covariance matrix for the NOAM angular velocity that we think is more realistic than the published covariance.