Ocean mass from GRACE and glacial isostatic adjustment

We examine geoid rates and ocean mass corrections from two published global glacial isostatic adjustment (GIA) models, both of which have been used in previous studies to estimate ocean mass trends from Gravity Recovery and Climate Experiment (GRACE) satellite gravity data. These two models are different implementations of the same ice loading history and use similar mantle viscosity profiles. The model results are compared with each other and with geoid rates determined from GRACE during August 2002 to November 2009. When averaged over the global ocean, the two models have rates that differ by nearly 1 mm yr-1 of ocean mass, with the first model giving a correction closer to 2 mm yr-1 and the second closer to 1 mm yr-1. By comparing the two models, we have discovered that 50\% of the difference is caused by a global (land + ocean) mean in the first model. While it is appropriate to include this mean when subtracting GIA effects from measurements of sea level change measured by tide gauges or satellite altimetry, the mean should not be included when subtracting GIA effects from ocean mass variations derived from satellite gravity data. When this mean is removed, the ocean mass corrections from the two models still disagree by 0.4 mm yr-1. We trace the residual difference to the fact that the first model also has large trends over the ocean related to large rates in its predicted degree 2, order 1 geoid coefficients. Such oceanic trends are not observed by GRACE nor are they predicted by the second model, and they are shown to be inconsistent with the polar wander rates predicted by the first model itself. If these two problems are corrected, we find that the two model predictions agree at the 3\% level. On the basis of this analysis, we conclude that the ocean mass correction for GRACE is closer to 1 mm yr-1 than 2 mm yr-1, although significant uncertainties remain.