The materials contained in this section of the paper consist of Figures S1, S2, S3 and S4 plus the four tables referred to in the main text, respectively those labeled S1, SS1, and S2, SS2. Figure S1 compares the viscosity profiles VM2 and VM5a referred to in the text together with the VM1 viscosity profile that served as first guess profile in the Bayesian inversion that was employed to produce VM2 as described in Peltier (1996).The tables come in pairs. For example, Table S1 lists the observed results for the vertical and horizontal rates of motion of the crust for all of the North American and Greenland sites for which GPS data is available based upon the reanalysis of the global data set of Desai et al (2011). Also listed in Table S1 are the predictions of the rates of vertical motion of the crust of the new ICE-6G_C (VM5a) model. Immediately following this table is Table SS1 which lists the locations from which North American sea level data have been selected and which have been employed to test the multi-millennial year predictions of relative sea level history for the new ICE-6G_C (VM5a) model of the global process of glacial isostatic adjustment. Following the table listing the locations and references to the data sources for these RSL histories, is a listing of the citations to the peer reviewed publications in which the data for these sites is found. The additional tables in this Supplementary Materials section are the corresponding sets of tables of GPS observations and model predictions and sea level bibliographies for Fennoscandia which are labeled S2, and SS2.. Figure S1 is shown first followed by Figures S2, S3 and S4. The latter three figures compare maps of the vertical motion predictions for North America, Fennoscandia and Antarctica with approximations to these maps based upon the empirical approximation to the vertical motion field suggested by Purcell et al (2011) based solely upon the Stokes coefficients in terms of which the time dependence of the gravitational field is described based upon GRACE satellite observations. Approximations to the vertical motion field are shown on these figures using Stokes coefficients for both degree and order 60 and for degree and order 256. Also shown on these figures are the differences between the exact vertical motion solution for model ICE-6G_C (VM5a) and these two Stokes coefficient based approximations. These difference fields allow quantitative recognition of the errors associated with the use of the empirical approximation. These figure are followed in this Supplementary Materials file by the two sets of two Tables discussed above which list the GPS observations and model predictions of vertical motion for the two target regions as well as the names and data sources for the sites from which relative sea level data have also been employed to produce the new ICE-6G_C (VM5a) model..
Figure S1. Comparison of the radial viscosity profiles VM1, VM2, and VM5a discussed in the text.
Figure S2. (a) the rate of vertical motion of the crust predicted for the North American continent by the ICE-6G_C (VM5a) model of the glacial isostatic adjustment process, which is based upon a spherical harmonic expansion complete to degree and order 256. (b) the approximation to the correct vertical motion field shown in (a) based upon the empirical formula of Purcell et al (2011) that is in turn based upon the geoid Stokes coefficients of the ICE-6G_C (VM5a) model listed in the Supplementary file SStokes_256 but using only Stokes coefficients up to degree and order 60. (c) same as (b) but using the complete set of Stokes coefficients to degree and order 256. (d) the difference between the approximate field in (b) and the exact field in (a), that is (d)=(b)-(a). (e) the difference between the approximate field in (c) and the exact field in (a), that is (e)=(c)-(a). Note that the scale of the color bar for plates (d) and (e) is linear whereas that in plates (a)-(c) is not.. The point of this figure and those which follow for Fennoscandia and Antarctica is to demonstrate that the errors evident in plates (d) and (e) are not significantly diminished when the empirical formula of Purcell et al. (2011) is applied to the complete set of geoide Stokes coefficients rather than only to the geoide Stokes coefficients up to degree and order 60 which is the limited range over which the authors considered the empirical formula to most reasonably apply. Errors in the empirical prediction are small over the continental interior (<~1mm/yr) but significant in regions in which the water load is continuing to change.
Figure S3. Same as Figure S2 but for Fennoscandia
Figure S4. Same as Figure S2 but for Antarctica. It is in this region that the errors in the prediction using the formula of Purcell etal (2011) are especially large, so large as to apparently render the formula inapplicable for the prediction of vertical motion of the crust on the basis of the geoide Stokes coefficients. Further analysis which is outside the scope of the present paper will be required to determine the reason for the degradation of the accuracy of the empirical model in the polar region.
Table S1. North American observed site velocities and ICE-6G_C (VM5a) vertical predictions