Surface Deformations from Glacial Isostatic Adjustment Models with Laterally Homogeneous, Compressible Earth Structure

The zipped file contains global 1-degree grid files of four different surface deformation parameters: Horizontal velocity, North component (vnorth), in mm/a Horizontal velocity, East component (veast), in mm/a Vertical velocity (vup), in mm/a Geoid change (dgeoid), in mm/a calculated from a set of 26 different glacial isostatic adjustment models applying 10 different radially varying (=layered) earth structures and 3 different global ice models. The different earth structures and the available combinations with ice models can be found in the readme.pdf. File naming is simply {ice model}_{earth model}_{parameter}.grd. For example, anu-ice_f72_vup.grd is the global vertical velocity grid file calculated with a GIA model with ANU-ICE ice history and 60 km lithospheric thickness, 4E20 Pa s upper mantle viscosity and 2E21 Pa s lower mantle viscosity. Grid files (NetCDF format) were generated with GMT6 (Wessel et al., 2019), thus can be directly used. Ice thickness histories of ICE-6G_C (Argus et al., 20214; Peltier et al., 2015) and ICE-7G_NA (Roy & Peltier, 2017) were downloaded from W. R. Peltier’s data website at the University of Toronto, Canada: https://www.atmosp.physics.utoronto.ca/~peltier/data.php Note that the velocity field of ICE-6G_C(VM5a) can be compared to the one available from W. R. Peltier’s data website. The files provided here are not a substitute for the ones by W. R. Peltier and colleagues! Analyzing the difference between the files from this work and the ones available on the data website can help getting an error estimate from the two GIA model implementations (see further below). The user will find minor differences in the uplift component but larger ones in far field areas of the horizontal components. ICE-7G_NA(VM7) results are added as complement for interested users. However, note that ICE-7G_NA contains ice thickness history modifications in North America only and a fully global re-optimization of the ice thickness is warranted. Hence, excessive use and interpretation of these grid files, especially on global scale, should be avoided. ANU-ICE is a global 1-degree ice thickness model merged from several regional models (Lambeck, 1995; Fleming & Lambeck, 2004; Lambeck et al., 2010; 2014; 2017) kindly provided by Anthony Lambert and Kurt Lambeck, ANU, Canberra, Australia. The regional models contain differing spatial and temporal resolutions that were unified to fit the global 1-degree spatial resolution at mainly common time steps (500–1000 years). The Antarctic Ice Sheet part contains changes in the last time steps, thus some larger changes in the velocities can be found there. The software ICEAGE (Kaufmann, 2004) is used for calculating the grids, which applies the viscoelastic normal-mode method (Peltier, 1974; Wu, 1978). The sea-level equation is solved in a pseudo-spectral approach (Mitrovica et al., 1994; Mitrovica & Milne, 1998) in an iterative procedure in the spectral domain. See further details in Kaufmann and Lambeck (2000; 2002). The spherical harmonic expansion in the spectral domain is truncated at degree 192, which corresponds to ~1° spatial resolution. The models are spherically symmetric (1D), compressible, with Maxwell-viscoelasticity, rotational feedback, and time-dependent coastlines. The Earth’s core is, as assumed to be inviscid, incorporated as lower boundary condition. Rheological parameters such as depth-dependent density, Young’s modulus, etc., are taken from PREM (Preliminary Reference Earth Model; Dziewonski & Anderson, 1981). Acknowledgments HS would like to thank Jeff Freymueller for discussions on model selection. References Argus, D. F., Peltier, W., Drummond, R., Moore, A.W. 2014. The Antarctica component of postglacial rebound model ICE-6G_C (VM5a) based on GPS positioning, exposure age dating of ice thicknesses, and relative sea level histories. Geophysical Journal International 198, 537–563, doi:10.1093/gji/ggu140. Dziewonski, A. M., Anderson, D. L. 1981. Preliminary reference Earth model. Physics of the Earth and Planetary Interiors 25, 297–356, doi:10.1016/0031-9201(81)90046-7. Fleming, K., Lambeck, K. 2004. Constraints on the Greenland ice sheet since the Last Glacial Maximum from sea-level observations and glacial-rebound models. Quaternary Science Reviews 23, 1053–1077, doi:10.1016/j.quascirev.2003.11.001. Kaufmann, G. 2004. Program Package ICEAGE, Version 2004. Manuscript. Institut für Geophysik der Universität Göttingen. Kaufmann, G., Lambeck, K., 2000. Mantle dynamics, postglacial rebound and the radial viscosity profile. Physics of the Earth and Planetary Interiors 121, 301–324, doi:10.1016/S0031-9201(00)00174-6. Kaufmann, G., Lambeck, K., 2002. Glacial isostatic adjustment and the radial viscosity profile from inverse modeling. Journal of Geophysical Research Solid Earth 107, ETG 5-1-ETG 5-15, doi:10.1029/2001JB000941. Lambeck, K. 1995. Late Devensian and Holocene shorelines of the British Isles and North Sea from models of glacio-hydro-isostatic rebound. Journal of the Geological Society London 152, 437–448, doi:10.1144/gsjgs.152.3.0437. Lambeck, K., Purcell, A., Zhao, J., Svensson, N.-O. 2010. The Scandinavian ice sheet: from MIS 4 to the end of the last glacial maximum. Boreas 39 (2), 410–435, doi:10.1111/j.1502-3885.2010.00140.x. Lambeck, K., Rouby, H., Purcell, A., Sun, Y., Sambridge, M. 2014. Sea level and global ice volumes from the Last Glacial Maximum to the Holocene. Proceedings of the National Academy of Sciences of the United States of America 111 (43), 15296–15303, doi:10.1073/pnas.1411762111. Lambeck, K., Purcell, A., Zhao, J. 2017. The North American Late Wisconsin ice sheet and mantle viscosity from glacial rebound analyses. Quaternary Science Reviews 158, 172–210, doi:10.1016/j.quascirev.2016.11.033. Mitrovica, J. X., Davis, J. L., Shapiro, I. I. 1994. A spectral formalism for computing three–dimensional deformations due to surface loads: 1. Theory. Journal of Geophysical Research Solid Earth 99(B4), 7057–7073, doi:10.1029/93JB03128. Mitrovica, J. X., Milne, G. A. 1998. Glaciation-induced perturbations in the Earth’s rotation: a new appraisal. Journal of Geophysical Research Solid Earth 103, 985–1005, doi:10.1029/97JB02121. Peltier, W. R. 1974. The impulse response of a Maxwell Earth. Reviews of Geophysics and Space Physics 12(4), 649–669, doi:10.1029/RG012i004p00649. Peltier, W., Argus, D., Drummond, R. 2015. Space geodesy constrains ice age terminal deglaciation: The global ICE-6G_C (VM5a) model. Journal of Geophysical Research Solid Earth 120, 450–487, doi:10.1002/2014JB011176. Roy, K., Peltier, W. R. 2017. Space-geodetic and water level gauge constraints on continental uplift and tilting over North America: regional convergence of the ICE-6G_C (VM5a/VM6) models. Geophysical Journal International 210(2), 1115-1142, doi:10.1093/gji/ggx156. Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H. F., Tian, D. 2019. The Generic Mapping Tools version 6. Geochemistry, Geophysics, Geosystems 20, 5556–5564, doi:10.1029/2019GC008515. Wu P. 1978. The response of a Maxwell earth to applied surface mass loads: glacial isostatic adjustment. MSc thesis, University of Toronto, Toronto, Ontario, Canada.

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