W12a GIA Model, version 1: Notes -------------------------------- [last updated 6th November 2012] All queries to Pippa Whitehouse (pippa.whitehouse@durham.ac.uk) When referring to the W12a GIA model, please use the citation 'Whitehouse, P.L., Bentley, M.J., Milne, G.A., King, M.A., Thomas ,I.D., 2012. A new glacial isostatic adjustment model for Antarctica: calibrated and tested using observations of relative sea-level change and present-day uplift rates. Geophysical Journal International 190, 1464-1482.' doi:10.1111/j.1365-246X.2012.05557.x The ice model used is described in Whitehouse P.L., Bentley, M.J., Le Brocq, A.M., 2012. A deglacial model for Antarctica: geological constraints and glaciological modelling as a basis for a new model of Antarctic glacial isostatic adjustment. Quaternary Science Reviews 32, 1-24. doi:10.1016/j.quascirev.2011.11.016 Introduction ------------ This directory contains model predictions for present-day changes in geoid and uplift rates, derived using the W12a Antarctic glacial isostatic adjustment (GIA) model (Whitehouse et al., 2012a; 2012b). Geoid rates are provided as files of time derivatives in Stokes coefficients (the 'grate_X_v1.clm' files; standard normalisation) and as a lon/lat grid of geoid rates (the 'grate_X_v1.txt' files; units of mm/yr). Uplift rates are provided in grid format only ('urate_X_v1.txt'; mm/yr). Columns in the .txt files are longitude, latitude, geoid/uplift rate. The lon/lat grid extends from 90S to 55S, and is defined at 0.5 degree intervals in both longitude and latitude. Results are provided for three different GIA models (denoted by 'X' in the file names) to give a total of 3 x 3 = 9 data files. The three GIA models define the 'best' model ('B'), and lower ('L') and upper ('U') bounds for the GIA correction across Antarctica (see the section entitled Uncertainty-1). These three models are identical to the models that were used in the Ice sheet Mass Balance Inter-comparison Exercise (IMBIE)(Shepherd et al., in press). Information relating to the ice history and Earth models used in the three GIA models is given below. In addition, the file urate_envelope.txt contains more conservative lower and upper bounds for GIA-driven uplift rates across Antarctica, as used in King et al (2012). Stokes coefficients for these bounds will be added to this directory soon. Further details are given below in the section entitled Uncertainty-2. Please note that the Stokes coefficients should only be used in Antarctic GRACE analyses. The GIA model is a global model, but has not been tuned to fit far-field sea-level records, and so should not be used in the 'far-field' (i.e. north of 55S) or for global analyses. GIA Model --------- A GIA model must be driven by an ice model. The deglacial ice model used in the W12a model has two components; an Antarctic component and a far-field component. The Antarctic component is the model published by Whitehouse et al. (2012a). It is derived using a numerical ice-sheet model (Glimmer) forced by the Vostok/EPICA Dome C climate records and calibrated to match observations of ice extent. Whitehouse et al. (2012a) derive 16 deglaciation reconstructions that all give a reasonable fit to the ice extent data. The reconstructions differ slightly in the climate forcing, basal heat flux, Earth rheology and sea-level forcing used. Please see the original publication for further details. The model that gives the smallest rms misfit to observations of former ice extent is defined to be the 'best' deglacial reconstruction (Whitehouse et al., 2012a). However, all 16 models are used to define bounds for the final GIA model (see below). Each Antarctic deglacial reconstruction is embedded in the far-field component of the ICE-5G model (Peltier, 2004). This creates a set of global deglaciation models that can be used to drive a GIA model. The global deglacial models are combined with an 'Earth model' (a parameterisation of the rheological response of the Earth to loading) in order to solve the sea-level equation (Farrell and Clark, 1976), and make predictions of relative sea-level change, uplift rates and geoid rates. 297 different Earth models are tested; see Whitehouse et al. (2012b) for further details. The single deglaciation history/Earth model combination that gives the best fit to the Antarctic RSL data set is sought. This combination defines our 'best' (labelled 'B', see below) GIA model for Antarctica. The GIA model output includes the influence of ocean loading (sea-level changes) and GIA-induced perturbations to Earth rotation. The rotational component is based on the revised theory described in Mitrovica et al. (2005). To compute to ocean loading, we solve the sea-level equation presented in Mitrovica and Milne (2003) using the algorithm described in Kendall et al. (2005). Points to Note -------------- 1. The rates provided only account for the viscous response at present due to load changes (ice and ocean) up to 100 years ago. More recent ice-load changes can strongly influence the GIA signal, especially in low viscosity regions (e.g. Nield et al., 2012). 2. Uplift rates are provided in the centre of mass (CM) reference frame, and do not include present-day mass change effects. Both factors should be taken into account when comparing model output to GPS rates. 3. Degree zero and degree one terms are both zero in our solutions. 4. We re-iterate that the Stokes coefficients should only be used in Antarctic GRACE analyses. They should not be used for global analyses, and they do not provide an accurate correction for e.g. GIA in Greenland. W12 versus W12a ----------------------- The 'best' deglaciation model of Whitehouse et al. (2012a) is referred to as the W12 deglaciation model in Whitehouse et al. (2012b). In developing the final GIA model, after combining the W12 deglaciation model with an Earth model, GIA model output was compared with GPS data. Following initial comparisons, an adjustment was made to the deglacial history in the Antarctic Peninsula during the last 1000a to reflect changes not captured by the numerical ice model, and to give a better fit to GPS data in this region (Whitehouse et al. 2012b). The deglacial model that includes this adjustment is referred to as the W12a model (Whitehouse et al., 2012b). This latter version is incorporated into all the GIA models contained in this directory, and the GIA model should therefore be referred to as the W12a GIA model. The details of the modification to W12 to provide W12a are described in full in Whitehouse et al. (2012b). Note that in this release we do not include the modification to W12a along the Siple Coast, which was used in King et al. (2012)(See their Supplementary Information (section 3)). Uncertainty-1 ------------------ In addition to providing the model that best fits the RSL data, two further models that fit the RSL data well (95% confidence) were provided to the IMBIE exercise: Both these models form a self-consistent solution to the sea-level equation, and they describe the upper ('U') and lower ('L') bounds for the GIA model insofar as they are the models, chosen from all of the deglaciation history/Earth model combinations, that give the largest and smallest maximum geoid rates. All three models use the 'best' deglaciation model (Whitehouse et al., 2012a). Brief details of the Earth models used are given below, further details can be found in Whitehouse et al. (2012b). Model 'B' (best model): lithospheric thickness (LT) = 120 km upper mantle viscosity (UM) = 1.0 x 10^21 Pas lower mantle viscosity (LM) = 10 x 10^22 Pas Model 'L' (lower bound): LT = 120 km UM = 1.0 x 10^21 Pas LM = 5.0 x 10^21 Pas Model 'U'(upper bound): LT = 96 km UM = 0.8 x 10^21 Pas LM = 20 x 10^21 Pas Uncertainty-2 ------------------ More conservative bounds on the GIA correction have also been determined by seeking the maximum and minimum predicted uplift rate at each grid point (0.5-degree grid) for all deglacial history/Earth model combinations. This was achieved in three steps: 1. Uncertainty due to the deglaciation history was determined by seeking the maximum/minimum predicted uplift rates across all 16 deglacial models defined in Whitehouse et al. (2012a). In each case the deglacial model was combined with the 'best' Earth model (model B above). 2. Uncertainty due to the Earth model was determined by seeking the maximum/minimum predicted uplift rates across all 17 Earth models that gave a good fit (95% confidence) to the Antarctic relative sea level (RSL) data set (Whitehouse et al., 2012b). In each case the Earth model was combined with the 'best' deglaciation history (Whitehouse et al., 2012a). In both cases, the upper and lower bounds of the resulting 'envelope' of uplift rates were expressed as the difference between the max/min uplift rate at each point and the uplift rate for the 'best' ('B') GIA solution at each point. Therefore, lower bound values are <=0, and upper bound values are >=0. 3. Upper and lower bounds for the uncertainty due to the deglaciation history and the uncertainty due to the Earth model were summed at each grid point, to give conservative upper and lower bounds on the total uncertainty, expressed in terms of uplift rates. Note that the surfaces of this envelope do not form a self-consistent solution to the sea-level equation. Uplift rate differences that describe the envelope of solutions are given in urate_envelope.txt; the columns of this file are longitude, latitude, lower bound, upper bound, where the bounds are in mm/yr. The uplift rates defined by the above analysis were used to define the 'systematic error' on the solutions presented in King et al. (2012). In order to determine this systematic error, the uplift rates were converted to geoid rates following the method of Purcell et al. (2011). A file containing these geoid rates, and further details on their calculation, will be added to this directory soon. Pippa Whitehouse November 6th 2012. References ---------- Farrell, W.E., Clark, J.A., 1976. On Postglacial Sea Level. Geophysical Journal of the Royal Astronomical Society 46, 647-667. Kendall, R.A., Mitroviva, J.X., Milne, G.A., 2005. On post-glacial sea level: II. Numerical formulation and comparative results on spherically symmetric models. Geophysical Journal International 161 (3), 679-706. King M.A. et al., 2012. Lower satellite-gravimetry estimates of Antarctic sea-level contribution. Nature, doi:10.1038/nature11621. Mitrovica, J.X., Milne, G.A., 2003. On post-glacial sea level: I. General theory. Geophysical Journal International 154 (2), 253-267. Mitrovica, J.X., Wahr, J., Matsuyama, I., Paulson, A., 2005. The rotational stability of an ice-age earth. Geophysical Journal International 161, 491-506. Nield, G.A. et al., 2012. Increased ice loading in the Antarctic Peninsula since the 1850s and its effect on glacial isostatic adjustment . Geophysical Research Letters 39, L17504. Peltier, W.R., 2004. Global glacial isostasy and the surface of the ice-age earth: the ICE-5G (VM2) model and grace. Annual Review of Earth and Planetary Sciences 32, 111-149. Purcell, A. et al., 2011. Relationship between glacial isostatic adjustment and gravity perturbations observed by GRACE. Geophysical Research Letters 38, L18305. Shepherd, A. et al., in press. A Reconciled Estimate of Ice Sheet Mass Balance. Science, in press. Whitehouse, P.L, Bentley, M.J., Le Brocq, A.M., 2012a. A deglacial model for Antarctica: geological constraints and glaciological modelling as a basis for a new model of Antarctic glacial isostatic adjustment. Quaternary Science Reviews 32, 1-24. Whitehouse, P.L., Bentley, M.J., Milne, G.A., King, M.A., Thomas ,I.D., 2012b. A new glacial isostatic adjustment model for Antarctica: calibrated and tested using observations of relative sea-level change and present-day uplift rates. Geophysical Journal International 190, 1464-1482.