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.