Note: use paragraph below… The ice sheet provided for PMIP3/CMIP5 LGM experiments is a blended product obtained by averaging three different ice sheets: * ICE6G provided by Dick Peltier * MOCA provided by Lev Tarasov * ANU provided by Kurt Lambeck A short description and references for the different ice sheets is provided under the link below: LGM icesheet description This solution was proposed by PMIP bureau in light of a community checking. Given the uncertainties that still exist on the reconstruction of the ice-sheet, resulting from uncertainties in datation for the data used for global or regional constraints, climate intput from ice core temperature reconstructions or climate model simulations, etc… it sounds reasonable to consider that the average is a best estimate of the LGM ice-sheet.

Several PMIP participants were in favour of using a new ice-sheet reconstruction for PMIP3/CMIP5 that better matches the geomorphologic and glaciological constraints than the ICE-5G reconstruction used in PMIP2.

Therefor we have decided to have

• a) A reference ice-sheet for the core CMIP5 simulations
• b) alternatives ice-sheets propositions for groups interested to run sensitivity experiments in order to discuss the sensitivity of the model results to the uncertainties in boundary conditions. If you are interested by participating to these coordinated sensitivity experiments, please contact Ayako Abe-Ouchi (abeouchi@ccsr.u-tokyo.ac.jp)

Several documents and figures, as well as discussion and comments from the community can be found on the PMIP ice-sheet discussion page Ice Sheet discussion

Procedure to make the averages.

0. Sources:

1. <H, RSL> ANU ice model (2009) incl. British area (*1)
2. <s, mask> ICE-6G v1.02
3. <H, s> GLAC-1 nn454 model for North America, and ne8234 for Eurasia

 H:    thickness
 s:    surface topography
 mask: ice or not

*1 Only the ice thickness at 20ka is provided for the British region

  at the moment.  RSL is computed with assumption of mantle density
  4500 kg m-3.
  Surface elevation at LGM is computed as follows:
    s[LGM,ANU] = s[present,ICE-6G] + H[LGM,ANU] - RSL[LGM,ANU]

1. Interpolation on to ICE-6G domain

/ICE-6G domain/
  lon [0, 1, ..., 359]
  lat [-89.5, -88.5, ..., 89.5]

Gridpoints out of the sources are set `Undefined'

• Resolution Notes*

ANU Antarctica [-179,180] x [-89.5,-61.5] 1 deg

         Eurasia            [0,115.5]       x [50.25,83]      0.5 deg
         North AMerica      [-139,-7]       x [38,84.5]       0.5 deg
         British            [-10,-2]        x [52,59]         1 deg
  GLAC-1 North America      [187.5,354.5]   x [34.75,84.25]   1 x 0.5 deg
         Eurasia            [347.25,479.25] x [48.125,83.125] 0.5 x 0.25 deg

2. Average

The average is computed as follows:
  X(ave) = [X(ANU) + X (6G) + X(GLAC-1)] / <Number of `defined' grids>

X(ANU or GLAC-1) = X (if defined)
              or = 0 (if undefined)

3. Plots

antarctica21ka.pdf

In the surface topography plots, light green indicates that the
elevation at the gridpoint is below zero;  brown is above zero but
not covered by ice; grey or blank region are `undefined' gridpoints.

Number of `defined` grids are plotted besides the average in the
NH figure.  Red = 1, Blue = 2, Magenta = 3.
By this configuration; Magenta corresponds to the ANU domain,
magenta and blue to GLAC-1 domain, and all region to the ICE-6G
domain, respectively.
There is a region of isolated red at the north of Alaska.  This is
because of the `undefined' grids in the GLAC-1 source.  I have no
idea why this isolated region is undefined in the GLAC-1.

Average surface topography shows straight coastline at the Bering
strait on the Alaska part.  This reflects the original GLAC-1 data.
I think this region should be skipped when averaging, but this is
just a quick-look.

Number of `defined` grids are NOT plotted in the SH figure.
But, this is easily deduced by other two plots. 

For those interested in sensitivy experiments below is more details of the different ice-sheets anf the acess to the corresponding files.

Using new calibrations and a revised version of his model, Dick Peltier proposes a revised version of the ice-sheet that should better match the different paleo data. The following figures are based on data supplied by Dick Peltier and Rosemarie Drummond (Sept 4th 2009 version).

Note: get in touch with Jean-Yves Peterschmitt in you need a copy of the following papers. * Peltier, W.R., 2009, Closure of the budget of global sea level rise over the GRACE Era: The importance and magnitudes of the required corrections for global glacial isostatic adjustment. Quat. Sci. Rev. 28, 1658-1674.

• Donald F. Argus and W. R. Peltier, 2009. Constraining models of postglacial rebound using space geodesy: A detailed assessment of model ICE-5G (VM2) and its relatives, Geophysical Journal International, submitted.

• W.R. Peltier and R. Drummond, 2008. Rheological stratification of the lithosphere: A direct inference basd upon the geodetically observed pattern of the glacial isostatic adjustment of the North American continent. geophys. res. Lett., vol. 35, L16314, doi:10.1029/2008GL034586.

• W. R Peltier, D. F. Argus, R. Drummond, R Gyllencreutz, J. Mangerud, J-I Swensen, and O. S. Lohne, Space Geodesy Constrains Ice-Age Terminal Deglaciation, Nature, submitted

• Get in touch with Jean-Yves Peterschmitt if you want to download the netcdf files

A comparison between the different versions of ICE-nG is provided on the pdf document ice-ng_compare_polar.pdf(56 Mb, 77 pages)

The Greenland model is from Tarasov and Peltier (2002 and 2003), a glaciological model with hand-tuned climate adjustments to enforce fit to Relative Sea-Level (RSL) records and the GRIP borehole temperature record. It was also validated against observed rated of present day uplift for 3 sites and against GPS measurements for horizontal ice surface velocity. A variant of it is the Greenland component of ICE-5G and ICE-6G.

The North American and Eurasian reconstructions are objective Bayesian calibrations of the MUN/UofT glacial systems model. The latter incorporates a 3D thermo-mechanically coupled (shallow) ice-sheet model, with permafrost resolving bed-thermal model, asynchronously coupled down-slope surface drainage/lake depth solver, and various other components such as a thermodynamic lake ice, sub-glacial till-deformation, bouyancy and temperature dependant calving law, ice-shelf represention, …, some of which are described in Tarasov and Peltier, QSR 2004, and Nature 2005, and a more complete description is currently being written up). The visco-elastic bedrock response uses either the VM2 (as used in ICE-5G) or VM5a (used in ICE-6G) earth rheologies. Relative Sea Level is computed using a gravitationally self-consistent formalism similar to that of Peltier, except for an eustatic approximation for dealing with changing ocean masks and the lack of accounting for rotational effects (which are mostly significant for far-field RSL records, ie records that do not locally constrain ice load history).

Climate forcing involves an interpolation between present day observed climatologies and the set of highest resolution LGM fields from PMIP I and II data sets. The interpolation is weighted according to a glaciological inversion of the GRIP record for regional temperatures over the last glacial cycle.

The calibration involves approximately 30 (currently 36 for North Am, 29 for Eurasia) ensemble parameters to capture uncertainties in deglacial climate and ice dynamics. The majority of these parameters are used for the climate forcing, including weighting the inter-model (ie between PMIP models) EOFs for LGM monthly precip and temperature, regional desert elevation effects, and LGM atmospheric lapse rate. Other ensemble parameters adjust calving response, effective viscosity of subglacial till, strength of margin forcing, and flow parameters for ice-shelves. Model runs are forced to stay within uncertainties of the independently derived ice margin chronologies (Dyke, 2004 for North Am, Gyllencreutz et al, in preparation for Eurasia).

Model runs cover a full glacial cycle. North America and Eurasia are calibrated separately. Calibration targets include a large set of RSL observations, geologically-inferred deglacial ice-margin chronologies, and geodetic constraints. For the case of North America, the calibrated ensemble is further scored with respect to strand-lines (paleo lake level indicators) and Marine Limit (maximum level of marine inundation) observations. A key point is that model runs are penalized in proportion to the amount of margin forcing required. So the calibration is directed towards a climate forcing that is consistent with the margin chronology.

The model was calibrated using the ICE4G ice load reconstruction for Antarctica and the VM2 earth rheology because the ICE6G Antarctic chronology and VM5a earth model along with a much expanded geodetic dataset were provided by Dick Peltier only in early September, which left too little time to recalibrate the models. There is the added issue that the ICE6G Antarctic chronology lacks error bars. The expanded geodetic data-set for North America included significant revisions to the previous geodetic constraints. This along with the significant reduction in LGM ice volume in ICE6G Antarctic as compared to ICE4 and 5G rendered a significant misfit with the far-field Barbados RSL record. With the limited time, a somewhat blind and largely random 2000 member ensemble was generated along with a rerun of the best 300 previously calibrated parameter sets and some 200 attempts at hand-tuning. nn450 is the weighted distribution of 7 model runs that passed certain hard threshold constraints. nn9021 is the best (though “best” depends to a certain extent on the weighting between various constraints) single run from the previous calibration and nn445 is the weighted ensemble mean for that previous calibration.

The Eurasian calibration did converge, and aside from issues with the Norwegian fjords (the latter are also a problem for ICE6G), the calibration was generally successful. nn8234 is one of the best runs with the largest 26ka RSL contribution to the Barbados record. A single run was chosen to ensure consistency between drainage fields and the surface topography. The mean distribution for the calibration can be made available upon request.

In summary, the GLAC-1 submission provides a set of glaciological models that are derived from a plausible climate forcing based on PMIP1 and PMIP2 results for LGM and that fit independently derived ice margin chronologies. This provides strong constraints throughout deglaciation. For Eurasia, the smaller set of constraints (among other more speculative reasons) resulted in a successful calibration that reasonably well covered the available constraint set. North America has a much larger and much more diverse set of constraints (and I suspect a much more complicated ice/climate interaction history), so the calibration has never been able to fully satisfy the whole set of constraints (strandlines are for instance a challenge to fit given their high sensitivity to drainage choke point elevations).

Unfortunately, these glaciological models in combination with the ICE-6G chronology for Antarctica (and Patagonia) and Dick Peltier's VM5a earth rheology have at best a weak fit to the the LGM segment of the Barbados record. There is a significant tradeoff between Barbados fit and fit to other constraints. What is unclear at this stage is the extent to which this is due to deficiencies in the glaciological models, to problems with the ICE-6G Antarctic ice chronology, or possibly with inferred uncertainties in the Barbados record and with the VM5a earth rheology.

One possibility for resolving Barbados, is to take the 1.5 sigma upper limit of the previously calibrated ensemble for North America which almost reaches the inferred Barbados record for 26 to 21 ka. Dick Peltier and Rosemarie Drummond will cross-check this dataset. The problem with using ensemble bounds is that this is no longer a glaciologically self-consistent model and RSL fits have also deteriorated.

• Tarasov, L., and W. R. Peltier, Greenland glacial history, borehole constraints, and Eemian extent, J. Geophys. Res., 108(B3), 2143, doi:10.1029/2001JB001731, 2003
• Tarasov, L., and W. R. Peltier, Greenland glacial history and local geodynamic consequences, Geophysical Journal International, Volume 150, Pages 198-229, doi:10.1046/j.1365-246X.2002.01702.x, 2002
• Tarasov, Lev and Arthur S. Dyke and Radford M. Neal and W. R. Peltier, A data-calibrated distribution of deglacial chronologies for the North American ice complex from glaciological modeling, Earth and Planetary Science Letters, Volumes 315–316, 15 January 2012, Pages 30-40

• Get in touch with Lev Tarasov or Jean-Yves Peterschmitt if you want to download the following NetCDF files:
  • NetCDF of 21 to 10ka surface elevation, thickness, basal velocities for the nn454 North Am model and nn8234 Eurasian model: NAnn454.nc, EAnn8234.nc
  • NetCDF of 21 to 10ka for nn445 ensemble means and 1.5 sigma range: NAnn445.nc
• Other data available upon request from Lev Tarasov

The ANU Ice Model description and data have been supplied by Kurt Lambeck

The ANU ice sheets are based on the inversion of geological sea level and shoreline data supplemented by observational evidence of ice margin locations and, in a few instances, by limiting ice thickness estimates.

These models have evolved over a period of years in an iterative fashion. Broadly, the first iterations are based on the analyses of far-field data where the sea-level signal is predominantly a measure of the changes in total ice volume (the ice-volume equivalent sea level or esl) with the principal isostatic component often being the water-load term and a function of the rate at which water is added into or removed from the oceans. Simple models are initially used for the ice sheets. The separation of mantle rheology from the esl function is achieved by using the spatial variability of the far-field sea-level signals (Nakada and Lambeck, 1990 #127 see http://rses.anu.edu.au/people/lambeck_k/index.php?p=pubs for references). The resulting ice function is then redistributed between the ice sheets by using simple scaling relations in the first place and the process is iterated to ensure some convergence (Lambeck, Yokoyama and Purcell, 2002 # 228).

In parallel inversions are attempted for the individual ice sheets using data from within and close to the ice margins. These observations are most sensitive to the ice models and mantle rheology. For the northern hemisphere these analyses are carried out separately for Scandinavia (Lambeck, Smither, and Johnston, 1998 #187, Lambeck et al., in press), Barents-Kara (Lambeck, 1995, 1996 #166, 170), Greenland (Fleming and Lambeck, 2004 #238), British Isles (Lambeck, 1993; 1995 #164, 156) and North America (as yet unpublished). In all cases new compilations of the field data have been made. These separate solutions allow for lateral variability in mantle viscosity. Some interactions between the ice sheets occur and the solutions are therefore iterated.

The Antarctic field data is insufficient for a similar analysis for the southern hemisphere and we use the difference between the global esl and the northern hemisphere esl to estimate the volume changes for Antarctica eslant (allowing for mountain deglaciation in both hemispheres, Lambeck and Purcell, 2005 #247). The ice in Antarctica is then distributed according to the LGM ice margins proposed by Anderson et al. (2002) and on the assumption that the ice profiles followed the quasi-parabolic function proposed by Paterson. The retreat history is determined by the eslant function. These models are not meant to be accurate reflections of the Antarctic ice history but as a convenient way of disposing of the ice volume that cannot be attributed to the northern hemisphere, in a way that will not impact in a major way on the far-field and northern hemisphere analyses.

With the new ice models the far-field analysis is repeated and the individual ice sheet analyses are also repeated. Several such iterations have now been carried out but the successive results have not yet been published. The LGM results provided here represent the most recent (2009) solution. The full solutions for some of the ice sheets extend back to MIS-6 (Lambeck et al., 2006 # 252).

The rebound inversions result in the changes in ice thickness compared to the present day ice volumes. Thus the LGM ice thickness is obtained by adding the present-day ice thickness. The LGM ice elevation, with respect to sea level at the LGM is obtained by subtracting the sea-level change (geoid change beneath the ice sheet) from the palaeo ice thickness.

The esl function as used in the ANU solutions is defined as all land ice and grounded ice on the shelves and the ocean margin at the LGM is defined by the ice grounding line (Lambeck et al., 2003 #233).

• Lambeck & Johnston, 1998: The viscosity of the mantle: evidence from analyses of glacial rebound phenomena. “The Earth's Mantle” (ed. I. Jackson). Cambridge University Press, Cambridge. pp 461-502

• Lambeck, Purcell, Johnston, Nakada & Yokoyama, 2003: Water-load definition in the glacio-hydro-isostatic sea-level equation. Quaternary Science Reviews, vol. 22, pp 309-318

• Lambeck, & Chappell, 2001: Sea level change through the last glacial cycle. Science, 292, 679-686.

• Lambeck, Yokoyama & Purcell, 2002: Into and out of the Last Glacial Maximum: sea-level change during Oxygen Isotope Stages 3 & 2. Quaternary Science Reviews, vol. 21, pp 343-360

The following plots have been prepared by Ayako Abe-Ouchi and Saito Fuyuki:

• Antarctica plots
• Northern Hemisphere plots

The plots show the combined Surface Altitude and Fraction of Grid Cell Covered with Glacier, and use data from:

• for ANU ice model (2009)
• for ICE-6G v1.02
• for GLAC-1 nn454 model for North America, and ne8234 for Eurasia

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