the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Quantifying the Uncertainty in the Eurasian Ice-Sheet Geometry at the Penultimate Glacial Maximum (Marine Isotope Stage 6)
Oliver G. Pollard
Natasha L. M. Barlow
Lauren Gregoire
Natalya Gomez
Víctor Cartelle
Jeremy C. Ely
Lachlan C. Astfalck
Abstract. North Sea Last Interglacial sea level is sensitive to the fingerprint of mass loss from polar ice sheets. However, the signal is complicated by the influence of glacial isostatic adjustment driven by the Penultimate Glacial Period Eurasian ice sheet and its geometry remain significantly uncertain. Here, we produce new reconstructions of the Eurasian ice sheet during the Penultimate Glacial Maximum (PGM), for use as input to sea-level and climate models, by employing large ensemble experiments from a simple ice-sheet model that depends solely on basal sheer stress, ice extent, and topography. To explore the range of uncertainty in possible ice geometries, we use a parameterised shear-stress map as input that has been developed to incorporate bedrock characteristics and ice-sheet basal processes. We perform Bayesian uncertainty quantification to calibrate against global ice-sheet reconstructions of the last deglaciation to rule out combinations of input parameters that produce unrealistic ice sheets. The refined parameter space is then applied to the PGM to create an ensemble of plausible 3D Eurasian ice-sheet geometries. Our reconstructed PGM Eurasian ice-sheet volume is 51.16±6.13 m sea-level equivalent which suggests a 14.3 % reduction in the volume of the PGM Laurentide ice-sheet. We find that the Barents-Kara Sea region displays both the largest mean volume and relative variability of 26.80 ± 3.58 m SLE while the British-Irish sector’s volume of 1.77 ± 0.11 m SLE is smallest, yet most implausible. Our new workflow may be applied to other locations and periods where ice-sheet histories have limited empirical data.
Oliver G. Pollard et al.
Status: final response (author comments only)
- RC1: 'Review of the paper by Pollard et al.', Evan Gowan, 09 Feb 2023
-
RC2: 'Comment on tc-2023-5', Lev Tarasov, 24 Apr 2023
(note my quality/impact/... ratings on the review form are based on the current version)
The Pollard et al submission is an attempt of applying history
matching to the Penultimate Glacial Maximum (PGM) for Eurasia. The
choice of history matching is appropriate, however the implementation
is limited and currently inadequate to match the claims. Critical, the
submissions claims via the title to quantify "the Uncertainty in the
Eurasian Ice-Sheet Geometry at the Penultimate Glacial Maximum", and
via the abstract to "robustly quantify uncertainties" and yet it only
partially does so. It fails to account for the structural uncertainty
of their static perfectly plastic ice sheet model. It also fails to
account for uncertainties in the MIS 6 ice margin. A key point is that
MIS 6 maximum ice extent has poor age control. It is unclear to what
extent parts of the margin represent short term surge events (which
are not going to be well represented by a perfectly plastic ice sheet
model), nor is it clear to what extent the maximum ice margin extent
was synchronous. Nor is the potentially large uncertainty associated
with the assumption of an equilibrium ice sheet addressed.The work is of potential value, but it first needs to make claims that
are defensible. This includes clarity and accuracy on the extent to
which uncertainties are addressed and that this is a very approximate
history matching as the parameter sampling is far from
complete. History matching typically relies on emulators to adequately
sample the parameter space. 200 samples for 7 parameters is far from
adequate unless the response is very linear with minimal interaction
between parameters (which would have to be shown).Secondly, the chosen model uncertainty estimate has no
justification. Futhermore, it is clear that there is a bias error that
also needs to be addressed in the implausibility function given the
mean NROY misfits to the GLAC1D and ICE6G ice sheet chronologies.
However, this can be rectified. Select at least 20 of your simulations
that have the least RMSE error for GLAC1D (and separately for ICE6G if
that is fully from a glaciological model). Use the variance of the
residuals as your minimum structural model variance error estimate and
use the mean bias as your minimum model bias error estimate in the
implausibility. Note, these values will clearly vary around the ice
sheet. You can either make the error estimates a field (ie depending
on relative location in the ice sheet), or you can choose the maximum
value across the ice sheet (easier but at cost of wider
uncertainties). As both of these ice chronologies have their own
limitations, expanding the resultant variance and bias estimates by
some fudge factor, would still be needed. To account for errors
growing with a larger PGM ice sheet, scale the uncertainties for ice
thickness by the ratio of mean ice height.Thirdly, the authors are conflating NROY with plausible. This is a
problematic stretch. Showing something as being NROY, ie not
implausible, doesn't necessarily make it plausible.Finally, the authors do not adequately address the limitations of
the perfectly plastic approximation and make a number of inaccurate claims,
some of which are detailed below (running late on this review, I figured
it's better to give you something to work with now than a completely detailed
evaluation).# some specific comments
Quantifying the Uncertainty in the Eurasian Ice-Sheet Geometry at
the Penultimate Glacial Maximum (Marine Isotope Stage 6)# The title is misleading, as uncertainties are inadequately quantified.
51.16±6.13 m sea-level equivalent
# The significant digits given for results are meaningless, correct this to
# an appropriate amount.We perform Bayesian uncertainty quantification
# History matching is not Bayesian (where do you invoke Bayes Rule?)
# cf https://www.physics.mun.ca/~lev/revCalG.pdf
# for an explanation of what Bayesian is and entails.Finally, the simple ice-sheet model approach is designed to generate
ice geometries based on simple, steady-state ice-sheet physics for a
prescribed margin# Misleading as stated. The perfectly plastic ice sheet model is
# is derived from "steady-state ice-sheet physics" but it doesn't
# reflect it, only provides a limited approximation.simple ice-sheet model whose minimal input requirements
# The specification of a 2D basal shear stress map for each timeslice
# is far from minimal.However, reliance on poorly constrained rebound data required for GIA
inversion modelling (Lambeck et al., 2006) or assumptions of highly
uncertain climate data used in dynamic ice-sheet simulations
(Abe-Ouchi et al., 2007; Peyaud, 2006) make these approaches
challenging to constrain for the Penultimate Deglaciation and give
only a very limited view of possible pasts with no grasp on the vast
range of plausibility# The last claim is incorrect. I'm using a glaciological (hybrid
# shallow shelf/shallow ice) model with large degrees of freedom in
# the climate forcing. Though not perfect, I suspect I've generated a
# larger range of history matched simulations for last glacial cycle Eurasian ice
# sheet evolution (in early process of write-up) than is offered by
# the methodology of this submission, as evidenced by my current 50
# ensemble parameters (versus 7 in this submission).a simple ice-sheet model whose minimal input requirements enables the
production of large ensemble simulations with controlled sources of
uncertainty (Gowan et al., 2016a).# If the sources of uncertainty are "controlled", then they should be
# fully assessed.generate physically plausible ice-sheet reconstructions
# Given the approximations involved, I don't see how you can call
# these physically plausible.
since our simulations
505 are process based# The perfectly plastic approximation is not a process based model but
# a diagnostic tool. What processes are you actually modelling?The model has been successfully applied where large uncertainty in
inputs required for dynamic ice-sheet models, such as climate, have
reduced the confidence in using the outputs of such models as inputs
to sea-level models due to misfits against ice extent and volume
distributions that impact GIA, and where large numbers of runs are
required making computation efficiency 105 paramount, such as in the
exploration of variable global ice-sheet configurations (Gowan et
al., 2021)# What do you mean by "successfully"? Instead of vague descriptors,
# be precise or do you want to be stuck with my definition of "successful"?Limited constraints on climatic conditions, the requirement for large
ensemble simulations to explore the range of plausible scenarios, and
a need for well-defined sources of uncertainty make ICESHEET an ideal
choice for exploring uncertainty in ice sheet configurations during
the PGM.# Again, given the statement above, a full uncertainty assessment
# should be provided to match the claim. Without seeing that assessment,
# I see no basis for calling ICESHEET an "ideal" choice, or even a defensible choice.In order to account for GIA, we assume that the Eurasian ice sheet at
the PGM had been at its maximum extent sufficiently long for the solid
Earth underneath to be at (or close 180 to) an isostatic equilibrium
with the ice load, an assumption we consider reasonable given the lack
of constraints during this time# this is a large assumption, contributing another source of unassessed uncertainty
# One main reason for your lack of constraints, is your missing of full glaciological
# physics of the ice and earth system which provide some pretty strong constraints
# on the system.We run 200 simulations for each reconstruction and each of the 4
selected time periods (22, 20, 18, 16 ka), totalling 1600 simulations
(Figure 5 and Figure A1).# so you are assuming minimal interactions between your parameters,
# but do not provide evidence to support this. If this were not the
# case, then even just a 3 value min/median/max grid search over 7
# parameters would entail 3^7= 6561 simulations for 1 timeslice.eq 1
# The denominator for implausibility should include variance for model
# structural error. The numerator should include model structural bias
# error. You are choosing to specify model structure error as simply
# some fraction of ensemble variance. On what basis do you justify
# such a choice? To understand why this can be problematic, cf the
# simple example in subsection 2.5 of
# https://doi.org/10.5194/egusphere-2022-1410
# The above reference also provides guidance some guidance on how model
# structural uncertainty can be defensibly assessed.Bayesian History Matching
# Looking at the first page of googled hits for "Bayesian History Matching", the actual papers
# describe Bayesian emulation used in history matching. As you are not using emulators, your
# description is inaccurate. This needs to be corrected throughout.We restrict our NROY space to parameter values that correspond to
models runs with implausibility I(ˆp) higher than 3, following the
Pukelsheim (2012) three-sigma rule typically used in Bayesian History
Matching
# Should be less than 3 not "greater than 3" for NROY. You should also
# state clearly what assumptions you are making about the residual distribution
# to justify the choice 3 sigma (the modelling community relies too much on "this
# is what others do"). cf the above https link for the assumptions made.
Figure 5# please add a few contours to each frame as its hard to discern the
# colour map values within even 300 m Also, I can't make sense of the
# colour scale for the first two columns. How can you have negative
# ice thickness or ice surface elevation (not clear what is being
# plotted) a km below sealevel?Our work has expanded this methodology to include the cold-based ice
and active ice streaming basal processes which have had a strong
impact on the implausibility metric, improving the simulation fit
during history matching when applied to the Last Deglaciation, with
the exception of the British ice sheet (Figure 4) where simulation
mismatch is likely due to discrepancies in ice-margin extraction.# You need to be honest about exactly what the perfectly plastic
# approximation entails and how far what you implement is from
# the physics of ice streams.Citation: https://doi.org/10.5194/tc-2023-5-RC2
Oliver G. Pollard et al.
Oliver G. Pollard et al.
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