Dear authors,
thanks for revising your manuscript for the Cryosphere. Given that the reviewers accept the detailed response to their thorough review of your paper, I will be happy to accept your manuscript for publication.

However, please consider these additional points in your final revised manuscript:
- assess the impact of inflow/outflow of ice along the flowline
- discuss the impact of uncertainties in the bedrock topography
- compare the estimated enhanced HTM precipitation to simulations of HTM climate

as well as these technical corrections:
Page 3, line 29: remove "the"
Page 4, line 21: missing figure number;
Page 4, line 30: incomplete sentence "causing"?

Sincerely,
Kerim Hestnes Nisancioglu
University of Bergen and the Bjerknes Centre for Climate Research

Dear authors,
thanks for the detailed response and revisions of the manuscript.

Dear authors,
thanks for the detailed response and revisions of the manuscript.


Additional referee report:
"*** response to responses

However, given the uncertainties associated with paleo climate
reconstructions, we are at a loss as to how to improve this
relation. The precipitation anomaly P is intended to account many
unknown climate factors that are not captured in by Equation (4). We
now discuss this at greater length in Section 2.3.

# cf Bahadory and Tarasov, GMD 2018 for an example.

Sensitivity tests suggest that this complexity may not be necessary
because the precipitation anomaly is not particularly sensitive to the
rate factor and consequently to ice temperature. Modeled retreat is
controlled primarily by surface mass balance rather than ice
dynamics. These points are now included in the section on model
limitations.

# you are assuming continuous frozen base then? If there is a
# transition between cold and warm based conditions, then your
# statement is no longer apriori valid.

Parameter values for the positive degree day model were selected to be
consistent with previous paleo-modeling efforts. The lapse rate is from
Abe-Ouchi et al. (2007), and we will add a reference.

# Given the attention to uncertainty quantification, there should be
# some consideration of the uncertainties introduced from the above.
# If you review there relevant litterature, there are other choices
# for treating these components. Just stating you chose something
# because somebody else used it is crappy science that ice sheet
# modellers have too often relied on.

This is correct. We do not model runo or refreezing rain, only
refreezing of melt as superimposed ice.

# Need to explicitly state so in the text


Comment
\We randomly sample curves from a multivariate Gaussian with the same covariance structure
as the GMRF prior outlined in Section 2.5.3" justication as to why the GMRF provides an
appropriate distribution for this context?

As for P, the GMRF prior is a \smoothness" prior. We have edited the text for clarity.

# not addressing the stated query


Comment
is not a full edged substitute for MCMC methods, which can compute 30
expectation inte- grals to higher levels of accuracy" And which do not
need to assume a Gaussian distribution

Response The mean and covariance estimates obtained via the unscented transform
can be accurate even if the underlying posterior distribution is not
normal. Of course, the mean and covariance may not fully characterize
the distribution (e.g. if it is multimodal). Perhaps we could include
a normality test to address this?

# not addressing point. You are assuming that mean and covariance
# fully characterize the distribution. This implies you are assuming
# an underlying multivariate normal distribution.

*** comments wrt revised text

On a global scale, the moisture content of the atmosphere increases by
roughly 7% for every degree of warming, according to the
Clausius-Clapeyron relation

# incorrect. If you do the math with the observed mean global
# temperature (278K) and the simplification of Clausius-Clapeyron
# using the ideal gas law, you get a 10% increase per K.

While there are important differences between HTM and modern climate,
the history of retreat in West Greenland may help understand how the
GrIS will respond to a warmer and possibly wetter future climate.

# If find this claim almost vacuous within the context of this study. You are explicitly assuming ice dynamical changes don't matter, ie
your inference is focussed on inferring past precip changes with a 1D
isothermal flowline model with time idependent sliding. How does this
relate to inferring future changes in the GRIS in response to future
changes in climate when the largest uncertainties are local climate
change, ice dynamical (ie surges/destabilization), and submarine melt
and grounding line retreat where relevant.

observed terminus positions in a flowline ice dynamics model

# -> observed terminus positions in an isothermal flowline ice dynamics model

Even state-of-the-art MCMC methods require drawing many thousands of
random samples, each of which corresponds to a single forward run of
the ice dynamics model

# Scientific writing needs to be precise and accurate. The above statement
# is not correct if emulators are used.


Previous modeling studies indicate that Holocene retreat in land
terminating regions of the GrIS were controlled primarily by surface
mass balance rather than ice dynamics (Cuzzone et al., 2019;
Lecavalier et al., 2014)

# I don't know how you can infer this from the cited studies. I'm
assuming you are equating that the sensitivity to relevant tuning
parameters is higher for SMB than basal sliding. But that is not the
same as your claim. Those models did not assume an isothermal
structure and therefore had basal temperature controlled switching of
basal sliding.

Isostatic uplift and relative sea level changes are accounted for
using output from a Glacial isostatic adjustment model (Caron et al.,
2018).

# Need to be clear that you are introducing another source of
# uncertainty given that the GIA output from Caron et al, is unlikely
# to be self-consistent with your changing ice sheet load.

determined by the Clausius-Clapeyron relation given by
...

# that is not the Clausius-Clapeyron relation

We use the 1D, isothermal, flowline model with higher-order momentum
balance described in Brinkerhoff et al. (2017)

# I see little point in bothering with a higher-order momentum balance
# if you are likely introducing larger uncertainties from the use of
# an isothermal model

Consequently, on a high end desktop, the iterative optimization
process requires computation time equivalent to three successive
forward model runs.

# Seriously, you are doing Bayesian inversion with only 3 model runs?
# In this case, if this inversion is so fast, then the cost of running
# a full 3D ice sheet model should be irrelevant.


Exploring surrogate modeling approaches to solving inference problems
in glaciology is a promising avenue for future research

# Should cite past applications thereof, eg Tarasov et al, EPSL, 2012,
# and pollard et al, GMD, 2016


reduced Arctic sea ice or
changes in atmospheric circulation during the HTM

# -> .. and/or changes .."

Dear authors,
I am happy to accept your revised manuscript for publication in the Cryosphere.

Sincerely,
Kerim Hestnes Nisancioglu