Please find my report attached.

Dear collegues

This is an interesting and important analysis of the flow behavior of

a firn-covered large glacier, where an ice core for climatic analysis

has been drilled. The paper is nicely written and comprehensive. The

discussion needs some more consideration of the shortcomings of

neglecting bubble close-off and a static climate. 

My recommendation is to publish the manuscript after taking into

account the comments below.

General comments

- The abstract is quite long and should be considerably shortened. It

  contains repetitions and too many details.

- "full Stokes" does not exist (but seems to be marketing jargon of Elmer Ice)

  -> these are just the Stokes equation from fluid mechanics.

  There exist "reduced" equations, omitting some terms due to scaling arguments.

- "ice age" usually means a geological epoch. Better replace this term

  everywhere with "the age of the ice"

- citation style should be adapted: Often \citet or \citep!

- Section 3 is out of place, and is also partly repeated in Section 4.

  Maybe convert to a table, or relate it better to the rest of the manuscript.

- also in section 4 and 5 information is not given in a logcial order.

  You should rater describe, in this order:

  - geometry, density, temperature etc

  - numerical approach & solver etc

  - discretization

  - boundary conditions

To obtain a reasoable age of the ice at the base, the air bubble

pressure after close-off has to be taken into account. This was

pioneered by Pimienta, and implemented in e.g. Lüthi & Funk (2000).

Without that effect, the ice at the botton cannot be dated correctly,

and the age is much too old. Also, varying basal melt could easily be

used to control the age of the ice at the bottom. If it is too old in

the model, just slightly increase the melt.

Overall, this is a very nice and conclusive study on the important

topic of dating a climatologically relevant ice core. The study has a

few shortcomings, especially wrt. the model. These problems are mostly

discussed, and are largely due to the lack of data to constrain the

model. These include flow velocities and climate data to constrain the

long-term thermal and dynamical evolution of the glacier. I think that

at this stage it is not useful or necessary to implement bubble

close-off in the Elmer Ice code base (but this needs urgently be done

for subsequent studies). 

The discussion should not only list, but also clearly work out the

effects of neglecting in the model the effects of bubble close-off,

and of assuming a high and constant basal heat flow, as well as

assuming steady climate conditions.

Specific comments

22 If the area is so large and encompasses North Africa and Asia, it

   is not representative for any of those.

34 does the part after "while" refer to measurements? Or the model?

39/45/54 and other places "full Stokes" -> Stokes

40 "the accumulation record"

49 "Mt. Dôme du Goûter" -> leave away Mt.

50 " Blank," -> Blanc

61 the glaciated area

62 a stray parenthesis

74 Better put the information on Pleiades in the Acknowledgements (does

   not fit in the main text)

79 Here, I was expecting the Pleiades DEM for the surface 

79 How do you get a 10x10 m bedrock from a radar survey? Was this somehow gridded?

Figure 1, caption: Coordinates are NOT given in UTM, but this would be much more useful!

89 So, this is a triangulation of the domain. How was this done, with

   Triangle? You should also mention that you need this grid for the FE-model.

92 Does this mean that you have prismatic elements, which are

   problematic for the incompressible flow due to LBB stability criterion?

   Also, the mesh resolution with depth is wildly varying. I can see

   the advantage of extruding a mesh in the vertical, but a TET4 mesh

   would likely be much more suited for the computations at hand.

95 This argument is not clear. It would be trivial to shift the

   bedrock up by 5 m, and then retain the exact horizontal position of

   the borehole. This is crucial, since mainly surface slope drives

   ice flow, especially in delicate saddle-like topographies like the

   one modeled in this study. Point a is on a clear slope, while point

   b is not.

   Also, radio echo data was likely not correctly interpreted

   (vertical instead of perpendicular to the surface), and depends a

   lot on the velocity model assumed, which depends on the density

   structure & temperature.

   

99, Tab 1 "Mathematical model"   better: "Numerical model" or "Ice flow model"

Tab 1: there is way too much information in this table

   at the same time it is totally unclear what type of relations were used.

113 This "full Stokes..." appears here for the 3rd time. Rather

    describe it properly at some point.

120ff please show the data and the approximations in a figure.

125 Show the equations that are solved (maybe in an appendix). Not

    everyone wants to look up these equations. Are these the exactly

    same equations? Then why show them. If not: what is different?

130 The derivation of the tensor invariant makes no sense if it is not

    presented in the context of the flow relation used. Either show

    all, or nothing (but show in the appendix what exact equations were used).

130 It is confusing using "D" for several things, and also "T". 

145 This is wrong in the context of a compressible flow relation. "p"

    is a Lagrange multiplier in a purely incompressible flow law. Here

    a compressible law is used, were isotropic and deviatioric parts

    are mixed. See e.g. Gagliardini & Meyssonnier (1997), Lüthi & Funk (2000)

147 This is Glen's flow law for INCOMPRESSIBLE ice. You should write

    down the proper Duva-Crow flow law!

150 References for the parametrizations of c and \kappa should be

    given. Is T in K or degC?

    Also, these values can be deleted in Tab 1. It is important to

    notice that both thermal quantities are strongly dependent on

    density.

154 This equation is wrong, it is k, not \kappa (diffusivity) Sorry, I

    see that \kappa is used for conductivity here, but it is convention

    to use \kappa for diffusivity and k for conductivity.

156 these are the conservation of mass equation (the volume is changing!)

165 Are these b.c. varying with depth? Already mention it here, I see Eq (26).

179 What is the rationale for a non-zero vertical velocity, but a zero

    horizontal velocity?

198 This shape of the velocity profile is only reasonable below the

    firn-ice transition, as can be seen e.g. in Fig 4a.

207 This is not a reduced flow model, you solve the full flow model

    for a time-constant T-distribution.

211 The viscosity must be dependent on the density. This is absolutely

    crucial. If you use Duva-Crow it is given by a(phi) and b(phi).

213 This section should be part of the Methods section, and most of

    the text appears here for the 4th time.

230 What is the role of the flow-enhancement factor? Is this needed at

    all? How is it applied, to firn and ice simultaneously? This would

    lead to densification values that are not compatible with the

    measured densities anymore. 

245 Figure 4C merits some attention. This temperature profile is truly

    exceptional with 18 K temperature difference on only 180 m! Such

    high temperature gradients and heat fluxes are truly remarkable.

    Why are they occurring? Is the assumed basal heat flux of 340

    mW/m2 really realistic? In mountains, the vertical heat flux is

    often much reduced due to topography.

251 Write out "Figure" everywhere in the text, and abbreviate it in

    parentheses.

255 Since we cannot see anything useful in Fig 4b, please indicate

    what deviation the age of the basal ice has. Is it too old? 

280 wrong parens

280 But they nicely agree for other sites, such as Colle Gnifetti and

    Col du Dome, with similar model setups (Lüthi, Liciulli, Gagliardini, ...).

    The problem with the deepest layers is that they might be remnants

    from a time when the geometry of the glacier was very different,

    the ice divides were shifted and the flow regime was altered.

    Also, as mentioned above, neglecting the effect of bubble

    close-off (not yet implemented in Elmer-Ice?) strongly affects the

    age at depth.

Figure 4b: There is nothing useful to see in this figure. Show the top

    and bottom parts separately. Additionally/alternatively, you could

    use a logarithimc age scale. Also indicate the reference dates

    (volcanoes) with dots.

Figure 4c: Please indicate 0 degrees, and also the pressure melting

    temperature at the base. From the plot one cannot determine the

    basal temperature.

    For a steady state model with density variation you will

    never get a straight line, since the vertical heat flux is

    constant, but you need a higher gradient in firn. The measured

    temperature profile also looks advective, which should have been

    captured by the model. Finally, the spatially constant vertical

    heat flux b.c. in the model is not realistic in a mountain

    topography (e.g. Lüthi, 2001).

Figure 4 caption: what is this stray "vertical a"??