The authors use airborne laser altimetry (from airborne topographic mappers (ATM)) over Antarctic Peninsula (AP) and Amundsen Sea (AS) ice shelves, plus models of surface mass balance and firn compaction, to measure ice shelf thinning rates and assign these rates to individual terms in the mass balance.
The study is complementary to several previous studies that used satellite altimeters. The coverage of ATM is poor prior to Operation Icebridge (OIB). However, it has some advantages in terms of dedicated tracks, in particular allowing measurements to get close to grounding lines. It is therefore a valuable study, and dataset, to provide to the community.
RESPONSES TO ANONYMOUS REFEREE #1
“We did not compare with Pritchard et al. (2012) as the data is not provided in a compiled form. Rignot et al. (2013) do not provide publicly available data.”
This is true; however, data sets are available from these authors on request.
However, laser altimetry datasets have more accurate surface determination and can more accurately track over regions of abrupt topographical change. ICESat-2 should provide a valuable extension to the laser altimetry record and help separate short term oscillations with long-term change.
It is true that lasers track the true surface better (much better!) than radar. However, if your firn density model (providing the correction for firn air content) is wrong, it is possible that the radar provides a *better* estimate of basal mass balance than you get from laser.
The authors have carried out a major overhaul of their manuscript in response to the first round of reviewer comments, including much better organization. However, I still have issues that I think need to be addressed.
1. Figures are not ordered correctly. This made it hard to follow at some points.
2. As I think I now understand, *all* thickness change rates are cited in Lagrangian terms. Even “Eulerian TINs” have been corrected for divergence. However, the authors need to appreciate that at least some of their readers are going to default to “thickness change means Eulerian” (i.e., evidence that mass/volume of the ice shelf is changing). I still contend that the “standard” use of Lagrangian methods is to smooth out the individual estimates of height change before *removing* the divergence term to get back to thickness change in Eulerian terms, rather than reporting on Lagrangian changes where all of it *might* be divergence with no SMB and BMB contributions. Hence, I still argue for using the Lagrangian derivative symbol (DH/Dt) rather than the words “thickness change”, so readers are constantly reminded what they are looking at.
3. Related to this: One way in which Lagrangian methodology “smooths” thickness change is when changes due to divergence dominant over SMB and BMB variability. That is, even ignoring surface topographic variability that is subsequently advected to create “noise” in the method, Lagrangian processing might produce a smoother field just because the thickness-change numbers are larger and more coherent. I’m not arguing against Lagrangian processing, but the manuscript should explain in more detail the effects of different processing options.
4. Minor general comment: consistent units (either m or meters, not changing), and space between values and units (200 m, not 200m)
p.1/l.8-9: See general comments. The first part of this sentence sort-of makes sense in terms of Lagrangian DH/Dt, but is then violated by the second part which says that other processes also play a role. Maybe it is “dominated by flux divergence” but certain times and places show other important terms?
p.1/l.21: I still don’t think Rignot et al. 2013 is a good citation for evidence of buttressing. There are many others that focus more on the mechanics of this process rather than just asserting it. The same goes for Shepherd et al. 2003 and Fricker and Padman 2012.
p.1/l.21-24: This would flow better if you started with something like “The mass budget of an ice shelf is the sum of several mass gain and loss terms (Thomas 1979). Mass is gained by, … Losses are associated with …
p.2/l.1: Isn’t mass rather than volume the important term? I think Paolo et al. 2016 used volume because of concerns over firn models, but the other two papers there are attempting *mass* balance calcs.
p.2/l.4: “at accelerated rates FOR SEVERAL years following the collapse”
p.2/l.7-9: I think I pointed this out last time: It’s the *increase* of CDW heat that would drive accelerated thinning, not just the presence of CDW heat. Unless you think it wasn’t there at all, the last time these glaciers were in balance, or you are referring to changes *after* the irreversible onset of MISI (in which case you need more words.)
p.2/l.18: What is “Icessn” after “Atm”? If it’s important, it’ll need to stay with the “ATM” name later on.
p.2/l.28: delete “be in reference to”; okay just to say “converted to the 2014 solution …”
p.3/l.22: Scambos et al. 2001 is a very early cite for delineation of ice-shelf extent
p.3/l.27: “corrected for ice strain effects” following …”. Clearer, and more precise, might be to say “have been corrected to Lagrangian thinning rates by adding in the effects of strain.” Also, I think Moholdt *removed* strain (to get to Lagrangian-processed, *Eulerian* dh/dt), rather than adding in strain.
p.5/l.14-15: “firn-column heights” is a bit vague. Something like Fig. 3 would have been a good place to outline what everything is. Is this height relative to “pore close-off depth” (defined as some density?), or the equivalent of “firn air content”, or ???
p.5/l.29: I’m assuming everything is Lagrangian, but saying “the change in ice thickness of” always implies, to me, a change in the volume/mass of the ice shelf. But in fact you conclude that it’s fairly close to steady state, and these “changes” are just because ice diverges.
p.5/l.30: Cite to Figure 6 is wrong; or at least, Fig. 6 should be moved to Fig. 4, and this cite should be to Fig. 4 (it is the first figure cite after Fig. 3).
p.6/l.3: Again “is thinning” means something different from what you want people to be thinking in your Lagrangian FoR.
p.6/l.10: wrong figure cite. (last one I’ll point out.)
p.6/l.11: “Wilkens” => “Wilkins”
p.6/l.14: Not clear what other way it can “ablate” other than through basal melting. What other explanation do you have in mind, that you are discounting?
p.6/l.16: Many readers will not know whether 6000 km^2 is a lot or not. Maybe add “, from xx,xxx to yy,yyy km^2”
p.6/l.19-21: This is an interesting case where basal melt rate greatly exceeds Lagrangian thinning. But I struggled to understand how it could be, since Lagrangian thinning includes the basal melt. Since DH/Dt<BMB, flow is CONvergent, and/or SMB is quite large. But then you could tell us that it isn’t large enough to prevent *Eulerian* rates from being negative (ice shelf thinning).
p.6/l.26-31: This discussion is convoluted. You need to tell us first about the existence of a “once grounded (when?) but not any more (after ???)” region. Then explicitly discuss the “always ungrounded” and the “sometimes ungrounded” parts separately.
(same area): On l.31 you say “significantly weaker”, but I don’t know “than what” ? Part of the trouble is that you are jumping back and forth between basal melting and “ice shelf thinning rates”. Because of this, I don’t know whether I’m meant to be comparing rates in regions, or rates in the same region between epochs.
p.6/l.34-p.7/l.1: I really don’t think Rignot and Jacobs 2002 tell you that GL melt rates have the highest impact on glacial flow dynamics; they just base their decision to analyze near-GL melt on that assumption. They say “We focus on melt rates near the grounding lines of deep-draft outlet glaciers because continental ice discharge is principally controlled by the channeled flow of these ice streams into the ocean (Fig. 1). If these regions are the locus of high basal melting, the potential exists for substantial ocean control over ice shelf, if not ice sheet, mass balance (11213). Indirect observations and computer models have suggested high basal melting in the proximity of deep grounding lines and have shown that melting efficiency will decrease as buoyant plumes lose heat and rise to shallower depths along ice-ocean interfaces (14, 15).”
p.7/l.5-6: I don’t see how this is a “However, …” statement, since it essentially repeats the content of the previous sentence. Maybe it doesn’t matter, but it seems to point to your wanting to tell us about *mean* conditions, *then* variability, but that isn’t the distinction I get from these two sentences.
p.7/l.11-12: Rewrite sentence starting “Ice thickness …”. You cannot cite figure panel IDs before the reader even knows what figure to look at. This might be because I recommended *not* starting sentences with “Fig. X shows that …”, but there are other ways around it.
p.7/l.19-21: “much less noise compared with …”. I get what you’re saying, but it is dependent on the content of the next sentence to remind us *why* this is true. It also assumes that the benefits outweigh the “costs” of Lagrangian processing. These might include fewer data (depending on flight path choice (and orbits, for satellite application)), and dependence on velocities that might not be well enough known to calculate divergence (think of a shear margin where spatial scales of velocities are smaller than what you can comfortably get out of InSAR).
p.8/l.25: Adusumiili et al 2018 expanded on Paolo work by adding in CryoSat-2, but they didn’t expand coverage; instead, they limited themselves to just the greater AP area.
p.9/l.11: I thought the data set used here is more than IceBridge: Figure 1 shows data going back to 2002, well before OIB.