This study uses averaging of Cryosat-2 data to produce an 11-year record of centered-in-time annual DEMs for Pine Island Glacier, and then uses these to investigate the evolution of basal channels, primarily through a Lagrangian change analysis. Overall, I find the methods to be sound and the conclusions to be well-supported. I was particularly interested in the relationship between the pinning point and channel evolution. I think this will be a valuable addition to the literature on DEM methodologies, basal channels, and PIG.

The main concern I have with this manuscript is that some of the analyses, while technically correct, have strayed away from the physical processes that they are trying to represent. Specifically, the calculation of anomalies, given the language used, makes it very difficult to ascertain the physical meaning of the results.

If I’ve understood correctly, anomalies in elevation and basal melt rate are calculated by using a 7 km Gaussian filter, and then subtracting the results from the unsmoothed values. So, this is a neighborhood operation, and these anomalies are saying whether the ice base and melt rate are higher or lower than nearby points. For melt rates, as is described in lines 239-240, “A positive ice loss anomaly means more thinning and a negative ice loss anomaly shows anomalous thickening.” It is technically correct to use this language; a negative ice-loss anomaly means thickening in the same way that a slightly weaker northerly wind is a southerly wind anomaly. However, the language is misleading, because based on the map in Figure 5, and from what we know about the PIG system, there should be no freeze-on occurring. So, in fact, there is no actual thickening due to melt (freeze-on). The anomaly values themselves are also not particularly meaningful, since they are comparisons to a fairly arbitrary section of ice-shelf base.

What I think can be said based on the anomalies is that, first of all, they are really only relevant if you’re interested in the relative evolution of a distinctive basal feature such as a basal channel, and that a negative anomaly within the channel indicates that the amplitude of the channel is decreasing, i.e. the channel is filling in. That’s interesting and important, but is currently obscured by the presentation in the manuscript.

I think this can probably be addressed by being more careful with language within the current structure of the manuscript. However, I also think that a careful look at the results presented will reveal that not all of the discussion is relevant to the conclusions. Ideally, I think the results could be shortened quite a bit after reconsidering the meaning of the results and linking them to the conclusions.

Scientific/clarification points:

The length scale over which ice-flow divergence is calculated should be explicitly stated and justified.

In general, there is little to no treatment of error. While I don’t know that a rigorous treatment of error is necessary, some discussion at least seems warranted. For example, calculations are made right up to the 2011 grounding line. It is not established how the grounding line has evolved after 2011 and throughout the record developed here. If it has retreated substantially, then using the 2011 grounding line is conservative and probably okay. If it has retreated slowly or not at all, then the measurements close to the grounding line are likely substantially influenced by not being fully in flotation, and these need to be discussed in the results and/or removed from the analysis. I’m also concerned that there appears to be no temporal interpolation of velocity fields during point migration – rather, it sounds like the velocity of a migrated point is pulled directly from the annual ITS_LIVE velocity grid for the year into which the point fits. On an accelerating ice shelf, this can introduce large errors in migration location, which should probably be quantified. If the ice shelf is accelerating fairly steadily, linear interpolation between velocity grids would reasonably solve this issue. If I have misunderstood the method, it would be helpful to clarify the text.

Lines 200-201: “A dashed line is also plotted in Figure 4c and d. These correspond to the depth of the smoothed ice base in 2011 and 2017, respectively, and represent the ice base if channels did not exist.” I’m not convinced of this equivalency – it’s just a smoothed ice base, not necessarily one devoid of influence from channels.

The use of directions is confusing. The abstract uses east and west, lines 242-243 use north and south, and the description of Coriolis-influence melt uses northeast and southwest. This needs to be standardized. I realize that PIG is not directly N-S aligned, but since we normally think of ice as flowing from south to north in Antarctica, I’d personally stick to east and west.

Line 279-280: “…and the surface elevation and melt anomaly are now in phase.” I’m not sure what the point of this is, physically speaking. It’s true that the graphs in Figure 7 go in the same direction at this point. But a negative melt anomaly means less melting, which would lead to relatively thicker ice, while a negative ice-thickness anomaly means thinner ice. So, physically, they are at odds with each other. While this is a mathematically correct statement, it doesn’t seem to help much with the physical interpretation

Line 281: “…where Channel 1 is carved, and a few kilometers downstream, where it is eroded.” These terms don’t make much physical sense. Carving is okay, but I assume the term “eroded” is supposed to mean where the channel is filling in (as the opposite of “carved”). Since erosion typically refers to taking material away, this would be a very confusing way to say it. Similarly, line 309 “indicating channel calving” – I assume carving was meant? Calving would not make physical sense here.

Figure 7 and the text show both Eulerian measures of change and a Lagrangian measure, but it is unclear what differing conclusions can or should be drawn from these differing analysis styles, and it is not brought into the discussion/conclusions. I do think there are some interesting implications about the persistence of a channel imprinted on an ice parcel vs. the influence from Eulerian features such as plumes and pinning points that are hinted at in the manuscript, but could be stated much more explicitly.

Line 293: I believe these features are discussed in some detail in Bindschadler et al. (2011), https://doi.org/10.3189/002214311797409802

Figure 8 shows a few spots where the algorithm has marked the western flank as being shallower than the apex. I suggest that the algorithm is not working well in these cases, and perhaps these points should be excluded.

Line 413: Sergienko (2013) is a modeling study that clearly shows deflection of channels from flowlines.

Minor grammatical points:

West Antarctica abbreviated as WA: Since this is only used a small number of times in the first paragraph of the intro, it seems better to just write out “West Antarctica”

“data” should be plural throughout – e.g. line 86: “The 12 months of data that are required to create a single DEM are centred around…” (note also that “created” in this line should be “create”

Line 195: “transects” should be “transect”

Compound adjectives or nouns used as adjectives should technically be hyphenated – e.g. “kilometre-scale gradients” in line 223. Even terms like “sea-level rise” and “ice-shelf stability” should technically be hyphenated, although I realize that this isn’t necessarily in style. If two nouns are not used as adjectives, they should not be hyphenated – e.g. remove hyphens from “ice-shelf” in lines 206 and 207

Figure presentation:

Please replace rainbow color maps, which introduce false perceptions of high gradients, with a visually consistent color scheme

In general, it’s helpful if figure captions stand mostly on their own, so that a reader glancing through the paper can make sense of what you’re doing. To that end, it would be helpful to define acronyms within captions (e.g. DROT in figure 1), and although it’s fair to say that basemap and grounding lines are the same as in figure 1, it’s a pain to go back through to find figure 1 to figure out when the basemap and grounding lines are from. Perhaps consider a legend within the figure for the grounding lines at least, and/or put the date of the basemap in the captions.

Figure 3: The color bar appears to be very saturated, which limits the amount of information we can get from the figure.

Figure 4 (discussed in text): I wouldn’t call those lines light blue, blue, and dark blue – at very least the first line is much more green than blue.

Figure 5: Titling this figure “The main variables needed to calculate basal melt rates” is odd when one of those variables is basal melt rates themselves. Although using “ice loss” as the color bar title is technically correct, it’s a little confusing when on one color map it refers to basal melt (ice is completely lost and turned into water) and on another it’s divergence (ice is lost from the pixel but just moves next-door). Consider “ice-thickness loss” instead, here and in the text.

Figure 5 (described in text): “basal channels are clearly present within the thickness map.” It would be helpful to mark them.

Figure 7: I struggled a lot with this figure. The caption jumps around a lot, which doesn’t make it easier to follow.

• First, I’m not sure why the time-averaged elevation anomalies (and please clarify in the caption that these are anomalies) are plotted twice; I think it would either be better to plot them once on the same graph with the melt, or to plot the melt and elevation on separate graphs, but I spent a while trying to figure out why those were different.
• Please also move the legend so it does not cover up some of those data.
• Consider moving those averages to the right-hand side, since they’re calculated from the Hovmöller data (just seems more logical, but this is a minor preference).
• The caption statement “(b), (d), and (f) are overlaid with the zero contour line from (a), (c), and (e), respectively” has me confused. The zero contour line should come straight out of the Hovmöller, without need for averaging, so I’m not sure why it’s linked to the averages. There’s also what appears to be a zero contour line on the rest of the Hovmöllers, which aren’t mentioned.
• It would be easier to spot your cyan and pink arrows marking the basal channels if they were always on one side – probably on the right, since that’s where the channels are consistently seen. It would also be helpful if the same locations were marked on the melt diagrams in d, h, and l.

Review: Spatio-temporal melt and basal channel evolution on Pine Island

Glacier ice shelf from CryoSat-2

Katie Lowery et.al.

In this study a new approach to calculate ice shelf basal melt rates on monthly resolution for Pine Island Glacier is presented. The study is a case study to demonstrate the new approach which uses CryoSat-2 swath data to derive monthly melt maps with a 250 m spatial resolution. The results show, that near the grounding line basal melting is 50% stronger on the western flank of a channel that on the eastern flank. In addition, findings suggest that the channelized geometries on PIG are triggered upstream and that the channel geometry facilitates ephemeral re-grounding as it moves downstream, potentially influencing ice-shelf stability.

In general, the paper is well written, clearly structured and the presented idea to derive melt rates is novel and worth to be published in TC. Equations used are correct and figures are of good quality while mostly supporting the analysis.

While reading I think that the results part is very voluminous and already includes sections which should be more presented in the discussion section (e.g. L202 – L225). Please check carefully.

I do have some questions and concerns about two aspects in the methodology (see below), which I think need to be discussed with respect to the derived findings.

Shean (2019) used high resolution Tandem-X DEMs to derive melt rates of PIG. They found a higher melting associated with basal channels and deep keels near the grounding line and relatively shallow keels over the outer shelf and do not discuss a more pronounced western flank melting. It would be nice and important to see if you can confirm and discuss the findings of Shean in more detail and also if this Coriolis dependent melting as it was not discussed in Shean (2019) might be a result your processing methodology.

As a general remark. How much is the velocity changing throughout the observed time period? Can you please make a figure in the supplements showing the difference of the x and y components of each single velocity field to an averaged velocity. To my opinion it would be much better to use an averaged field in the whole processing as long as the velocity is more or less constant throughout the time period. This would substantially minimize errors in the Lagrangian shift, which is based on pixel to pixel shifts and therefore very sensitive to noise of the velocity components on the pixel scale. I think this is important, especially as you try to analyze small scale melt differences within a channel.

Suggestion for all overview figures: I think the western part of the ice shelf doesn’t need to be included as it is never discussed in the paper. Please zoom in to the main fast flowing part which you are focusing on (Fig 1, Fig2, Fig3, Fig4b, inlet Fig9, Fig A1, A2)  

In addition, the choice of the selected along and across flow segments which are varying in the paper make it difficult for the reader to follow. Can you please include in your overview Fig1 also the cross section X-X’, Y-Y’, Z-Z’ and the box S-S’ and U-U’

Z-Z’ seems to be very similar to B-B’ – why not using the same.

Can you please slightly enlarge S-S’ that it includes Y-Y’, Z-Z’ and B-B’ and please also mark in Figure 5 and 6 the position of those cross sections. This would help to understand better otherwise it’s a bit confusing.

Please don’t use rainbow color scale for elevation and thickness.

Detailed:

L70

here you claim that the new method can be applied on every ice shelf or terrain. I think this is not correct. You still need sufficient data coverage of the swath data to form this DEMs based on 1 year of acquisition data. And this is not the case for most of the ice shelves. For PIG or Dotson it seems to work.

Usually from theory quasi nadir swath processing is affected by phase ambiguities and low coherence over flat terrain, where across track slope is less than half the antenna beamwidth – which usually is the case over ice shelves. As Cryosat2 has a small mis pointing of 0.1° this left and right looking phase returns are not completely canceling, allowing to detect some coherence and therefore to derive elevation estimates across track in some places like PIG. I think it is important to be mentioned.

L100

Here you argue that the time centering method is more accurate than just binning and compare both DEMs in A1. How do you know which one is better? Of course you reduce the averaging of across flow features but with the time centering method you also introduce errors which are related to the velocity field and it‘s derivative, which I assume is very noisy when using yearly velocity fields (see comment above).

I would suggest to compare to other high resolution DEMs like the Tandem-X DEM presented in Shean (2019) to evaluate which method is better. I would also like to see a typical point cloud coverage of one month of swath elevations to get an idea of the general data coverage. As you use the median as a very robust averaging method, I would like to see the standard deviation for each pixel to get an idea of how much the swath elevation point cloud elevations are varying within one pixel. Do you filter or exclude outliers of the swath data before averaging?

L113 ff.

Can you please exactly explain where H is coming from? Due you use the mean(h) of both contributing DEMs, or h of the first DEM or a constant h for all time steps?

L133 is the noise of the monthly melt maps maybe related to the noisy velocity field?

L134 ff

The averaging of monthly data to reduce noise is a well know procedure. However, I do not understand why you advect the melt maps. To my opinion this is not correct. The overall melt pattern is not moving in a Lagrangian sense with the ice. The melt is triggered by ocean water masses and the ice is moving. This means that the melt pattern can locally change with time due to changes in warm water supply through the ocean but this warm water supply is decoupled from the ice movement. Therefore, an averaging of monthly melt maps should be done without advection. I also think because of this additional advection you change the melt distribution across a channel. And this change is correlated to the across flow component of the velocity field.

Therefore, I would like to recommend to redo the analyses based on not advected averaging and see new figures 6,7,8. Will this change your conclusion of pronounced western flank melting and support the findings in Shean of high keel and channel melting in areas close to the grounding line?

Please also give the equation of how you derive ice shelf base showing in Figure 4.

L173 ff pinning point

This is an interesting finding, that you are able to see an un- and regrounding in the CS2 data. Can you please confirm that DROT also see an ungrounding of section Z-Z’ in 2023?

In Fig 4b you only show DROT grounding of 2017. I would suggest to zoom in in Fig 4B to only show the relevant ice shelf section and enlarge labelling in 4B. Maye provide another figure like 4B with DROT grounded areas of 2023 to further support the CS2 data.   

L225 ff Channelized melt + Coriolis favoured melting

As mentioned, please redo the analysis with not advected averaged melt maps.

L312 ff

As suggested. Why not use a constant averaged less noisy velocity field to avoid effects of changing and noisy divergence.

L317 Coriolis favoured melting

Could you please include in your analysis and Figure 8c the melt rate within the channel apex as well as the melt rates of the western and eastern keel.  It would be interesting to see if this Coriolis effect, as proposed, is only dominant in the channel and if  in the neighboring keels a different melt rate is observed. Furthermore, this would also show whether Shean's observations of higher melt rates at the Keels can be confirmed.

Fig 9

Can you please mark with a grey bar the position and extend of the channel you discuss in L379 ff