Dear Yaowen Zheng and co-authors,

Thank you very much for uploading your responses to our two referees. In their reviews, both referees recommend making the paper more concise, simplified, and clarified in places. I agree with these general comments, which should be reflected in your revised manuscript.

I appreciate your efforts to address both reviewers’ concern about the impact of biases in satellite/climate model products on estimating “optimal” PDD parameters (T0 and DDF). Please, make sure that your proposed sensitivity experiments remain consistent with the new local estimates of PDD parameters (grid-cell scale) that you suggested to reviewer #2. It remains however unclear how this procedure change, i.e., estimating PDD parameters locally (grid-cell scale) instead of regionally (sector scale), could impact your results.

It is also unclear how additional Figures displayed in your response letter will fit in the revised manuscript, as they are not always discussed or referred to in your answers. Are these illustrations for the reviewers’/editor understanding, if so this should be clarified in your response letter. When using new Figures in your revised manuscript, please comply with the above comment on conciseness, i.e., focusing on relevant results that best convey your message. For instance, additional Figure 2 in the review of referee #1 shows details that may not be essential.

As a general note, please answer each comment separately (even with a brief sentence), and avoid combining them as in Comment 6, 21, 23 and 24 of reviewer #2. Doing so makes it hard to assess how each point comments are addressed. The same holds for removed or restructured sections as in Comment 24 of reviewer #2. You will find some minor comments from the editor below.

Note that both referees and the editor will re-assess your revised manuscript before potential acceptance in TC.

Best wishes,
Brice Noël

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Minor editor comments:
When preparing your revised manuscript, please pay particular attention to the wording to avoid confusions.

In your response to reviewer #1, please consider the followings:

L56: “overlapping period” instead of “overlapped period”

L65: “reconstructing” instead of “replicating”

L68-68: Do you mean: “However, biases in satellite products are likely due to frequent equipment replacements, i.e., at least 4 times in the period YYYY-YYYY” or something equivalent?

L70-79: Do you mean? “To explore the sensitivity of PDD parameters and model outputs to biases in both the satellite and RACMO2.3p2 products, we perform two sensitivity experiments. In the first sensitivity experiment, we explore the response of T0 and the PDD melt-day (and CMS) outputs to perturbations in satellite estimates. We increase/decrease (HIGH/LOW run) satellite CMS estimates by 10% (Figure 1a) for each grid-cell then repeat the T0 parameterization as described in Section 3.2.1, respectively. In the second sensitivity experiment, we explore the sensitivity of the DDF and the PDD melt amount outputs to perturbations in RACMO2.3p2 melt estimates. We increase/decrease (HIGH/LOW run) the RACMO2.3p2 melt estimates by 10% (Figure 1b) for each grid-cell then repeat the DDF parameterization as described in Section 3.2.2, respectively. Based on these experiments, we obtain an optimal parameterization for T0 and DDF which are thereafter used in the CONTROL run.” Please, clarify what you mean by “satellite estimates” (i.e., CMS) and “RACMO2.3p2 simulations” (melt amount estimates) to avoid confusions.

L80-84 These lines are unclear. Do you mean? “In addition, these sensitivity experiments enable us to explore potential applications of our PDD model to predict Antarctic surface melt in the future. Although our PDD parameters remain stable for the contemporary climate, it is uncertain how they could change in a warmer climate. Exploring the variations in PDD parameters by performing the above sensitivity experiments provides some insights on the model ability to simulate melt under future warming scenarios. “

L186-187: "… calculated by multiplying the cell area (km2) by the total annual melt days (day) in that same cell…"

In your response to reviewer #2, please consider the followings:
L70: What do you mean by “fidelity”?

Comment 4: I agree with the two reviewers that L29-47 could be shortened to focus on the impact of melt on the mass balance (e.g., runoff and ice shelf hydrofractures).

Comment 5: Here, referee #2 means that previous studies show that surface melt has not shown a significant increase/acceleration since 1980, but rather even a decrease as mentioned by referee #2. In view of this, the sentence “surface melt has most likely been accelerated by the rapid increase of atmospheric temperatures” could be inappropriate, please elaborate.

Comment 8: “ERA5 performs better at representing near-surface temperature than its predecessors …”

Comment 9: in L298-300, why not simply stating that 151 numerical experiments were carried out for T0 ranging from -10ºC to +5ºC with a 0.1ºC interval?

Dear Yaowen Zheng and co-authors,

Thank you very much for submitting your revised manuscript, which has been reviewed by our referees. The editor joins the referees to acknowledge the great effort you put into revising the manuscript. However, the paper remains too detailed/wordy in places, and sometimes overly technical, which can distract the reader. The manuscript also requires additional clarifications, notably on the selection of a grid-cell parameterisation approach, which should be better motivated. As noted by referee #2, it is currently unclear how the latter parameterisation remains valid for independent applications, i.e., future projections.

As a general comment, the introduction should be more focused. For instance, comparing Greenland to Antarctica is not strictly necessary (L17-19, L26). As suggested by referee #2, I recommend elaborating on the impact of surface melt on ice shelf viability, e.g., via hydrofracturing, and AIS mass balance (L24-25). The research question/objectives should be more clearly formulated: this study consists in a statistical exercise assessing the robustness of the PDD method to estimate AIS present-day melt.

Sections 3.3.1 and 3.3.2 are currently too technical. I invite the authors to reformulate these sections with a more appropriate level of detail. Referee #1 provides constructive ideas about this. Both referees spotted inconsistencies in the result section that should be checked. L270 states that the PDD model is “particularly well suited” to estimate melt over the Peninsula sector. L289-292 and L298-299 draw the opposite conclusion.

Based on the above, I deem that major revisions are required. Note that referee #2 and the editor will re-assess the revised manuscript before acceptance in TC.

Below, the authors can find additional minor suggestions.

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Section 2.2: Here the authors should mention that satellites detect the presence of surface liquid water, not necessarily surface melt.

L110: Remove “the” in front of “RACMO2.3p2”. This holds for the whole manuscript.

Section 3.1: Here the authors should (at least briefly) mention limitations of the PDD method. Otherwise, the reader only learns about shortcomings at the very end of the manuscript (Section 4.3).

L190: “The cross-validation (CV) technique …”

L217: Here you use the acronym CMS, which is defined for the first time in L277. Please define CMS here first.

L224-227: These lines could be removed as they anticipate on results discussed later in the text. For instance, you state that PDD parameters remain stable in the contemporary climate, which is discussed much later in the text.

L257-262: These lines are unclear. Could you remove or reformulate?

L311: Here you use the acronym SAM, which is defined for the first time in L345. Please define SAM here first.

From Section 4.2 onward: consider using “bias” instead of “mismatch” in the main text and figures/captions.

Dear Yaowen Zheng and co-authors,

I join the reviewer to congratulate you on a revised manuscript that clarifies remaining concerns and much improves the robustness of the results. The reviewer has a few minor suggestions, that I invite the authors to consider in a revised version. You can find below some additional edits. When the authors have addressed these minor comments, I am in principle happy to accept the manuscript for publication in The Cryosphere.

Best wishes,
Brice Noël

Editor minor comments:
L8: I suggest “… (PDD) model, forced with 2-m air temperature reanalysis data, and spatially parameterized by minimizing …”
L15-16: PDD estimates of what? Please clarify: melt amounts / extent?
L28-29: Do you mean “that increase ice shelf vulnerability, as meltwater can pond, drain and further contribute to the structural weakness of ice shelves.”?
L36: The authors could in ‘one sentence’ introduce Regional Climate Models that use SEB modules to estimate surface melt. See e.g. Wessem et al. (2018), Agosta et al. (2019) and models presented in the model intercomparison of Mottram et al. (2021).
L65: Please add a reference to the RACMO2 data set.
L155: “in the overlapping years.”
L219: 0 should be a subscript in ‘To’.
Table 3 and 4 captions: Please add “Ordinary Least Square” to define the acronym “OLS”.
L343: I suggest “… because of the correlation between …”
L370: Here and elsewhere could you consider “we show that” or “we find that” instead of “we see”.
L370: Replace ‘statistically significantly, strongly’ by ‘significantly’.
L373-377: Cut this long sentence into two sentences.
L383: I suggest “might explain” instead of “might be”.
L388-389: “To that is parameterized by … data sample used to parameterize … data length used to estimate …”.
Figure 8 caption L5: “shaded areas indicate …”.
L396: Do you mean “is expected to increase the occurrence of temperatures above …”.
L401-403: “sensitive … to” instead of “sensitive … on”.
L402: “while” instead of “when”.
L443: “surface melt estimates from using uni-PDD.”
L472-473: The link to IMBIE-3 data does not work, please update.
Figure E1 c, f and i and caption: ‘ERA5’ instead of ‘EAR5’.
L518: “first decade and almost overlap for the rest”

Wessem et al. (2018): https://tc.copernicus.org/articles/12/1479/2018/
Agosta et al. (2019): https://tc.copernicus.org/articles/13/281/2019/
Mottram et al. (2021): https://tc.copernicus.org/articles/15/3751/2021/

Dear Yaowen Zheng and co-authors,

Thank you for submitting your revised manuscript and response letter. Your clarifications and corrections have addressed all remaining comments. Therefore, I am happy to accept your manuscript for publication in The Cryosphere. Before publication, you should consider the technical corrections listed below.

Congratulations on the acceptance of your manuscript, and on your thorough revisions!
Thank you again for publishing your research with TC,

Best wishes,
Brice Noël

Editor technical corrections:
L382: “estimates are not significantly correlated” statistically is not necessary as you provide the statistics in brackets.
L406-409: “is less sensitive to the low melt scenario than the satellite estimates, as the dist-PDD ... while the satellite ...” and “is less sensitive to the high melt scenario than the satellite estimates, ...”.
L420: “that is reported by other studies”.
L440-441: “We have constructed a PDD model with spatially varying parameters (dist-PDD) and with spatially uniform parameters (uni-PDD) based on the temperature-melt relationship”.
L449: “We found that our dist-PDD model improves the accuracy of Antarctic surface melt estimates compared to the uni-PDD setting, and has ...”.
L511: “Our dist-PDD model shows significant negative bias in both surface melt days and amounts compared to ...”.