The methodology of this paper is flawed. Not only are the atmospheric rivers (AR) included in the climatologies used, and thus cannot exceed 100% of the budgets, but the local fluxes within the bounds of the AR are calculated as an anomaly without consideration of the budget for region as a whole i.e. reflecting the fractional area of the AR to the area of the region as a whole (e.g. Greenland, marginal seas  etc. 

Additionally, the authors to not make the case for AR vs extratropical cyclones. AR are not a standalone feature and thus the tropical cyclone itself is the story not the AR.

Some other line by line points

Line 46. The argument here is that atmospheric rivers are a distinct feature when they are simply associated with extra-tropical cyclones. It is the cloud associated with the cyclone warm front that is leads to the excessive LW-down. The detrainment of water vapor from the cyclone could be adding to LW-down, but the authors are not distinguishing the two characteristics here. Include further references to add to Ralph et al., 2018 to show that there is considerable mechanistic literature on the cause of ‘atmospheric rivers’.

Eiras-Barca, J., Ramos, A. M., Pinto, J. G., Trigo, R. M., Liberato, M. L. R., and Miguez-Macho, G.: The concurrence of atmospheric rivers and explosive cyclogenesis in the North Atlantic and North Pacific basins, Earth Syst. Dynam., 9, 91–102, https://doi.org/10.5194/esd-9-91-2018, 2018.

Zhang, Z., Ralph, F. M., & Zheng, M. (2019). The relationship between extratropical cyclone strength and atmospheric river intensity and position. Geophysical Research Letters, 46, 1814–1823. https://doi.org/10.1029/2018GL079071

Dacre, H. F., P. A. Clark, O. Martinez-Alvarado, M. A. Stringer, and D. A. Lavers, 2015: How Do Atmospheric Rivers Form?. Bull. Amer. Meteor. Soc., 96, 1243–1255, https://doi.org/10.1175/BAMS-D-14-00031.1.

If you accept that ‘atmospheric rivers’ are manifestations of subtropical cyclones, as the above papers suggest, then reference to previous Arctic budget analysis is required.

Villamil-Otero, G.A., Zhang, J., He, J. et al. Role of extratropical cyclones in the recently observed increase in poleward moisture transport into the Arctic Ocean. Adv. Atmos. Sci. 35, 85–94 (2018). https://doi.org/10.1007/s00376-017-7116-0

Line 68. In any estimation of energy budget on needs to calculate the impact of snowfall associated with the cyclones on sea ice and land energy budgets, because of the high albedo of snow in spring.

Webster, M.A., Parker, C., Boisvert, L. et al. The role of cyclone activity in snow accumulation on Arctic sea ice. Nat Commun 10, 5285 (2019). https://doi.org/10.1038/s41467-019-13299-8

Line 79. There are other mechanisms for extremes (which have a disproportionate impact) of the energy budget eg.

Papritz, L., S. Murto, M. Röthlisberger, R. Caballero, G. Messori, G. Svensson, and H. Wernli, 2023: The Role of Local and Remote Processes for Wintertime Surface Energy Budget Extremes over Arctic Sea Ice. J. Climate, 36, 7657–7674, https://doi.org/10.1175/JCLI-D-22-0883.1.

But it may be sensible not to extend the length of the submission by avoiding discussion of extremes as this is whole topic in itself.

Line 95. You should note here that ECMWF does not directly assimilate tropospheric water vapour over land or sea ice, except for radio occultation which does not have the capability to detect AR, and so there is no actual measurements 

Line 96. If you just did explosive cyclone tracking, would you get the same answer? After all, it is the clouds that matter for LW-down rather than the water vapour itself.

Line 175. Rewrite such that Figure 1 is not the subject of the sentence but supports the statements e.g. ‘The seasonal frequency of AR occurrence (Fig 1) shows…

Line 176. Avoid putting detail in the text which should be in the figure caption (eg. The index used and the limitation of the period 1980-2019. Otherwise, you are repeating what should have been in the methods section. Have a new sentence to introduce the topic of Table 1

Table 1. I do not understand this table. The AR are already included in the seasonal climatology so how can they contribute more than 100% of the LWD or surface energy budget? E.g. Greenland. The only way to do this properly is to total the number of J/m2/s for the time without AR and then sum over the time with AR.

General comments

This study is a comprehensive examination of the atmospheric river (AR) influence of the surface energy budget (SEB) across the entire Arctic. Using an AR detection algorithm based on relative monthly integrated vapor transport (IVT), the authors identify the distinctions of AR SEB influence across land, open ocean, and sea ice regions. Their results help confirm and build upon previous understandings about AR impacts on Greenland surface melting and especially the hampering of winter sea-ice growth. Regarding this AR impact on winter sea-ice growth, the observation that this process is highly sensitive to the choice of AR detection algorithm is a great distinction between the impacts observed while using an AR detection algorithm designed to capture extreme events and an algorithm designed to capture more frequent events. There is a clear line of progression from the authors’ previous first work on Arctic AR climatology to this study on Arctic AR SEB behavior. The methods are clear and well formulated, and the results are exhaustive and detailed. To my knowledge, previous studies have looked at localized Arctic SEB impacts from ARs, but this is the first study to make a comprehensive analysis on this topic across the entire Arctic. After some minor revisions, this manuscript will serve as an excellent reference for other researchers looking to understand the overall influence of ARs on the polar SEB. I would be happy to see this manuscript published after some global comments and a series of minor comments are addressed.

Specific comments

1. Section 2.3: Please consider including the equation for the SEB so the reader can quickly understand the various SEB components presented in this manuscript.
2. Sec 3.1: Please discuss how the AR frequency results presented here compare to the analysis in Zhang et al., (2023). Assuming that this is a similar analysis as Zhang et al., (2023), it may be helpful to mention that you have repeated this AR frequency analysis to help contextualize your later SEB results. I do like that you made this a small section as to not detract from the SEB analysis.
3. Figure order: Consider changing the order of the results so that the net SEB is presented first and followed by the components of the SEB. This could improve the readability since currently Figure 7 is referenced before Figures 3-6 when discussing the LWD results.
4. Section 4.2: This is a good discussion comparing the melting implications of your study with previous works, but it could use some more elaboration and clarity. In the beginning, you mention is disparity between the results of Mattingly et al., 2020 which found ARs delivered large sensible heat fluxes while your study links ARs to smaller turbulent heat fluxes and more net longwave anomalies. You attribute these differences to the focus on stronger ARs in Mattingly et al., 2020, but could elaborate on why a focus on stronger ARs might cause these differences?

Then you discuss your findings in Northeast Greenland which point to a larger influence of turbulent heat fluxes which actually agrees a bit with Mattingly et al., 2020 and aligns closer to Mattingly et al., (2023) which discusses more the foehn effect from ARs. It would be good if you can mention this agreement with Mattingly et al., (2023) and how your sensible heat flux results might be picking up on the AR-related Foehn contribution in the region.

1. Section 4.3: Naturally, some readers will wonder if you would get similar results using a cyclone-detection algorithm to study SEB impacts. I’m not suggesting you make an additional analysis with a cyclone-detection algorithm, but perhaps it could be beneficial to add a few sentences to the end of this section relating your results with other studies that did track SEB-impacts from cyclones and then argue why it is more informative to use ARs instead of cyclones to quantify SEB-impacts.

Minor comments

Line 29: First sentence is a run-on. Consider breaking it up.

Line 41: “Remote perspective” is slightly vague. Maybe “remote forcing perspective”

Line 47: Consider distinguishing the studies that focus on Antarctic ARs and Arctic ARs.

Line 53: Add an oxford comma after “ocean”

Line 67-68: It’s good you cited the importance of the AR impacts on the SEB in relation to sea ice. But since this paper also discusses the SEB over land, you should also state the importance of the AR SEB impacts over land ice.

Line 68: “accelerate or decelerate ice growth” you should clarify that you refer to sea ice growth here.

Line 80: Correct “AR’s impact” to “AR impacts on the Arctic surface energy budget”. Surface energy budget should be singular unless you reference multiple locations in the sentence.

Line 86-91: This is a really long sentence. Consider breaking it up around when you describe MERRA-2 being the source data for ARTMIP.

Line 100: Can you briefly say why you only choose dates during neutral or weak ENSO events?

Line 133: It seems odd that surface energy budget is first abbreviated here and not earlier in the introduction on its first use.

Line 159: Consider changing to “underscores the potential role of ARs driving net SEB fluctuations”

Line 164: Comma after “To do this”

Section 3.2: Just wanted to say that I appreciate you outlining the different figures and tables here before continuing to the sub-sections. This is very helpful for the reader to follow along.

Line 227-228: Nice result here. You could comment that ARs are nearly the exclusive cause of LWD over Arctic land areas during winter. This would make them the main cause for warming during the winter since winter warming is driven by LWD

Figure 2c,3c,5c,6c,7c: On both ends of the color bar, there is a gray color to represent values exceeding -100 and 100%. In Figure 2c, the caption says these gray areas represent percentage results greater than 100%. However, in some other figures, the gray areas represent percentages less than 100%, but this isn’t mentioned in their figure captions. Please clarify this either in the Figure 2 caption or the following figure captions.

Line 257: Figure 7 is cited before Figures 3-6. While I appreciate that this is meant to enhance the discussion of the results in Figure 2, it is disorientating to the reader since they haven’t had a chance to understand the meaning of Figure 7 and forces them to skip ahead in the manuscript. Please considering moving Figure 7 to Figure 3, moving this text to the discussion, or devise another solution to improve the order of results here.

Line 274: You mean the AR-related LWD contribution here?

Line 276-284: While I do like some reflection on the meaning of the results in the Results section, this paragraph feels more appropriate for the Discussion section. Especially since you are citing Figure 7 before Figures 3-6.

Line 294: This might be a question for the editor, but it would be helpful if there was some label or subsection break between the LWD and LWN results (and for the other SEB components). Even just “Net surface long radiation” written in bold would help the reader follow along.  

Line 328: You should cite Zhang et al., (2023b) here concerning the AR impacts on marginal sea ice zones

Figure 3: Is there a particular reason why it appears AR have a negative LWN contribution in this patch over central Siberia?

Line 360-361: Does this mean that AR-related warm air advection is more important than the AR-related SEB influence?

Line 394: Add space in (Fig.5b).

Line 408-409: Here and other places you should clarify that this warming role is confined to the SEB and does not include warm air advection related to ARs.

Line 414: Play not plays

Line 415: Add oxford comma.

Line 441: Comma after “Unlike other Arctic regions”

Line 456: Comma after “Arctic Ocean”

Line 474: Add “the” between “highlights AR’s”

Line 474-483: I was wondering why the AR contribution to turbulent heat fluxes is negative around the coastline of Greenland, but positive over the Greenland interior. Perhaps you can comment on this in this last paragraph of the section.

Line 506: This delay in sea-ice refreezing is also a result from Zhang et al., (2023b) and should be mentioned here.

Line 529: Comma after “central Arctic”

Line 559-561: I’m very happy to see these AR temperature anomalies quantified so extensively for the Arctic region

Line 657-659: This remark about the sensitivity of the AR effect on the hampering of the winter sea-ice freeze to the choice in detection method is one of the more compelling implications from this study. You make a great point about the risks of only capturing extreme AR events for studying impacts. Although not necessary, this would be a good point to include in the abstract if you can replace another sentence as the abstract is already long.

Line 675: “rely” not “relies”

Line 693-695: Suggest rewording this sentence.  “partially offsetting the large LWD anomalies, thus resulting in moderate impacts on the LWN anomalies”

Line 727-728: “especially during cold seasons, particularly winter”. Suggest rephrasing since most people would consider winter the cold season.

References:

Mattingly, K. S., Turton, J. V., Wille, J. D., Noël, B., Fettweis, X., Rennermalm, Å. K., and Mote, T. L.: Increasing extreme melt in northeast Greenland linked to foehn winds and atmospheric rivers, Nature Communications, 14, 1743, https://doi.org/10.1038/s41467-023-37434-8, 2023.

Zhang, C., Tung, W., and Cleveland, W. S.: Climatology and decadal changes of Arctic atmospheric rivers based on ERA5 and MERRA-2, Environ. Res.: Climate, 2, 035005, https://doi.org/10.1088/2752-5295/acdf0f, 2023a.

Zhang, P., Chen, G., Ting, M., Ruby Leung, L., Guan, B., and Li, L.: More frequent atmospheric rivers slow the seasonal recovery of Arctic sea ice, Nature Climate Change, 13, 266–273, https://doi.org/10.1038/s41558-023-01599-3, 2023b.

In this paper, authors aim to analyze the contribution of atmospheric rivers (ARs) to the seasonal surface energy budget (SEB) in the Arctic using ERA5 reanalysis data for 1980-2019. ARs are detected using the 85^th percentile of IVT and components of the seasonal SEB are anomalies are assessed for times when ARs are detected. The aim of improving understanding the importance of ARs in net SEB in the Arctic is important and interesting, and the authors provide a very detailed analysis with discussion of implications and connections to previous work. Analysis regarding absolute anomalies is thorough, but I am unsure of the appropriateness of the metric used to quantify the contributions of ARs to seasonal SEB (detailed in Major Comment 1). 

Major Comments:

1. The metric used for evaluating the contribution of ARs to net SEB may not be appropriate for the conclusions drawn. It is difficult to interpret the physical meaning of the contributions when the seasonal net SEB is very small. Please see the attached file for a description of a potential solution and further reasoning. Regardless of how the authors proceed, the equation used to calculate this metric should be included, rather than only described in words to make sure it is very clear what is being shown.
2. I am unable to reproduce the “contribution to SEB” values shown in Table 1 using the description of how it was calculated in Section 2.3. Since the AR frequencies, anomalies and net SEB values are provided for each region, the contribution should be able to be calculated without any further information (based on Section 2.3). Please see the attached document for an example of this calculation not resulting in the same value seen in Table 1.
3. Consider performing statistical testing to determine if the absolute anomalies during ARs are statistically different from the mean conditions (which could be shown in the b rows of Figures 2-7). Since ARs exist in a location likely for more than one timestep, there is some temporal autocorrelation which may be accounted for by randomly selecting a smaller sample of AR timesteps to compare to a randomly selected sample of non-AR timesteps. Determining the statistical significance of these anomalies may help to identify SEB components that are more important with more confidence.

Minor Comments:

• 45-46: ARs typically being associated with extratropical cyclones is mentioned here, but isn’t discuss it again. I think more discussion regarding the linkage between cyclones and ARs would be valuable here for context of when/how ARs occur in the Arctic.
• 100: It is mentioned that times are only used during neutral or weak El Niño-Southern Oscillation. I assume it’s because of IVT anomalies associated with strong ENSO events, but it is worth briefly stating in the text for clarity.
• 123-125: Is it necessary to give multiple names for these first 3 ERA5 variables?
• 147-149: This sentence uses both “three-hourly” and “3-hourly” referring to the data – I suggest picking one to remain consistent.
• 287-289: What is meant by “ARs make their most significant relative contribution to the average net SEB in spring, accounting for at least 45% of the net SEB, surpassing the corresponding AR frequency by more than 34%”? I don’t think subtracting the frequency from the contribution has a physical meaning since they are percentages of different things.
• 358: I suggest starting a new paragraph at “The results over the central Arctic” as this is a long paragraph, and a new topic is being introduced here.
• Section 3 is titled “Analysis and Results” and Section 4 “Discussion”, but Section 3 includes a lot of discussion (i.e., discussing potential impacts of the anomalies, comparing to previous work) and Section 4 still discusses some results (particularly temperature). A potential solution for this would be to rename Section 3 to focus on SEB and Section 4 to focus on impacts, and perhaps create another section for limitations/uncertainties (for 4.3 and 4.4).