General comments:

This interesting research documents the impact of different factors on changes in March SWE by analyzing two reanalyses products and 22 CMIP6 models. The study shows that SWE is decreasing over most of the Northern Hemisphere, as decreases in snowfall and snow-on-ground are more significant than the increase in total precipitation. However, there are large variations between the products analyzed. In general, the study is well-written and easy to follow, and I only have a few comments as outlined below.

As the author discusses, there are large differences between different models/reanalyses analyzed in this research and making definitive conclusions might be difficult but, as the paper discusses changes in SWE, I think it might be good to have a bit more clear statements about these changes in the conclusion. Also, some comments on how the changes in March mean SWE differ from the findings of other papers mentioned in the introduction (e.g., Pulliainen et al. (2020) and Mudryk et al. (2020)) might be good.

This research has some similarities to Kouki et al. (2022) which analyses SWE in CIMP6 models and the effects of different factors (temperature and precipitation), though this article covers a larger time span and includes also analyses of reanalysis products. This manuscript mentions that CMIP6 SWE exceeds the GlobSnow estimates similarly to Kouki et al. (2022) but maybe a few more words about any similarities/differences would be good...?

Specific comments:

L11: ’This is repeated…’ This sentence is a bit unclear, what is repeated?

L130: A sentence or two describing MERRA 2 might be good (as there is a short description of ERA5- Land).

Table 1.: Possibly line numbers have jumped to the last column of the table? Or what are the numbers (145, 150) in the table?

Figure 3: It might be interesting to see the difference in SWE between different versions? Different spatial trends are visible in the figures but the same figures showing the differences might be beneficial.

L520: Are there some areas where the spatial correlation is better? The average SWE values are larger in North America and some products have problems with this and thus have better performance in Eurasia.

L521-523: “However, compared with both ERA5L and MERRA2…” I find this sentence bit unclear, what does overestimating the SWE decrease mean?  

References:

Kouki, K., Räisänen, P., Luojus, K., Luomaranta, A., and Riihelä, A.: Evaluation of Northern Hemisphere snow water equivalent in CMIP6 models during 1982–2014, The Cryosphere, 16, 1007–1030, https://doi.org/10.5194/tc-16-1007-2022, 2022

Mudryk, L., Santolaria-Otín, M., Krinner, G., Ménégoz, M., Derksen, C., Brutel-Vuilmet, C., Brady, M., and Essery, R.: Historical Northern Hemisphere snow cover trends and projected changes in the CMIP6 multi-model ensemble, The Cryosphere, 14, 2495–2514, https://doi.org/10.5194/tc-14-2495-2020, 2020.

Pulliainen, J., Luojus, K., Derksen, C., Mudryk, L., Lemmetyinen, J., Salminen, M., Ikonen, J., Takala, M., Cohen, J., Smolander, T., and Norberg, J.: Patterns and trends of Northern Hemisphere snow mass from 1980 to 2018, Nature, 581, 294–298, https://doi.org/10.1038/s41586-020-2258-0, 2020.

The author compares how three contributing factors that influence March historical snow water equivalent trends are represented in two reanalysis products and in 22 CMIP6 models. The factors contributing to total SWE change are changes related to the total precipitation, the fraction of precipitation occurring as snowfall, and the fraction of accumulated snowfall which remains on the ground. The author determines that there is broad agreement in the subcomponents over the long analysis period assessed (1951-2022) but that internal variability and model biases reduce the agreement between historical trend estimates and the CMIP6 multi-model mean over the shorter 1981-2022 period analyzed.

General Comments: Overall this paper is well-written and provides logically argued results. The framework used to attribute SWE changes to changes in precip, snowfall fraction, and snow-on-ground seems to works well and provide reasonable results. I only have a  few issues I’d like to see addressed or commented on.

Specific comments:

The snow-on-ground term G absorbs a wide range of processes that will vary substantially from model to model. While inter-model difference in snow melt will be a key component of this term, differences in sublimation and any other structural differences in how a particular model treats snow will also affect it (e.g. vegetation-snow interactions, differences in how well snow water mass is locally conserved in a given model). Thus, it isn’t surprising that the models disagree the most on the changes in this term. I think it’s worth pointing this out in the text when you first discuss the equations and also at line 270 where you attribute the differences in G primarily to snow melt.

Line 186: I believe you are defining X1=X_clim and X2 = X_clim + dx where dX is the monthly anomaly. Using these definitions x-bar is the monthly mean value plus half the monthly anomaly. If you actually used G_bar = G_clim + 0.5dG, F_bar = F_clim + 0.5dF, P_bar+0.5dP in equation (2) please state this more explicitly. If you assumed the additional ½ dG/dF/dP components of G_bar/F_bar/P_bar would be absorbed into the non-linear term as second-order terms and approximated G_bar = G_clim, F_bar=F_clim, etc, please state this instead.

I think the MMM trends you show are probably a good representation of the ensemble average given the range of models. But it would still be good to check that the figures look similar if you plot the median trend value at each location in case there is any undue influence in the mean from outlier trends. 

Minor comments:

L541: Please rephrase. I don’t think snow melt occurs more efficiently as the climate warms. There’s just increased snowmelt in a warmer climate.

The manuscript “Changes in March mean snow water equivalent since the mid-twentieth century and the contributing factors in reanalyses and CMIP6 climate models” uses a decomposition-based approach to evaluate and diagnose changes in historic snow water equivalent (SWE) trends in the northern hemisphere for two historic periods in two reanalysis products, the GlobSnow product, and the CMIP6 ensemble. SWE is decomposed into contributions from total precipitation, snow fraction, and snow-on-ground fractions. The primary findings include high degrees of spatial correlations but individual variation due to model-to-model differences in snow-on-ground fraction. Total SWE has gone up in many far northern locations due to increases in precipitation, though CMIP6 appears to overestimate SWE increases. Biases in all data sources are discussed, and the paper highlights how difficult SWE is to correctly simulate in climate models. The topic is within the scope of The Cryosphere.

Overall, I like the methodology as an interesting approach to breaking down drivers of SWE. However, my first major concern centers around choices in the spatial aggregation step and the monthly time step that may lead to very different results. Huge efforts and computational resources have been expended on improving spatial resolution of snow (and many key climate system variables) in global models, and it is unfortunate to not see how finer resolution may improve the insight provided by the work (it also may not, but it needs to be shown). My second major concern is the lack of energy balance components in SWE trends is perhaps implicit in the G term, but this is not apparent from the methodology description.

The paper is written well. For the audience I expect to find this paper of the most benefit (e.g., modeling and observational groups focused on snow processes), the figures are satisfactory. There are numerous occasions where qualitative information is given (e.g., L232 “slightly larger”) or implied (L235 “exceeds”) when numerical values would be welcomed as they are more informative. The paper would also benefit from additional citations to shore up arguments and to increase its comprehensive coverage of the topic. With revisions to address the major, minor, and specific comments, I believe this manuscript will make a solid contribution to the literature.

Major Comments:

1. The aggregation via interpolation of observational data and CMIP6 simulations to 2.5° horizontal resolution likely will cause a lot of loss of potentially valuable information, especially in mountainous areas where SWE can vary over much smaller spatial scales. I am concerned that the results and interpretations may be very different if different resolutions are used. There may be good reason to do this aggregation as performed, but this needs to be shown. In other words, how much do the results vary if the ERA5, MERRA2, CMIP6, and GlobSnow are all re-gridded to 50 km instead of such a coarse 2.5° resolution? This exercise may also highlight where models are doing better/worse across locations in the Northern Hemisphere and be valuable to modeling groups who want to improve their results.

1. What physical components control the SWE on the ground (the G term in eq 1)? Does this term accumulate the effects of the surface energy budget? More explanation is needed as this is a critical component of SWE trends (the “demand side” whereas F and P are the “supply side”). While the focus on the supply side of SWE trends is valuable, adding an analysis of G, especially if broken down into its physical components, would greatly elevate the papers contribution to understanding what is driving SWE trends as well as be helpful for the modeling community to improve the representation of these key processes (L270 and L349 acknowledges the challenges of snowmelt modeling and role of how this step leads to differences in results). This would allow the paper to nicely ‘bookend’ the supply and demand sides in the CMIP6/historic reanalysis framework.

Minor Comments:

1. It was unclear what timestep of observational and model output was used, was it monthly March means or the date of peak snow water equivalent in March (daily). Similar to Major Comment #1, how sensitive are the results to the use of monthly versus daily values? After reading further, it appears March monthly mean was used, but was this necessary for some reason? Why not use the peak March value (which likely would vary in time across the month by latitude, elevation, a given year, etc)?

1. L229: This difference in mean SWE could be readily examined by using finer (native) resolutions, making a stronger point than the speculation provided at present.

1. It would help to have a bit more comprehensive literature review on SWE comparisons between reanalysis products such as MERRA2 and ERA5L across locations and scales; this may also be helpful when discussing the results found.

1. I liked the two directions posed in the conclusion, however the way the conclusion was organized, the paper felt like it ended abruptly. I suggest adding a short closing section to finish the article or reorganizing this section.

Specific Comments:

L23-32: Suggest to add citations to the first paragraph; all good info but offers opportunity to point readers to recent work on various sub-topics.

L41: Add “beneficial” before “ecological impacts”?

L45-54: This paragraph would be stronger with additional numerical quantification of historic change and more local specifics, e.g., what are the decreasing trends?

L69: Suggest removing “three-dimensional” as weather prediction and climate models are four-dimension (3-d in space plus a time dimension). Would also benefit to add some examples of these to give readers examples of their spatial and temporal resolution of output.

L81: add the scale this paper addresses (Northern Hemisphere) to “recent trends in SWE” just to set the stage for going into the questions.

L107-112: Instead of this table-of-contents explanation of upcoming sections, I think this text could be markedly condensed and some initial insights into what the work provides the community could be given, thus helping motivate the work better.

L138: Please quantify “thick”.

L138: How much is this underestimation of SWE?

L141, 167: Tables 1 and 2: Please add a column of the native spatial horizontal resolution of these products

L154: Please define the SSP scenarios briefly and add a reference.

L165: Please add a reference for conservative remapping (even if just the function used in the programming language) to ensure repeatability.

L172: Table 2: suggest making the delta-T subscripts hyphenated (51-22) to be more intuitive.

L180: What fraction of areas in the Northern Hemisphere have permanent snow cover? Has this number changed substantially? It would be OK to give the mean or median value for a given date range to give readers an idea even if this is calculated for each specific year.

L189: Please define “very small”.

L239: Alternatively, could the ERA5L SWE being “too large” be a product of it doing a better representation of SWE at high elevations as well?

L255: Missing period at end of sentence.

L281: Suggest to be more specific in terms of temperature (and radiation), also add citation(s) here unless this finding is directly shown, in which case please reference the figure or table here.

L284-285: Add references; also would help to provide some additional physical reasoning about the logic involved in this sentence.

L317-320: Would help to give trend values in the text for easy comparison.

L331-334: Does this suggest the models are getting temperature signals correct? I see later this is noted in a few paragraphs (L343); perhaps consider reorganizing the text in this section and the other to allow it to flow more naturally?

L370: change “Both” to lowercase

L371: all or nearly all, can you rephrase to give a specific number?

L396: Change to: “With regards to the components…” or “Regarding the components…”

L428: To what extent might relative humidity (or direct moisture variables) be at play in the snowfall fraction? There has been a lot of recent work highlighting the importance of atmospheric moisture in determining precipitation phase (see e.g., Jennings et al. 2018 Nature Communications). Could be worth mentioning here.

L465: Is this comparison of spatial correlation performed at 2.5° resolution or at finer scales?

L474: This is interesting discussion; have other authors suggested, found similar results, or further investigating these aspects in CMIPx? Worth adding if so.

L501: Instead of "Height" would  ”maximum extent” or “maximum depth” be better terms?

L513: Here’s a great example of where numerical values would help readers and would be useful for citing this work! How much compensation of increased SWE from precip is there in the other direction (loss) from FP and G declines? OK to give an average and the range (e.g., 1 standard deviation).

L540: Per Major Comment 2, did this approach address how snowmelt occurs and what drives it becoming more rapid or frequent as the climate warms (I’m not sure “efficient” is the right word here, either, though I suppose if SWE is broken down into melt and sublimation terms, water input to the surface from snowmelt would be less efficient per unit SWE if more water was lost to sublimation).