This work presents important updates to the GlobSnow data assimilation framework to best utilize long temporal records of spaceborne microwave data to improve global estimates of SWE. This manuscript proposes two key additions to the existing product including new snow course data, as well as a novel daily bias correction approach. I have included larger comments and smaller in-line comments in the sections below that I believe could help improve this manuscript. Most of my larger comments are directed at the new daily bias approach. With this being a new approach, I believe some added clarity would be beneficial to the readers. Once these comments are addressed I would strongly support this paper being reconsidered for publication. 

Larger comments to authors:

• Daily bias correction using linear (e.g., MLR) and non-linear methods (e.g., random forest) have shown success in previous work estimating SWE bias from SNODAS (King et al., 2020). With your ample amount of snow course data and large study domain, have you considered using such methods to estimate daily bias fields for PMW? The reason I suggest this is because you inherently lose valuable temporal information by first aggregating to monthly fields for the purpose of kriging, correct? If my statement is true, I think a more nuanced discussion may help inform present/future efforts? 
• Another point on the daily bias via monthly bias fields, and correct me if I am wrong, but this hinges on two things : 1) that DMSP SSM/I-SSMIS is a daily product (which is true), and 2) that snow course data is uniformly distributed across a given month, temporally? For example, if more snow course observations were present at the frontend or backend of a given month, there would be issues with interpolating based on the 15th? How might this impact your Eq 1-3?
• Is it common to fill missing values prior to avg monthly bias using this technique? It would seem this could potentially introduce a bias itself?  How does this gap filling impact your daily model? You return to this idea in Line 485 for example, where you state the end of May can have positive bias. Do you include June in the interpolation? Also, similarly does filling missing values impact December in a similar way? What is the purpose of filling and not just using the geometric mean? I think I would just like to see clarification in the reviewer discussion and not necessarily in the manuscript. 
• Clarification on 40 years of data which you mention in the text. However, you refer to analysis 1980-2018 (39 years). Is this a typo or is it 39 years of analysis ?

In-line comments to authors:

Line 10: Suggest changing “global snowpack” instead over “snow cover”?

Line 12: Define (PMW) here for the abstract.

Line 19: I’m not sure necessarily if these products need to be mentioned in the abstract but will leave it up to the authors. 

Line 25: GS has not been defined in the abstract. 

Line 35: 37GHz ~ 8 mm . I don’t think this statement is entirely true as most snow grains are between ~ 0.5-4 mm? It’s certainly closer than 19GHz, but I think I would like to see a response from the authors or to adjust the language just slightly. 

Line 45: At this specific frequency? Maybe it could be useful to specify. E.g., snow is a scattering medium in visible wavelengths for all values of SWE.

Line 49: Listing the 4 products like this is a little awkward, but perhaps could revisit the grammar to include them all together in a list.  

Line 56: GS has not been defined in the text.

Line 61: I suggest the authors consider if this paragraph is needed.

Line 72: I think you are missing GHz after 19.40?

Line 75: You mention masking complex terrain from retrieval but discuss results across mountains (e.g., US Western Mountains in Line 326), please explain?

Line 76: What method is used for wet snow to relate SD to SWE when the PMW algorithm is not used?

Line 79: There is often ambiguity and both are commonly used, please specify if you are referring to diameter or radius for effective snow grain size. I assume diameter based on d0 but would just like to clarify. 

Line 84: Should use previously defined d0 symbol.

Line 90: You mention later on that constant density = 240, I suggest adding here as well for the reader.

Line 94: Is it worth having the CDR acronym as it only is stated once in the paper?

Line 150: What exactly do you mean when you state, “filled from two closest”? Linear interpolation? If so, it would be nice to state this.

Line 151: typo, “Filling”

Line 174: Check grammar , “are” used?

Line 175-176: Suggest revising to simpler sentence structure here.

Line 180: Check grammar , ‘“are” not used’?

Line 194: Appendix A figure may be more supportive to your claim if you were to include a simple statistical trend test to assess for slope, significance levels, etc based on the data points shown here. 

Line 208: The updated SWE being larger is not visually apparent in the histograms, and could be aided by adding the colored mean values (red/blue) as text to the plot, and/or adding dashed vertical lines representing the mean SWE. 

Figure 1&2 can be combined if the authors would like. 

Figure 1&2: Please be consistent with “old” vs. “new”  / “updated” vs. “original”. You should stick with only one of these and stay consistent throughout the text to be more concise. 

Figure 1&2: What is being shown with the black/white and the green backgrounds?

Line 226: SCI? Do you mean SC?

Line 235-239: Revise run-on sentence. 

Line 244: Please provide reference to gamma SWE dataset if available. 

Line 246: You can add in this sentence, “because of gammas higher relative accuracy”, or something similar to this effect. 

Line 250: Not required to add, but may be insightful to add here for early-career readers to very briefly (~1 sentence) discuss “saturation effect” (see example in Cho et al., 2020) and the rationale for splitting validation metrics at 150 mm SWE. 

Line 256: This is the first mention of SnowPEx. Briefly introduce, as well as discuss why you are comparing this to your NH SWE estimates. (I understand after reading it for the first time, but extra background here I believe will strengthen your methods).

Figure 3: Is it not clear to me if the black/white areas are different snow climates? Extents of the model?

Line 267: It would be nice to stick with old/new or updated/original, for consistency. 

Line 269: SC.v31 typo.

Figure 5: Shouldn’t you also mention this is excluding complex terrain as done in Figure 8? Capitalize the Northern Hemisphere (check throughout text)?

Line 280: In the caption, “SCv3.0” should be changed.

Line 295: With the over-abundance of SD for informing inversion in Finland (and stable bias), I am curious if future work could try holding out SD/SWE for independent evaluation (if data available). 

Line 301: Non-mountainous correct?

Line 313: I suggest to be consistent and either use SCv3.1 or Snow CCI.

Figure 6: I think this may be a typo and should be “SCv3.1”?

Line 331: I was thinking a lot about this sentence, and have a suggested rewrite the authors may consider:

“Applying the updated snow course data to both GSv3.0 and SCv3.1, we show …” etc. 

Something like this?  The point is this is getting at the retrieval algorithm and so it may be helpful to lead with the updated snow course data being the same in this scenario. 

Line 337: It would be best not to say probably, and if you have these data you should be able to verify. 

Line 345: Be more specific, are these changes to the retrieval related to the variable snow density?

Line 348: Please add the years discussed in Mortimer et al 2022 in this sentence. 

Line 351: Instead of saying, “...to that of two suites of reanalysis products, as described in Sect. 2.5…” Please consider simply referring to SnowPEx here.

Line 359: Please check the typo, “SnowPEx”.

Line 370: Referring to section 2.5 like this is confusing since it also includes gamma data. Can you not just state SnowPEx reanalysis data here?

Line 371: I think you mean Table D1**. Also, I am curious if you tested the daily bias correction SCv3.1 and the monthly bias correction SCv3.1 against gamma. It appears in this table you have just done the daily? However, would it not be beneficial to show if there is improvement from your new approach over the prior method?

Table 1: Why isn’t V3.1 included in Table 1 against gamma SWE measurements? Or is this a typo?

Line 384: Table D1*

Line 394:  I know the reanalysis product is not a pure validation set, but I think it still may be helpful to see Pearson correlation for Figure 7. I’m thinking this decision is best left to the authors however. 

Figure 7: Is the light grey in this map the topography mask? IF so, this needs to be stated in the caption.

Line 429: check consistency throughout , “in-situ” vs. “in situ”. Also in L236 and  L241.

Figure 8: It seems the months are not aligning with the x-axis ticks (it aligns with the text)? Also there are three shaded areas? In the text you mention only the SnowPEx being shaded? 

Figure 8: It would be helpful to draw the mean/median SnowPEx as you refer “to center” often, however, it would be much more clear with it drawn on. Further, you may discuss the mean/median values and the differences between the SCv3.1.

Line 440: And perhaps areas for future testing could be with region specific reanalysis data, such as those presented in Fang et al. (2022)?

Line 447: But is the peak really indicative here? Wouldn't the percentage of observations over, say 150mm, be more physically meaningful? Similar to how you described the 3x increase in low-bin for the updated snow course data.

Line 452: Typo, SWE.

Line 455: If this is a question of differences in magnitude, there are validation metrics that account for this such as “relative root mean squared difference” or using percent differences ? Perhaps I am looking at this incorrectly. 

Line 478: Please add the word “SWE” after GSv3.0.

Line 490-491: I would avoid saying “might” here. If possible, would you be able to check the data and report with added certainty here?

Line 505: “Northern Hemisphere”,  capitalize, check throughout.

Line 506: Closer to the mean? Median? How much more accurate was your daily bias product vs. your improved monthly product. To reiterate on one of my points above, if you compared both the monthly and daily bias correction methods to the gamma dataset, you could get at a regional percent improvement, correct?

Line 511: Please consider adding “in relation to GSv3.0” after “for April and May”.

Line 572: Correct typo in reference Brown et al. 2018.

Line 632: A note to the authors that this work was published, here is the citation:

Mortimer, C., Mudryk, L., Cho, E., Derksen, C., Brady, M., and Vuyovich, C.: Use of multiple reference data sources to cross-validate gridded snow water equivalent products over North America, The Cryosphere, 18, 5619–5639, https://doi.org/10.5194/tc-18-5619-2024, 2024.

References

Fang, Y., Liu, Y., & Margulis, S. A. (2022). A western United States snow reanalysis dataset over the Landsat era from water years 1985 to 2021. Scientific Data, 9(1), 677.

King, F., Erler, A. R., Frey, S. K., & Fletcher, C. G. (2020). Application of machine learning techniques for regional bias correction of snow water equivalent estimates in Ontario, Canada. Hydrology and Earth System Sciences, 24(10), 4887-4902.

The manuscript by Venäläinen et al. entitled “Updated monthly and new daily bias correction for assimilation-based passive microwave SWE retrieval” presents a new version of the GlobSnow passive microwave data assimilation product (GlobSnow V3.0), updated with new snow course data for monthly bias correction and extended to daily bias correction (Snow CCI V3.1). The authors show that the new bias-corrected product provides better estimates of SWE over the northern hemisphere, especially in spring. The paper is well written and I have no major concerns about its publication as a research article. I have only one general comment regarding the structure of the Results section, which should be revised, and several specific comments aimed at improving the clarity of the manuscript. I recommend that the manuscript be accepted for publication after the authors have addressed these few points.

General comment:

The Results section is somewhat confusing and its structure should be revised. I suggest first discussing the temporal evolution of the bias and then its spatial heterogeneity. Then I suggest comparing the original and updated versions of the GlobSnow V3.0 and finally compare with the SCv3.1 bias field. Perhaps, it would also be helpful to present a table in the Methods section with the different products you are comparing.

Specific comments :

1. l. 34-35 Could you rephrase this sentence for clarity?
2. l. 38 It would be good to give explicit examples of “other SWE products”.
3. l. 44-45 This may be trivial, but I think some readers would appreciate a sentence or two explaining the physics behind this method limitation.
4. l. 52 Can you briefly explain why only the March SWE time series has been thoroughly evaluated by this method?
5. l. 68-92. This should be included in a new subsection of its own.
6. l.70 Can you expand on the source of the snow depth measurements.
7. l. 83. Can you explain why the average of the 6 closest snow depth measurements is calculated and what effect this would have on the variance if the measurement points were sparsely distributed?
8. l. 90 (and l. 106) How was this constant value of snow density defined?
9. l. 111-114. Please state the difference between the new and original threshold detection values.
10. l. 121. Consider “spatial interpolation and assimilation” as a sub0section of the first part of the method (see. Specific comment 7.).
11. l. 130-132. Snow courses may not be evenly distributed throughout the winter neither.
12. l. 132-133. Is the bias really stable over time? Please explain the implications of this assumption.
13. l. 171. I suggest to expand on the source of snow depth, SWE and snow density measurements.
14. l. 211. Figure 1:
    1. The figure can be enlarged to make it easier for the reader to read and interpret.
    2. I am struggling with the black and gray colors on the figure. What are these colors supposed to represent?
15. l. 227-228: Can you elaborate?
16. l. 256. Figure 2. Same comment as Figure 1 regarding the colors.
17. l. 268. Original = old and updated = new? Please be consistent throughout the manuscript.
18. l. 278-279. What would cause this negative bias in spring? Is it related to density assumption? Please elaborate.
19. l. 282; l. 361; Table 1. SCv3.1 instead of SCv3.0?
20. l. 293-294. This sentence is redundant. Can you please rephrase it?
21. l. 304. "...where the snow mass from the updated bias correction (blue line) is > 100 Gt larger than when calculated with the original reference data (black line)."
22. l. 307. Figure 5: Do you also see a similar difference between the products for April snow mass?
23. l. 313. Names can be somewhat confusing (see Specific comment 19).
24. l. 327-328. It would be interesting to discuss why the addition of new snow courses increases the negative bias between the two GS data products.
25. l. 332. Are the differences really most pronounced in May compared to other months? It is not possible to tell from Figure 6 alone.
26. l. 342. Figure 5 instead of Figure 4?
27. l. 352. Here you refer to figure 8 before figure 7, which makes it confusing. I think that reorganising section 3 (see General comment) would make it easier to refer to figures in the order in which they appear in the text.
28. l. 371. Table D1 (instead of Table B1).
29. l. 412 Figure 7:
    1. For consistency, I suggest using hemispherical maps as shown in the previous figures.
    2. What do the gray areas represent on the maps? Complex topography? Please state this clearly in the caption.
    3. The style of the caption for Figure 7 does not follow the requirements of the journal. Please revise.
30. l. 425-433. Consider adding a supplementary figure showing the locations of SWE > 150 mm and SWE > 200 mm. This would help the reader in interpreting your results.
31. l. 452. Typo. SWE instead of SEW.
32. l. 457-464. It would be interesting to further discuss how the new GSv3.0 and SCv3.1 data products may increase the bias in Quebec and Alaska (which are high snow locations).
33. l. 466-468. Is it the opposite in April and May (snow density higher than 240 kg m^–3). It seems so from the bottom row of Figure 4. Please expand on that.
34. l. 480. It would be interesting to further discuss the role of spatial resolution and how it affects the bias fields compared to the effect of other factors (such as a constant density assumption).
35. l. 502-504. As North America is presented before Eurasia throughout the manuscript, I suggest that this order be maintained in the conclusion.