General Comments:

This manuscript is fairly straightforward and logical.  It is mostly well written, but some sections could use clearer language or additional explanation.  The study seems worthwhile, because there is a large amount of uncertainty in global snow estimates and assuming a constant snow density over time and space (as in GlobSnow) is not realistic, so any method that could introduce empirical density estimates would be beneficial.  However, the improvements in SWE estimation did not seem all that significant/impressive, so I wonder if post-processing is not the best approach. I have some additional specific comments below about the methodology, interpretations, and presentation.

Specific Comments:

• The title is a bit misleading, because it makes it sound like the dynamic snow density is incorporated directly into the retrieval, when in fact it is applied in post-processing.
• Line 64: Do the authors have a citation that they can provide to show that the Sturm et al. approach did not improve retrieval skill?
• Lines 141-142: Why was there so much more validation data than implementation data in the Eurasian portion of the analysis, but the opposite in North America?
• Line 163: The method does not produce SWE estimates for mountainous areas, but most of the SNOTEL data come from mountainous regions. How do the authors justify using mountain snow to determine the density for snow that is not in the mountains?
• Line 224: How was the multi-decadal snow density field produced for only 2000-2009?  Is it a running average, or were the data actually produced using data from the full 1979-2018 time period?  If the data were limited to only 2000-2009, wouldn’t that make it the same as the decadal field? 
• Figure 5: When the authors compare the in situ densities used to reprocess GlobSnow to their nearest neighbors (used for ground truth), is a similar pattern seen, or does it better fit the 1:1 line? Is the interpolation smearing out the range/variability of the density values?  If so, the authors might search for a different interpolation method.  Additionally, by interpolating across large distances (which may have different land cover, elevation, etc.), the authors are effectively taking local density estimates assuming that they are representative of large areas.  Do the authors think this is a fair thing to do?  Might it be better to use an interpolation method akin to PRISM (Daly et al.) to take land surface properties into account?
• Line 244: “…SWE values up to 500 mm and SWE values up to 150 mm…”. This is a confusing sentence, and I was only able to understand what the authors meant by looking at Table 2.
• Line 269: Is GlobSnow calibrated to SWE in any way?  If so, then post-processing might not be a good idea?  The authors note in lines 338-349 that implementing densities directly into the retrieval may be more beneficial, as a wrong density may lead to reduced retrieval skill. So, then why bother with post-processing?
• Line 272: Calculating decadal density maps and applying them to the entire decade seems a bit arbitrary.  For instance, the density applied to data from 1981 would be from (approximately) the next 10 years into the future, while for 1989 the density would be from (approximately) the past 10 years.  Why not calculate a running decadal average, centered on the year of interest?
• Line 277-278: I don’t know what the authors mean in this sentence.
• Table 3: The improvements in post-processed SWE seem marginal, so I wonder if post-processing is worth doing at all.  Do the authors have any way to evaluate the statistical significance of the improvements in SWE?
• Figure 8: What does the colorbar in this figure show?  It is not labeled.
• Figures 8-10: Why are these 3 separate figures?  Why not one figure with 6 different panels?
• Lines 339-347: Do the authors have a citation(s) for this?
• Lines 350-351: To what methods are the authors referring?  This paragraph needs to be further explained.

Technical Corrections

• Line 17: “was found to produce the best results”?
• Lines 58-59: Snow also undergoes metamorphism that can cause density to increase.
• Line 130: “The North American dataset”?
• Line 133: “The SNOTEL dataset”?
• Caption of Figure 4: “for snow transects”?
• Line 231: “differs from the other two versions more” – could improve grammar
• Figure 8, y-axis label: “Estimated SWE”?
• Figures 8 & 9: The font sizes of the titles of these two figures are different.

SUMMARY OF THE PAPER

This study concerns the treatment of snow density in the GlobSnow SWE product (post-processing only). It develops and tests new dynamic snow density estimates based on data collected at snow courses and telemetered snow sites in the Northern Hemisphere. These estimates are compared to the existing approach, which assumes constant snow density in space and time. The new dynamic approach is first developed at a subset of measurement location. Snow density is averaged each day of winter over different periods (multi-decadal, decadal, and annual), then interpolated in time and spatially mapped using ordinary kriging interpolation. All three approaches show improved mapping of snow density against observations relative to the constant density assumption, however lower density values (300 kg/m3) are underestimated. The snow density estimates based on annual values are slightly improved over the multi-decadal and decadal versions. Post-processing of the GlobSnow SWE data is then conducted for each of the three dynamic density datasets, with SWE errors lowest for the multi-decadal and decadal values of snow density, and improved over the case of constant density. The decadal version was then applied to the northern Hemisphere GlobSnow and SWE was post-processed. This yielded slightly better agreement in SWE compared to ground truth data. SWE errors were consistently reduced at all reference SWE values in Eurasia but only at SWE greater than 100 mm in North America.

COMMENTS

1. The Sturm density method was briefly mentioned as a candidate approach, but found to not improve retrieval skill notably (Lines 63-64). Was that analysis published? If not, it could be worth including in the current study, as it would be an interesting point of comparison that would be of interest to the community. 

2. For the SNOTEL data, did the authors check to ensure that the snow depth sensor measures snow depth on top of the snow pillow? This is not always the case at SNOTEL stations, and when snow depth is recorded at a location next to the snow pillow, an estimate of density from the SWE and depth data may be biased. Unfortunately, documentation on the layout of sites is inconsistent. Careful inspection of site photos can reveal which SNOTEL stations may have collocated SWE and depth measurements.

3. The results in Figures 5 and 6 appear to be contradictory. Figure 5 suggests that that snow density estimation is improved (but only slightly) relative to decadal and multi-decadal across a range of ground truth density values. In contrast, Figure 6 suggests much larger SWE errors associated with the annually-derived snow density when compared to mulit-decadal and decadal versions. Given the post-processing (equation 5), the differences in SWE must be due solely to differences in snow density errors and not errors in baseline SWE. However, Figure 5 suggests the snow density errors are lower for the annual estimate. How do you rectify these conflicting results? Are you sure these have been analyzed correctly?

4. Overall, the discussion section is brief and does little to connect the current study to previous work (no other studies are actually cited in the discussion). For example, there have been other studies that have compared the constant density assumption versus dynamic snow density for passive microwave SWE retrievals and found improvements with dynamic snow density (e.g., Tedesco and Narvekar, 2010), and other studies have called for improved density representation for passive microwave (Kelly et al., 2003). How do the results of the current study build on established knowledge?

5. Ignoring the potential issues with SNOTEL-based values snow density (see comment #2 above), there are issues with the location of SNOTEL stations (mountains where snow is deeper and possibly denser, and GlobSnow does not produce SWE), and differences in temporal sampling. To the latter concern, it would be possible to check whether the temporal sampling of snow density influences the density curve development and validation, compared to the case of less frequent snow course measurements (e.g., Canada and Eurasia). The differences in GlobSnow SWE for constant versus dynamic snow density were smaller in North America (where SNOTEL are located) versus Eurasia (snow courses only), as seen in Figure 7. To what degree do the differences in daily snow density (SNOTEL) versus 10-15 day snow density (elsewhere) influence the result? This could be checked by sampling the SNOTEL density to a similar interval as snow courses and recomputing the statistics. 

6. The results seem rather marginal and potentially overstated. An example is Lines 292-293, which state “…the accuracy is considerably better with RMSE for the baseline being 31.87 mm and for the post-processed dataset, the error is 30.87 mm.” I question the significance of a 1 mm reduction in SWE error and whether this is “considerably better”.

GENERAL COMMENTS

- Please consider the number of significant digits for the error statistics reported in the text, figures, and tables. What is the measurement precision of the snow density observations? Are we really confident in density to the tenth or hundredth of a kg/m3? Are we really confident in SWE to the hundredth mm?

- A histogram of snow density values (development and validation data) would be useful context, especially for interpreting Figure 5. - Figures 8-10 are all referenced in the text before Figure 7 (see Lines 289-304). Consider reorganizing the text or renumbering/reordering the figures.

- The Discussion section and the Conclusion section are mislabeled and should be Sections 4 and 5, respectively.

- There is some discussion-like comments mixed into the results section (e.g., Lines 293-294, 302-304). Please consider reorganizing.

TECHNICAL CORRECTIONS

- Line 34: Should be “data are also available” since “data” are plural.

- Line 40: Should be “in deep snow”.

- Line 44: Should be “observations”.

- Line 59: The Maurice and Harold (1981) citation is not included in the References section. Please add.

- Line 62: Please rearrange parentheses such that it reads “Sturm et al. (2010)”.

- Line 91: Is a subsection required here? There is a 2.1.1.1 but no 2.1.1.2, so this subsection title may not be warranted.

- Line 101: Should be “were used”.

- Line 120: This should be “Figure 2”.

- Line 130: Add “The” before “North American”.

- Line 132: Should be “observations”.

- Lines 132-133: Can you state why only SNOTEL stations in Alaska and the northwestern USA were selected, and not SNOTEL stations farther south in the USA?

- Line 147: Please rearrange the parentheses here such that they are for the year only (two cases).

- Line 186: Add “the” before “variogram”.

- Line 208: Add “the” before “baseline”.

- Line 224 and Table 1: The period of validation reported here does not correspond to what is described earlier in Lines 100-105. The annual data do not appear to span 2000-2009, and the decadal was previously described as 1999-2009.

- Line 229: Should be “decadal” rather than “decal”.

- Line 243-244: Add “separately” after “performed” to indicate that the validation was done for two different cases of SWE values.

- Line 254: Should be “decadal” rather than “decal”.

- Line 282: Is this supposed to be “SWE values up to 500 mm and 150 mm” rather than “density values”?

- Line 291: Replace “improves” with “reduces”.

- Line 329: Should be “SWE retrievals” at the end of this line.

- Line 330: Replace “effects” with “errors”.

TABLE AND FIGURE COMMENTS

- Figures 5, 8, 9, 10: The vertical axis should read “Estimated” rather than “Estimates”.

- Figure 5 caption: Should be “decadal” rather than “decal”.

- Figure 7 would be more effective if a third panel was included that showed the different in SWE estimates from GSv3.0 vs. post-processed. In the current form, I can only tell subtle differences between the two maps.

- Figure 7: Note the title above each panel is overlapping text below (90 deg W). Please correct.

REFERENCES

Kelly, R. E., Chang, A. T., Tsang, L. and Foster, J. L.: A prototype AMSR-E global snow area and snow depth algorithm, IEEE Trans. Geosci. Remote Sens., 41(2), 230–242, doi:10.1109/TGRS.2003.809118, 2003.

Tedesco, M. and Narvekar, P. S.: Assessment of the NASA AMSR-E SWE Product, IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 3(1), 141–159, doi:10.1109/JSTARS.2010.2040462, 2010.