The study demonstrates the potential of assimilating L-band InSAR-derived snow depth retrievals to enhance snowpack simulations. The results showcase improved spatial and temporal resolution in capturing snowpack properties, leading to more accurate predictions of SWE/Snow Depth compared to open loop or control simulations. The paper is well-written and grounded in established scientific principles. However, some aspects of the methodology and analysis could benefit from further elaboration to strengthen the overall validity of the findings.

Major comment

The study utilizes L-band InSAR data to estimate changes in snow depth, which necessitates knowledge of snow density. As I understand it, the authors propose using an average density derived from bias-corrected ASO data. After evaluating the error associated with different time periods, they opt to employ this information to calculate incremental snow depth. By combining absolute ASO information with incremental L-band data, the data assimilation process is transformed into a traditional data assimilation problem. However, Equation 3, based on Liens et al. (2015), derives incremental SWE without requiring snow density but necessitates calibration of the parameter alpha. In the present form, I am not totally sure about the rationale behind assimilating Δz instead of ΔSWE. A clearer explanation of this decision would help to avoid potential confusion.

Specific comments

L101: NISAR mission was already introduced at L80

L112: This sentence is unclear due to the lack of context about the dataset. Please provide more details or consider removing it from the introduction.

L 228-230: for which snow density the value of 69 cm is valid?

Section 2.4 the source of the density estimation used to derived the snow depth from the InSAR data has to be clearly stated.

Section 3 To enhance the clarity and conciseness of the results, consider summarizing the key findings in a table (now only in the text as numbers). This will make it easier for the reader to compare different scenarios and draw conclusions.

L448 please revise the sentence

L492 To enhance clarity, please provide a more detailed explanation of how the density value was determined. This will help to avoid confusion and strengthen the overall understanding of the methodology.

Code availability: Some of the links provided in the code availability section are not functional. I strongly recommend making the data and code used to reproduce the results openly accessible. This includes model outputs and InSAR-derived snow depth data. Given that many of the results in this paper were made possible by the open access nature of the data used, it would be beneficial to maintain this level of transparency and openness.

Figure 5 a The legend seems a bit unclear. Could you please provide more details or clarify the meaning of the different colors used?

Fig 9 To better highlight the spatial variability, consider including a zoomed-in view of a specific region, similar to Figure 5.

This paper presents, to my knowledge, the first example of data assimilation over a spatial domain with L-band InSAR snow retrievals, and is an important step forward toward the operational use of L-band InSAR snow products.  This is of particular importance due to the upcoming launch of NISAR.  This paper demonstrates the usefulness of assimilation of L-band InSAR snow depth retrievals, and shows how it improves the accuracy of the author’s modeling results over flat topography on Grand Mesa, using data from the 2020 NASA SnowEx UAVSAR timeseries.   The challenges with retrievals in forest are shown, pointing to more work needed in these environments.  It would be worth mentioning more work is needed in complex topography too.

This work is a logical next step in the use of L-band InSAR for improving snow estimation at large scale, and it is important that this work is published.  There are however some major revisions I feel are needed before this work is ready for publication, as there are important details missing, many of which are outlined in detail with line-by-line comments below.

I have a few big picture concerns that I think are most important to address before publication, followed by a list of more minor things.

• The paper in general lacks details throughout on the snowpack model used, and some details on the data assimilation steps, how state variables are changed, etc. The paper “Shrestha and Barros, WRR, 2024” is often referenced, however this doesn’t have a complete citation and I couldn’t find it on the WRR site.  Is this in review?  If so, details in the WRR paper are needed for this TCD paper to be published.  This is also really critical since the code used to do all of the modeling and DA in this paper is not currently available.  There are many very widely used snowpack models that are open source and contain very detailed physics – how is this model different?  This model appears to not have been used outside this research group; if it was made open to the community as it appears the authors intended, I think it would likely be useful for many other researchers.  As an example of more detail: L272: “part of the data is used for assimilation, rest for evaluation”.  What is the split? Randomly selected? Or different regions?  How exactly are the snow depth changes assimilated?  What kind of error covariance model? Is mass changed? Is density changed? Just a few examples, more below.
• This work leverages multiple recently released open source software packages. Many of these packages were produced with great effort by students in the community, and were part of their research – please make sure the student authors of these packages you are using are explicitly given credit, not just a link to a repo (uavsar_pytools, herbie, etc).  Zenodo references would help here.  Many of these resulted from collaborations built at SnowEx Hackweek as well, which would be great to acknowledge maybe in the Acknowledgements section, along with mentioning the NASA SnowEx campaign there, in particular the field and airborne crews who collected all the data used in this paper.  Especially given all the open source software and community collected data that this paper uses, I strongly encourage the authors to make their model and data assimilation software open, as it appears they intend to (although link currently broken and repo appears to be private).
• There are several uses of snow pit data, taken in different locations, that need to be interpreted with caution. For example, changes in snow depth between two pits in different locations, when it is on the order of less than 10cm, can easily be due just to spatial variability, even when only a few meters apart.  Density changes between Feb 1 and Feb 12 from snowpit observations in different locations is likely due to spatial variability, not temporal change.  I know this trend is also in the ASO modeled and bias-corrected densities, however those will show the same trend as the field data, due to the bias correction applied to ASO SWE.
• Density used in the L-band InSAR inversion. The authors show that their reference model has significantly higher densities than the field data, but still use it in the inversion – why isn’t a field-measured density used here?  This was also a really hard detail to find in the paper – consider stating that you are using reference model densities more clearly and earlier in the paper – i.e. in the section on the UAVSAR retrieval.  Given the time series of depth and SWE from the nearby meteorological stations, it is unlikely there was much settlement of snow below the Feb 1 surface between Feb 1-12.  It seems therefore more appropriate to use the density of the upper part of the snowpack for the inversion, since this is the part that changed and caused the phase change in the UAVSAR data.  No modeled density profiles are shown, although it is mentioned that it was basically two layers.  Consider showing a comparison with field-measured density profiles, to help the reader see that the modeled density profiles are reasonable.
• This paper shows the same comparison with the same datasets between L-band InSAR depth retrievals and repeat lidar for the western part of Grand Mesa, as shown in Marshall et al., 2021, but some additional details would help compare these two studies. Why was VV used for this comparison, but then HH used for the rest of the DA results (HH used in the previous work)?  It would be better to evaluate the technique and then apply it with the same polarization.  A scatterplot would be helpful in Fig 5, and more quantitative comparison (R-value, RMSE).  The previous work found R=0.76, RMSE=4.7cm using the near surface field measured density observations in the retrieval – looks like similar results here, but hard to tell just from figure 5.  How big of an impact did the atmospheric correction have?  How exactly was this retrieval calibrated with the time-lapse snow pole depths?  Which ones were used and where were they?
• I understand why you focus on InSAR snow depth change retrievals, rather than the more direct SWE change retrievals – so you can compare with the unique coincident repeat lidar discussed in 5) above. But once that is done, why not assimilate change in SWE?  Then you remove the sensitivity to the density estimates.

Detailed suggestions/comments

• The abstract states that the inversion was “modified”, yet the common Guneriussen et al (2001) equation is used. The main difference I see is in the way the authors estimate the density and atmospheric delay, but the inversion seems the same?  If not, maybe more details help here.
• L76: refraction doesn’t cause the phase delay. The phase is delayed because the radar wave moves slower through snow.  The time of flight actually decreases due to the refraction, due to shorter path length, rather than delaying the signal.
• L80: great place to mention the 2020 NASA SnowEx campaign
• Note that accurate density estimates are not required for SWE inversion, just depth retrievals as shown by Leinss.
• L156: consider rewording. The domain was stratified into 9 classes based on tree density and snow depth.  Reference SnowEx experimental plan so readers can find more details.
• L175: Confusing. Are you using a single forecast or ensemble?
• L212: phase delay is an integral over phase changes in each layer, but total phase change is very similar whether you account for all layers or just use a bulk density – but again the appropriate density here is that from the upper part of the snowpack where the change in SWE/depth is occurring.
• L225: would be a good place to mention that the many SnowEx UAVSAR papers that have compared to lidar did the same approach here.
• L234-242: Calibration step here needs much more detail. Put the location of the calibration measurements (time lapse snow poles) on your maps.  Did you use the average measured change for calibration? Or something more complex?
• L275: How did you choose magnitude of the perturbation (standard deviations in U)?
• L386: It is interesting that the authors report almost the exact same error as Marshall et al., 2021 with this same dataset (~5cm), but different data (timelapse snow poles) used for the evaluation – encouraging that this is consistent between studies and worth mentioning here.
• L400: Forested areas showed HIGHER coherence? This probably a typo?
• L430: difference in DA and DAU negligible at pits…could this be partly due to disturbed snow around pits?
• L445-447: These results depend highly on the calibration approach, which was hard to evaluate due to a lack of detail. How different would your results be if you used the near-surface measured density? How big was the atmospheric impact?  Was this applied for each UAVSAR flight? More calibration details would help reader interpretation here.
• L459: how do you measure model improvement at the end of Feb/early March when there is no lidar? Is this with the pits or the time lapse snow poles?
• L493: More detail needed here – how are you doing depth-weighted averaging? And it says “or average between flights”? Did you do this differently in different situations?
• L553 – please fix link / make repo you are trying to share here public. This will be a huge service to the community, thank you!
• L591: Please acknowledge SnowEx participants, especially field observers and airborne teams. A shout out to Hackweek, which started collaborations between students and resulted in the open source software packages used in this paper, would be awesome here.  We really want to keep Hackweek going so more software and data can be published for others to use!  Thank you.
• It is stated that the UAVSAR retrievals do not agree with lidar in the dense forest, but does agree with the timelapse snow poles? Why is that?  Does the lidar not agree with the snow poles in the dense forest?
• Fig 1: why does land cover classification only cover part of the domain?
• Fig 3: consider putting the timing of the UAVSAR flights on this figure
• Fig 4: The locations of the snowpits used is needed on the map in Fig 1 for both dates
• Fig 5: add locations of the timelapse poles and snowpits used on this figure
• Fig 6: Are these validation sites? I thought these were used for calibration?
• Fig 7: see comment about interpreting snow pit depths at different locations in the context of temporal changes – some of these changes are less than expected spatial variability
• 8: Where is this comparison being done? Can you do it at the Mesa West weather station and show the measured snow depth time series?  Show the location of Mesa West on your maps.
• Fig 9: Hard to see changes at this scale. Consider showing a smaller domain, and/or a full-page figure for this many panels.

Excellent work here.  This is a super important next step for combining L-band InSAR and modeling!