This paper investigates data assimilation (DA) of Sentinel-1 snow depth (S1) and snow disappearance date (SDD) over the East River Basin in Colorado. Overall, the paper is well written and of interest to the science community. The authors find that assimilating S1 data provides limited benefit, whereas SDD assimilation significantly outperforms S1 DA in improving model performance.

Main comments:

I disagree with the authors broad statement that S1 snow depth (SD) assimilation has "limited utility." Instead, I encourage the authors to clearly explain why the S1 DA does not work well in THIS TEST CASE. These are some main points to support this comment:

1. We know that S1 has limitations in wet snow conditions (known issue) but can still be valuable for accumulation phases or early-season estimates. The authors say that “basins like the ERB receive significant snowfall after January, which reduces the early-season window's ability to predict SWE reliably later in the year (e.g., April-onward).” So, does this suggest that the East River Basin might not be the best place to test the utility of S1 in general?

2. Related to the above point, the current evaluation (comparing S1 DA to ASO lidar data in melt season) is not fair to the “good” (early season) S1 observations, which instead were taken earlier in the season. Consider: 1) Separating evaluation into accumulation and melt periods; 2) Reporting S1 DA performance specifically during accumulation when S1 is most reliable.

3. Some of the paper conclusions can be associated with the assimilation scheme and not entirely to S1. I think the error analysis (re their question #1) informs that the errors vary over time, is this analysis informing the choice of what measurement error is chosen in the DA scheme? Is the measurement error dynamic (varying with snowpack conditions as suggested by Fig. 4) or constant? The description and choice of the measurement error is of critical importance to indeed evaluate the utility of S1 data in a DA system.

4. In a DA experiment there are always three players: the DA scheme, the model, and the S1. It is not clear how each of them contributes to the results found by the authors. Much responsibility is given to the observations, which could be, but the contribution of DA scheme is not discussed (see for example previous point), nor the models errors/performances are reported. In all tables, authors should - at the bare minimum - inform the readers about the performances of the model. I recommend to always report model (prior to the assimilation) statistics alongside assimilation results. The readers should be able to see how much improvement/degradation is from DA vs. the model skill. I recommend adding model (prior) estimates in all relevant figures (especially Figs 5, 6, 7, 10) and tables (3, 4, 5).

A few more comments:

- Line 63: Also add the more recent paper by Lievens et al., 2022

- There is a contradicting reporting of errors in line 90 associated with S1 vs lines 162-165

- Line 237: “Lower and upper bounds values for precipitation are selected to ensure realistic” how are these bounds implemented? i.e., if a particle ends up being sampled higher than a bound is it set to the upper limit, resampled, or other? Please add explanation

- Fig. 4 :how  is the range of errors defined? From the daily values? Pelase add

- Figure 5: I assume the gray shading is the spread of the prior particles? What about the posterior? Is it ZERO? Can you add also the posterior spread? My fear is that the chosen meas. error (which is critical to know in this paper yet struggle to find what value was used) is likely just too small.

- Also in Fig 5, 8 legend, “particle” should not be a gray line rather a gray box and it should also be called “prior particle spread” or something like this.

- Table 4: how relevant is the correlation metric in this context? Isn’t this primarily driven by model and meteo forcings rather than the DA of snowpack early in the season? Similarly, for table 5, why would one observation only (SDD) lead to such a higher value with respect to the values reported in Table 3?? Wouldn’t the correlation values be just an artifact of the model temporal variability?

General comments:

In this work the authors devlop an independent validation of the snow depth S1 based products, and study their ability to update a snow model in a basin with high data availability using DA. The paper is generally well written and structured, and is a good contribution to the available literature.

The authors conclude that these snow depth products have a limited ability to update numerical models. Despite this, there does appear to be a signal in the products, albeit a very noisy one. Given the results, I generally agree with the authors, although probably with more sophisticated error models (perhaps with dynamic error models), there could be some potential in this product. The work would benefit from including in the discussion the possibility in the future of improving the quantification of the uncertainty of the observations, a critical point in DA and too often overlooked.

I have been surprised by the decision to assimilate SDD. I agree that it probably performs similarly to the more standard FSCA. Although I see some problems in areas with ephemeral snowpack, where several “seasons” may occur. Perhaps the reason is to facilitate manipulation of the data by reducing multiple observations to a single observation, but I would like to know if there is another motivation, and that the discussion reflects this possible source of uncertainty in the ephemeral snowpack areas.

From the DA point of view, the posterior simulations are treated as deterministic ones, while the posterior is a distribution. There are ensemble validation metrics such as the CRPS that are designed to account for the uncertainty of the posterior ensemble. Also, the authors compare the posterior runs among themselves, but it is important to compare with the reference run. Is the error after assimilating S1 equal to that of the reference (not DA), is it even worse? For example, if the error assigned to the observations is high, the prior ensemble  will not be constrained at all after analysis (which is not necessarily negative, it would indicate that the observations are noisier than the uncertainty associated with the forcing).These are important questions to be discussed.

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Specific Comments:

l.15 - Ensemble-based? all models can be run in ensembles. maybe physically based?

l.47- Maybe include https://doi.org/10.1029/2021WR030271 for a recent example of spaceborne photogrammetry and DA

l.65 - In my opinion, the biggest challenge of S1 based snow depth data is the accuracy of the product itself as proved by the recent independent validations.

l.71 - P.Broxton, remove P

l.76 - The authors are running 1D DA experiments, I would remove spatiotemporal since it may be confusing. Anycase, S1 DA has been tested before, showing little improvement as in authors work (eg https://doi.org/10.1029/2023WR035019)

l.100 - It shouldn't be a problem to DA S1 data even during melting, if a proper error model is developed. 

l.146 - This is the right citation for ERA5 Land https://doi.org/10.24381/cds.e2161bac 

l.148 - ERA5 land is available since 1950

l.151 - It is true that if sufficient information is provided, DA can be used as a downscaling tool. And it's a smart approach to avoid computational cost since one ensemble could potentially be used for many cells (for non-iterative schemes). But I am not convinced that this is the case for S1 according to the results. I would recommend adding something in the discussion about this, since the reference run (simulation without DA) will be very biased due to the complex topography.

l.154 - Is there any reason to choose PBS over other methods? PBS acronym not introduced yet

l.175 - … it is well established for guiding model… reference needed.

l.227 - FSM2 “more complex” parameterization uses a Monin-Obukhov stability adjustment

Table 1. What are the parameters of the lognormal distribution? 

eq.1 - Why the conditional operator Z|Y is repeated (not repeated in the caption)? Similar comment for pv(V).

l.284 & eq.286 - I am not sure about what you mean here. eq 1 is compatible with multiple observations of different nature. The number of observations of each quantity should not be a problem if the error is properly modeled. Also, should not be the joint likelihood the product (rather than the sum) of the independent likelihoods? Or were you referring to the log-likelihood, where summation (of log terms) is equivalent to multiplying the likelihoods?

Section 4.1 - I miss a visual map comparison between ASO and S1, please include it.

l.301- Please consider to include a metric that uses the posterior uncertainty, eg Continuous ranked probability score (CRPS)

Table2 - You can not use R2 for validation comparing timeseries (observed vs modeled) of variables that exhibit seasonality like the snowpack. The seasonal pattern forces R to be high (no snow in summer, some snow in winter). This is probably the reason why you are getting high R2 temporally, but low R2 spatially when comparing S1 against lidar. Also, if you're including summers or long periods without snow, the RMSE, and maybe other metrics, will be of course low. Please clarify/improve the validation strategy.

l.319 - Please provide the value here for the S1 uncertainty estimation

Fig5 - In legend, Particle? Is that grey shadow the ensemble standard deviation? maybe call it open loop or prior ensemble? What about the posterior spread? The inclusion of the posterior dispersion of the experiments probably makes the figure too complicated, but there is no mention of posterior uncertainty anywhere in the paper.

Table3 (and maybe other places as well) - Same comment as for Table2

Table4 - Control experiments? they are not there (despite they should)

Figure7 - Please include the reference run  and observations for comparison. c) how are they combined? This is not very standar

Table5. Consider to add Hs-F even if repeated, its annoying to scroll up and down for comparing

Figure10 c) please review caption Panel c shows the density plot comparing two experiments (Hs-F, SDD-Hs-F, and SDD). Similar comment as for Fig7c.

l.434 - This is very speculative.  If the poor spatial validation metric is because of the timing of the lidar, shouldn't the DA of the early season perform better?

l.449 For DA, it is not a real problem to use noisy observations, as far as you know that they are noisy. I would reformulate this sentence to highlight the importance of developing more sophisticated error models (which involves a proper understanding of the S1 signal, something that should be better investigated). 

l.470 Missing parenthesis

l.476 Maybe include https://doi.org/10.5194/tc-18-5753-2024

l.489 According to your results, why the biases are near and after maximum peak SWE? Since DA of Hs-F performs better than Hs-E, someone might argue otherwise.