In this paper, the authors expanded an originally developed Bayesian-based SWE estimation algorithm to a new Ku-band radar sensor applied in Canada. Several important improvements were made.

The achieved SWE estimation accuracy was below 20 mm, and could be improved to 15.8 mm if three additional observation angles are provided. 

The authors made great efforts to explicitly describe the influence of the prior mean and variance on the accuracy of the retrieval results and their MCMC-estimated chain uncertainties. They also described the ability of MCMC and a proper constraint setting to correctly characterize a layered snow stratigraphy. The discussions are in-depth, and most of them are correct.

I have only the following suggestions to post. 

Major:

1. In abstract, what is the physical snow RT model utilized to describe the backscattering in four incidence angles?

2. It is suggested to provide a false-color image, a DEM, and a land cover in addition to the backscatter image in Figure 1.

3. For Section 2.3, it reads unclear whether the SVS-2 simulation dataset is a full region map or one that covers only several individual points. Additionally, the description of the forcing dataset contradicts itself between line 126 (SM in Figure 1) and line 131 (neighboring weather stations). 

4. Can SVS-2 consider wind compaction and effectively model the wind slab layer for snow in Canada?

5. For lines 147-153, does it mean that all sites in Figure 1 use the same single snow profile as the prior? How did you determine the variance of the prior distribution?

6. Line 233: What does "top 30 ensemble members" mean? Are they the first 30 members closest to the study area, or those most similar to the measured snow profile?

7. Line 253: Could you use equations to describe the idea of DEMCZ for guiding the direction of chain evolution?

8. Lines 266-270: The methodology for implementing the constraints can be mentioned here.

9. Lines 335-337: Using the Arctic version of SVS-2 simulations, the uncertainties of MCMC retrieval results are reduced when the prior s.t.d. is reduced by narrowing down from all ensembles to the top 30 ensembles. This is reasonable. 

Additionally, in Table 1, is the s.t.d. of Hsnow(R) from the top 30 members (Arctic version) 9.5 or 0.95?

Actually, when comparing Fig.8(b) and Fig.7(b), I did not observe a reduction in the uncertainty (i.e., the range of the error bars on the Y-axis). Could you check the values?

10. For the low correlation of the retrieved SWE to the measured SWE in Figs. 7 and 8, could you check the correlation between SWE (or SD) and the original radar observation inputted to MCMC? Are they highly-correlated or scattered?

11. The corresponding content of (a) and (b) is not labeled in Figure 9.

12. Lines 341-346: This result indicates the considerable impact of the grain size prior on SWE retrieval—not due to the accuracy of the mean, but rather due to the tolerance that allows the MCMC retrieval system to better match the observations. Increasing the variance of grain size indirectly enhances the influence of radar observations on the retrieval.

13. Did Figure 10 utilize a single-angle radar backscatter, as in Figures 8 and 9?

14. Line 405: "other variables like thickness" -> Actually, I think what you really meant might be strategraphy, or strategraphy of layer thicknesses.

15. Lines 406-408: "It should be noted that when SWE is poorly estimated by the prior, the posterior SWE estimate has a higher error (Figure 8), where SWE estimates are concentrated around the initial modeled SWE and do not diverge from that initial." -> The accuracy of the prior SWE does influence the SWE retrieval, and this is truly reflected in the likelihood calculation. However, for the case in Figure 10(a), I think the key point is that the default SVS-2 gives a highly-underestimated bottom-layer SSA (i.e., overestimated grain size); with a small variance, the system is forced to trust this value excessively. This resulted in the underestimation of SWE. Additionally, the default SWE prior is underestimated and has a low variance. This helped to make things worse, slightly. 

The key point is not to overtrust the land surface model, allowing remote sensing to correct it. Trusting a wrong prior too much is the last thing to do, especially for radar-sensitive parameters.

16. Lines 428-430: "Similarly, when comparing the outputs from both SVS-2 versions, the prior density estimates for the R layer of the default version (Figure 10a), do not allow to sample values close to the measured ρsnow, which prevents the MCMC method to properly sample other variables, such as SSA for the same layer." -> I do not fully agree that the snow density influences SSA; rather, I think SSA influences itself. Or, they both influence both. This is because, in general, the sensitivity of radar signal to snow density is low.

17. Line 500: It also indicates that remote sensing and land surface model can work together to mutually improve their accuracies. Ku-band radar is sensitive to snow depth and the SSA of the depth hoar layer, which can provide important information in regions with sparse measurements.

Minor:

1. In the abstract, uncertainty should be described more clearly to distinguish it from the RMSE compared with in-situ data. For example, use the MCMC-estimated retrieval uncertainty.

2. In the caption of Figure 3, second line: but->by.

3. Line 489: We also show -> We would also expect?

4. Line 503: "that influence the most the radar sigma0"—maybe change to "that influence the radar sigma0 the most"?