In this paper, the authors conducted an important research to explore the data assimilation potential of the TSMM mission of Canada, which provides dual-Ku backscatter measurements in weekly intervals.

However, firstly, the authors didn't clearly present whether all weekly backscatter coefficients were input together to constrain the entire snow season, or the snow process was updated at weekly steps.

If it is the first case, previous studies would not recommend perturbing the seasonal pattern of snowfalls. Instead, an adjustable constant multiplication factor will be applied to the entire snow season.

The current assumption cannot enumerate all possibilities in the meteorological forcing errors for the entire snow season. Therefore, instead, it adds great noise into the SWE and backscatter ensembles (e.g., Fig.2h), which have made DA really difficult.

Due to the reasons mentioned above, the presented ensembles alone in Fig.2 fail to convince me that dual-Ku backscatter can work well to constrain SWE uncertainty, although it indeed could.

The simulations also have other problems: usually, if the snowpack is deeper, the snow will tend to melt more slowly under the same energy input (air temperature+radiation). It is unrealistic that the spread of snow-off dates is so narrow in Rogers Pass, which is even narrower than the very shallow snow at TVC in Fig.2(k). It should be noted that the largest and the smallest peak SWEs for Rogers Pass differ by over 300 mm, whereas that for TVC is only 20 mm. Therefore, I guess there is also some problem in the snow process modeling. If the snow-off dates are correctly simulated, even fractional snow cover from optical sensors can be used for DA; backscatter should be more powerful.

More points are listed as follows:

Major points:

1. Abs: In "Results indicate that assimilating backscatter observations reduced the mean continuous ranked probability score (CRPS) of SWE estimates by up to 32 % at the Arctic and humid continental climate sites compared to the open-loop ensemble, performing similarly to the assimilation of SWE with an observation error larger than 20 %", what is the source of the SWE directly assimilated?
2. Line 150: I feel, the temporal evolution equation (1) for meteorological forcing error is needed only if the observations are inputted into DA sequentially.
3. Follow point 2, and for lines 179-180: sequential assimilation had one problem in assimilating backscatter when new snowfall happens to occur at the observation time. It is related to the limited response of backscatter to small fresh snow particles, until the snow grains start to grow. How to avoid this problem?
4. Line 160: Although it may not be important, however, I feel additive perturbations may be more suitable for wind speed and shortwave radiation.
5. Line 170: Do you mean the autocorrelation of the error of HRDPS compared to the observations?
6. Line 192, Is Derksen et al.(2021) an indirect citation? Please clarify if this citation refers to more backscatter experiments in Canada or measurement experience.
7. Fig.2, the authors could try to enlarge the backscatter time series for Rogers Pass and Powassan. The separation between different ensemble runs is too small.
8. Lines 240-262, This is a new term. The authors are suggested to explain the cumulative distribution function clearly. In addition, what does a higher CRPS stand for?
9. Line 456, usually assimilating microwave observations directly should perform better. This is because the snow process model adds another group of constraints between snow depth and snow microstructure in addition to that from microwave observations, driven by the temperature gradient within the snow profile. Could you please check the correlation between snow depth (or SWE) and the snow microstructure parameter at some representative temporal points?
10. Line 465: for the saturation of backscatter for SWE>300 kg/m3, while your statement in general is true, it was not supported by the comparison between (a) and (c) in Fig. 2. The spread of backscattering from Jan to March is larger at Rogers Pass than Powassan.
11. Also for Fig. 2(c)-(f), the simulated backscatter is questionable in mid-Jan and mid-Feb. The jumps of backscatter for these 3 to 4 ensembles are difficult to explain.
12. Fig.4, it is the systematic bias of SWE, instead of uncertainties that will greatly influence the SWE DA result. Therefore, I think the current comparison between the backscatter and the SWE assimilations is unfair.
13. Line 224, what is the criterion to select THE particleS with the highest weights? How many samples were selected, and how were they combined to produce the final estimate?
14. In Fig.3b&3e, the spread of SWE was not narrowed down greatly using backscatter for this very shallow and backscatter-sensitive snowpack, because the ensembles are too noisy for this site (Fig.2h).
15. Fig.2: Should the reference run be a single curve for each case?
16. Line 390-395: It means if the SWE error retrieved from radar drops below 30%, assimilating backscatter directly will be unnecessary. However, in my experience, this is not true.
17. Lines 413-414, it is true that at a single time step, the sensitivity of MODIS-reflectance is limited to shallow snow, because only in this case, the light can penetrate through the snow medium and be influenced by the low-reflectance background beneath the snow. However, it is the time series of MODIS reflecting snow-off date (or snowmelt process) that makes it workable for deeper snowpacks.
18. Line 426, for the higher sensitivity to meteorological forcing (MF) uncertainties in the early snow season, is it because the snow is an accumulated result of snowfalls, and the noises of MF have not been "smoothed" before the mid snow season?
19. Line 614, the information for Madore et al.(2023) is not complete.

Minor points:

1. Lines 207-209: Fig. 2 shows ...
2. Line 212: reached a plateau - reads not academic.
3. Line 448: 10? or, 100?
4. Line 457: on par?