I am very enthusiastic about this paper, having experienced PBS ensemble collapse in assimilation of frequent and over-confident observations myself, and it has potential applications beyond cryospheric data assimilation. My comments are mostly more in the nature of discussion than requirements for revisions.

The broad review of assimilation methods relevant to the subject is interesting, but could possibly be shortened, and it is a little repetitive in places (e.g. MCMC is referred to as “gold standard” 15 times). There is much less in general terms on the nature of filter collapse that is central to this paper, but the simple illustration in Figure 2 could provide insight. I think that the PBS mean is suboptimal because the necessarily broad prior does not efficiently sample the narrow posterior, and the degeneracy is because of the prohibitive cost in Equation 4 for all except the nearest particle.

Isn’t the mode of the lognormal distribution for the precipitation multiplier in 3.2 equal to 0.86, i.e. not centred on being unbiased? It won’t make much difference, but why is a logit-normal distribution chosen instead for perturbing other strictly positive forcing variables in 3.3 (it would make sense for relative humidity, but that is not listed as a perturbed variable)? 

The banana-shaped posterior distribution in Figure 2 is the equifinality which is familiar (because easily visualized) in calibration of temperature index models. A hydrologist seeking to calibrate a 2-parameter model would not consider this challenging at all; a better solution than the degenerate PBS in Figure 2 could be found efficiently by any number of standard methods.

There are only a few snow depth measurements in Figure 2, so I guess that the ensemble collapse is due to the observations having high confidence. The assumed observation error should be stated in the text and shown on the figures.

Is the KDE in Figure 6 misleading? The PBS posterior approximation appears to be too wide, but it should actually be too narrow.

In situ meteorological data are available for all of the ESM-SnowMIP sites; is ERA5 used instead for generality? ERA5 grid elevations without downscaling can be expected to be considerably lower than most of the site elevations (Menard at al. 2019, Figure 9). The final version of Essery et al. (2024) is https://doi.org/10.5194/gmd-18-3583-2025. Of the parameters listed in Table 1, rgr0 and rhow will have no influence on snow depth simulations; this could be apparent from the posterior parameters. Can MuSA diagnose parameter importance?

It would be easy to add PBS RMSE and bias to Table 3, allowing the reader to judge for themselves how badly it is struggling. There will be enormous redundancy in hourly snow depth measurements because of autocorrelation; would decimated or averaged observations be less challenging?

Minor errors:

p3

“Ensembe Kalman”

p4-5

“comprehensive texts … for a comprehensive”

p12

“that we can easy generate”

p13

”samples form the target”

p15

“each iterations proposals density” (missing apostrophe)

p19

No reference in the text to Figure 1 (could be related to the steps in 2.6.1).

p20

“cryospheric sciene”

p22

“The idea being …” is an incomplete sentence as written.

p23

“FMSM2”

“7 perturbation parameters to correct the forcing” – only six are listed.

p26

The MCMC distribution in Figure 2 should have a colour scale.

p29

Figure 5 would be clearer if ESS in the legend was changed to N_eff as in the caption.

Rather than ending up selecting a threshold value, you must have started out by doing so if it is preselected (p16).