Refer to pdf for comments

This manuscript performs an assimilation experiment over the European Alps to investigate several advances to the modeling and assimilation scheme. Specifically, they consider the assimilation of a snow depth machine learning product based on Sentinel-1 observations and the development of a dynamic observation error for their Ensemble Kalman Filter setup. I find this study to be very compelling with interesting results, and I only have a few minor comments.

• Are the snow depth ML estimates available everywhere and thus assimilated everywhere or are there flags to exclude assimilation in higher uncertainty areas where SAR does not perform well, like dense forests?
• How representative are the in situ observations of the surrounding ~1km to match the modeled grid?
• Are there any spatial datasets, like lidar, for evaluating modeled snow depth over a broader area?
• In Figure 2b, the OL performs better than either DA scenario compared to the in situ, though DAvar performs better than DAconst. Is this similar behavior in other locations where the initial OL estimate is already close to the in situ truth?
• How does the DA perform when snow needs to be added to the system? Figure 2a shows the DA reducing the modeled snow down to match the observations. Though in later results, it appears that DA mostly reduces snow in the model.
• Lines 226-230: You mentioned that some of the increases in MAE at higher elevations could be due to limitations in the model during the melt season or biases from the assimilation. In your results, do you find that DA tends to add to remove snow at the higher elevations? How does the ML snow depth product perform at higher elevations where I assume the snow is deeper.
• Figure 4e: Do you have an idea why DAvar degrades performance around peak accumulation for the 2000-2500 m elevation band? Aside from that line, it appears like DAvar improves upon DAconst for each elevation band throughout the winter
• Figure 5: It appears like the modeled SWE almost reaches an asymptote around 600-700mm of SWE. Any ideas why the model is underestimating at the deepest SWE values?
• Figure 7: The difference plot for DAvar is much jumpier than that from DAconst. Can you explain that? Does DAvar have more ephemeral snow that comes and goes throughout the winter and spring? I assume much of that is from low elevation snow?
• Lines 264-268: Do you have any time series with snow cover comparisons to IMS or Copernicus?
• Figure 8: Does it make more sense to have the y axes on these plots be the percentage of sites within each elevation band so it is easier to compare against 25%, 50%, etc of sites?
• Lines 307-320: I think this would be better in the methods. It feels odd to introduce a new dataset in the discussion section.