Summary & General Comments:

This brief communication presents a novel approach to derive snow depth from low-cost temperature sensors deployed at the snow-ground interface using a random forest model. This method would hypothetically allow snow depth monitoring at far greater number of sites than currently available, a significant finding well within the remit of The Cryosphere journal. The manuscript is concise and well-written. I recommend this manuscript be published subject to minor revisions, as detailed below.

As an aside, I would be interested to see what you think the impact of snow stratigraphy may be on  the depth estimates from your model (particularly when it comes to evaluating snow depth at sites beyond the Arctic, such as the New Mexico site), but I understand that you are unlikely to have this data for comparison.

Minor/Technical Comments:

This is a broad and minor stylistic comment, but I would remove the italics for above and below ground throughout.

Section 2.1: Could you add a photo of one of your DTPs to Fig S1? Please also give an indication of how deep into the soil these profilers go, and when they were deployed relative to the start of the snow season.

Line 46: Please give the precision of the snow depth estimates.

Line 47: Is the value of the closest temperature sensor used as the value for T_SG, or is T_SG estimated from the sensor temperature using another method (such as a linear extrapolation)?

Line 76-77: Does “shallow subsurface” refer to the 1 - 5 cm temperature measurements from the previous sentence? Consider rephrasing these two sentences for clarity.

Line 84: Consider adding vegetation type for all sites to table S3 and refer to this after the statement “Vegetation also varied across sites”. Vegetation for 2 sites is given in the following text but this info isn’t currently in the table, whereas vegetation for other sites is included in the sensor details column. 

Lines 92-94: I am confused as to how you trained RF-Deep when you are unable to derive depth estimates for snowpacks deeper than the 1.77m length of the temperature probes. Please clarify what data was used to train the deep model.

Line 95: I would role this section into the previous one.

Line 115/Figure 1: My initial thought was that “temperature range” referred to the range of temperature measured along the whole depth of the DTP, not just as the snow:ground interface. Consider changing this to “daily T_SG range” in both line 115 and the red y-axis for plots g - i. Additionally, the use of blue and green to distinguish between the two different models is not accessible to those with colour vision deficiencies. Please change one of these colours – something like blue and orange or green and purple would work.  

Line 138: Could this poor performance for ephemeral snowpacks be improved by including more ephemeral snowpacks in the training dataset?

Line 149: The insulative capacity of some snowpacks has been shown to be reached at much shallower depths than 1 m (e.g., Slater et al, 2017), particularly in Arctic environments like where the original model was trained. Potentially reconsider the use of this 1m value.

Line 156/Figure 2: The figure caption refers to a colour bar for subplot f), when I think you mean the y-axis for subplot g). Please double check. Some units on the y axes are also needed. Please also clarify what the black lines refer to – measured snow depth? Also, as for the previous figure, the use of blue and green to distinguish between the two different models is not accessible to those with colour vision deficiencies. Please change one of these colours.

Figure S1: Please clarify what is meant by WY2023 and WY2022 in the figure caption. Can you also confirm that snow depth data shown in b) and d) is for a different year to the temperature data on which the snow depth model is based. Also see comments for Section 2.1 above.

References:

Slater, A.G., Lawrence, D.M. and Koven, C.D. (2017) ‘Process-level model evaluation: a snow and heat transfer metric’, The Cryosphere, 11 (2), 89–996. https://doi.org/10.5194/tc-11-989-2017.

This brief communication presents an interesting approach to derive snow depth through temperature data recorded with easy-to-deploy sensors. Authors exploit machine learning models (random forest) to predict snow depth from snow-soil interface temperature. While the brief communication reads well and it is suitable to be published in The Cryosphere, some points must be addressed before publication.

First of all, the approach tested is trained in two sites and then evaluated in these two sites, but also in 10 other sites, what I might highlight in both the abstract and the introduction. Through this test on model transferability it is clear that this approach works well in cold and high latitude areas, but in temperate areas where ROS events can occur or temperatures are milder, it fails.  This has to be highlighted in the abstract and the conclusions.

More details about the training study sites (spatial distribution of DTP’s within the domain), image of the DTPs, and photograph of them would be desirable. I guess number of figures are limited, but some of these can be included in Figure 1.

The application of the training, validation and evaluation datasets it is not clear. This point has to be clarified in methods section. Similarly, it is not clear if, for sites where the models are transferred, these are evaluated with a similar dataset of observation (DTPs spatially distributed) or just data compared with automatic weather station data from a single location.

Minor comments

Line 30: I assume you already know somehow the spatial distribution of the snowpack in the study area (lidar/uav data?) or you are just modelling and testing in the exact location of your DTP sensors? I think it is the second but it is not clear.

Line 38 and 39: Please include snow density units in the international system (Kg/m3).

Line 9. There are some works which have already exploited random forest to analyze, and simulate snow distribution, showing suitable performances. You might cite here: Meloche et al., 2022 (https://doi.org/10.1002/hyp.14546), Revuelto et al., 2020 (https://doi.org/10.1002/hyp.13951) and Hsu et al., 2024 (https://doi.org/10.31223/X57391)

Line 69-70: Did you apply an “out of the bag” approach to validate evaluate? I do not understand why you use a 24 DTP validation data and a 31 DTP evaluation dataset, which is the difference here? If not, why don’t you use an out of the bag test?

Lines 72-77: Impact of sensor burial. I would present this section on section 2.2.

Line 90: How many sensors are used to train RF-Deep in senator Beck Basin? is this a similar test area (i.e. same number of DTPs or equivalent sensors)?

Line 114. I would briefly state here how do you test these models. You are directly comparing the observed snow depth at the sensor location in different stations with that modeled, right?

Figure 2. Some symbols of the study area are quite difficult to identify (eg. Bayleva station or Siberian), please increase their size. Also captions and graphs sizes are too small, can this figure be extended and increase captions size. For instance, you can remove the names above the graphs and just include the letter inside each one (a), b), c),…).

Conclusions: It must be highlighted that this method is suitable to predict snow depth in cold regions and that its applicability in temperate areas must be further investigated.

Summary

This brief communication describes a new method to use inexpensive temperature sensors and machine learning to estimate snow depth in the Arctic, with cross-validation in temperate regions. The manuscript presents the results clearly and succinctly, and my only major comments relate to the presentation of information, rather than the analyses conducted. I recommend that this manuscript be published following minor revisions.

Major comments

The non-Arctic sites should be introduced somewhere in the methods – as it is, they come as a bit of a surprise in the results, making it difficult to track what data are used and how.

I’m sure space is short, but I worry that the description in the abstract noting that the model performed “well” is a little bit misleading, as the RMSE = 0.15 m is among the lowest you report, and whether or not that should be considered good performance is a matter of judgement. I’d like to see a little more nuance in the abstract – maybe a brief description of the conditions under which the model performs best and worst, with the relevant RMSE values provided. Percent bias could also be helpful here, given that snow depth is so important to model performance.

Minor comments

Line 19 – citation needed here, as this probably refers mainly to potential for increasing snow depth?

Line 25-26 – Sonic sensors are deployed at SNOTEL stations, along with snow pillows, but this currently reads as though sonic sensors and SNOTEL stations are two distinct types of monitoring equipment. Suggest rewording.

Line 28 – Can you say why these remain a challenge in Arctic regions? In fact, I would expect IceSat-2 to provide better observations in polar than temperate regions, due to the higher sampling density.

Line 59 – I don’t think this permutation importance is unique to RF; should remove as a reason for selecting RF. Your other reasons for selecting RF are perfectly good, though.

Line 90 – I think this is the first time the other training sites are being introduced. They should be briefly described somewhere.

Line 134 – I think you should define the zero-curtain period the first time you use the term.

Line 180-181 – I question whether future work should try to improve the technique for deeper snow – it seems that for physical reasons, this may be unlikely. Perhaps it would be more productive to discuss how the technique could be combined with other types of observations. I also wonder about discussing a more thorough investigation of the relative merits of different ML models; an LSTM would make more sense conceptually but is probably harder to implement, and we’re not given much information about the implementation you tried that didn’t outperform the RF.