This manuscript details the application of a simple energy balance model to a surface ice ‘cone’ geometry to simulate the dynamic melt and growth of a hypothetical ice stupa situated in the Oberengadin region, Switzerland. My feeling is that this manuscript does provide novel theoretical methods (subject to clarification from the authors of what the novelty actually is – see comments below) which are relevant to scientific investigations within the journal scope, and therefore should be published subject to recommended revisions. Specific comments are provided in the attached pdf. Below, I’ve provided a brief summary of my thoughts.

Overall, the manuscript is brief and to the point – well suited for a brief communication. However, I did feel that the work itself is not well-justified in the introduction. The author’s note that the work is complementary to the much more elaborate study of Balasubramanian at al. (2021), but they don’t elaborate on how this communication compliments it/provides novelty (i.e. why should this communication be published?). I wasn’t able to access this study as I believe it is currently under review, so it’s difficult to establish where the novelty lies. I therefore recommend that the author’s briefly and succinctly outline the novelty of the work and why it complements the more detailed work of Balasubramanian at al. (2021).

There are two occasions in the manuscript where the authors refer to their “belief” in the approach and “reasonable[ness]” of assumptions they employ without giving any specific justification. On another occasion, they postulate that the roughness parameter is, “expected to be larger than one, and could perhaps have a value of 2 or more”. This later forms the basis for selecting a value of 2 for the experiments presented. I appreciate that this text is a brief communication, but some justification for these assumptions is, I think, important (there is still lots of space to cite previous work as justification).

Finally, clearer definition of equation terms and units are required.

I believe these issues, along with the more detailed attached comments should be relatively easy for the authors to address and, therefore, subject to these minor revisions, I recommend that this brief communication is published.

This is a nice study. I make just a request for clarification:

When calculating the SW radiation flux in equation 5a, the impinging direct SW is calculated from the area of the stupa base. Because the sun in winter is always below vertical, this is a systematic (and perhaps fairly large) underestimate. Is it in fact negligible?

On a similar theme, the direct and diffuse downward SW fractions are assumed to be equal (q=0.5). Is there any particular reason to assume this?

Finally, line 96 has a spurious apostrophe in "stupa's".

This is an elegant and simple model description of stupa growth and decay based on a cone shape and standard energy balance terms. The stated goal is to estimate the speed of growth and melt of such features, while evaluating factors responsible. The model is described, and then applied to a region in Switzerland where continuous measurements allow for energy balance terms to be generated. Overall, the note is a nice contribution, and alludes to a more complete model that is in consideration for publication that takes variable surface temperature into account (Balasubramanian et al., submitted).

The study stops short of comparing the model output with actual stupa mass evolution apart from noting a similar 12 m height. The provided photos are nice in describing the stupas, but were there not any additional photos to show the evolution of the ice (accumulation, and decay) to qualitatively validate the model? In particular, the assumed constancy of the 'shape parameter', ie ratio of cone height h to base radius r), and the evolving albedo, could be substantiated or perhaps not with a time series of photos.

Moreover, the further value of the model beyond rates of growth/decay might be more fully demonstrated, given the compelling context: ultimately testing the effectiveness of stupas as seasonal water storage.

line edits:

L23: should be "are grown"

L24: they yield water, not deliver

L28: used to make

L29: the more effectively; delete second 'effective'

L30: insert comma after summer

L31: Start new paragraph at, "In this note…"

L34: use "elevation" or "altitude" rather than "height"

L35: end: most important for what?

L55: Is there empirical evidence or physical properties to justify the assumption that the shape parameter stays constant?

L89: insert colon at end

L132: was eq. 5a used or should that be 5b for the explicit albedo?

L133: faster "now" is not clear; delete it.

L178: "solid" is awkward; actual?