The authors have done a very interesting work. The simulation of the depth distribution of glacial lakes has been less addressed in previous studies, but it is crucial for the simulations of outburst floods for vast glacial lakes without measured depth data. Therefore, the scientific value of this study is unquestionable. However, I have some questions about the study, and I hope the authors will provide reasonable answers.

1. In the abstract it is stated that there are 10 standard conceptual models, 4 in Section 2.3, 5 in Figure 3a, and 4 standard curves in Figure 3b, so how many standard conceptual models are there in this study as defined by the authors?
2. The authors classified glacial lakes as supraglacial, proglacial, periglacial, extraglacial, and ice-dammed types based on the topological positions between the glacial lakes and their parent glaciers. Of the three glacial lakes for in model validation, Cirenmaco and Jalongco are defined as periglacial lakes. The authors are requested to describe the specific topological relations of the five glacial lakes with their parent glaciers or to indicate the references in the article.
3. The general curve generated must pass through points A and C, and the C is the maximum depth of a glacial lake. So how do we get the maximum depth of a glacial lake for a lake that has no actual bathymetry? Is it by an empirical formula? In your study, what is this empirical formula?
4. In figure4, how can we obtain the different standard conceptual models in five lake types?
5. Zhang et al., (2023) published bathymetric data for 16 glacial lakes on the Tibetan Plateau (https://doi.org/10.1038/s41561-023-01150-1). Could you apply your conceptual model to more glacial lakes for validation?
6. In figure6, the order of Figure b and Figure c in the title should be switched.
7. In figure7, the display of the standard conceptual model and the general conceptual model in the figure on the left lacks the necessary legends, such as what does the fill color represent? What is the color of the lines of each standard conceptual model? and the dashed line representing the general conceptual model is not visible in Figure 7b.
8. The expressions in lines 157-160 are not easy to understand. What means "the SCMs of proglacial lakes to be half of the preceding four SCMs"? How is one half divided? “We ultimately designed two SCMs: the semi–cone structured by the straight side and the triangular cone (V = 1/3A·D).” Are these two SCMs applied to the previously mentioned proglacial lakes and ice-dammed lakes, respectively? I think the description here should be improved to make it easier to understand. 

This study presents the approach of geometrical approximation of glacial lake bathymetry, considering different types of glacial lakes. I’m convinced that this might be an important contribution towards filling apparent research gap and addressing the need for lake bathymetries in GLOF and lake evolution studies. I have two major and a couple of minor concerns regarding this study.

My first concern is associated with the novelty methodological aspects of this study. Please correct me if I’m wrong, but from reading your manuscript, my feeling about your methodology is that:

• You approximate the max. lake depth from empirical equations
• You place this deepest point in the middle of the lake polygon
• You interpolate the rest of the lake basin (with possible use of different curves such as straight, parabola or ellipsoid)

According to my knowledge, various GIS software offer different interpolation tools too. Could you please explain and highlight the advantage and novelty of your approach? This is especially important considering that your code is only provided on request.

My second concern is associated with the validation procedure of this approach. The authors compile global bathymetric dataset and claim that their method could be applied around the globe (L320). However, only three lakes with very similar characteristics (all moraine-dammed, all large, all from Himalaya) are used for the validation. More experiments are needed to evaluate the performance of your approach considering: (i) different lake types; (ii) different lake sizes; (iii) different geographical contexts.

Personally, I would very much appreciate distinguishing between moraine- and bedrock-dammed lakes, because while a bedrock-dammed lake is the one that occupies a depression carved in a bedrock by a glacier, a moraine-dammed lake is trapped behind a wall of material deposited by a glacier – and so the bathymetries of those two types are likely to be different (as e.g. Muñoz et al., 2020 dataset from Peru confirms). This could actually help you to solve the problem with low R2 values of so called extraglacial lakes.

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L26: I would not call your three lakes typical, also because two of them produced a GLOF in the past, decreasing ‘natural’ lake water level; this further undermines the validation (see my general comment)

L41: when talking about these 50%, please mention that this only applies to glacial lakes located within 1km buffer from the RGI glaciers; overall regional figures differ substantially.

L46: you might want to refer to the latest GLOF inventory compiled by Lützow et al: https://essd.copernicus.org/preprints/essd-2022-449/

L51: attenuates instead of proceeds?

L60: Tibetan Plateau and the Himalayas are different regions

L76: if you mention ‘several studies’, you should refer to more than just one study

L105: what about the location of this deepest point? I have not figured out how you treat this in your study? Is the maximum depth always placed in the lake center?

L107: how do bathymetric data help to understand lake evolution (unless you have repeated bathymetric surveys)? Please clarify

L109: please consider schematic figure of these different expansion mechanisms

L116-120: I don’t understand why/how is this relevant for the rest of the study? The key for the bathymetry of periglacial lake is what morphological glacial lake type it is (bedrock- vs. moraine-dammed) rather than how the lake water level possibly changes with precipitation or meltwater input? Or maybe I’m just missing your point here.

Figure 1: please consider changing the visualization in a way it is recognizable how many bathymetries you compiled from individual regions

L185-191: the difference between standard and generalized model is not clear

Figure 5: is the deepest point located always in the middle of the lake? Because many glacial lakes tend to be deepest in their rare part (beneath the icefalls where the erosion is the most intense)

L244: see my comment to L26

Figure 6: in fact, you do not cover central part and half of the lake area for the Jialongco with your bathymetrical profiling; I’m not sure such data are suitable for the validation of the bathymetry approximation (a lot of interpolation had to be used, right?)

L265: relatively deep compared to what?

L273: in the model description you talk about maximum depth but here about the mean depth, this is bit confusing

Figure 7: is this validation done against really measured points only or against interpolated points too?

L310: please refer to a study supporting this assumption

L318-L320: I would not agree that using the datapoints from around the globe will make your method globally-applicable; it may be the other way round too if you assume individual regions differ (and they do if you compare surrounding topography of glacial lakes in Tropical Andes and Southern Alps, for instance)

L324-329: please see my general comment about the validation

L328: how did you come to this estimation? Please explain

L334: do you mean outliers?

L358: there are other problems in predictive GLOF modelling that may introduce much higher uncertainty than simple empirical equations-derived volume, for instance dam breach scenarios (see e.g. https://doi.org/10.5194/nhess-22-3041-2022)

L365: yes, and I’m sceptic to this ‘worst case scenario’ approach, because complete lake drainages are very rare (and should be only considered in well-justified cases) while incomplete drainages are much more common (https://doi.org/10.1016/j.gloplacha.2021.103722)

L407: it is actually not clear to me how partly glacierized lake basins (i.e. proglacial lakes) are treated in your model?

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To sum up, I recommend major revisions and I hope that my comments will help you to improve your study.

Kind regards

Adam Emmer