Response to Adam Emmer,

Thank you very much for your review. As we have added some revised figures, please see the attached file for details.

Response to Reviewer,

This paper presents a novel method for estimate the water storage of moraine-dammed glacial lakes (MDLs) by using geometric approximations. This method addresses the significant challenges posed by traditional bathymetric surveys, which are often difficult and costly, particularly in remote and high-altitude regions. By utilizing the outline and surrounding terrain of a glacier lake, and assuming a parabolic lake bottom and constant hillslope angles, the model achieves a lower average relative error (~14%) compared to other models (>44%). The paper validates the model with data from newly surveyed glacial lakes on the Qinghai-Tibet Plateau and other recently measured lakes, proving its robustness and potential for global application in glacial lake management and GLOF risk assessment. Additionally, the study's classification of MDLs into glacier-contacted and glacier-uncontacted lakes, based on their geometric properties, enhances the model's applicability. Overall, this paper offers a significant advancement in glacial lake management, providing crucial insights for hazard mitigation and water resource management in glaciated regions.

Explanation and revision: Thank you very much for your positive feedback.

Besides, some minor problems in this manuscript should be thought by the authors:

1. Line 237 | The author did not mentioned how the threshold of m and n was determined, it should be given more explanations.

Explanation and revision: Thank you very much for your affirmation and questions. We first simplified the model into four equations, with their solutions all dependent on the correct selection of m, n, and r. Based on the geometry of the glacial lake, we established a proportional relationship between m, n, r, and the glacier lake length (l). This proportional relationship is empirically defined and essentially represents a geometric segmentation of the glacial lake. The lake is divided into three sections, and the volume of each section is calculated separately. The total water storage of the lake is then obtained by summing the volumes of these three sections.

Therefore, we first used measured data from four glacial lakes to validate whether this proportional relationship was appropriate. After validation, we found that the empirically derived proportional relationship performed well. Hence, this study adopts this proportional relationship as the standard for the model's input parameters. No calibration or adjustments were made during this process. We have added the following explanation in lines 243 to 248 of the original text: " Based on the geometry of the glacial lake, we established a proportional relationship between m, n, r, and the glacier lake length (l). This proportional relationship is empirically defined and essentially represents a geometric segmentation of the glacial lake. The lake is divided into three sections, and the volume of each section is calculated separately. The total water storage of the lake is then obtained by summing the volumes of these three sections."

1. Line 263 | The author mentioned ‘we trained our workflow on ...’. According to this paper, there is no parameter that needs to be trained or optimized, all parameters can be measured through the glacial lakes and their surrounding topology. The author should consider modifying the description of  the workflow.

Explanation and revision: Thank you very much for pointing out the issue; we have revised the description of the workflow. The modified sentence is as follows: “We executed our workflow (Figure 6) on 44 MDLs in High Mountain Asia that have known depths and water storages.”

1. Line 349 | The total volume of water storage in HMA is not accurate, since this is a method used to estimate the water storage of MDLs, while there are other kinds of glacial lakes such as ice-dammed glacial lakes supraglacial lakes etc., of which volume is accurate using this method.

Explanation and revision: Thank you very much for pointing out the issue; we have revised this sentence: “Over the past three decades, the overall MDL’s water storage increased by 8.94 km³ from 28.24 km³ in 1990, representing a growth of approximately 32%.”

1. Line 433| MDLVL is not mentioned before.

Explanation and revision: Thank you very much for pointing out the issue. We have reviewed and revised the entire text, changing "MDLVM" to "our model."

Response to Reviewer,

This paper presents a novel method for estimate the water storage of moraine-dammed glacial lakes (MDLs) by using geometric approximations. This method addresses the significant challenges posed by traditional bathymetric surveys, which are often difficult and costly, particularly in remote and high-altitude regions. By utilizing the outline and surrounding terrain of a glacier lake, and assuming a parabolic lake bottom and constant hillslope angles, the model achieves a lower average relative error (~14%) compared to other models (>44%). The paper validates the model with data from newly surveyed glacial lakes on the Qinghai-Tibet Plateau and other recently measured lakes, proving its robustness and potential for global application in glacial lake management and GLOF risk assessment. Additionally, the study's classification of MDLs into glacier-contacted and glacier-uncontacted lakes, based on their geometric properties, enhances the model's applicability. Overall, this paper offers a significant advancement in glacial lake management, providing crucial insights for hazard mitigation and water resource management in glaciated regions.

Explanation and revision: Thank you very much for your positive feedback.

Besides, some minor problems in this manuscript should be thought by the authors:

1. Line 237 | The author did not mentioned how the threshold of m and n was determined, it should be given more explanations.

Explanation and revision: Thank you very much for your affirmation and questions. We first simplified the model into four equations, with their solutions all dependent on the correct selection of m, n, and r. Based on the geometry of the glacial lake, we established a proportional relationship between m, n, r, and the glacier lake length (l). This proportional relationship is empirically defined and essentially represents a geometric segmentation of the glacial lake. The lake is divided into three sections, and the volume of each section is calculated separately. The total water storage of the lake is then obtained by summing the volumes of these three sections.

Therefore, we first used measured data from four glacial lakes to validate whether this proportional relationship was appropriate. After validation, we found that the empirically derived proportional relationship performed well. Hence, this study adopts this proportional relationship as the standard for the model's input parameters. No calibration or adjustments were made during this process. We have added the following explanation in lines 243 to 248 of the original text: " Based on the geometry of the glacial lake, we established a proportional relationship between m, n, r, and the glacier lake length (l). This proportional relationship is empirically defined and essentially represents a geometric segmentation of the glacial lake. The lake is divided into three sections, and the volume of each section is calculated separately. The total water storage of the lake is then obtained by summing the volumes of these three sections."

1. Line 263 | The author mentioned ‘we trained our workflow on ...’. According to this paper, there is no parameter that needs to be trained or optimized, all parameters can be measured through the glacial lakes and their surrounding topology. The author should consider modifying the description of  the workflow.

Explanation and revision: Thank you very much for pointing out the issue; we have revised the description of the workflow. The modified sentence is as follows: “We executed our workflow (Figure 6) on 44 MDLs in High Mountain Asia that have known depths and water storages.”

1. Line 349 | The total volume of water storage in HMA is not accurate, since this is a method used to estimate the water storage of MDLs, while there are other kinds of glacial lakes such as ice-dammed glacial lakes supraglacial lakes etc., of which volume is accurate using this method.

Explanation and revision: Thank you very much for pointing out the issue; we have revised this sentence: “Over the past three decades, the overall MDL’s water storage increased by 8.94 km³ from 28.24 km³ in 1990, representing a growth of approximately 32%.”

1. Line 433| MDLVL is not mentioned before.

Explanation and revision: Thank you very much for pointing out the issue. We have reviewed and revised the entire text, changing "MDLVM" to "our model."

Response to Reviewer 2,

The authors developed a model to improve lake water estimation by simplifying the shape and depths of moraine-dammed lakes. The model showed better performance compared with other existing models. The author also used this model to calculate the water storage changes of moraine-dammed lakes in the past 30 years in High Mountain Asia. I think this study is a significant advancement in glacial volume estimation and it is worthy of being published after minor revision. Some major comments are shown as below:

1, Four types of moraine-dammed lakes are considered in this study. In fact, as shown in Figure 4 and Figure 10, the shape of MDLs is much more complicated. If the authors can classify the MDLs in more types in the future study, the estimation may be further improved.

Explanation and revision: Thank you very much for your suggestion. We will carefully consider improvements in this regard.

2, Line 165-169, the authors gave the core assumption of the model. In the discussion section, the authors add some discussion about this assumption using the available data. It is helpful, but we can also see that the underwater bathymetry is complicated so the model can be further improved in the future study.

Explanation and revision: Thank you very much for your affirmation and support. As you mentioned, the morphology of moraine dammed lake beds is complex, closely related to glacial erosion processes. In our model, we first proposed a hypothesis and validated it with measured data, striving to approximate the actual basin morphology of moraine-dammed lakes as closely as possible. However, this inevitably comes with certain limitations. We will prioritize improvements to the model in our future work.

Minor comments

1, Line 126-127, the sentence is not clear enough for me, please further rephrase it.

Explanation and revision: I sincerely apologize for the misunderstanding my wording caused during your reading. So, we have revised the sentence as follows:

“If R is less than 0.1, it may indicate the presence of glacial lakes with lengths exceeding 10 meters but widths of approximately 1 meter.”

Response to Reviewer,

Thank you very much for your review. As we have added a revised figure, please see the attached file for details.