Review Reports - Refined Reservoir Routing (RRR) and Its Application to Atmospheric Carbon Dioxide Balance

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript entitled Reservoir Routing and its Application to Atmospheric Carbon Dioxide Balance analyzes the reservoir routing framework, extends it to find approximate solutions for nonlinear cases, and then applied it to describe the mass balance of atmospheric carbon dioxide and determining characteristic residence times. Although the framework is very novel, the experiment design and organization look problematic. I provide some detailed comments below and recommend Rejection of it.

(1) The abstract and the main text lack quantitative conclusions to answer the questions proposed around carbon dioxide characteristic residence times.

(2) The topic is inconsistent, which includes both reservoir water balance and atmospheric carbon dioxide mass balance. One paper should have only one topic. Please focus on one topic to express the whole study, especially for the introduction part.

(3) In addition, the introduction reads very casual. Please use scientific and professional language to organize the manuscript.

(4) The proposed method which studies the carbon dioxide characteristic residence times, outflow and inflow lacks validation and assessment of its suitability. This is major deficiency of the experiment design.

(5) The results part of Section 3 contains both method (e.g., Equations (50-65)) and background (e.g., 3.1.1) introduction. These do not belong to the results, even is not closely linked to this study topic. Please refine this part thoroughly.

Comments on the Quality of English Language

Please refine the language and orgnization.

Author Response

Please see attached report.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Line 9, the expression is not accurate. Some nonlinear problems can be analytically solved.
The present study proposes an analytical method for Reservoir Routing problem. It is suggest refining the article title with a more specific title, including the name of the proposed method.
Some quotes are unnecessary (for instance lines 24-26, 55-59).
What is the mathematical fundamental on the proposed method?
Is the proposed method applicable to 2D or 3D problems? Please clarify it.

Author Response

Please see attached report.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript proposes a simplified and extended reservoir operation framework and applies it to the mass balance study of atmospheric carbon dioxide. The application results align well with actual data, allowing for easy quantification of atmospheric carbon exchanges and providing reliable and intuitive results without resorting to complex climate models. However, the current version requires improvements before publication. It is recommended to make minor modifications based on the following comments:

1.The introduction provides a general description of the mechanisms of carbon dioxide exchange between the atmosphere and water bodies, lacking detailed discussion and explanation of how these processes are influenced by hydrological factors.

2.Although the model shows good consistency with specific datasets, comparing it with predictions from existing complex climate models could strengthen the validation of the proposed simplified model.

3.The theoretical analysis section is dense, potentially challenging for readers unfamiliar with the concepts in this field. Simplifying explanations or providing visual aids could enhance understanding.

4.The abstract and conclusion are relatively simple and lack a systematic summary. For example, the practical significance of this innovative study in estimating carbon emissions or influencing policy formulation could be elaborated.