Fitting Nonlinear Equations with the Levenberg–Marquardt Method on Google Earth Engine
Round 1
Reviewer 1 Report
The authors should better discuss why the presented methodology seems to work well.
In the conclusion, the authors should mention the limitations of their study and how these could be handled in a future work.
Author Response
Thank you for reviewing my manuscript
Author Response File: 
Author Response.docx
Reviewer 2 Report
The authors provided a revised version of the manuscript. They refer to review round no. 1 by changing th manuscript adequately. The subsequent repsonse letter explains the changes made, and the argumentation is clear. Against this background, I would like to recommend this manuscript for publication.
Author Response
Thank you for reviewing my manuscript
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Authors address the problem of fitting nonlinear models in the context of Google Earth Engine for processing geospatial data, such as remote sensing and climate data. They compared two commonly used non-linear fitting methods, the Levenberg-Marquardt (LM) and Nonlinear Least Square (NLS) methods, and found that the LM method was superior to the NLS method according to the convergence speed, initial value stability, and the accuracy of fitted parameters. The developed non-linear fitting function for the GEE platform has been further tested by fitting a double-logistic equation with the global leaf area index (LAI), normalized difference vegetation index (NDVI), and enhanced vegetation index (EVI) data on the GEE platform. They claim that this function is fast, stable, and accurate in fitting double logistic models with remote sensing data and can also be used to fit other types of nonlinear equations with other sorts of datasets.
This seems to be a very challenging topic and authors have solidly proven their findings. Nevertheless, many points need to be clarified before this submission can be accepted.
More specifically, the preliminaries, the algorithm as well as the mathematical types are detailed in a thorough way showing readers the potential of this area; also, the research appears to be complete in terms of thorough explanations.
On the other hand, I think that the paper should ideally be enriched with some figures so as to further explain to users who are not very familiar with this field, the purpose of appreciating the precise contribution made by this paper. Specifically, authors could analyze more in detail some definitions by providing analytical frameworks.
In the introduction, authors should mention their contribution and not to repeat the abstract. Authors have also omitted to discuss the problem at hand. Also, they have not stated the differences of their work with others in bibliography.
Moreover, authors did not discuss at all the algorithm. It must be places within the text with further analysis and not in the appendix.
The dataset analysis is somehow missing. Please provide link or reference along with dataset characteristics.
Why these two methods?
Finally, authors should mention their planned future work.
Reviewer 2 Report
The authors should compare the produced results of Levenberg–Marquardt (LM) with linear regression models of GEE platform.
A statistical test should be used for the comparison of the examined methods.
The authors should also compare the time complexity of Levenberg–Marquardt (LM) with linear regression models of GEE platform.
Reviewer 3 Report
This methodological oriented study is worth publishing in this journal. While the methodology appears sound to me, I have one comment on the discussion of the study results: When discussing the advantages of the Google Earth Engine cloud-computing platform, you only refer to a general on the GEE (Gorelick et al. 2017). However, you not discuss advantages of the GEE approach with reference existing studies. Without this linkage, your study results remain unconnected to the state-of-the-art debate. In a revised version, you should establish this link. This would help to improve your interesting manuscript.
