Dear Editor and authors,

The manuscript "Multifractal structure and Gutenberg-Richter parameter associated with volcanic emissions of high energy in Colima, México (years 2013–2015)" by

Marisol Monterrubio-Velasco, Xavier Lana, and Raúl Arámbula-Mendoza is an interesting piece of research about the applications of multifractal detrended fluctuation, scaling and statistical analysis to volcanic emissions time series.

I think that, although interesting, the paper cannot be considered for publication in Nonlinear Processes in Geophysics in the current version for the following reasons:

1) Methods are not complete (it is not clear how the b-value and completeness of catalogue are calculated), uncertainties and fit quality and outputs are not always reported;

2) The abstract and introduction should be rewritten in a clear way, improving language quality (avoiding repetitions ...)

3) The quality of figures is not optimal

4) Discussions are mixed to results and a quantitative summary is missing.

Therefore, I suggest reconsidering the manuscript after major revision; however, the decision must go to the editor.

Below I attach a pdf file of the manuscript with comments, suggestions and corrections.

The study attempts to justify the hypothesis that by studying the temporal variation of some multifractal parameters, together with the extension of Gutenberg-Richter law to volcanic energy emissions, one is able to forecast the imminence of high energy emmissions.

The work is interesting and worthwhile of the attention of the academic community. However, the manuscript and results need to be presented in a clearer way.

The following are my major concerns, other issues are highlighted in the annotated pdf annexed.

Abstract is too cumbersome. 

It is not t clear why the authors only show the behavior of some moving windows and not others.

There is no apparent difference in the curves of Fig. 6,

The employ of the algorithm based on reconstruction theory is not clearly explained and objectively justified.

Labels and captions on some figures are misleading or confusing.