REVIEW ON THE PAPER“Uncertainties, complexities and possible forecasting of the volcán de Colima energy emissions (México, years 2013-2015) based on the fractal reconstruction theorem” by Xavier Lana, Marisol Monterrubio-Velasco, Raúl Arámbula-Mendoza

The paper “Uncertainties, complexities and possible forecasting of the volcán de Colima energy emissions (México, years 2013-2015) based on the fractal reconstruction theorem” contains an interesting analysis of the seismic activity of a Mexican volcano using fractal, informational, nowcasting and dynamical systems techniques. Results show occasional persistent patterns in volcanic activity but limited predictability.

While both the content and scientific approach to the subject of a so rich and integrated analysis make this paper an interesting and significant contribution, the manuscript is riddled with several minor and major mistakes throughout the main text, figures and in its structure itself which do not allow publication in the present version:

1. The abstract is mainly devoted to methods without providing information about the content (volcanic activity), goals and results.
2. The introduction is confusing and definitely a better and wider background should be provided to the interested reader. More references should be added.
3. The section about data is a mix of discussions, analysis, and methods, while no link or reference is given for the data analysed in this study.
4. The quality of some figures is poor; moreover, references to subfigures are sometimes missing and the measure units as well.
5. Conclusions are not clear enough: what is the final output of authors’ analysis about the possible forecasting of the Colima volcano? I have read the paper and at the end I was not able to answer this crucial question without looking more times for information throughout the text and pictures.
6. The quality of language is poor with misspellings, inaccurate terms, and sometimes convoluted sentences. I strongly suggest that the authors carefully read their draft and try to make it enjoyable to read.

Therefore, I think that, even though the content is intriguing, a really deep revision is needed to before the manuscript be eligible for publication in Nonlinear Processes in Geophysics and I am not sure that the amount of work required is suitable for a “major revision”; however, the decision must go to the editor.

Major and minor comments, request of improvements, corrections and suggestions are listed as comments in the main text, figures, and captions throughout the pdf file I attached.  

The article discusses methods for analyzing time series representing the power (the amount of energy released per unit time) of volcanic eruptions in Mexico. The general goal of such an analysis is to predict a certain number of time steps ahead. It is proposed to use an approach based on the use of nonlinear methods. The reason for this choice is that the data distribution satisfies the Gutenberg-Richter recurrence law, that is, it has self-similarity properties. To describe the data, such statistics as the Hurst exponent, Kolmogorov entropy, exponential Lyapunov exponents, and estimates of the hidden attractor dimension using the Grassberger–Procaccia correlation integral are used. Together, these methods represent a standard set of tools for analyzing the behavior of time series and estimating the depth of data memory, assuming the existence of some hidden non-linear mechanism that generates its time samples. For the actual prediction, a method is proposed, previously developed for the analysis of seismic catalogs, and called nowcasting. This method is based on calculating the average number of events whose power is less than a given threshold, which defines a "strong" event. The distribution function for the number of small events makes it possible to estimate the "seismic" potential, which, in relation to the analysis of volcanic activity, means an assessment of the level of danger of a strong eruption. Such nowcasting curves are shown in the article (Fig.10). However, they do not use in any way the previously made estimates of the nonlinear statistical characteristics of the time series of eruption intensity. Below are graphs of changes in the nonlinear parameters of the time series (Fig.11). The main remark to the content of the article is that it is necessary to more clearly indicate the relationship between the curves in Fig.10 and Fig.11. I have the impression that no such connection has been established at the present time. If so, then this should be written more specifically. The authors write that they plan to conduct further studies that may help to identify such a relationship. But now the content of the article is divided into 2 independent blocks: an estimate of the nonlinear parameters of the time series of eruption intensity and brief considerations regarding nowcasting, in which the remark is made that this method is apparently less effective for estimating the probability of strong eruptions than for earthquakes.