Dear Editors,

I carefully read the manuscript by Rojo-Garibaldi et al.

It is an excellent work on a very important topic, the data used are new and the data analysis is also innovative, and the results are relevant. Methodologically the paper is very strong.

Thus this work needs only minor revisions

List of Minor Points:

1. In the introduction authors ought to add some considerations on the impact of el nino on human life, and, in particular, on human health. This would enhance the relevance of their work and increase its readership
2. Section 2.1.2 needs more bibliography.
3. Section 2.1.2: the final sentence on Friedrich et al must be anticipated and also expanded: it is not good to say the readers: go and read that paper. Moreover, the journal is on a topic that is very different from the one of this journal, thus maybe readers could incur in some difficulties in reading that paper. For example, in section 2.1.3 authors succintlu but clearly describe the main content of various papers
4. In section 2.1.3 the discussion of the bibliography ought to be anticipated or intermixed with the formulas: this would increase the readability of the work
5. Authors explain that they use “a neural network model of the map F and of its Jacobian J”. This is a key point of the whole paper and, in particular, of sections 2.2 and 3. In section 3 we also read that the ANN has a single layer. Authors must provide further details, such has the number of neurons of the layer, the training procedure, the global minimization algorithm used and the activation functions
6. A lot of important details are in the appendix, especially in appendix A5. Authors ought to consider to move some materials of the appendix in the full text

Extended editor comment of Nonlinear Time Series Analysis of Coastal Temperatures and El Niño–Southern Oscillation Events in the Eastern South Pacific

Dear authors, 

The editorial process has been abnormally long, as one of the promised reviews did not come in. In agreement with one of the editors-in-chief, and to avoid further lengthening the process, I have myself proceeded to a review. 

Along with the first review, I consider that the manuscript will be acceptable for Earth System Dynamics, but a significant edition will be necessary. 

Perhaps at odds with usual practice, I will focus first on the minor comments, and then proceed to the bigger picture.

Abstract:

'the station that displays very regional characteristics'. The sentence is a bit cryptic. On the one hand, they both correlate with ENSO, but one is "very regional". The message should be more specific and accurate. 

l. 25: "negative trend observed in the PDO" : is this a trend in the mean or in the variance ? 

l. 50: "rigorously": use a more specific word. In what sense is this 'rigorous'

equation p. 7:

The equation only makes sense if $\delta$ is a line-matrix (meaning a vector), while it is defined as a norm p. 6. There is also confusion about the old / italic convention. The  $J_{m-t}$ is a Jacobian (a matrix), and so should $T_M$, but $T_M$ appears both in boldface and in plain. 

While the development is classical, many readers might not get why only the largest eigenvalue $\nu_1$ (and not the other ones) survives under the limit $M\rightarrow\infty$. 

p. 7: You mention the 'first approach', .... but never the 'second approach'

Methods have not been fully presented before the Results section. At this point, the reader understands the definition of the short-term Lyapunov exponent in a dynamical system where the Jacobian is available, but not the algorithmic methods and choices that allow for the estimation of the short-term Lyapunov exponent from an empirical (uni-variate) time series, and how critical are these algorithmic choices. Little to nothing is said about the feed-forward neural network model (l. 220) and the BIC that are central to the results. 

p. 12: "this does not happen". Not clear what "this" refers to (negative LLE for all time series ?). Using positive wording (LLEs are positive for AST) might help. 

The discussion on p.15 is not easy to follow. I understand that LLE may increase or decrease during an El-Niño

event, and this depends on the epoch. l. 259 one refers to a "marked decrease" during the 192-1973 event but the reader will not know how well it is "marked" and what this means.

More broadly, I would strongly encourage the authors to reconsider their choices of figures. On the one hand, the boxplots (Fig. 6) linking the short-term to long-term Lyapunov exponents are interesting but perhaps they can go in the appendix or supplementary material. By contrast, the presentation p. 15 describing the evolution of indices through time must be supported by figures (especially given that, l. 273, you acknowledge that the result presentation so far lays upon a "visual comparison", which the reader cannot reproduce). 

The spectral analysis section 4.1 should be part of the result presentation, not the discussion. 

Attributing spectral peaks to forcing or processes (lunar perigee subharmonic, QBO) is a delicate task, with significant risks of misattribution. Using the conditional (with the magic phrase "may be") is a wise precaution, but somewhat unsatisfactory. For example, in this particular case, can you check the phase coherence of the signal with these processes? 

The discussion of the nonlinear analysis (section 4.2) is also a bit tedious, some would say speculative. It is fine to formulate hypotheses, but consider the following advices: 

 - refer to figure numbers when you describe a specific feature (to help the reader make its own judgments. For example, when you write "it is also possible to observe similar dynamics", "it can be noted by eye")

 - discuss and describe possible ways to verify your hypotheses. What would it take to verify the teleconnection processes; verify the role of the atmospheric teleconnections, the role of the Pacific anticyclone, or the fact that disturbances coming from the equator only influence the northern part of Chile). 

 - avoid non-necessary conditional (e.g.: "it is also possible to observe" : you observe it, or you don't). 

l. 412 : "but rather Southern Annual Mode" :  the sentence is unclear. 

l. 450 : a table with cross-entropies would help. 

These line-by-line comments bring me to the broader  editorial concern. 

Overall, I consider that you need a better discussion strategy for section 4.1. The section is lengthy, and it leaves the reader unsatisfied because many hypotheses are expressed but the reader will struggle to make his/her own opinion. 

Once you have presented the methods (and again, consider that at the reader  lacks algorithmic details,  with  a discussion of the critical aspects of the algorithmic choices) my advice would be to focus  on fewer elements that emerge out of your analysis,  but treat them in a way that effectively helps future studies to build on them. 

Remember that ESD's focus on the functioning of the Earth system. This is not the journal for presenting tons of data nor focusing on overly local aspects. 

Use the figures in a way that helps the reader. Refer to them effectively in the text. Perhaps not all A5-A10 are needed (have the data available, though, for example using an institutional repository such as Zenodo), and put in the core text what the reader needs to reproduce your reasoning. 

Most sincerely, 

Michel Crucifix.