Three Kinds of Butterfly Effects within Lorenz Models

Round 1

Reviewer 1 Report

Dear editor and authors.

This work is a review on the 3 kinds of butterfly effects present in chaotic dynamics. It takes a look at each phenomenon and describes it, along with a brief history behind it.

I found this work overall very interesting and enjoyable to read. I certainly believe it has merit for the community and should be considered for publication.

Given the nature of the journal, I believe though some effort should be made to make it more accesible for a general physics audience. For example, I found hard to follow the BE3 phenomenon, from line 233 onward and in (3). I believe some explanation is required here.

In addition, here are some remarks and thoughts.

--line 95, 'materials'.

--Figure 1, I would suggest to also give the initial conditions x0,y0,z0. And also, I would suggest also plotting the x,z states as well, to visualize that despite the initial divergence appearing only on y, i.e. x0,y0+e,z0, the divergence in the trajectory appears in all three dimensions.

--line 172, 'release of instability by the atmosphere'. The term 'release' I am not sure if it is appropriate here.

--line 211, 'Such a closure produces inconsistent properties and unphysical results''. The term unphysical results, I think is worth explaining further.

--line 209, 'approximation'

--The vese in line 280, do you believe is more suitable to explain the BE2, in terms of transfering a change from smaller to higher scales? (wing flap-->tornado, nail-->kingdom). This to an extend though, since it still falsly describes this as a monotone increase.

--Much like the BE1, can the BE3 be visualized?

Author Response

Please see the attached file for details. 

Author Response File: Author Response.pdf

Reviewer 2 Report

The exploration of atmospheric predictability on a range of time scales (including short-range weather forecasting) is of great practical importance and keep attracting attention of researchers over time. The authors of the manuscript under review provide their theoretical explanations in support of the article “Mesoscale predictability in moist midlatitude cyclones is not sensitive to the slope of the background kinetic energy spectrum”, published in JAS this year (the authors are D.L. Lloveras, L.H. Tierney, and D.R. Durran). In this article, using simplified f-plane model, the authors shown that the error-grow time for atmospheric wave with given wavenumber is not proportional to the eddy turnover time. The authors of the peer-reviewed manuscript mathematically correct and physically soundly presented their arguments in favour of this conclusion.

Apart from that, they, using mathematical analyses, provide additional discussion which can help researchers better understand and proper interpret the equation for the lead time represented in the form of time series (equation (5) in the original article of Lloveras et al.).

I have no objection to the publication of a peer-reviewed manuscript written at a high scientific level.

Author Response

Please see the attached file for details. 

Author Response File: Author Response.pdf

Reviewer 3 Report

The study is based on three Kinds of Butterfly Effects Within Lorenz Models. The model consists of three 1st order ordinary differential equations (ODEs) for three variables (X, Y, Z) which describes the time evolution of the amplitudes. Each case is explicitly defined and discussed very well. It further clarifies some inaccurate understandings of BE1 and BE3 with valid supporting arguments.

I would like to sugest that Table 1:The Three Kinds of Butterfly Effects. can be placed under discussion and can be referenced in the conclusion.  

The paper is of high quality and I recommed it be accepted for publication after the minor change.

Author Response

Please see the attached file for details. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have addressed my remarks. I still believe Fig. 1 should have been updated (yes, surely similar images can be found in other papers for this well known phenomenon, but still the paper should be self contained.) but as this does not affect the essence of the work, the authors have the freedom to decide for themselves. Thus the work can now proceed to publication.

Author Response

Figure 1 has been revised accordingly. Thanks very much!

Reviewer 3 Report

I am happy with the changes and recommend this manuscript be accepted for publication.

Author Response

Thanks very much!

Round 3

Reviewer 1 Report

The updated image is fine