Dear Dr Kwasniok,

you paper was sent back to the two referees who reviewed the first version. One of them was unable to review the paper again, so I decided to sent the paper to another expert. His/her report is included together with the second report by one of the former referees. The reports indicate that, while worth publishing, your manuscript still needs some work in several aspects. Please, read the reports very carefully and consider one by one the referee recommendations.

Dear Dr Kwasniok,

your paper has been re-reviewed by the Referee. I agree with him/her concerning the use of the word "Amplitude" in Fig. 4. If I understand correctly this plot shows the three main principal components (EOF) of the perturbation field, y_j^{(\tau}) for j=1,2,3 in Eq.(21) as a function of the ith degree of freedom (spatial components) for different values of \tau. Your response to the previous Referee report saying that this plot shows "the amplitude of an eigenvector e_j" is certainly confusing because e_j is defined as a orthonormal basis and as such the amplitude of e_j is always unity. I guess you meant to say the amplitude of the fluctuationprojection in the e_j direction, that is Eq.(21). The Referee, and I agree, asks to write y_1, y_2, and y_3 explicitly in the Y-axis, instead of using an ambiguous term as "amplitude".

I recommend you to:

1) write y_1, y_2, and y_3 explicitly in the Y-axis, instead of using an ambiguous term as "amplitude",

2) mention in the figure caption Eq.(21), so that the reader could easily link the plot with the quantities defined in the text,

3) in Fig. 4 also replace j in the X-axis by i to be consistent with the notation of the paper.