Review Reports
- Kai Yu1,2,3,*,
- Changming Dong4 and
- Jin Wang4
- et al.
Reviewer 1: Anonymous Reviewer 2: Leonid Piterbarg
Round 1
Reviewer 1 Report
See the attached PDF.
Comments for author File: 
Comments.pdf
Author Response
Please see the attachment
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper addresses statistical properties of SST at the Kuroshio Extension derived from high accuracy satellite data via a relatively new techniques developed by Vogelzang et al. One of the main results claims fractal properties of the SST field based on estimating the Hurst exponent of temperature time series which is typically walks around 1/3. The region in question is mapped accordingly to the slope p of the partial variance V (r) (or structure function
D(r)). That map supports conclusions on multiscale and fractal features of SST.
In general, the results are interesting and methods in use are adequate and mathematically consistent.
A few comments which could improve presentation.
1. In the Kolmogorov theory r =sqrt(x2 + y2 + z2 ) and k =sqrt(kx2+ ky2+kz2) are the magnitudes of the 3D displacement and wave vector respectively while in the paper context r and k are one-dimensional characteristics (length and wave number respectively). A remarkable and highly non-trivial fact is that eq. (1) holds true in both, 3D and 1D cases. That should be noticed somewhere (say, right after the equation) to avoid confusion.
2. The expectation symbol in (2) should be deleted because M1(r) and M2(r) are non-random characteristics (statistical moments).
3. Calculations given in Appendix A can be found at almost every textbook in Probability or Statistics. Please remove that Appendix. Furthermore, the words ’correlation between S2(r) and moments’ are incorrect because the former is a random variable while the latter are deterministic quantities.
4. Please check spelling on figures. Example: In figure 7 we see ’saptial’ instead of ’spatial’.
Comments for author File: Comments.pdf
Author Response
Please see the attachment
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
See the attached PDF.
Comments for author File: Comments.pdf
Author Response
Author Response File: Author Response.docx