Review Reports - An ISOMAP Analysis of Sea Surface Temperature for the Classification and Detection of El Niño & La Niña Events

Round 1

Reviewer 1 Report

Review of the manuscript ‘An ISOMAP Analysis of Sea Surface Temperature for the Classification and Detection of El Niño & La Niña Events’ by John Chien-Han Tseng.

The manuscript examines the efficiency of the ISOMAP data coordinates to obtain distances which are corrected by the curvature of the low-dimensional manifolds where data lie. Distances are compared with geodesic distances. The same assessment is performed with Euclidean distances obtained by the PCA coordinates. The comparison is performed on the space spanned by the leading PCS of the SST variability evaluated in the El-Niño Pacific region.

The manuscript is generally clear providing a good application of the ISOMAP method. The conclusions are well supported and new. In order to obtain a publishable manuscript, some phrases shall be corrected in terms of grammar and some considerations and minor shall be addressed.

In the abstract and lines 68-69, the reference to the Lorenz ‘butterfly effect’ is somehow abusive because it should be accompanied by a study of the evolution of trajectories starting from nearby initial states and also the computation of Lyapunov exponents. However, this study is not performed and therefore the text must refer this limitation.
Lines 43-44 Rephrase: ‘Inevitably, this explanation not well situation always happens in the real data analysis’
Line 45 Give references for each PCA type analysis
Line 45 Refer alternative techniques to PCA of the data compression and dimensionality reduction, which are based on Information Theory, looking for components or subspaces which are the most statistically independent as possible when data follow non-Gaussian probability distributions, like the ICA (Independent Component Analysis):

Hannachi, S. Unkel, N. T. Trendafilov, and I. T. Jolliffe, “Independent component analysis of climate data: a new look at EOF rotation,” Journal of Climate, vol. 22, no. 11, pp. 2797–2812, 2009.

and ISA (Independent Subspace Analysis):

Pires, C. and Hannachi, A. 2017. Independent subspace analysis of the sea surface temperature variability: non Gaussian sources and sensitivity to sampling and dimensionality. Complexity 2017, 1–23. doi:10.1155/2017/3076810

Lines 54-55 In the phrase: ‘When these linear coordinates are used to determine nonlinear variation, the data points are found to concentrate in some places and to separate in some places’, the meaning of ‘concentrate’ and ‘separate’ is ambiguous in this context. Rephrase please.
Line 62: ‘data points can be pushed away more than that with the traditional linear PCA’. Explain. The reverse can also happen i.e. data points can be pulled together.
Line 73 Explain the acronym NWP (Numerical Weather Prediction) at the first use.
Line 89, 90 Refer here the number N of instants used in the analysis
Line 116 Provide reference for MDS (e.g. Cox, T.F.; Cox, M.A.A. (2001). Multidimensional Scaling. Chapman and Hall.)
Line 118 In the Algorithm of ISOMAP explain what are the yi and yj vectors, its dimension, and indices. Are I,j temporal indexes?
Line 123 For the sake of better understanding, write explicitly the correspondent expression for the residual variance using the distances obtained from PCA components
Lines 191-192 In the discussion of temporal PCA components and temporal ISOMAP components, check in which measure the ISOMAP components are more statistically independent than PCA components. Check if zero correlation in ISOMAP different components is preserved. Moreover, like in ISA (Independent component Analysis) we look for more independent rotated components when the probability distribution of data is Non-Gaussian. In this regard, check for instance if certain nonlinear correlations decrease when ISOMAP components are taken instead of PCA components.
Line 218 Correct ISOMPA
Lines 240-244 Explain better how the values were obtained for the cases described in the rows of the Tables: ‘El Niño and non-El Niño’ and ‘La Niña and non-La Niña’
Lines 270-272 Explain the reason of the phrase ‘With a neighbor number 270
greater than 480, the classification results are similar to those of the PCA method. The reconstructed data points are closer to each other, and the advantage of using the ISOMAP is lost.’
Line 311 Is matrix D the same as DM? Please check.
Line 312 Give the reason why the number of 44 of neighbors is chosen
Figure 4 Explain the meaning of color arrows in the caption
Line 314 Give reference for the Dijkstra’s algorithm

Author Response

Dear Reviewer,

Please see the attachment.

Sincerely,

John Tseng

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript deals with the ENSO events. The authors accepted that the ISOMAP method is sensitive to region. However, at present, the ENSO event is preferred to take place in the central Pacific Ocean. The readers did not understand the specially of ISOMAP to distinguish the various flavors of EL-Nino/ENSO. Thus, the advantages of the method is required to mention in the manuscript.

Author Response

Dear Reviewer,

Please see the attachment.

Sincerely,

John Tseng

Author Response File: Author Response.pdf

Reviewer 3 Report

Review report on ‘An ISOMAP Analysis of Sea Surface Temperature for the Classification and Detection of El Niño & La Niña Events’ by John Chien-Han Tseng,

In this study, the Author described the Isometric feature mapping (ISOMAP) analysis for classification and detecting the different phase of ENSO such as El Niño, La Nina and Neutral events from NOAA Sea surface temperature data. The Author also compared the ISOMAP classification with the traditional PCA method. Further, the author tested these classifications with the Niño 3.4 index. Overall, the manuscript is written well and nicely presented.

The ISOMAP can help to identify the extreme ENSO cases. Previously this ISOMAP analysis was applied to investigating the monsoon intra-seasonal variability and well explained. Even though I am not a mathematician and not expert in these different mathematical analyses, the paper looks promising and easy to follow. In my opinion, the present study will provide some insights into the understanding of the ENSO classification methods. Thus, I recommended this paper in the Atmosphere journal with following few corrections.

Corrections

The captions and labels for axis (x and y axis) in the figures should be improved. Please increase the size of labels and axis ticks for improving the quality of the figures.

Line 51-54: Please change ‘geopotential height’ to ‘Geopotential height’

Line 98: ‘average SST exceeded 0.5°C’ is it SST? Or SST anomaly? Please clarify it.

Line 103-104: Follow either ‘Fig. 1’ or ‘Figure 1’ in the entire manuscript.

Author Response

Dear Reviewer,

Please see the attachment.

Sincerely,

John Tseng

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The author have thoroughly answered to all questions and made the necessary corrections. I recommend publication after the mention of a reference described below.

In the section 'Introduction', describing the state of the art and the several techniques of blind source separation, the author has decided not to mention the ISA (Independent Subsapace Analysis). However, it is important to cite that as a generalization of ICA (Independent Component Analysis) when multivariate non-Gaussian data are not linearly separable into one-dimensional independent subpaces, i.e the independent components extracted from ICA but they rather separable into independent subspaces of dimension (one or more).