The authors developed a new method for detecting oceanographic fronts by employing PCA, GMM, and I-metric. By utilizing B-SOSE, they have demonstrated that their new methods successfully detect fronts, which vary in time and space. In general, I think their scientific discussions are sound. I think this manuscript is well-written. However, for readers who do not know much about these analyses methods, some parts of the text are difficult to follow. I suggest that minor revision  before publications.

Minor comments

Section 2.1 For those people who do not know much about ECCO, it would be great if authors can elaborate a bit about what other ECCO products are available and why authors choose B-SOSE. 

Lines 117-126: This part of the text is difficult to follow without reading Pauthenet et al., 2017 carefully. A bit more explanation (e.g., equations (1) in Pauthenet et al., 2017) and something similar to Fig. 4 in Pauthenet et al., 2017 would be helpful for better understanding. 

Line 147-170: If I am not wrong, I think PCA is used just to compress the data (reduce its number of dimensions), rather than to investigate the structure of its covariance matrix. This point is not stressed in this paper. The authors should clarify this point if this is correct. 

In addition, it becomes easier to understand if the authors can elaborate on (1) why GMM is used rather than PCA (advantages and disadvantages) and (2) the difference (or relations) between vertical modes of temperature and salinity obtained from PCA analysis and figure 5. For me, this manuscript was initially very confusing because it took me a while to understand that PCA is only used to compress the data but main analysis was conducted using GMM. 

Abstract and Summary : 

Authors conduct analysis using Sobel edge operator but they do not argue how it can be useful in the abstract and conclusion. A sentence describing how it can be useful and comparisons with GMM is going to be useful. 

The authors propose a new method to quantitatively define the Southern Ocean fronts. The new metric,  I-metric, searches boundaries of water masses in the space spanned by the principal components of the Southern Ocean hydrography. The water masses are classified by the Gaussian mixture modelling. When applied to the output of the Southern Ocean State Estimate (B-SOSE), the newly defined fronts correspond well to the traditional definitions of fronts both in monthly snapshots and in 5-year average.

I find the definition of the I-metric (equation (3)) is intuitive and natural, and am convinced that the new method has an advantage over the traditional front definitions in its ability to allow "for a wider variety of transition types between regimes" (ll.198-199). The paper is well written except for a few places where exact meanings of technical terms are not obvious (see below). I think only a minor revision is needed before acceptance.

l.95: Doesn't B-SOSE also solve the salt conservation equation?

Table 1. It is stated that "a state estimate ... the changes in ... mixing parameter" (l.90). Are the mixing parameters listed in Table 1 the initial values? Or are they fixed? Or are they after adjustment?

l.120: Explain the use of the word "normalise" in more detail. Did you calculate the spatial standard deviation at each depth at each time step in the entire region south of 30S and divide temperature with the standard deviation? Or the standard deviation includes the time dimension?

l.180: I believe this term "posterior probability" is used in the Bayesian probability. If this is the case, it would be helpful to explain what is the prior probability here.

ll.183, 190, etc. also equation (3):  Is "maximum" right word here? The word "highest" (l.185) sounds more appropriate since all Gaussian are "maximum" (l.165) in the sense of minimum mode-data misfit.

l.246:  By "central" and "eastern" export pathways, I interpret the former corresponds to the equatorward path around the dateline and the latter along the 120W meridian. If the "eastern" means the I-metric blob off the South America coast, more detailed explanation is needed to clarify the ambiguity.

ll.277-278: I do not understand what is meant by "correlation coefficient between Gx and x gradient." Is this the correlation between the result of Gx operator and the result of d/dx applied to the gridded PC data?

l.283: What is "*" operator? How is it defined? Convolution in space?

Equations (B4)(B5)(B6):  c_n seems undefined. mu in the 1st line of (B6) should be in bold face.

Equation (B7): Is k defined?

L.450: What is w here?

Appendix A1.

(A2) and (A5) are identical. The content is very elementary and can be found in any textbook. I do not think this appendix is necessary. I found Appendix A2 is very informative.

This paper proposes a concise and effective metric for identifying ocean fronts. The authors provide thorough background and reasonable discussion of certain considerations when using the metric.

Comments:

• While the metric does appear to effectively highlight when water masses are not clearly assigned to a single cluster – the authors remain ambiguous on what is a ‘low’ metric and what is a ‘high’ metric. Toward the goal of removing ad hoc decision making, a more quantitative description of how the I-metric is classified would be helpful.
• Similarly, in figure 2b, low I-metric points are not shown – what was the threshold used and how was it chosen?
• Figure 3 caption should be rephrased to read as complete sentences.
• Figure 5 legend should be fixed to be easily readable.
• Figure 5 caption should be rephrased somehow, e.g. “Envelope indicates one standard deviation to either side.”
• First sentence after equation 5 (line 277) should be rephrased more clearly.