Response to Reviewer 1

We thank the reviewer for carefully reading our manuscript and offering many constructive comments.  We have endeavored to revise the manuscript through incorporation of nearly all of those comments.  We detail our responses, and highlight revisions in the resubmitted manuscript, in the following responses.

Response to Major Comments:

1) New Figure 4 (old Figure 3) presents the distribution of the core isertel values over the time series for each jet from each data set.  The purpose of showing this distribution is to make the point that the two layers do have robust, identifiable peaks in their respective distributions that mirror those found in a similar analysis of NH wintertime jets.  The figure can be interpreted as evidence that the PV-based categorization of the tropopause-level jets as physical features is a robust method as it returns very similar results in both hemispheres.  Text has been added in the revised manuscript to better assist in interpretation of this result.

2) We agree that the short section regarding possible coupling between the troposphere and stratosphere is not substantial enough to be included in the analysis.  Though comparison of the waviest and least wavy years may be of interest, these ideas are not sufficiently well developed to take their place next to others that are more fully formed.  And you are absolutely correct in stating that ALD does not make distinctions among various waves, their locations, or their individual amplitudes.  It perhaps could be altered to allow such distinctions, but we have not considered that refinement to date.  We have dropped this short section in the revised manuscript and taken up a more substantial discussion of the relationship between our results and characteristics of the Southern Annular Mode (SAM) as suggested by you and another reviewer.

3) We enthusiastically took up your suggestion of looking at any possible relationship between our ALD metric and characteristics of the SAM.  As one example, we considered the three winter months with the most positive and most negative SAM extremes since 1979 (June 2009, July 1998, and August 1994 for the former and June 1992, July 1995, and August 1981 for the former).  New Fig. 10 is a spaghetti plot of core isertels for each pair of winter months that illustrates the clear distinction between the extremes.  Positive (negative) extremes of SAM show a poleward encroachment (equatorward displacement) of the SH polar jet.  In June, the POLJ waviness is larger in the POS SAM extreme but that relationship is reversed in both July and August when the POS SAM extremes are less wavy than their NEG SAM counterparts. 

We also considered the JJA 3-month average SAM index (calculated after Gong and Wang (1999)) to the winter ALD from the JRA-55 reanalysis (new Fig. 9).  The correlation between the two time series was 0.053 suggesting almost no relationship between SAM and the seasonal averaged ALD.  Both of these analyses are presented with new figures in the revised manuscript.

Finally, we calculated the average latitude of the core isertel for both the STJ and POLJs from each data set.  Based upon the hemispheric distribution of these average core isertels, we have calculated the climatological ALD for both jets and report that now in the revised text.  These average core isertels, along with isotachs of the 200 hPa jet (for the STJ) and 300 hPa jet (for the POLJ) are shown in new Fig.  3 and described in the accompanying text.  The core of the STJ isotach maxima around the hemisphere is a near-perfect fit for the nearly indistinguishable core isertels of the STJ.  The fit between the core isertels of the POLJ and the 300 hPa isotachs is not quite as stunning, but is convincing nonetheless. 

4) Application of the sinuosity metric to the jet stream was my original idea and yet, for various reasons, I was not included as an author on that Cattiaux et al. (2016) paper to which you referred.  Sinuosity in this context suffers an incurable resolution dependence, since the calculation depends entirely on measuring contour length. Such dependence is at the heart of the famous “coastline” problem of Richardson in which measuring the length of the coastline of England depends entirely on the desired resolution.  ALD sidesteps part of this problem by only depending once on contour length (in the calculation of circulation that leads to identification of the core isertel).  After that core isertel and its equivalent latitude are identified, ALD simply measures the latitudinal displacement of the core isertel from the equivalent latitude.  This step is NOT resolution dependent.  In addition, the ALD method is premised on dynamical identificadtion of a physically relevant, feature-based characteristic of the tropopause-level flow - the region of strongest horizontal PV gradient. With sinuosity one has to assume that a set of geopotential height contours at a given level are well chosen to describe the feature of interest – and one is restricted to consideration of the waviness of the geostrophic flow, not the total flow.  My sense is that ALD is superior to sinuosity as a metric of waviness for these reasons.

Minor Comments:

1) You are right about this – the original intention of this sentence was to set the reader up for the sentence that follows, but it is not needed.  We have removed it without any ill effect on the message conveyed in the abstract.

2) This is a very good suggestion but that portion of the text has been removed in the revised manuscript.

3) Using the three data sets of varying lengths (72 years for NCEP, 62 years for JRA-55, and 41 years for ERA-5) we have 175 annual time series of the ALD of both jets.  This statement means that 163 of those pairs are correlated with magnitudes less than 0.3.

Response to Reviewer 2:

We thank the reviewer for carefully and thoughtfully reading our manuscript and for offering a number of excellent suggestions for its revision.  We have attempted to incorporate all of the suggestions into the revised manuscript which stands much improved as a result.  We offer our point-by-point responses below.

Minor Comments:

1) Manney et al. (2017) and Manney and Hegglin (2018) have done excellent work on identifying the polar and subtropical jets and investigating the trends in their various characteristics over the past decades.  Their approach identifies the jets diagnostically as volumes within which the wind speed is  >= 40 m s^-1.  Our work is premised on having identified isentropic layers wherein the wind speed maxima (of greater than 30 m s-1) is located.  This allows our method to hunt for dynamical signals (i.e. the horizontal PV gradient) that identify the core of the two jets.  Manney’s work is more diagnostic and employs latitude criteria for differentiating between POLJ and STJ that include well considered definitions based upon the tropopause height, the latitude of the jet maxima, and other considerations.  They also celebrate the agreement amongst the different reanalysis data sets as evidence of the robustness of their results as we do here.  Though not presented in this paper, Martin (2021) found that the NH POLJ is shifting poleward in direct contradiction to the result from Manney and Hegglin (2018).  Our results in this paper bear a closer correspondence to those in Manney and Hegglin (2018) with both the SH POLJ and STJ shifting poleward and both studies note an increase in the STJ core speed as well.  We have added reference to these differences and similarities to the Discussion section of the revised paper.

2) The trend discussed in relation to new Fig. 5 is the trend from the JRA-55 data, chosen as representative.  The revised text includes mention of the trends from the other two data sets for completeness and they are – NCEP POLJ (from 1958), 0.023 deg/year; NCEP STJ (from 1958), 0.0125 deg/year; ERA5 POLJ, 0.0088 deg/year, and ERA5 STJ, -0.001/deg/year).  The figure in the revised manuscript does not include a separate trend line for each reanalysis time series.

3) We have added a reference to the suggested connection between poleward migration of the SH jets and the ozone hole as suggested.  Thank you for pointing this possible connection out to us.

4) This is an excellent suggestion but, as both other reviewers were also critical of the lack of substance in the very short troposphere/stratosphere section of our analysis, we have decided to remove any reference to possible dynamical explanations from this manuscript and take it up in separate work that will require development of some new expertise on our parts.

Technical:

1) We have removed that sentence from the abstract per a suggestion from Reviewer 1 – but have combed through the text of the revised manuscript to ensure that we use “trends” rather than “tendencies” as you suggest here.

2 This is a very good suggestion but that portion of the text has been removed in the revised manuscript.

3) This sentence has been rewritten to clarify – it now says “It is important to note that 53.8% of all qualifying columns (to 380K) in the 0-40S bin (STJ) were in the 340-355K layer while 46.8% of all qualifying columns in the 40-65S bin (POLJ) were in the 310-325K layer offering strong support for the isentropic assignments for the two species mentioned previously.”

4) We have made the suggested change.

Response to Reviewer 3

We thank the reviewer for carefully and thoughtfully reading our manuscript and for offering a number of excellent suggestions for its revision.  We have attempted to incorporate all of the suggestions into the revised manuscript which stands much improved as a result.  We offer our point-by-point responses below.

Major Comments:

1) We enthusiastically took up your suggestion of looking at any possible relationship between our ALD metric and characteristics of the SAM.  As one example, we considered the three winter months with the most positive and most negative SAM extremes since 1979 (June 2009, July 1998, and August 1994 for the former and June 1992, July 1995, and August 1981 for the former).  New Fig. 10 is a spaghetti plot of core isertels for each pair of winter months that illustrates the clear distinction between the extremes.  Positive (negative) extremes of SAM show a poleward encroachment (equatorward displacement) of the SH polar jet.  In June, the POLJ waviness is larger in the POS SAM extreme but that relationship is reversed in both July and August when the POS SAM extremes are less wavy than their NEG SAM counterparts. 

We also considered the JJA 3-month average SAM index (calculated after Gong and Wang (1999)) to the winter ALD from the JRA-55 reanalysis (new Fig. 9).  The correlation between the two time series was 0.053 suggesting almost no relationship between SAM and the seasonal averaged ALD.  Both of these analyses are presented with new figures in the revised manuscript.

Finally, we calculated the average latitude of the core isertel for both the STJ and POLJs from each data set.  Based upon the hemispheric distribution of these average core isertels, we have calculated the climatological ALD for both jets and report that now in the revised text.  These average core isertels, along with isotachs of the 200 hPa jet (for the STJ) and 300 hPa jet (for the POLJ) are shown in new Fig. 3 and described in the accompanying text.  The core of the STJ isotach maxima around the hemisphere is a near-perfect fit for the nearly indistinguishable core isertels of the STJ.  The fit between the core isertels of the POLJ and the 300 hPa isotachs is not quite as stunning, but is convincing nonetheless. 

2) We agree that the short section regarding possible coupling between the troposphere and stratosphere is not substantial enough to be included in the analysis.  Though comparison of the waviest and least wavy years may be of interest, these ideas are not sufficiently well developed to take their place next to others that are more fully formed.  And you are absolutely correct in stating that ALD does not make distinctions among various waves, their locations, or their individual amplitudes.  It perhaps could be altered to allow such distinctions, but we have not considered that refinement to date.  We have dropped this short section in the revised manuscript and taken up a more substantial discussion of the relationship between our results and characteristics of the Southern Annular Mode (SAM) as suggested by you and another reviewer.

Minor Comments:

1) We will keep the NCAR-NCEP reanalysis in the study as it provides a symmetry with the Martin (2021) study of the wintertime NH tropopause-level jets. 

2) As you surmised, getting the ERA-5 data back to 1940 is too onerous for the short period allotted for response to reviewers comments in this case, but we look forward to acquiring that data set for future analyses.

Specific Comments:

1) This is an excellent correction – the EQLAT very nearly approximates the zonally averaged latitude but they are not the same thing.  We have changed the wording here to state “ . . the jet core’s equivalent latitude which closely approximates its zonally averaged position.”

2) Since there is no substantive difference between what we have done and what you suggest, and that the suggestion does not make interpretation of the various numbers any more readily available, we have opted to not make a change here.

3) We have made this amendment, an excellent suggestion, to Figs. 4, 6, and 7.

4) Addition of new analyses comparing ALD to the SAM, in other parts of the paper, allow us to comment only briefly on the apparent wave-3 look to these composite difference fields.  We do make those comments in the revised text.