Tracing the second stage of ozone recovery in the Antarctic ozone-hole with a "big data" approach to multivariate regressions

de Laat, A. T. J.; van der A, R. J.; van Weele, M.

doi:https://doi.org/10.5194/acp-15-79-2015

Articles | Volume 15, issue 1

https://doi.org/10.5194/acp-15-79-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/acp-15-79-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 15, issue 1

Research article

|

08 Jan 2015

Research article |

| 08 Jan 2015

Tracing the second stage of ozone recovery in the Antarctic ozone-hole with a "big data" approach to multivariate regressions

A. T. J. de Laat, R. J. van der A, and M. van Weele

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Final revised paper (published on 08 Jan 2015)
Supplement to the final revised paper
Preprint (discussion started on 14 Jul 2014)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC C5880: 'Review', Anonymous Referee #3, 14 Aug 2014
- AC C8267: 'Response #R1', Jos de Laat, 20 Oct 2014
RC C6015: 'Review', Anonymous Referee #2, 18 Aug 2014
- AC C8268: 'Response #R2', Jos de Laat, 20 Oct 2014
RC C6221: 'Interesting paper, needs clarification of a few points', Anonymous Referee #1, 26 Aug 2014
- AC C8269: 'Response #R3', Jos de Laat, 20 Oct 2014
AC C8270: 'General comments by authors regarding reviews of acp-2014-428', Jos de Laat, 20 Oct 2014

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Adrianus de Laat on behalf of the Authors (20 Oct 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (21 Oct 2014) by Martin Dameris

RR by Anonymous Referee #3 (05 Nov 2014)

RR by Anonymous Referee #1 (08 Nov 2014)

Suggestions for revision or reasons for rejection

\section{General rating of revised version}

It is good to see that the authors have taken the reviews of the 1st version serious, and have substantially revised their manuscript. It is also good that the authors have discovered and corrected an error in their piecewise linear trend calculation (already suspected by the reviewers).
Omitting the use and discussion of not-connected linear trends has also helped to make the manuscript clearer and more succinct. I think the manuscript is now much clearer, the main messages are clearer, and this version is almost ready to be accepted for ACP.

\section{Points still to be corrected, or improved}
I think the authors still have an error in their uncertainty estimates for EESC based trends, e.g., in Table 3 (2nd column from the right): Uncertainty for the 1979 to 1999 EESC-based should be about four times larger than uncertainty for the 2000 to 2010 (or 2000 to 2012) EESC-based trends, because both trend and trend uncertainty essentially are the EESC change per time multiplied by EESC coefficient and its uncertainty obtained by the multiple linear regression. Since EESC shape is fixed, the ratio of EESC based trends before and after EESC turnaround and ratio of their uncertainties must be the same.

Following the authors' notation from the equation in lines 150 to 156, the EESC based term will be
\begin{equation}
C_5 EESC(t)
\end{equation}
where $C_5$ and its uncertainty $\Delta C_5$ are determined from the regression. The 1979 to 1999, and 2000 to 2010, EESC-based trends $dO_3/dt$ then are
\begin{equation}
\frac{dO_3}{dt}(1979,1999) = C_5 \frac{dEESC}{dt}(1979,1999)
\end{equation}
\begin{equation}
\frac{dO_3}{dt}(2000,2010) = C_5 \frac{dEESC}{dt}(2000,2010)
\end{equation}
Their uncertainties are
\begin{equation}
\Delta \frac{dO_3}{dt}(1979,1999) = \Delta C_5 \abs{\frac{dEESC}{dt}(1979,1999)}
\end{equation}
\begin{equation}
\Delta \frac{dO_3}{dt}(2000,2010) = \Delta C_5 \abs{\frac{dEESC}{dt}(2000,2010)}
\end{equation}
The ratio between the EESC-based ozone trend uncertainties, therefore, must be the same as the ratio between the ozone trends and the ratio between the EESC trends (slopes).
\begin{equation}
\frac{\Delta \frac{dO_3}{dt}(2000,2010)}{\Delta \frac{dO_3}{dt}(1979,1999)} =
\frac{\frac{dO_3}{dt}(2000,2010)}{\frac{dO_3}{dt}(1979,1999)} =
\frac{\frac{d EESC}{dt}(2000,2010)}{\frac{d EESC}{dt}(1979,1999)}
\end{equation}

This is clearly not the case in Table 3 for the authors' result. However, it is correct in the Kuttipurath et al. result reported in Table 3. This needs to be fixed in Table 3, and the discussing text also needs to be fixed (in several places).

Line 21: I do not understand why an EESC-based trend should not take fit residuals into account. In standard multiple linear regression, the uncertainty (e.g. $\Delta C_5$) is estimated from the fit residuals! I do agree with the 2nd part of the sentence (line 22), though. Because of the fixed temporal change (I would say "shape") of the EESC curve, no independent statement about ozone trends before and after turnaround can be made. So, fitting an EESC curve can only determine that, overall, ozone follows the EESC curve, but it cannot determine whether ozone has a positive trend after EESC turns around. This should be fixed, here in the abstract and in corresponding parts of the main text.

Line 28: Please also specify which time intervals are meant: E.g. "significant 2000 to 2010 trends"

Lines 34, 35: Antarctic ozone "recovery" (to levels like before 1984) is not expected until 2060 to 2100.
I think the word "recovery" is misleading here. The authors probably mean "beginning recovery as indicated by significant positive trends in Antarctic ozone". Should be reworded.

Line 70 to 71: I think that sentence is misleading, is not necessary, and should be dropped. The general assumption, also in these papers, is that some of the ozone variation is deterministic, can be accounted for (e.g. by (multiple) linear regression), and some ozone variation is (auto-correlated) noise, and essentially determines the statistical uncertainty. This is no different in the references model papers.

Line 202, 203: I think that only 2002 in the Southern Hemisphere really qualifies as an outlier year. In the NH there are many more warm and cold years, and I would not claim that 2011 was an outlier year because 1997, 2000, and several others were cold years in the NH. Should be reworded.

Lines 515 to 517: Needs to be corrected, as discussed above.

Lines 560 to 562: I think this should be Table 3, not Table 2. There are other places in the text where the wrong Table or Figure is referenced. The authors should check that carefully!! (Or use the \label{} and \ref{} in \LaTeX.)

Lines 563 to 565: The authors might want to add/ clarify this even more: The Table 3 uncertainty is due to regression residuals only. If these are small, uncertainty will be low. Also: For the authors PWLT method, the uncertainty of the 1979 to 1999 trend is essentially the uncertainty of the underlying 1979 to 2010 (or 2012) trend - which will be small because of the underlying 32 years. So the 1979 to 1999 trend estimate in Table 3 tends to be low, AND DOES NOT account for uncertainty / variation of the other proxy time series used in the regression. For the 2000 to 2010 trend, the uncertainty from the regression residuals happens to be comparable to the uncertainty estimated using the big-data approach of the current work. This is good to see - but it is coincidence!

Line 626: I do see a trimodal distribution in the middle panel of Figure 4 (not 3!), but nowhere else really. As mentioned above, Figure and Table references have changed due to dropping/ adding of Figs. and Tables in the revised version, and need to be checked.

Line 638: I suggest to add "specific" before SAM and "specific" before solar flux. While it may be that the SAM and solar flux proxy variations correctly predict the ozone variations, this could also be lucky coincidence. There is enough noise and non-linearity in the system - so if things work really well in a multi-linear regression, there is also a good bit of luck involved.

Line 652: Replace "better" by "correct", or by "more appropriate". I would argue that beginning recovery can never be proved with a fitted EESC curve, because the answer is already built into the EESC curve. (Circular conclusion). EESC can be used for many things, but not for investigating this specific question.

Line 653/654: Do EESC fits not use ozone fit residuals for their significance calculation?? Please correct the wording. The main point to me is that PWLT trends do have the necessary degree of freedom to answer the question, whereas EESC fits do not. It is not a question how significance is estimated.

Lines 707 to 711: Looking at Table 9, I find this a very negative formulation of the results. To me Table 9 says that nearly all regressions show statistically significant ozone increases, except those where 21-30 Sep. ozone, or July or August only EP fluxes are used. So unless you select the worst parameters, most regressions do actually show ozone going up. I realize that this conclusion is different from the conclusion of the 1st version of the manuscript. However, now that the authors have fixed errors in their PWLT calculation - results do look substantially more like increasing ozone. To me that must be reflected even more in the text of the 2nd version!

Lines 724 to 727: Following my EESC trend comments from above, I think this sentence needs to be reworded.

Line 735: The authors might want to add that the PWLT based increases (+1.66 to +4.74 DU/year) are actually larger than expected from EESC fits (Fig, 4, middle panel). This is, in fact, something to wonder about: Are the PWLT trends picking up ozone increases that are due to something else than declining EESC?

line 774: Replace "will" by "may"?

Table 5: Please state in the caption what break/ ending years are used. (Compared to Table 6, which states that explicitly.)

Line 977: Also state the magnitude of the wind speed anomalies, to give context for the 1.5 to 2 m/s uncertainty.

Line 982: Should be "McCormack"

Line 1000 to 1026: Is this appendix really needed? I think a reference in the main-text to the website would be enough.

Figures 6 and 7: Like in Fig. 4, it would be good to give typical regression residual based uncertainties (e.g. from regressions giving coefficients near the mean).

Figure 7: It is encouraging to see that EESC and PWLT regression give nearly the same SFxQBO, SAM and EP-Flux coefficient values - as expected for orthogonal predictor time series.

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RR by Anonymous Referee #2 (10 Nov 2014)

ED: Reconsider after minor revisions (Editor review) (11 Nov 2014) by Martin Dameris

AR by Adrianus de Laat on behalf of the Authors (20 Nov 2014) Manuscript

ED: Publish as is (25 Nov 2014) by Martin Dameris

AR by Adrianus de Laat on behalf of the Authors (01 Dec 2014)

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Short summary

Recent research suggests the Antarctic ozone hole has started to shrink due to decreasing ozone-depleting substances. Because it could be questioned how robust these results are, we provide an assessment of uncertainties in both the underlying ozone observational records and the detection-attribution method. Although Antarctic ozone concentrations are definitely increasing slowly, the formal identification of recovery is not yet justified, although this will likely become possible this decade.