the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical Note: A best-practice approach to calculating the Southern Annular Mode index
Laura Velasquez-Jimenez
Nerilie J. Abram
Abstract. The Southern Annular Mode (SAM) strongly influences climate variability in the Southern Hemisphere. The SAM index describes the phase and magnitude of the SAM and can be calculated by measuring the difference in mean sea level pressure (MSLP) between mid- and high-latitudes. This study investigates the effects of calculation methods and data resolution on the SAM index, and subsequent interpretations of SAM impacts and trends. We show that the normalisation step that is traditionally used in calculating a non-dimensional SAM index leads to substantial differences in the magnitude of the SAM index calculated at different temporal resolutions, and that the equal weighting given to MSLP variability at the mid and high southern latitudes artificially alters temperature and precipitation correlations and the interpretation of climate change trends in the SAM. These issues can be overcome by instead using a dimensional formulation of the SAM based on MSLP anomalies, resulting in consistent scaling and variability of the SAM index calculated at daily, monthly and annual data resolutions. The 10 dimensional version of the SAM index has improved representation of SAM impacts in the high southern latitudes, including the asymmetric (zonal wave-3) component of MSLP variability, whereas the increased weighting given to mid-latitude MSLP variability in the non-dimensional SAM incorporates a stronger component of tropical climate variability that is not directly associated with SAM variability. We conclude that a best-practice approach of calculating the SAM index as a dimensional index derived from MSLP anomalies would aid consistency across climate studies and avoid potential ambiguity in the SAM 15 index, including SAM index reconstructions from paleoclimate data, and enable more consistent interpretations of SAM trends and impacts.
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Laura Velasquez-Jimenez and Nerilie J. Abram
Status: open (until 09 Nov 2023)
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CC1: 'Comment on cp-2023-64', Elio Campitelli, 23 Aug 2023
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This is an nice paper. I have to admit that I'd always thought that these indices were always computed using the raw anomalies and share the authors' confusion on why this method is used. (I prefer EOF-based methods). MSLP difference is, to me, the self-evidently physically relevant variable. The authors here also demonstrate empirically other benefits.
The results in Figure 7 are particularly intriguing, since I would've not expected for the signal-to-noise ratio to change so much.
I do think that having a dimensionless index is useful, especially for comparing models among themselves and model with observations. So I'd use a dimensionless SAM defined as:
(P'_40 - P'_65)/sd(P'_40 - P'_65)
That is: the (dimensional) difference between MSLP anomalies divided by the standard deviation of such difference computed in the reference period.
This index is essentially the same as the dimensional index in this paper but scaled by a constant factor, so it should share all its good properties of plus it has the advantage of being easy to compare between models.
Some comments below:
Figure 3b shows that the correlation of the annual non-dimensional SAM indices is essentially 1. A correlation of 0.9998 between indices is basically perfect and is much greater than the correlation of SAM indices computed using different datasets, different reference periods, different latitude bands, different levels, or slightly different methods. Therefore, they are basically equivalent except for a constant scaling factor (shown as the slope). Being dimensionless quantities, this scaling factor is not relevant. Particularly, it's not relevant for correlations.
This can be seen in the correlation differences shown in the bottom left panel of Figures 5 and 6, which are tiny (on the order of 0.01). These differences are probably not statistically significant and, IMHO, most definitely not physically significant. They are likely much smaller than the standard error of their estimations or the difference between various reasonable SAM indices.
Figure 3d: Why are not the three time series exactly equal? The monthly mean of the difference between daily values must be exactly the same as the difference between monthly mean values. If they are not equal, what's their correlation?
Figure 4: What's the correlation between the dimensional and non-dimensional indices at the annual, monthly and daily resolution? It would be helpful to have a number attached to these differences.
Figure 5: There's a strange artefact in the top-left panel near the dateline. A vertical discontinuity in the shading. The artefact might also be present in the other panels but harder to see.
Figure 5 and 6: Would it be better to plot the difference in r2 between each panel? Right now, to interpret the figure one needs to look also at the sign of the correlation in the original panels. By plotting the difference in r2, negative values would be directly interpretable as a decrease in the strength of the (linear) relationship and vice versa.
Are the differences in correlation statistically significant?
Figure 4 and 7: How are these plots created? By definition, the units of the dimensional and non-dimensional indices are not the same so their alignment should be arbitrary (in other words, the y axis has two different units). Did you standardise both indices to show them on the same scale?
Figure 7: It's surprising, at least to me, that both indices are almost exactly the same before ~1950. Why is that? Was there a change in the ratio of the standard deviation of MSLP between 40ºS and 60ºS?Citation: https://doi.org/10.5194/cp-2023-64-CC1 -
RC1: 'Comment on cp-2023-64', Anonymous Referee #1, 25 Sep 2023
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This paper explores how the normalization component of calculating the Southern Hemisphere Annular Mode (SAM) impacts its magnitude and relationships with climate.
I thought that a lot of the manuscript was ‘stating the obvious’: e.g., the dimensional SAM produces consistent indices across different temporal resolutions. Having said that, no doubt there are many researchers who have correlated something against the SAM without fully understanding how it was produced and how that might impact their findings (e.g., the incorrect Dätwyler methodology). So, in that sense, I think it is a useful addition to the literature, perhaps particularly for the paleoclimate community.
I have a few issues with some of the language used, both the tone and some of the terms used.
One might argue that what the authors are calculating is simply the mean SLP difference between 40°S and 65°S and that this is not the SAM at all. This has been done for other climate indices, such as the NAO, when it is termed the ‘natural NAO’. So, maybe this could be referred to as the ‘natural SAM’ to distinguish it? I agree that in many cases this might be a more useful metric than the SAM (see also Elio Campitelli’s comment).
The normalization is done, as it is for many climate indices such as the NAO or SOI, to adjust for seasonal differences in both the average and in the year-to-year range of variability at each of the latitudes, so that each latitude always contributes equally to the index. For certain studies this may be an important criterion. You could argue that the ‘natural SAM’ is basically a SLP index at the higher latitude, because of the significantly larger variability there, and maybe if you are interested in how the SAM impacts lower latitudes this is going to swamp the local signal in SLP variability.
I don’t like the use of ‘best-practice’ and ‘biases’, which comes across as arrogant (how about ‘alternative methodology’ and ‘differences’?): present the positives of your method of producing the ‘natural SAM’ (which I agree are several) and let the reader decide if they want to use it instead of the standard method. There are also other issues to think about when calculating the SAM, such as using SLP versus say 700-hPa geopotential height as used by the Climate Prediction Center to calculate their SAM/AAO:
(https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/history/method.shtml).
I also concur with Elio Campitelli’s comment that a dimensionless SAM is useful when comparing models, which may have differing biases in representing the SH extratropical SLP field.
Specific points
Given that many authors prefer to use an EOF-based SAM index, it would be helpful to do a comparison with this method of deriving the SAM too.
I also looked at Fig. 7 and wondered why the differences between the two SAM indices are so much less prior to the reference interval than afterwards. It would be helpful if the authors could investigate this a little more: does it say something about temporal changes in circulation or is it simply biases in the historical model fields?
Citation: https://doi.org/10.5194/cp-2023-64-RC1
Laura Velasquez-Jimenez and Nerilie J. Abram
Laura Velasquez-Jimenez and Nerilie J. Abram
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