Guest essay by Craig Lindberg
Abstract: The change in the relationship between the hemispheric sea ice anomalies appears to have a sinusoidal nature with a wavelength that is a function of North Atlantic and North Pacific sea surface temperature oscillations. There is also a repeating signal observed in both oceans going back at least 100 years. The pattern of this signal appears to be correlated with the sea ice area in both hemispheres and the ENSO.
Background
With only a cursory look at the sea ice anomaly trends in Figure 1, it might be surmised that that the Northern and Southern Hemisphere (“NH” and “SH” respectively) anomalies are negatively correlated; that is as the anomaly in one hemisphere increases, the anomaly tends to decrease in the other.
![Figure1[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure11.png?quality=75)
Figure 1 – Northern and Southern Hemisphere sea ice anomalies over time (Cryosphere Today / Arctic Climate Research at the University of Illinois).
Simply plotting the relationship between the Northern and Southern Hemisphere sea ice anomalies won’t do much to change a perception of a negative correlation. As illustrated in Figure 2, overall it is negative (r^2 = 0.08). Notwithstanding, it appears that an inverse relationship does not accurately characterize the data, and in fact there seems to be a different, and much more interesting, relationship hidden just below the surface as Figures 2 and 3 begin to suggest.
![Figure2[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure21.png?quality=75)
Figure 2 – plot of the NH vs. SH sea ice anomalies and the trend across all data points. Color coding by year suggests that the relationship may have changed significantly over the duration of the satellite record.
![Figure3[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure31.png?quality=75)
Figure 3 – the NH vs. SH sea ice anomalies by calendar year. Black lines are linear best-fit (same color coding as in Figure 2).
The Sea ice Anomaly Oscillation
Figure 3 shows that the relationship between the NH and SH sea ice anomalies has changed meaningfully over time in both sign and magnitude. To study how this relationship varies continuously rather than in arbitrary discrete windows, I calculated the slopes of the best-fit lines (in the least squares sense) beginning with the most recent 356 days of the record (2014.0137 – 2013.0165). I then slid the calculation window backwards across the entire sea ice anomaly record one day at a time, stopping at the final 356 days of the record. This produces a 34 year long daily record of the trailing 365 day relationships between the NH and SH sea ice anomalies (Figure 4).
Any point in the series represents the sign and magnitude of the relationship between the NH and SH sea ice anomalies for the preceding 365 days. I named this index the Sea ice Anomaly Oscillation (the “SAO”).
![Figure4[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure41.png?quality=75)
Figure 4 – the SAO compared to the NH and SH sea ice anomalies. When the SAO is positive, the hemispheric sea ice anomalies generally moved in the same direction (either up or down) over the previous 365 days, and when the index is negative, they generally moved in opposite directions. 49.5% of the series is positive.
The SAO appears to oscillate with an approximately 32 year period that is almost exactly half that of the AMO (Figures 6 and 7). I also compared the SAO to a similar SST index for the Pacific: the mean North Pacific SST anomaly (20N-65N, 100W-100E) with the linear trend removed. I will refer to this index as the Pacific Multidecadal Oscillation (the “PMO”). The roughly 64 year wavelength of the PMO is almost identical to the AMO with the two little more than 3 years out of phase.
![Figure5[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure51.png?quality=75)
Figure 5 – the approximately 32 year SAO oscillation period.
The SAO appears to be directly related to the AMO and PMO. SAO minimums and maximums occur at approximately the intersection of the AMO and PMO and the maximum separation of the AMO and PMO respectively. Zero crossings occur at approximately 1) the intersections of the AMO and inverted PMO, and 2) the maximum separation of the AMO and inverted PMO. A relationship, if any, between the SAO and the PDO is not readily apparent (Figure 6).
![Figure6[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure61.png?quality=75)
Figure 6 – the SAO trend compared to the AMO, PMO (top), inverted PMO (middle), and PDO (bottom) trends.
The SAO and ENSO
When I first plotted the SAO, I noticed it looked similar to any of the standard ENSO indexes such as the Oceanic Nino Index (“ONI”) or the Multivariate ENSO Index (“MEI”). In fact, simply inverting the SAO at its zero crossings matches it up to either of these indexes tantalizingly well (Figure 7).
![Figure7[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure71.png?quality=75)
Figure 7 – the SAO inverted at its inflection points compared to the ONI. (R^2 =0 .13)
Relationship to Atlantic and Pacific SST
While studying the AMO and PMO, I noticed that after removing the main sine components, the residuals (which I will refer to as the “AMO2” and “PMO2” respectively) also had a sinusoidal nature, and that they appeared to be carrying information; the general pattern of the SAO appears to repeat multiple times across both series. To deconvolve the relevant segments into the SAO, I simply inverted them at the fitted SAO zero crossings and then smoothed with a 3-month centered SMA filter.
Deconvolving the AMO2 and PMO2 signals into an ENSO proxy was somewhat of a bigger challenge primarily because the data is fairly noisy (as should probably be expected given the nature of the data). I ended up building a model to deconvolve the signal and then optimized for a frequency solution using the ONI as a reference to minimize variance against. The optimized AMO2 and PMO2 frequencies were 0.1% and 1.0% different from the sine waves fit with R respectively. Deconvolving involved inverting the signal at the AMO2 and PMO2 zero crossings and at the AMO2-PMO2 intersections. The deconvolved signals were smoothed with a 3-month centered SMA filter.
The r^2 of the deconvolved AMO signal segment in Figure 8 compared to the ONI is 0.23 (0.24 MEI and 0.20 vs. NINO3.4). This doesn’t sound too bad when I consider that the AMO is calculated from the average of the entire North Atlantic and that the data used goes back between 74 and 114 years.
I ran several other AMO2 and PMO2 segments through the same algorithm and used the same frequencies, and while they didn’t correlate to the ENSO record nearly as well as the first segment I extracted from the AMO2, visually there were still many similarities. One example of a segment from the PMO2 is given in Figure 9.
![Figure8[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure81.png?quality=75)
Figure 8 – a segment (1900 – 1940.3) taken from the AMO2, shifted forwards in time to the present, and deconvolved into an SAO proxy (middle, r^2 = 0.17) and into an ENSO index proxy (bottom), shown here compared to the ONI (r^2 = 0.23).
![Figure9[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure91.png?quality=75)
Figure 9 – a segment (1945.5-1989.3) taken from the PMO2, shifted forwards in time to the present, and deconvolved into an SAO proxy (middle, r^2 = 0.24) and into an ENSO index proxy (bottom), shown here compared to the ONI (r^2 = 0.02).
Forecast
If these relationship hold, it appears that the next couple decades will see a generally warmer Nino3.4 region. With respect to the sea ice anomalies, I’m not sure how to translate the SAO forecast into km^2 or changes in the gap between the hemispheres – or if it is even possible to do so for that matter. It would appear however that the anomalies will be moving in generally opposite directions for the better part of the next two decades.
![Figure10[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure101.png?quality=75)
Figure 10 – forecast ONI and SAO based on the AMO2 signal post-June 1940.
Discussion
These observations would seem to further call into question the idea that GHGs are the driving force behind the contraction of Arctic sea ice area over the past few decades. If repeating SST patterns can predict the relationship between the hemispheric sea ice anomalies more than 100 years later with the resolution illustrated in Figures 8 and 9 (middle charts), which is the more likely cause: GHGs or natural cycles?
Likewise, perhaps winds do explain much of the recent Antarctic sea ice expansion as several recent journal articles have suggested (http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00139.1 and http://www.nature.com/ngeo/journal/v5/n12/full/ngeo1627.html), but if so, this would suggest such winds are part of processes set in motion a long time ago – as was whatever mechanism has caused the corresponding contraction in the Arctic.
Notes
Fitting sine cures to the signals in this analysis was performed with R in the y=a*sin(b*t+c)+d form. No adjustments were made to the AMO or PMO fit and only minor adjustments were made to the AMO2 and PMO2 frequency as described above. Constant values are presented in Table 1 below:
Table 1 – Curve fit constants.
![Figure11[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure111.png?quality=75)
Figure 11 – AMO, PMO, and PDO curves as fit. The SAO is shown in Figure 5.
The r^2 of the individual points of the SAO are fairly low. More than half are 0.07 or less. Notwithstanding, over 80% of the results are statistically significant at the 0.05 level and almost 73% at the 0.01 level. Of course, many of the points that are not statistically significant are where the SAO is zero (thus r^2 is also zero), and you would not expect the results to be significant.
![Figure12[1]](http://wattsupwiththat.files.wordpress.com/2014/02/figure121.png?quality=75)
Figure 12 – SAO Index r^2 and Sig. F. Red lines identify the points of the SAO that are not statistically significant at the 0.05 level.
All of the data and methodologies used in this analysis can be found in two Excel files here:
http://lindbergs.us/SAO/SAO1.xlsx
http://lindbergs.us/SAO/SAO2.xlsx
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What a fantastic paper! Can someone peer review this essay? It’s clear, terse, documented, and everything a short communication should be. This website is turning into a journal, of sorts.
And for those of us on our lunch-hour, who don’t have the time or intelligence to decipher, what will happen to the Arctic in the next 10 years or so? Sorry, I know it’s all there somewhere.
Nice. That AMO is detrended. Here some graphs with raw AMO monthly index and not detrended annual anomalies from 1885:
http://www.climate4you.com/images/AMO%20GlobalMonthlyIndexSince1979%20With37monthRunningAverage.gif
http://www.climate4you.com/images/AMO%20GlobalAnnualIndexSince1856%20With11yearRunningAverage.gif
I thought the prediction left out what will occur as the sun makes its decline into cycle 25, not sure we can predict from a somewhat short timescale
While interesting, I see a number of issues here. I would be careful about saying too much about ice extent/area/volume/concentration between the two poles. There are several differences between them, including circumpolar waves in one and not the other, large topography and geographic differences, and perpendicular incoming and outgoing currents in one but not the other. That is not to say they are not both affected by ENSO oscillations. It is just that ENSO events may set up cause and effects showing up in sea ice data that may be quite different between the poles, though may result from time to time in the seesaw currently evident in the sea ice data. I would also be careful interpreting your data using statistical significant difference algorithms. You have heavily manipulated your data. Any errors will be magnified thus producing spurious results in terms of significance. Not to mention the number of variables (see third sentence) you have in the data would require significant amounts of raw data to decrease your errors.
What relation/difference is there between your PMO. and the PDO? Are they one and the same?
I’ve thought for a while, as do others that I’ve read, the climate operates as multiple loosely coupled charge-pump oscillators.
Waters at the equator warm, winds and pressure zones develop which then push that warm water into other areas of each ocean. At some point the replacement of warm water with cold, an increase of clouds, or ? stop the pumping action, resetting into the charge mode. Since the tropical area is different for each ocean, they would have different time constants.
I see the melting of Arctic ice as a self regulating system, where warm water melts the ice, and large exposed warm ocean waters radiate more energy into space than they absorb.
Each of these major events change the state of the collective system.
I could see that the period of the oscillators change as the speed of the warming increases or decreases due to solar output and possibly Co2. This will be telltale of the energy accumulation of the system.
The problem with decoding this complex system, we just don’t have enough good data for a long enough period of time, we have bits and pieces.
Well done Craig!
Oh come on, the NHvsSH scatterplots are indeterminate at best. The distributions on the yearly plots do not lend themselves to linear fits. On most of them you could fit in almost any direction and get an answer – doesn’t mean it is right. “best fit” is a misnomer here. The data are very noisy and certainly not near enough to draw the conclusions the author have drawn.
I have to agree with Pamela about the manipulation of data and lack of data to give any real confidence.
Heavy manipulation? He just did some correlations and some frequency-removal.
I think the idea of the essay is that the “moving correlation” between NH sea ice and SH sea ice can be predicted by SSTs and ENSO.
It is only human to see connections in nature but i assure you that there is no connection between northern and southern hemisphere sea ice. That is because they are controlled by different physical processes. The only well defined oscillation is the ENSO and it has no long-term connections. I look askance on any long-term oscillations that are poorly defined and a clear physical driver is absent, As to the sea ice anomalies, Arctic warming has been reducing sea ice from two to four times faster than climate models predict. Small wonder because all the models have greenhouse warming built into their code while Arctic warming is caused by warm water carried into the Arctic ocean by currents. You simply can’t use greenhouse warming to predict the course of a non-greenhouse warming. Take that away and both temperature curves become identical. It started suddenly at the turn of the twentieth century, after two thousand years of slow, linear cooling. Its likely cause is a rearrangement of the North Atlantic current system that started to carry warm Gulf Stream water into the Arctic Ocean. It paused in mid-century for thirty years, then resumed, and is still going on. Arctic is actually the only part of the world that is still warming while the rest of the world is enjoying a hiatus-pause that is actually a permanent cessation of warming. Natural warming, that is, because greenhouse warming never existed. In the twentieth century there were only two spurts of warming – the first in 1910 raised global temperature by half a degree Celsius, the second in 1999 raised it by a third of a degree Celsius. ENSO does not count because it periodically returns to its base temperature.
I’ve got a number of problems right from the beginning.
1) You base your analysis based on the idea of correlation between the hemispheres’ ice extent. But there is no correlation. Figure 2 shows that quite clearly.
2) In figure 3, you attempt to show that the alleged correlation changes over time. The problem is that none of the individual years appear to have any real correlation. Sure you can get a best fit line through the points, but that best fit is still a really lousy fit.
3) Based on the flawed idea of a significant one year correlation, you then come up with figure 5. Since none of the individual data points are meaningful, as described in my point 2, the graph that is made from those points lacks any real meaning.
4) For the sake of the argument, lets say that figure 5 was meaningful. You then fit a sine wave to it, and used that to extrapolate it to 1900 (Figure 6), and use that extrapolation to draw all of your conclusions. Is there really a sine wave? Maybe, but we can’t tell yet. We have at this a point a maximum of one complete cycle on the theoretical, and very noisy, sine wave. Go back and read some of Willis’ criticisms on curve fitting and then come back and tell how reasonable it is to fit a sine wave to a single cycle.
Polar vortex unchanged. 17 km.
http://earth.nullschool.net/#2014/02/17/1200Z/wind/isobaric/70hPa/orthographic=-89.63,92.89,318
Joe Bastardi has been saying something very similar for some years but not a bad paper.
Isn’t this just a demonstration of the Law of Conservation of Polar Ice?
Thanks Graig, very interesting and complex too.
Not surprisingly, nature seems to be well-connected!
The author concluded in part “These observations would seem to further call into question the idea that GHGs are the driving force behind the contraction of Arctic sea ice area over the past few decades.” A reasonable and appropriately cautious statement. He also said “It would appear however that the anomalies will be moving in generally opposite directions for the better part of the next two decades.” Something of a prediction, but not really a bold one, is it? The current trends in N. and S. graphs support that more or less “by inspection.” I applaud the exercise, and find little to object to in the author’s conclusions.
Wiggle matching with an r^2 = 0.08??? Be still, my beating spleen! I’m underwhelmed.There may be something here, but I’m afraid it’s lost in irrelevant numerology.
The NS and SH correlation looks to be 0.0 +/- 1.0.
Interesting, but it looks like a remedial course in Stats is required. The elephants tail is NOT longer.
In fact, simply inverting the SAO at its zero crossings matches it up to either of these indexes tantalizingly well (Figure 7).
What does that mean? It looks like you merely multiplied every point in the curve by -1.
Take any two independent autoregressive time series over a finite time span and the odds are that they will be correlated. This is explained in the soon to be published book by Kass, Eden and Brown, Analysis of Neural data (here: http://www.springer.com/?SGWID=0-102-24-0-0&searchType=EASY_CDA&queryText=kass%2C+eden%2C+brown&x=0&y=0; the is also available in pdf form from Rob Kass’ website at the Carnegie-Mellon University Statistics Department. I can provide more information if anyone asks, such as page number.) You have taken a bunch of autoregressive time series, and shown that they are correlated, as expected. What you have not done is shown that they are not independent.
rats. “the book is also available in pdf …”
The sharp rise and fall temperature at a height of 30 km. Please compare with January 2013.
http://www.cpc.ncep.noaa.gov/products/stratosphere/temperature/10mb9065.gif
Sorry, r square less than 0.5 is rubbish. Try looking at max. temps.
Ionizing radiation indicates the area of lowest pressure over the the Arctic Circle.
http://oi62.tinypic.com/ang8xw.jpg
This is a very interesting idea, however, there is one important technical flaw in the method.
This is a classic misuse of OLS linear regression that is widespread in many fields of study but especially in climatology.
The basic problem is that the maths behind OLS “best fit” assumes and REQUIRES minimal error in the x-variable. This is fine in controlled lab experiment or for a time series where dates are usually accurately known.
However, it is not correct once you bang two error loaded datasets onto X and Y for a scatter plot.
Then there is an effect called ‘ regression dilution ‘ and the slope usually comes out too low. And on this kind of data it can be WAY too low. To see the problem just plot the graph the other way around and do the OLS . The two slopes should have a product of unity : eg 3 in one sence would give 0.33 in the other if they were consistent. Usually you will get something 0.25 and 2.5 , both being lower than the correct value. How much generally depend upon the spead of the data. Here there is a huge spread and the error will be significant.
I would highlight 2006 as one year that will give a grossly different value fitted the other way around.
Here is an example :
http://climategrog.wordpress.com/?attachment_id=631
A first guess at the true ‘best estimation’ value is to take some middle value of the two slopes or bisect the angle.
For example if the slopes are m1 and m2 : m_ave = sqrt (m1/m2)
That would be good enough for this exercise.
Since this error will be degrading any relationship which is there it would be well worth rerunning the process and using something like the m_ave shown above.
This same error applies to a scatterplot of TOA radiation and surface temperature that is often used to estimate climate scesitivity, real and model based. This ‘matters’ since an erroneously low slope leads to a higher value of CS (which is taken as the inverse of the dRad / dT slope).