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.
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.
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.
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.
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”).
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.
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).
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).
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.
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).
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).
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.
Figure 10 – forecast ONI and SAO based on the AMO2 signal post-June 1940.
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.
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.
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.
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: