On Friday I was pointed to another Internet posting that purported to show that the recent warming is due to changes in the PDO. It was probably based on the writings of D’Aleo at Icecap. I’ve written before that the PDO cannot contribute to global warming for the simple reason that for the ‘classical’ definition of PDO, the trend is removed (eg, at the University of Washington). There will still be variations about the mean, and those variations may mask or enhance the global warming signal in the global mean surface temperature, but it cannot contribute to a trend.

This post was originally just going to be a short rant about not understanding the definition of PDO and its implications. But as I was making some figures to include with this post, it began to evolve into something different. The ‘classical’ definition of PDO excludes any trend in the data. But what would happen if the trend were not excluded? How would that influence the shape of the PDO time-series and its corresponding EOF (empirical orthogonal function; basically, what the PDO looks like in space instead of time)?

Principle Components Analysis of PDO Region

To do this, I needed sea surface temperature anomaly data. I used the Kaplan Extended SST V2 available from NOAA ESRL. I then created a ‘mask’ that would zero out all the values outside of the PDO region. For this exercise, that involved looking at the Pacific Ocean north of 20N latitude, and using reasonable limits on the longitude. Due to the high correlation between adjacent grid cells, the choice of the boundaries should not vastly influence the results.

After the masking, the data was input into a principle components black box. The output is shown below.

At first glance this may not look at all like the traditional PDO (UW link above). However, there are qualities that support the notion that this is the PDO with a trend. I’ve included the slope of the first PC as the red dashed line as a visual reference. In the 1940s, the PDO is larger than the red line, during the 50s and 70s its below or near the line, and during the period from the 1980 to present it is mostly above the line. But usually, the PDO graph is not shown as a simple line like above, but blue and red colors are added to indicate when the PDO is in the ‘warm’ or ‘cold’ phase.

This graph would be equivalent to the PDO graph produced on the UW website. Except I’ve added the cyan line to indicate that the mean value has been changing. (The slope is about 0.5 standard deviation per century.) If we simply remove the slope, the far past will ‘warm’, and the near past will ‘cool’, and it will look almost exactly the same as the UW graph. When presented as above, the ‘phase shift’ that occurred in 1977 is not notable compared to other ‘phase shifts’ during the period of record.

To further convince you that this is really capturing the PDO signal, I present the EOF (spatial pattern) of the first principle component.

The figure corresponds to the PDO ‘warm phase’. Note that during the ‘warm phase’, the majority of the Pacific is actually cooler than normal, while the area near the coast of California is warmer. This is exactly the same spacial pattern as the PDO on the UW website. A note about the colors in the above figure; the blue colors make up a larger number of the contours, and thus it appears that there is more cooling that in reality. As with all figures, check the values presented in the color bar and note that the highest warm color (orange) is much larger than the lowest cold color (dark blue).

Principle Components Analysis of World SSTa

So what? You’ve included the trend of the data in the principle components analysis (PCA) and it resulted in a trend in the first principle component. Duh. It would be ‘duh’ if I left it there. But what if I do a principle components analysis on the entire sea surface temperature data?

Notice the same pattern as the figure above! There is cooling in the central Pacific Ocean and warming along the coast of California. Interestingly, the first mode of variability of the northern Pacific has the same pattern as the first mode of variability for the entire ocean.

This is the same figure as above, except shown using a Mercator projection instead of a satellite projection. This allows us to see what the pattern of variability looks like for the entire world. The ‘warm phase’ of the PDO is still evident, but there are areas with larger variability such as the Indian Ocean, which shows almost twice as much warming as the cooling in the north Pacific. In general, this pattern shown an overall warming of the worlds oceans with a few isolated spots that are cooling.

There appears to be a PDO signal in the north Pacific whether we use only the north Pacific in the PCA or the entire world SST. And the spacial pattern appears to be very similar. Therefore, we should expect the principle component time-series to be the same too shouldn’t we? Thankfully no. Which is why this post turned into something other than a short rant.

This is exactly the same figure as the first in this post: the first principle component time series. However, this is for the entire world, instead of just the north Pacific Ocean. Again, I’ve added the linear trend as a visual aid to show that the mean value is indeed changing. Although in this plot it is much easier to see. Overall, when comparing qualitatively comparing the values to the trend line, the plots are similar. There is a positive deviation in the 30s and 40s, a negative deviation in the 60s and 70s, and another positive deviation from the 80s to present.

PDO and Global Mean Surface Temperature

But when I plot the same data as the previous figure in the method traditionally used for the PDO, the plot looks different. Here we see that much of the time series before 1940 is blue, and much of the time series after 1940 is red. Notice that all of the years after 1980 are in the red, even though some of the monthly values dip below the trend line. Does the shape of that line look familiar? It should.

The first PC from the world sea surface temperature anomaly data is shown in blue. I noticed that it had the same structure as the global mean surface temperature, so I plotted GisTemp in blue on a different axis. The agreement is very good. Although in retrospect, it should be expected that the first PC of SST would be almost identical to the global mean surface temperature. The oceans cover about twice the surface area of the Earth compared to the land masses. If you’re interested, I’ve also included a scatter plot of the same data.

This implies that the mode of variability known as the PDO has the same spatial and temporal characteristics as the mean global surface temperature anomaly. The PDO doesn’t cause global warming, the PDO is global warming. (Insert all the caveats of PCA; statistical relationship not causal, linear, etc.) One reason that the time series of the PDO may look so noisy compared to the time series of the mean surface temperature anomaly is simply because it has less area, and therefore less data.

Characteristic Periodicity of PDO and GMST

Sometime, it’s said that the PDO has a characteristic time scale, hence the word decadal in the acronym. The UW website states that “Shoshiro Minobe has shown that 20th century PDO fluctuations were most energetic in two general periodicities, one from 15-to-25 years, and the other from 50-to-70 years.” To evaluate this, we can look at a wavelet analysis of the PDO with trend derived in the first part of this post.

Areas that are shaded darker have a higher significance than the lighter shading. Since the beginning of the record, the 15-25 year period does appear to be statistically significant at the 99% level. There is also a dark region in the 40-70 year period, but much of that is below the pink confidence line, meaning there isn’t enough data yet to determine if this apparent periodicity is significant or not.

This is the wavelet analysis for the first PC of the world sst anomaly. Compared to the wavelet for just the PDO region, there appears to be less periods of statistical significance. However, there is still significant periodicity at 15-25 years. But this frequency is not what is usually cited as being the ’cause’ of global warming. Instead, it is the longer 70-year periodicity. Since the time-series is so short compared to 70 years, we cannot know whether there is in fact a significant 70 year period in the global mean surface temperature unless we use a proxy reconstruction (which I’m sure someone already has done).

Second Mode of Variability: ENSO

The second PC/EOF of the world sea surface temperature anomaly is also interesting.

This is the characteristic signature of the El Nino-Southern Oscillation (ENSO); there is a warming of the tropical Pacific Ocean and a cooling in the western Pacific with little change elsewhere. I mention this not because it’s interesting that ENSO is a dominant mode of variability in the world SST data, but because of the corresponding principle component time series.

At first glance, this does not look like an ENSO time series. However, there is a large spike in the year 1998 which was the year of the super El Nino. Also indicative of an ENSO signal is the peak for the 1983 ENSO, and the current La Nina. But the main signature of this figure is the downward trend. Looking at the EOF figure above, we can interpret what this means. Since the early 1900s, the temperature in the tropical Pacific has been decreasing (the EOF is positive and the trend is negative), while the western Pacific has been warming (a negative EOF and a negative trend).

Conclusions

We’ve seen that the first mode of variability in the world sea surface temperature anomaly is the same as that seen in global mean surface temperature. In addition, the spatial and temporal pattern in the north Pacific are the same whether only use the area in the PDO region or the entire world. This may suggest that the first principle component of the northern Pacific Ocean sea surface temperature, now commonly referred to as the PDO, is a manifestation of global warming. Or the two phenomenon are linearly related.

The time scales associated with the PDO (15-25 years, and 50-70 years) are the same as those that are shown in the wavelet analysis of the global mean surface temperature. The shorter of the two time scales has statistical significance for both the PDO region and the world sea surface temperatures. The longer is not due to the shortness of the temperature record.

Finally, the second mode of variability has the same spatial patterns as ENSO. The principle component for this mode also has a trend. It shows that there is more warming in the western Pacific, and cooling in the central/eastern Pacific. There is a stronger temperature gradient across the Pacific now than 50 years ago.

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