Curious Correlations

Reblogged from Watts Up With That:

Guest Post by Willis Eschenbach

I got to thinking about the relationship between the Equatorial Pacific, where we find the El Nino/La Nina phenomenon, and the rest of the world. I’ve seen various claims about what happens to the temperature in various places at various lag-times after the Nino/Nina changes. So I decided to take a look.

To do that, I’ve gotten the temperature of the NINO34 region of the Equatorial Pacific. The NINO34 region stretches from 90°W, near South America, out to 170° West in the mid-Pacific, and from 5° North to 5° South of the Equator. I’ve calculated how well correlated that temperature is with the temperatures in the whole world, at various time lags.

To start with, here’s the correlation of what the temperature of the NINO34 region is doing with what the rest of the world is doing, with no time lag. Figure 1 shows which areas of the planet move in step with or in opposition to the NINO34 region with no lag.

Figure 1. Correlation of the temperature of the NINO34 region (90°-170°W, 5°N/S) with gridcell temperatures of the rest of the globe. Correlation values greater than 0.6 are all shown in red.

Now, perfect correlation is where two variables move in total lockstep. It has a value of 1.0. And if there is perfect anti-correlation, meaning whenever one variable moves up the other moves down, that has a value of minus 1.0.

There are a couple of interesting points about that first look, showing correlations with no lag. The Indian Ocean moves very strongly in harmony with the NINO34 region (red). Hmmm. However, the Atlantic doesn’t do that. Again hmmm. Also, on average northern hemisphere land is positively correlated with the NINO34 region (orange), and southern hemisphere land is the opposite, negatively correlated (blue).

Next, with a one-month lag to give the Nino/Nina effects time to start spreading around the planet, we see the following:

Figure 2. As in Figure 1, but with a one month lag between the NINO34 temperature and the rest of the world. In other words, we’re comparing each month’s temperature with the previous month’s NINO34 temperature.

Here, after a month, the North Pacific and the North Atlantic both start to feel the effects. Their correlation switches from negative (blues and greens) to positive (red-orange). Next, here’s the situation after a two-month lag.

Figure 3. As in previous figures, but with a two month lag.

I found this result most surprising. Two months after a Nino/Nina change, the entire Northern Hemisphere strongly tends to move in the same direction as the NINO34 region moved two months earlier … and at the same time, the entire Southern Hemisphere moves in opposition to what the NINO34 region did two months earlier.

Hmmm …

And here’s the three-month lag:

Figure 4. As in previous figures, but with a three month lag.

An interesting feature of the above figure is that the good correlation of the north-eastern Pacific Ocean off the west coast of North America does not extend over the continent itself.

Finally, after four months, the hemispherical pattern begins to fall apart.

Figure 5. As in previous figures, but with a four & five month lag.

Even at five months, curious patterns remain. In the northern hemisphere, the land is all negatively correlated with NINO34, and the ocean is positively correlated. But in the southern hemisphere, the land is all positively correlated and the ocean negative.

Note that this hemispheric land-ocean difference with a five-month lag is the exact opposite of the land-ocean difference with no lag shown in Figure 1.

Now … what do I make of all this?

The first thing that it brings up for me is the astounding complexity of the climate system. I mean, who would have guessed that the two hemispheres would have totally opposite strong responses to the Nino/Nina phenomenon? And who would have predicted that the land and the ocean would react in opposite directions to the Nino/Nina changes right up to the very coastlines?

Second, it would seem to offer some ability to improve long-range forecasting for certain specific areas. Positive correlation with Hawaii, North Australia, Southern Africa, and Brazil is good up to four-five months out.

Finally, it strikes me that I can run this in reverse. By that, I mean I can find all areas of the planet that are able to predict the future temperature at some pre-selected location. Like, say, what areas of the globe correlate well with whatever the UK will be doing two months from now?

Hmmm indeed …

Warmest regards to all, the mysteries of this wondrous world are endless.

w.

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