Mar 14 2008
First, Assume a Spherical ENSO…
The price of milk had been dropping. To make matters worse, Farmer John’s cows weren’t producing as much milk. He was becoming desperate to keep his farm afloat. Last year, he invested in a new as-seen-on-TV feed that was supposed to make the cows happier and thus produce more milk. It didn’t work. A year before that, he tried Beethoven for Bovines - no luck with that either. His attempts at solving the problem experimentally did not work, so he decided to see if a theoretician could help. His local university veterinary department did not have any bovine theoretician on staff. As a joke, they suggested the physics department. Farmer John, not in on the joke, asked Professor Honcho why his cows weren’t producing milk. Honcho replied that this should be an easy problem; not more than a day or two. Three weeks later, Honcho called the farmer and said, “I found your answer. It was more difficult that I first thought, but the result is interesting, and I’ll be presenting it at the department seminar this week.” As the talk begins, he goes to the blackboard and says, “First, assume a spherical cow…”
The point of the story/joke is that sometime we can increase our understanding by making a simplifying assumption. In the story/joke above, that was to assume that a cow was a sphere. In the world of climate, that assumption won’t help us much. So instead, I’m going to assume a “spherical ENSO”. It doesn’t make sense that ENSO is spherical, but I can assume that it is a perfect sinusoidal cycle. Using this simplification, we can look at how ENSO will affect the temperature trends.
First, I assume that our time series has a trends of 0.02 C/year. Our ENSO signal has an amplitude of 0.3 and a period of about 12 years. Since ENSO actually has a “period” of around 3-7 years, it’s clear that we’re not talking about the real ENSO. These values were chosen to highlight certain points about calculating trends.
Below is a plot that shows how the temperature trend varies as a function of how many years used to calculate the trend. Anyone getting tired of these plots yet? Me too. So I made this one into an animated GIF. The red line is the calculated trend, and the black line is our temperature time series. Click the image for a slightly larger view.
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The prescribed trend is 0.2 C/decade, but it’s obvious that the red line dances with slopes larger and smaller than that. There are extremely negative values even though the overall trend is positive. The amount that the red line fluctuates gets larger as less points are used in calculating the trend. This is because in this case the noise has fluctuations that are larger than the changes caused by the trend.
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Another way to look at the results is by plotting the trend as a function of the length of the trend measured in the number of cycles of our cyclic process. This is displayed above; the black line is the trend. The magenta horizontal line at 0.2 is our prescribed trend. Horizontal dashed lines represent the percent error in the calculated trend from the prescribed trend. The colors are for different errors: blue = 10%, green = 50%, red = 100%. These are not errors in the trend. When the black line crosses the red line, this means that the calculated trend has an error of 0.2.
There are several interesting things about this figure. First, the black line is above the bottom red line if the trend length is longer than one cycle. This means for us to be assured that our calculated trend is within 100% (0.2) of the prescribed trend, we must use more than one cycles worth of data. In the climate system, ENSO has a period of 3-7 years, and its amplitude is large compared to the background trend. This means that trends calculated for less than 7 years will be dominated by the ENSO noise.
Other oscillatory features in the global temperature will need more or less years in the calculated trend depending upon their length. For instance, the PDO has a period of about 20 years. This means that at least 20 years are needed in the trend to assure us of being within 100% of the actual trend. This assumes that the effects of the PDO are large compared to the background trend.
Currently, short-term trends are near zero or slightly negative. We are also in the middle of a fairly strong La Nina. This is going to make the trends lower than in actuality because ENSO is noise. The sea surface temperatures in the Pacific will rise back to their levels from before this event. They will then most likely enter a positive phase of ENSO. Then the short term trends will be biased towards higher than the actual trend.
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12 Responses to “First, Assume a Spherical ENSO…”
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Very good illustration and explanation. There is a lot of information on ENSO and PDO at the University of Washington, JISAO site:
http://jisao.washington.edu/pdo/
Yes, nice post, and the graphic is nice, Tufte-lovers would be proud of you. Any chance you can add one of, like from http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt ?
Also, as a minor nit, in case you do another, think about reversing the X axis on the second chart, so that the graphed position corresponds directly above to the left end of the trendline, which is useful as one can read the slope at any point. [Tufte-lovers would be even happier.]
[Response: I thought about that, but originally decided that this was more clear since we usually think of 'time' increasing from left to right. I'll try to do the GISTemp one tomorrow.]
Also, although it is clear from the chart that you did it correctly, it might be worth reminding some readers that this is a linear regression slope, i.e., Excel SLOPE, which takes into account all of the intervening points, not just drawing a line between the endpoints, which many seem to think is meaningful. (And if you graph that one, it really jumps all over the place.)
Considering that the ENSO period is only a few years, we can expect reasonable confirmation that the predicted warming will show itself when we move into the next El Niño, or not. That should shake off another wave of doubt.
Using a large cyclic ENSO as the explaination for the recent trends is a slippery slope for people who believe in the CO2 catastrophe hypothesis because we don’t really understand how the ENSO works or why it exists.
If one accepts the hypothesis that ENSO can produce large global temperature oscillations over 20 and 70 year timeframes then one must also accept the hypothesis that that ENSO could operate over longer timeframes (e.g. 1000 years) and that a long term ENSO oscillation could explain a large portion of the recent warming.
Data. ENSO is an observation, not hypothesis.
No data. We don’t have to accept a hypothesis where there is no supporting data.
See, that’s not so hard, is it?
“Data. ENSO is an observation, not hypothesis.”
Atmoz is using a periodic ENSO to explain the statistically implausible trend that has occurred over the last 7-8 years. That makes it a hypothesis based on an observed trend.
The historical temperature data also indicates that warming cycles occur with a 1000 year intervals. Those warming cycles are unexplained and could easily be another manifestation of the ESNO effect. You cannot not prove that ENSO has not caused the recent warming just like you cannot prove that ENSO is the explanation for the recent cooling.
Nice Post ATMOZ, I really enjoyed the way you tackled this problem.
Have a read of some of UC’s stuff over at CA on 1/f noise and the issues of LTP and the old old Robock paper is a nice place to start for issues of internal variability.
> The historical temperature data also indicates that warming
> cycles occur with a 1000 year intervals
Data (of the real, not made-up, variety)?
“> The historical temperature data also indicates that warming
> cycles occur with a 1000 year intervals
Data (of the real, not made-up, variety)?”
Yep. Take a look at the ice core data from greenland. This is supported by other types of good temperature proxies in locations around the world. Of course, some people prefer to focus on data from bad temperature proxies like bristle cone pines but ignoring inconvient data does not change the facts.
Data, I think Raven is relying on the Singer/Avery “unstoppable warming” idea. Not too respectable, IOW.
[...] recently posted an interesting analysis that explains why one must always be aware of the properties of weather when doing statistics. I agree with that. I would go further. I would say one must always be aware of the properties of [...]
Steve Bloom,
UC’s discussion on 1/f noise over at CA has nothing whatsoever to do with the Singer/Avery work.
Of course, you could have found this out by looking it up beforehand, but it is so much easier to criticise something from ignorance.