Wednesday, March 03, 2010

Insignificant warming trends: why 1995 was chosen

Deep Climate, a blog promoting panic about AGW and specializing in criticisms of the Canadian skeptic groups, asked the question why the BBC has inconveniently asked Phil Jones whether there had been a significant global warming since 1995. Recall that he had to answer that there was none - because it's damn too easy to check that there was none.

According to Deep Climate, your humble correspondent has "played a key role in getting the question asked in the first place."

Together with Richard Lindzen and Anthony Watts, I was quoted as the inspiration for the BBC. Once Phil Jones answered the BBC's questioned, he became our friend denier, so the Deep Climate article talks about Lindzen, Motl, and Jones. ;-) I am honored but yes, Deep Climate has a point. I helped to promote this way of thinking - about "statistically significant trends" - although I have obviously neither invented it nor brought it to climatology. :-)

My modest contribution was a simple calculation (thanks to Wolfram Mathematica), No statistically significant warming since 1995, that I wrote in December 2009 and that was reposted on Anthony Watts' blog which increased the nonzero but relatively modest TRF's reach by one order of magnitude.

Jeff Id showed us an article from November 2009 where he discussed the same question with the same result so I was surely no pioneer in the content, at most in the presentation. (But it does seem to me that our detailed calculations of the confidence levels etc. may differ a bit.)

Why 1995, why the answer is important

Deep Climate correctly writes that Richard Lindzen has been the main person who has thought about the statistical significance of the trends. He is often ahead of us, and ahead of everyone else. Let me mention a few elementary words about the statistical significance.

The "amateurs" would buy the superficial way of reasoning that has spread in the media. They would ask whether a warming trend in a period was positive or negative. They would usually end up with the trend since 1998 which were cooling, but that could have been blamed on a single El Nino, so the big conclusion remained obscure. (UAH shows cooling since 2001 and most other years, too.) And they (the amateurs) thought that this information was scientifically interesting by itself.

Except that it's not too scientifically interesting. It's clear that there's always some change. However, most changes of the atmosphere (and many other systems) may be interpreted as "noise". Almost by definition, detailed properties of "noise" can't have any implications: they're random. If we want to figure out whether the data support the idea of a warming - a trend that exists for a reason, whatever the reason is - we need the data to show not only some warming.

We also have to show that it is a "signal" and not just "noise". In other words, we need to show that it is unlikely for the change to have occurred just by "chance". The concept of statistical significance is designed to do exactly this job. When we look whether an event had a "real" reason, we employ various statistical methods to compute the probability that it could have occurred by chance.

If this probability is smaller than 1% or 5%, i.e. if we really see some "signal" that doesn't seem to be just "noise", it's pretty unlikely that the observed pattern is a result of chance. Such a conclusion weakens the "null hypothesis" - that the data are explained by "noise" - and strengthens another hypothesis, one that adds a new effect (an underlying warming trend, in this case).

That's the logic how new effects and new particles including the top quark were being discovered, too.

If the probabilities above are calculated to be smaller than 1% or smaller than 5%, we say that the conclusion about the existence of the trend (or anything else) is statistically significant at the 99% or 95% confidence level. That doesn't quite "prove" that the underlying trend is real but it makes it likely. It is a "fuzzy" kind of evidence - and science often needs to take similar "incomplete proofs" into account.

When you apply the methodology to the annual satellite temperature data, choose the "white noise" as your null hypothesis (you need to specify the "color" because "noise" is not a complete information how the random numbers for the temperatures should be chosen), and "white noise with a trend added" as the other hypothesis, you will find out that the satellite warming trend in the last 15 years doesn't even reach the 95% confidence level. Of course, it follows that it doesn't reach the more ambitious 99% confidence level, either.

15 years is a nice number. But if you happened to choose 16 years and you began in 1994 which was detectably cooler than 1995, you would probably have a trend that would be significant at the 95% level, although not yet at the 99% level. I forgot the exact number. So you would be marginally able to extract the conclusion that the climate has seen some "non-random" change since 1994.

So why 1995 was chosen as the beginning? Yes, it's not only because "15 years" sounds nicer than "16 years". It was chosen because it's the maximum recent period in which no statistically significant global warming may be seen, even with the most modest definition of "statistical significance". For "16 years", the answer would already be messy: it would depend how you exactly define statistical significance.

The conclusion about a "trend" since 1994 would still fail to be "robust", because a change of 1994 to 1995 would destroy it, but some people could already argue that the trend was there. For 1995, it's indisputable that the trend is statistically insignificant.

So was it cherry-picking when we chose 1995? Of course that in some sense, it was. The goal was to find the maximum period of time for which even the 95% statistical significance test fails. For the UAH data, the answer turns out to be 15 years. For periods longer than 15 years, we can see some glimpses of statistically significant trends. We can show that the white noise doesn't explain the data well if the intervals are longer than 15 years.

However, better hypotheses - red noise, pink noise, or a more complex theory with a stochastic element - could also explain the data longer than 15 years, without any need for an underlying warming bias, without any need for a "systematic explanation" why the trend was mostly warming, without any new "major effect", man-made or otherwise. It could have been just weather, even during the recent 30 years.

I was only checking the "white noise" explanation (which is the easiest one to "falsify", so with the "white noise" choice, it's most likely that you find a statistically significant trend) because I know that people are looking at the random numbers in this way: I surely never believed that white noise was a good null hypothesis. Also, this choice makes us Devil's advocates because we may falsify the ("white noise") null hypothesis even if the underlying numbers are random, but with a different color. In this way, we're trying to get as alarmist a result as we can: and we still fail.

So in some sense, we were cherry-picking. But before we found the lack of warming in 1995-2009, we asked a very interesting question and a very important answer. They actually tell us how "urgent" the global warming is, assuming that a trend exists. And the answer is that at the timescale of 15 years, the problem surely can't be urgent because the phenomenon leading to this "urgency" doesn't even exist as a statistically significant observation! It can't even be reliably distinguished from the normal, trend-less evolution.

So if we wait with the proposed "mitigation" for another 15 years, the conclusion of the calculations above implies that nothing statistically significant will take place. Not only there won't be any catastrophes in 15 years: it's likely that we won't even be able to detect any change from the present world!

After periods longer than 15 years, it's conceivable that the annual global mean temperatures will deviate in one way or another in such a way that can't be explained as a "white noise" deviation from the conditions that exist today. But even if that's the case, it is still very far from having a dangerous change. A change that you can barely observe - with the best thermometers and the most accurate methods how to calculate the global averages - is usually not yet dangerous.

And of course, none of these changes - even if you picked longer intervals where trends could be seen - would include evidence that there is an important man-made component of the "trends". In fact, we have seen lots of data from Central England, Central Prague, and others that make it completely clear that the rate of warming or cooling has been matched or surpassed many times in the last 360 years.

So realistically speaking, even if all of us were making some silly error and the warming were substantial, it can't be a problem for another 100 years or so.

And that's the memo.

Unrelated: Obama plans to triple the price of gasoline

According to a Harvard research mentioned by Sindya N. Bhanoo at the New York Times blog of Andrew Revkin,
Fuel Taxes Must Rise, Harvard Researchers Say,
Obama's plans to lower the CO2 emissions in the U.S. require the price of the gasoline to triple, from $2.30 today to $7 per gallon. Welcome to the Middle Ages or Kenya, Yankees. ;-)

I wonder how insane someone has to be to agree with such a future, without any rational reason.

Pachauri recognizes the criticism

More than three months after the collapse of the credibility of the IPCC-linked climatological community and three months when Rajendra Pachauri denied that anything bad has been revealed about the IPCC, Rajendra Pachauri "recognize[d] the criticism that has been leveled at us and the need to respond." He's so amazingly fast: just three months and he already recognized the criticism. He had to be excellent as a railway engineer.

In his porn book, he also reincarnated into a snail (there's a lot of reincarnation in the book) and raped a turtle. The cops asked the turtle: "Madam, could you please describe how the incident with the snail occurred?" And she said: "Unfortunately no, Sirs. It was s.....o...... f.......a.......s........t." :-)

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