I started working on a post about feedbacks, an interesting and important topic recently raised in reader comments. But I’ve been sidetracked by the revival of one of the favorite false claims of denialists, one of those pieces of garbage that never dies. Occasionally I look at the stats provided by wordpress, and I noticed I was getting a lot of hits from the science blog Deltoid. That’s because Deltoid commented on an open letter in the National Post signed by a collection of scientists which includes many, if not most, of the usual list of denialists. The open letter has some rather outrageous claims; possibly the most egregious (and most easily proved false) is this:
Consistent with this, and despite computer projections of temperature rises, there has been no net global warming since 1998. That the current temperature plateau follows a late 20th-century period of warming is consistent with the continuation today of natural multi-decadal or millennial climate cycling.
Regarding the claim that there hasn’t been any global warming since 1998, I’ve already posted about it, the claim is demostrably false. What’s really surprising (well, maybe it isn’t so surprising) is that some of the signatories to this drivel are trained in statistics, including Ross McKitrick and Edward Wegman.
But why, you may wonder, does this claim (in one form or another) keep rearing its ugly head? Whether it’s “global warming stopped in 1998″ or “the satellite trend is flat over the last 13 years” or “this year’s hurricane season was a dud,” I keep hearing so-called “statistics” that are touted as evidence against the reality of global warming. The reason lies in the fact that there are two things which contribute to data: the signal and the noise.
Noise is the “random” part of the data. It may be measurement error, or a random physical process, or even a deterministic physical process which mimics a random process. But it’s there. For the layman, it’s often unexpected; if global warming is real, how can global temperature fail to rise enough to break the 1998 record for hottest year ever (according to HadCRU data — according to NASA GISS data the hottest year is 2005)? But in the real world, noise is unavoidable. If I were to see temperature data which didn’t have noise in it, I’d be immediately suspicious that the data were faulty. Still — how can it be that we haven’t broken the 1998 record yet (according to HadCRU, because according to GISS we broke it in 2005)? It’s been nearly 10 years! Doesn’t that cast some doubt on global warming?
The “modern global warming era” is from about 1975 to the present. If you study the yearly global average temperature 1975-now, you’ll find that it shows a statistically significant upward trend, the planet getting hotter by about 0.018 deg.C/yr. You’ll also find that in addition to this signal, there’s noise which has a root-mean-square value (a “standard deviation”) of about 0.1 deg.C.
Is global temperature data really indistinguishable from a steady trend with random fluctuations? Is a steady trend with random fluctuations really indistinguishable from global temperature data? To get some perspective I decided to generate artificial data to mimic this, so I created a time series of 100 years length which is the sum of a signal plus noise: the signal consists of a steady trend at a rate of 0.018 deg.C/yr, the noise is random numbers with standard deviation 0.1 deg.C. Then I chose one of the values that had a particularly large positive random part and called that the year “1998″ in order to match the record-setting temperature actually observed on earth in 1998. Finally I shifted all the values by a constant, so the data would be on the same scale as actual temperature data. Using this artificial data, here’s what the modern global warming era looks like:
Just like real temperature data, it shows a distinct (and statistically significant) rise. Linear regression indicates the rate of increase is 0.014 +/- 0.004 deg.C/yr, so the error range includes the true value.
What if we looked only at data from the 1998 peak to the present? Now it looks like this:
Oh my God!!! Suddenly we have “no global warming since 1998″!!! Linear regression actually indicates cooling at a rate of -0.007 deg.C/yr!!!
But we know, without any doubt whatsoever, that the signal is still increasing, at a rate of exactly 0.018 deg.C/yr. It’s the noise that shows cooling — and for such a short time span, the cooling in the noise overwhelms the warming in the signal.
What does the future hold for this artificial temperature data? Here’s the data from the start of the global warming era, to 28 years from now:
It looks like we’ve got some serious warming on the way. Linear regression indicates that for this data, the rate of warming is 0.018 +/- 0.002 deg.C/yr. But of course, we already know that the warming rate is exactly 0.018 deg.C/yr — the artificial data is designed that way.
Noise exists. Anyone who tells you different isn’t just selling something, they’re lying. The noise we observe in annual global average temperature is big enough that it’s easy to get an entire decade which will give a cooling trend. And I didn’t have to work hard to make this happen; I didn’t generate lots of 100-year signal+noise series until I found one that made my point, I only generated a single series, and there it was. But the cooling trend so determined will not be statistically significant. The warming trend in longer time spans is statistically significant.
The right approach is to look for the trends, not the wiggles, and to apply statistical significance testing to determine whether they’re real changes in the system or just accidental fluctuations. There’s always noise mixed in with the signal, and disentangling the two can be very tricky. But it can be done.
Another way to get a better picture of actual trends is by taking averages, not over very brief 1-year periods, but over longer stretches of time. Here’s the actual global average temperature (from NASA GISS) averaged over each 5-year interval (the last average is incomplete, since we haven’t yet finished the 2005-2010 interval):
Now we see a much more steady progression. That’s because taking longer-term averages actually reduces the effect of the noise without affecting the trend. But there’s still noise! By taking averages over longer time spans we don’t eliminate the noise, we just make it smaller.
Global average temperature isn’t the only global-warming related variable which shows wiggles. In fact, just about all measured quantities show wiggles similar to what is seen in global temperature. Because of this, we can expect that there will always be several climate variables which are wiggling in a direction opposite to the long-term trend. Hence there will always be one or more measures which are — momentarily — going the “wrong way” according to global warming. And because of that, we will continue to hear about them from denialists. 2007 wasn’t as hot as 2005; Argentina had a colder winter this year than last; arctic sea ice anomaly isn’t as negative as it was this summer; hurricane activity this year was less than predicted; etc., etc., etc. As long as physical variables show wiggles — and they always will — there will be plenty of fodder for denialists. They’ll never run out of something that they can spin to make it look like global warming isn’t happening.
As long as there’s noise, denialists will exploit it to paint a false picture of the changes earth’s climate is experiencing. And there will always be noise — both in climate data, and from denialists.
UPDATE UPDATE UPDATE
The issue has arisen, are not the fluctuations seen in global temperature data since 1998 below the preceding trend? Is such deviation statistically significant?
The answers are, no and no. Let’s take GISS global temperature data, and use only the data from 1975 through 1998 to estimate the trend. By ending with 1998, we’ll get an especially high trend rate, so the following data will have a high trend to “live up to.”
We can then extend that trend line to the present, to see whether or not the most recent data depart from that trend. Here’s the result:
It’s rather clear that the data after 1998 are well in accord with the trend before 1998. We can also compute residuals, the difference between the observed data and what the value would have been if it followed the 1975-1998 trend exactly:
We see that the data since 2001 are actually a little warmer than what we would have expected from the 1975-1998 trend. But the deviations are not statistically significant.
UPDATE #2 UPDATE #2 UPDATE #2
Here’s the surface temperature record according the GISS and HadCRU, smoothed on a 5-year time scale: