In a previous post, I stated that the current trend in global temperature increase is sufficient that by 2015, data will probably establish that the planet’s temperature has definitely not stabilized or begun to decline. Specifically:
By 2015, the expected temperature from the regression-line fit and that expected from the “no change” hypothesis will be far enough apart that we’ll probably be able to distinguish between them with statistical significance. In other words, by 2015 either we’ll know that global warming has changed (possibly stopping, possibly reversing), or there’ll be no more of this “global warming stopped in 1998” malarkey.
It’s entirely possible that the numbers may give us statistically significant evidence even before 2015. If so, I’ll report the result. If it turns out that global warming is not continuing (which I seriously doubt), then I’ll readily admit that I was wrong. In fact, I’ll be keeping a close eye on the future evolution of global temperature and actively looking for such results, so if we do get valid evidence that global warming has stopped, I just might be the *first* one to say so.
If 2015 rolls around, and temperature have [sic] risen above present-day levels by enough to be demonstrably significant, I’ll announce that too. Will those who have so often chanted the “no more global warming” mantra admit that they were wrong? Somehow, I doubt it. I suspect that instead, they’ll be flooding blogs, newspapers, magazines, and Faux News reports with claims that “global warming stopped in 2013.”
I didn’t intend this as a “challenge,” but the idea was loosely based on various proposals I’ve seen for “bets” about future global average temperature. The “challenge” aspect has taken on a life of its own among readership; therefore I’m willing to make it official. I will also reiterate that the divergence between warming and no-more-warming isn’t married to the year 2015! That was a choice of a future year in which it’s likely that the issue will be statistically distinguishable, but a significant result might be available before then, or not until after. Also, the choice was based on intuition, not on any quantitative analysis. Eventually a significant difference will emerge; if not by 2015, then not long after.
I’ll also emphasize that I’m not interested in betting money on it. I have a family to provide for, and I can’t afford to have my money tied up in escrow while waiting years for a bet to be settled. Besides, I don’t gamble. Although if I did …
So I’ll outline more precisely what terms I would suggest for a wager, challenge, or whatever you like to call it, on the question “Is global warming continuing or has it ceased?” I’ll try my best to be fair to both sides, so that if you firmly believe that global temperature will continue to rise and you’re eager for a wager, I suggest this is the one to make, and likewise, if you’re firmly convinced that global temperature has peaked and is not going to continue and you’re eager for a wager, this is the one to take. The winner will definitely be decided by the reality or not of continued warming, not by any clever design of the terms and conditions of the wager. In my opinion, settling such a challenge should be based on statistical significance, not on choosing a specific year, so this proposal is based on statistical significance rising above the noise level, not on the temperature at a fixed future time (but as we’ll see, there is a time limit to how long the bet can last).
First let’s review the data leading up to the statement. Here are global average temperature estimates, all set to the same zero point (using the reference period 1950.0 to 1980.0), from NASA GISS, NCDC, and HadCRU:
The trend lines are determined from the data covering the time span 1975-2000. The graph is intended to show that the data after 2000 are not inconsistent with the claim that the trend is continuing, in fact they’re following the line with “wiggles” (i.e., noise) that make trends impossible to identify over short time periods but clear over longer time periods. (and indeed that is so). For the terms of this wager, it is not necessary to recompute the data using the 1950.0-1980.0 reference period I’ve used in this graph. This graph just gives us the essential idea behind it.
And the idea is this: if global warming is continuing, global temperature will continue to follow a rising trend plus noise. If global warming has ceased, it will stay at its present level (or decline) plus noise. So we should outline what global temperature will be in those two cases.
First let’s look at annual average temperature. I used the trend from 1975 to the present to estimate the trend, and used the standard deviation from the residuals (after subtracting the trend from the data) to estimate the noise level. The trend is upward at 0.018173 deg.C/yr, and the standard deviation of the residuals is 0.0959 deg.C. Here in fact are the annual averages (black dots), together with the trend (solid red line), and (dashed) lines two standard deviations above and below that trend line:
This gives the expected range of annual averages — between the dashed red lines — and 95% of all years should fall within those lines. If one wishes to be precise, these limits should be modified to account for the red-noise character of the data, but in this case it’s a small correction and I’m going to ignore it. Note that all the annual averages from 1975 to the present fall within the dashed red lines. As an aside, the above graph is about as clear a graph as I’ve seen showing that there’s really no evidence — none whatsoever — that global warming has stopped.
We can of course extend those lines into the future. We can also quantify the hypothesis that global temperature hasn’t changed since 2001; the average from 2001 to the present is 0.5432 deg.C, so we can simply draw a line at that value and dashed lines two standard deviations above and below it. Putting the “no-more-warming” range in blue, we get this:
If the “continued warming” hypothesis is correct, future values should fall between the dashed red lines. If the “no more warming” hypothesis is correct, future values should fall between the dashed blue lines. If the earth has actually started cooling, future values will eventually dip below the blue lines.
So here’s the bet based on annual averages: the still-warming side wins if temperature goes above the top dashed blue line; the not-warming side wins if temperature goes below the bottom dashed red line.
If temperature rises above the upper dashed red line, we have evidence that the planet is warming even faster than the present trend. In that case the still-warming side also wins. Alternatively, if temperature falls below the lower dashed blue line, we have evidence that the planet is actually cooling, and the not-warming side wins.
Finally, I’ll add one last condition. It’s unlikely but possible that a value can fall outside either range just because of noise. So, my “bet” is that as soon as there are two years (not necessarily consecutive) which are in either decisive region, the side with two decisive years is declared the winner. Therefore:
If annual average global temperature anomaly (land+ocean) from GISS exceeds 0.735 deg.C for two (not necessarily consecutive) years before it falls below the value (where t is the year) for two (not necessarily consecutive) years, then the still-warming side wins; if it falls below the above equation for two years before it rises above 0.735 for two years, then the not-warming side wins.
By the end of 2015, it is in fact likely but by no means certain that one or the other side will have won. Eventually, the two regions get far enough apart that it’s certain to happen. In fact, by 2028 we’re sure to have two years outside the limits of one or the other side, so the bet can’t take longer than 2028 to be decided. But this test isn’t based on a particular future year; it’s possible (but highly unlikely) that either side could win if 2008 and 2009 both fall into its winning region.
Although it’s unlikely, it’s possible that this bet could be undecided until the end of 2028. This is because the noise level is very high compared to the signal level; the noise level is about 5 times as large as the present annual trend! We can reduce the noise level without affecting the trend rate by using, not annual averages, but 5-year averages. That gives us a graph like this:
It’s straightforward to modify the terms of the test in order to base it on 5-year averages rather than annual averages. It’s also straightforward to adopt the test method to the use of HadCRU data, or NCDC, rather that NASA GISS.
I’ve seen other proposals for wagers, some of which strike me as perhaps unfair, having what seem like overly complicated conditions which may be designed to take advantage of statistical naivete as much as depend on the future progress of global temperature. On the other hand, some seem like fair but poorly chosen (too much chance of a false result due to random noise). If any part of this proposal favors one side over the other for purely statistical rather than climate reasons, I swear that it’s an oversight, not intentional. This proposed test is designed to be a fair test of competing ideas, and to be settled by a genuinely significant result, not by accidental changes due to “noise” in the climate system.
A final note: in further reader comments it was pointed out, quite correctly, that even if AGW is completely correct it’s still possible for temperature to show no increase long enough for the “no-further-warming” side to win this wager, IF unexpected events happen to alter the behavior of the climate. For example, large volcanic eruptions will cover the world with aerosols which will lead to significant cooling (such as seen after the Mt. Pinatubo and el Chicon eruptions) even if AGW is completely correct and uninterrupted; a series of large eruptions in succession may cause enough cooling to put future temperatures into the “no-warming” region. Likewise if sulfate aerosols from the booming economies of India and China get so great as to overwhelm the warming influence of greenhouse gases. I leave it to those who have money to bet, to estimate the probability of such things happening, and what additional conditions to impose to account for such a possibility. As for me, I suspect (even though I haven’t estimated the probabilities!) that it’s unlikely enough, that I’d still take this bet (for continued warming) without additional caveats. Of course that’s easy for me to say, since I’m not a gambling man.
If, however many years from now, the no-more-warming side wins the bet, and no unequivocal caveats are identified, then I’ll admit that our understanding of global climate is insufficient and that we can’t rely on the prognostications of the climate science community. I doubt it’ll happen. If, on the other hand, the still-warming side wins the bet … what will be the response from the skeptic side?