To Tell the Truth: Will the Real Global Average Temperature Trend Please Rise?
A guest post by Basil Copeland
Before proceeding, I want to thank Anthony for allowing me to guest blog at Watt’s Up With That? Anthony is doing some remarkable work in trying to insure the integrity and quality of the surface record, and it is an honor to be able to use his blog for my modest contribution to the debate over climate change and global warming.
In Part I we looked at seasonal differences in the four global average temperature metrics Anthony has recently been blogging about, and demonstrated that since around the end of 2001 there has been no “net” global warming, that positive seasonal differences have been offset by negative seasonal differences. More recently, negative seasonal differences have dominated, suggesting the possibility of a recent negative trend in global average temperatures.
Reader comments to Part I were interesting. It was obvious from many that they were struggling to understand what I was getting at, and that this was a different perspective on the data than usual. Others quickly raised the specter of cherry picking the data, or suggesting a hidden agenda of some kind. That some would jump to such conclusions without giving me the courtesy of waiting until I was finished is a sad commentary on what’s happening to the field of climate science. Science is supposed to be all about the freedom to engage in critical inquiry without being impugned with false motives, the freedom to hold scientific consensus up to the critical scrutiny of falsifiable hypotheses. When voices immediately seek to shut off avenues of inquiry, or impugn motives for questioning scientific consensus, I don’t know what that is, but I know that it is not science..
Resuming where we left off with Part I, if there is evidence of a recent negative trend in global average temperature, is it “statistically significant,” and if so, in what sense? That’s the question I left hanging at the end of Part I, and is the question we will address in Part II. There are various ways we might go about investigating the matter. I chose one that comes from my particular field of experience and expertise (economics, though it is perhaps worth noting that my training was in environmental and resource economics): the Chow test. The Chow test is used to test for “structural breaks” in time series data. Just as correlation does not prove causation, a “structural break” doesn’t necessarily prove anything. It merely suggests that things were different in some way before the “break” than afterward. It doesn’t answer the question of “why” things changed. Or, given the venue, we might say that it doesn’t answer the question Watts Up With That? But it does answer the question of whether the change is “statistically significant.” And if it is, then perhaps inquiring minds might want to know about it, and consider whether it makes any difference to matter under discussion.
The Chow test involves fitting a regression to the sub parts, and comparing the sum of the mean square error (MSE) of the sub parts to the mean square error of a regression fitted to the entire time period. If the sub parts come from sufficiently different regimes or circumstances, splitting the time series into two parts will reduce the total MSE, compared to the MSE of a single regression fitted to the entire time period. The Chow test follows the F distribution, and is a test of the null hypothesis of no change, or difference.
Table 1 summarizes the Chow test for each of the four metrics under consideration, for a structural break at 2002:01. The Chow test was statistically significant in all four cases, though in varying degree. In Table 1 I describe the level of statistical significance using the same likelihood terminology used by IPCC. Evidence for a structural break is “very likely” from the UAH satellite dataset, “extremely likely” from the GISS and RSS datasets, and “virtually certain” from the HadCRUT land-sea dataset.
I cannot say that, though, with remarking about how silly it is. I do not know of any other field where statistical significance is interpreted this way. In my field, anything less than a 95% level of confidence is considered weak support of a tested hypothesis. Instead of “very likely,” for support at the 90% level of confidence I’d say “probably.” Instead of “extremely likely” at the 95% level of confidence, I’d say “likely.” And instead of “virtually certain” at the 99% level of significance, I’d say “very likely.” In other words, to my way of thinking, the IPCC likelihood terminology is shifted about two orders of magnitude in the direction of overstating the likelihood of something. But even with my more cautious approach to characterizing the results, the evidence is somewhere between “probably” and “very likely” that a structural break occurs in the data after 2002:01.
However we choose to put it, there is statistical support for modeling the trends with a break at 2002:01. This is done, statistically, with dummy slope and constant variables, and the results are shown graphically in Figures 1, 2, 3, and 4. In each figure, there are three “trends” noted. The first, to the left and above the data, is the trend for 1979-2001. The third, to the right and below the data, is the trend for 2002 through 2008:01. In the middle, labeled “dT” is a trend for the entire period derived from the delta, or difference, in the end points of the the trend lines, with a number in parentheses representing the decadal rate of change from fitting a single trend line to the data. This overall trend, based on the difference in end points of the trend lines, is a “best estimate” of the overall trend using all 29 years of data (thus refuting any notion of cherry picking).
Figure 1 – click for larger image
Figure 2 – click for larger image
Figure 3 – click for larger image
Figure 4 – click for larger image
Many readers will probably be familiar with the use of 30 years as a basis for a “climatological norm.” While we do not have 30 years of data here, we’re close, close enough to refer to the overall trends as a climatological normal for the past three decades. As I look at the results shown in the four figures, two things stand out.
First, the dT of the final “best estimate” is 0.025C/decade (UAH_MSU) to 0.047C/decade (HadCRUT) lower than what we’d expect from fitting a straight trend line through the data. That is perhaps the major point I’m trying to make in all this: that over the period for which we have satellite data to compare to land-sea data, the rise in global average temperature is not quite as great as one would think from fitting straight trend lines through the data.
Incidentally, this not entirely owing to fitting a downward trend through the data since 2001. Separate slope and constant dummy variables are also included for the 1998 El Nino, and this accounts for some of the difference. In fact, somewhat surprisingly, when a constant dummy is added for the 1998 El Nino, it reduces the slope (trend) for the non-El Nino part of the time series through 2001. We usually expect a constant dummy to affect the model constant term, not the slope. But in every case here it reduces the slope in a significant way as well, so some of the difference in the “dT” and the result we’d get from a straight trend line owes to the effect of controlling for the 1998 El Nino.
The second thing that stands out, of course, is the downturn since 2001. Whether this downturn will continue or not, only time will tell. But if it continues, then the “dT” will likely decline further.
Other things may stand out to other observers. The differences within the two types of metrics are notable. GISS implies more warming than HadCRUT, and RSS_MSU implies more warming than UAH_MSU, with the latter showing quite a bit less warming in the period up to 2001 (given the way we’ve modeled the data). In the case of GISS vs. HadCRUT, the trends are actually quite similar in the period up to 2001; it is after that that the difference emerges, making one wonder if something has changed in recent years in the way one or the other is taking its measure of the earth’s temperature.
Just a final comment, as a way of putting this all in some perspective. In AR4 IPCC projects warming of 0.2C per decade for the next two decades in a variety of its climate change scenarios. That will take a lot more warming than we’ve seen in recent decades. And with the leveling off of the trend in recent years, even if an upward trend resumes, at present it seems highly unlikely that we will see a rise of 0.4C over the next two decades. Of course, the future has a way of humbling all forecasts. But perhaps the apocalypse is not as near at hand as some fear.