Recent Climate Observations Compared to (IPCC) Projections

There’s been some hoopla in the blogosphere lately about comparing projections of temperature from the IPCC TAR (third assessment report), published in 2001, to observed temperature. The comparisons have been made to temperature data since 2001, on the basis of the claim that that’s when the projections start so that’s when the comparison should start. It appears such claims are in error.

In a previous post, I addressed some simple ways to account for the effect of autocorrelation on estimating trends (in particular, the probable errors in such estimates). I applied those methods to global temperature data from NASA GISS, from which it emerged that the data since 2001 do not contradict warming at a rate of 0.02 deg.C/yr (or 0.2 deg.C/decade), the warming rate claimed to be the projection of the IPCC TAR.

As a reader pointed out, the IPCC TAR projections actually don’t start in 2001. That’s when the TAR was published, but the individual studies on which they’re based were published before that, and of course the computations were done before publication. It turns out that the models used to make those projections begin their independent (from any observations) computations in 1990. A proper comparison of projections with subsequent observations appeared in Rahmstorf et al. (2007, Science, 316, 709, hereafter referred to as “R07″), which examines not only global temperature, but CO₂ concentration and sea level as well. The authors clearly state, “Although published in 2001, these model projections are essentially independent from the observed climate data since 1990.” The temperature data used for comparison in R07 are annual average land-ocean surface temperature from GISS and HadCRU, from 1990 through 2006.

Pointing out that comparison of IPCC projections with observed temperature has already been done in the peer-reviewed literature, has led to questions about the origin of this temperature graph in R07 (I’ve added labels to the x-axis to indicate which years are graphed):

Lucia, for instance, makes a query on her blog which is well described as pleading for an explanation. This leads to considerable speculation in reader comments. I too was curious about the origin of this graph, but I took a different approach than asking my blog readers. Forgive the twisted logic of my bizarre approach, but the strategy I adopted was: ask Stefan Rahmstorf.

His reply was to the point: the graphs were made using actual data which was provided by the IPCC authors. Imagine that. The grey range and scenarios in R07 are exactly those famous future scenarios shown in the IPCC TAR Summary for Policy Makers in Figure 5. Here’s an updated version of the graph which includes more current observed temperature data (click the graph for a larger, clearer view):

The solid blue and red lines are the trends from GISS and HadCRU data, the dashed lines are the IPCC projections included in the TAR. The graph speaks for itself rather well.

The models used for the TAR were developed in the mid-1990s. They’re not statistical models based on fitting observed data, they’re models based on the equations of thermodynamics and hydrodynamics. They weren’t “tuned” or updated using any observed climate data subsequent to 1990. Furthermore, it’s just irrational to claim (as some have suggested) that model developers would subsequently have used observations post-1990 to change their models; in the mid-90s, the period after 1990 would have been way too short to be meaningful for model tuning, just as the period starting in 2001 is today too short for us to draw any conclusions about trends (which we’ll see shortly). The period 1990-2006 used in R07 is just about long enough for a meaningful comparison — that’s why R07 published it at the time.

The projections shown in R07 don’t follow the strict 0.2 deg.C/decade rate of increase claimed to represent IPCC projections. So what are the actual projections from IPCC TAR? The TAR states in more than one place that we can expect “about” 0.2 deg.C/decade warming over the next few decades. Note the qualifier “about,” and that the quoted figure is accurate to only 1 significant digit. The logical conclusion is: between 0.15 and 0.25 deg.C/decade, in which case flatly stating 0.2 deg.C/decade as though that were an ironclad exact figure isn’t an honest representation of the IPCC projection. But we needn’t be satisfied with so imprecise a figure. Using the actual data from model runs used in IPCC TAR and referred to in R07, we have these estimates for trend rates from 1990 to 2010, and for that matter from 2000 to 2010:

Note especially the final entry, which gives the average of the included scenarios. For the two decades following 1990 the average rate is 0.0165 deg.C/yr (0.165/decade), for the decade following 2000 the average is 0.0174 deg.C/yr (0.174/decade). Hence if we want to compare observation to projection starting in 1990, we should use the more precise figure 0.0165 for IPCC projection, and if we follow others by starting at 2001, we should use 0.0174. Considering how close the error ranges come to the purported projection of 0.02/yr, it makes quite a difference.

And what is the observed trend rate since 1990? R07 display both GISS and HadCRU data, so I’ll look at both of them. I’ll estimate the trend from ordinary least squares (OLS), but I won’t compensate OLS using a simplified estimate of the impact of AR(1) autoregression, or Cochrane-Orcutt estimation, both of which assume an AR(1) model for the random fluctuations. For the AR(1) model, the autocorrelation at lag j is given by

.

However, as a reader pointed out in comments to the preceding post, the autocorrelations at lag greater than 1 depart from this pattern, tending to be greater than their AR(1) values. The result is that although the AR(1) model certainly gets us in the ballpark, giving a realistic estimate, it underestimates the error range, which is larger than indicated by the AR(1) model. Since the final result of that analysis is rather a “close call,” it turns out that the AR(1) model, while sufficient for many purposes, won’t do for this job; it’s necessary to apply more realistic estimates of the autocorrelations. I’ll also use the exact formula for the impact of autocorrelation on the probable error in an estimated trend rate from OLS (see Lee & Lund 2004, Biometrika, 91, 240).

Results? For GISS data the trend estimate since 1990 is deg.C/yr, for HadCRU it’s deg.C/yr. The midpoint value from both data sets is greater than the TAR projection, but both error ranges include the TAR value of . Hence a proper comparison of observed data to IPCC TAR projected temperature (start in 1990 when the projections start, use a realistic autocorrelation model, and an exact formulation of its impact) confirms, rather than falsifies, the projection. If anything, it’s “more likely than not” that actual warming has been greater that the TAR projection.

I’m sure many readers are interested in results using only post-2001 observations. GISS data indicate deg.C/yr while HadCRU indicate deg.C/yr. Note that the error range for HadCRU data is just about 3 times as large as the estimated value itself, and that for GISS data is nearly 14 times as great as the value. Note also that both data sets give error ranges which include the TAR projection of deg.C/yr. In fact, both error ranges include the purported TAR projection of deg.C/yr. Here are the results presented graphically:

Finally, it must also be mentioned that even these error ranges, based on exact methodology and a realistic autocorrelation model, are still too small because they don’t include the uncertainty in estimating the autocorrelation parameters. So the error bars really should stretch even further than they do in this graph, which serves to emphasize the failure of observed data to falsify the IPCC TAR projection. It’s more work than I care to undertake to incorporate the impact of this final uncertainty into the numbers, but in this case it’s not necessary because we know that the error bars will get bigger — and they’re already big enough to rule out any falsification of IPCC TAR projection.

It also serves to emphasize the tremendous uncertainty is trend estimates from a mere 7 years of data with a signal-to-noise ratio as small as that we see in global temperature. Over a longer time span, the signal can emerge from the noise with sufficient precision to make meaningful comparison of projection to observation. But over such a short time span the long-term trend is swamped by the effect of the noise, so we effectively end up comparing random fluctuation in observed data to long-term trend from projections. That invites faulty conclusions — and in this case, unless one applies considerable rigor to the analysis it actually spawns faulty conclusions.

How, then, do some conclude that temperature data falsify IPCC TAR projections?

• Use the wrong start date, so that you
• Compare short-term fluctuation to long-term trend
• Make the rate projected by IPCC too high.
• Make the error range, even when compensated for autocorrelation, too small

I’ll close by quoting an important summary paragraph from R07:

Overall, these observational data underscore the concems about global climate change. Previous projections, as summarized by IPCC, have not exaggerated but may in some respects even have underestimated the change, in particular for sea level.

I couldn’t have said it better myself.