Mann and Emanuel 2006 presents an interesting alliance of Emanuel with Michael "I am not a statistician" Mann to carry out calculations purportedly "using a formal statistical analysis to separate the estimated influences of anthropogenic climate change from possible natural cyclical influences". It will come as little surprise to readers of this blog that there appears to some hair on this particular article. Here’s something that I noticed in a first read.
Here is their Figure 1a.
T(t) is the "net SST variability T(t) is represented using the tropical Atlantic HadISST2 observational SST dataset [Rayner et al., 2003]. The SST data from 1870 to 2004 are averaged over the season most relevant to tropical cyclone formation (August-September-October, or ASO), and over the main development region (MDR) of 6⸭18⹎, 20⸭60. "
"G(t) represents global mean SST over the same ASO seasonal window and time interval. "
R(t) are the residuals.
Intuitively one expects the variability in the tropics to be less than in the extratropics – this is certainly what one observes in their Figure 1a, which shows that tropical Atlantic regional SST has gone up less than global SST. Since global SST is a weighted average of tropical SST and extratropical SST (and Christy’s satellite data show a tight coupling of all 6 tropical SST basins), it is hardly surprising that there is a substantial correlation between global SST and tropical Atlantic SST. Mann and Emanuel report that a regression of tropical Atlantic T(t) on global SST G(t) has a coefficient yields the following:
T[t) = 0.93 G(t) + R(t)
and that this relationship "resolves 70 percent of the decadal variance and roughly two thirds of the net warming in T(t)". Mann-speak is always a bit tricky, but "resolved variance" here is probably Mann-speak for r2. The coefficient of 0.93 implies that the tropical Atlantic SST goes up a little bit less than global SST - a result that is intuitively unsurprising.
Mann and Emanuel 2006 Figure 1a.
Now Mann and Emanuel observe that the residuals from this relationship have significant autocorrelation. Again this is unsurprising. If you did the same exercise using VZ data, you would get a similar result. The regression here is not a regression of effect against cause. To the extent that both series are both forced in some fashion, autocorrelated residuals are what you'd expect. However, in this case, Mann argues that he can get rid of the autocorrelation by introducing aerosol forcing.
To represent potential enhancement of ASO tropospheric aerosol cooling over the MDR, the estimated Northern Hemisphere anthropogenic tropospheric aerosol forcing series available through 1999 [Crowley, 2000] was included as an additional predictor S(t):
Regression of tropical Atlantic SST against both global SST and Crowley aerosols yielded an equation:
T(t) = 1.7 * G(t) + 0.79 * S(t) +R(t)
The coefficient is now greater than 1 – which they report as "implying a projection of global warming onto the MDR (Figure 1a) that is significantly greater than the global mean". A "projection of global warming" – has to be Mann-speak. The new model is said to "resolve 85.5 percent of the decadal variance" – up from 70% and the autocorrelated residuals are gone.
But think about what this says: Mann and Emanuel conclude that the true temperature increase in tropical Atlantic SSTs should
actually be significantly greater than the increase in global SST and that the observed values have been damped by aerosol forcing. Actually not just aerosol forcing but "enhanced aerosol forcing". They say:
Model estimates [Hansen et al., 2005] indicate that this forcing is especially pronounced over the MDR during the crucial ASO season wherein the net estimated cooling is 1.12⹃, while the global mean ASO cooling is 0.71⹃, indicating a regional enhancement of –0.41⹃ for the MDR.
Now let’s think about the comments of the Georgia Tech students about Climate Audit – "rudimentary statistical analysis" with no attempt at physical understanding. Hey, I agree that most of the statistical analysis done here is rudimentary – had originating paleoclimate authors adequately performed such analysis, we wouldn’t have so many amusing exercises here. I submit that this toy regression in Mann and Emanuel 2006 qualifies as "rudimentary" statistics. I’m sure that Jean S or UC’s hair will curl when they look at this. It’s actually worse that rudimentary statistics since, as so often in these articles, it gives a false assurance that a "formal" statistical analysis has been done.
As to physical interpretation – I don’t purport to be qualified to make physical interpretations of these results and generally avoid doing so. However, I’m going to make an exception here. I think that it’s quite possible that increases in regional tropical Atlantic SST are less than global SST because the region is in the tropics and not because of aerosol forcing. Thus the introduction of aerosol forcing to explain the lower rate of temperature increase in this sector is simply irrelevant and the entire statistical analysis of Mann and Emanuel 2006 to this point is a crock. Over to you, Georgia Tech.
Update: Here is a graphic showing standard deviations by gridcell for the von Storch-Zorita Echo-G model (the graphic is my collation from original output.) You will see that the standard deviation in Mann’s MDR (Main Development Region) is rather low. Thus any conclusion from a "formal statistical" study purporting to show that variability in this region is especially great – and damped by sulphate emissions is rather suspect.