In the first two parts of this series, I demonstrated how multiple regression methods that assume an underlying linear "signal" are unable to properly reconstruct a pause in surface temperature warming when attempting to remove the volcanic, solar, and ENSO components from my simple energy balance model. That is, for an approach similar to Foster and Rahmstorf (2011), the method will tend to underestimate the warming influence of volcanic recovery and overestimate the cooling influence of solar activity over recent decades to compensate for the pause. With the improvement Kevin C mentioned, there is some ability to detect a longer tail for the volcanic recovery (indeed, it does so nearly perfectly if the underlying signal is actually linear), and the solar influence is no longer over-estimated. Unfortunately, it still underestimates the recent warming influence from volcanic recovery in my energy balance model in the "flattening" scenario 2.
I had thus wondered whether this long-tailed volcanic recovery was merely an artifact of my simple model, or indeed may have contributed substantial warming from 1996 (when the Pinatubo stratospheric aerosols were virtually gone) onward. There are not that many models that have contributed volcanic-only experiments to CMIP5 (I showed 1 in my part 1, and Gavin showed an ensemble for GISS-EH at RealClimate in response to this discussion). However, there is plenty of data from the natural-forcing only historical experiment, which, by averaging several of the runs for a particular model, can give us a good idea of the forced volcanic + solar influence in those GCMS.
In the figure below, I have shown the mean of the historicalNat runs for 7 individual CMIP models that have 4 or more of these experiment runs. As such, this should give an idea of the forced response in these models without much additional unforced variation. I have also plotted on the same chart the volcanic + solar influence as diagnosed by the FR11 and Kevin C methods when using the HadCRUTv4 dataset.
As can be seen, the volcanic response in all of these AOGCMs is far larger and has a longer tail than diagnosed by the multiple regression methods. Now, certainly it is possible that these volcanic responses in AOGCMs are too large, as there is evidence to suggest that the CMIP5 runs don’t properly simulate this response. However, the fact that the FR method shows far lower sensitivity to volcanoes while simultaneously showing a much larger sensitivity to solar influences than both GCMs and simple energy balance models would indicate would seem to suggest that it may be compensation for the recent flattening. Indeed, it is quite difficult to conceive of a realistic, physics-based model that does not indicate a substantial volcanic-recovery-induced warming contribution after 1996, despite it being virtually non-existent in the FR11 diagnosis (the increase around 1998 in the FR line is actually solar-induced).
The table below highlights the warming contribution of the model ensembles (in K/Century, so be careful!) from the indicated start year through 2012 (I have an * by CCSM4 because the runs end in 2005).
For comparison, the HadCRUTv4 trends over these same periods are
1979-2012: 1.55 K/Century
1996-2012: 0.91 K/Century
2000-2012: 0.38 K/Century
If one believes that this range of GCMs represent the true forced response of solar+volcanic, it would suggest that these natural forcings were responsible for 15% to 51% of the warming trend from 1979-2012. If I had to bet, I would probably put it on the lower end, as the AOGCMs appear to be a bit too sensitive to these radiative perturbations and suggest too much ocean heat uptake, which probably creates longer tails on the early volcanic eruptions than is warranted. However, I do think the contribution is probably greater than 0%, which is about what the FR method puts it at.
From 1996 to present, and 2000 to present, however, are where I think we see the larger misdiagnosis. Whereas all models (including my simple energy balance model) indicate that the solar+volcanic influence from 1996 to present was positive, comparable in amount (median: 0.81 K/century, mean: 1.05 K/century) to the actual HadCRUT trend, both regression methods either suggest a slight negative or nor-zero influence from these components. And from 2000 to present, while the models are more split (with only 6 of the 7 suggesting a positive influence, and the range varying more widely), it is difficult to believe that the actual influence of solar+volcanic is as strongly negative as the FR method indicates. This is why it looks to me like the multiple regression method underplays the influence of volcanic recovery in order to partly compensate for a recent pause.
Essentially, we are left wondering if the GCMs are too sensitive to volcanic eruptions, and/or if the multiple regression method is underestimating their influence to compensate for a recent pause. Again, if I had to bet, it would probably be in the middle – the GCM response is generally a bit too large, but the response is not nearly as small (or short) as the FR11 method would indicate.