Per request, I’ve tested the model of global temperature with el Niño, volcanic aerosols, and solar variations. It was suggested using a 15-year time span as a “hold-out” period for validation, but I decided to use longer hold-out period. Hence the model was fit with data from 1951 through 1989, and the period from 1990 to the present to investigate whether or not the model could match data with which it was not trained. I also decided to do this test with the NASA GISS data set.
The results are rather impressive. Here’s how the original data compares to the model fit for the “training period” from 1951 through 1989:
When we use the model it generates to compute the temperature post-1990, and compare that to the observed data, the fit is excellent:
What might be most impressive is that the model for post-1990 uses only the effect of el Niño, volcanic aerosols, solar variations, and a purely linear trend (to estimate the greenhouse-gas impact), and by doing so it faithfully reproduces both much of the fluctuation due to short-term factors and the continuing trend since 1990.
We can also compare the observed data to the model with their linear trends removed, to see how the model fits the short-term effects:
Of course the fit isn’t perfect, but with a correlation coefficient of 0.67 (and remember, that’s after the linear trends are removed) it’s pretty darn good. It’s also reassuring that the model coefficients are well within the uncertainty range of the coefficients fitting the entire time span (as in the previous post).
The model compares to the data over the entire time span 1951-to-present thus:
Impressive indeed, remembering that the model fit is computed using only the data prior to 1990.
All of which confirms that the model is doing a good job matching the effect of el Niño, volcanic aerosols, and solar variation. This means it gives us a realistic appraisal of what’s been happening to global temperature besides those exogenous factors. When we remove them, we get “adjusted” data which better isolates the global warming signal. It looks like this:
Annual averages of same are here (the vertical red line marks the transition between pre-1990 data used to fit the model and post-1990 used for validation):
The essence is the same as emerged from fitting the model to the larger data set: that there has been a steady warming of the planet since about 1976, one which has not shown a “pause” or “hiatus” or “slowdown” — like the eveready bunny, it keeps going, and going, and going …
Which puts the lie to such “pause” claims. But they were already dead anyway; even without removing the influence of exogenous factors, there was no real evidence for a “pause.”
Which leaves us with two inescapable conclusions. First, man-made global warming continues apace. Second, deniers will continue to deny, despite proof their claims are false.
A good bit of work went into this … those who want to support this effort are encouraged to follow the link below and make a donation.
This blog is made possible by readers like you; join others by donating at Peaseblossom’s Closet.
Open Mind 
Always happy to donate…
For those who have not noticed, the AVISO Sea Level website has added new features that allow for making 5yr and 10yr graphs of GMSL.
What do you use for the “Solar”, “Volcanic”, and “ENSO” exogenous variables? TSI from the data page seems like a good guess for Solar, but what about the others?
[Response: For volcanic I use the aerosol optical depth from Sato (available from NASA GISS), for ENSO I use the MEI (multivariate el Nino index).]
That is indeed an impressive match. Foster and Rahmstorf 2017?
I’d vote for them.
While the MEI data only runs from 1950, there is an extended MEI data set that the MEI folk are happy to call being on a “sister website” and to provide the link. And that extended MEI goes back to 1871.
The Sato aerosol data goes back to 1850 and the TSI reconstructions even further.
Now the further back in time we go, I would expect the fit between a ENSO&Sol&Vol model of global temperature and the instrument data to be showing some significant differences. But we do have Gistemp’s LOTI back to 1880. And, as I have argued on another thread recently, those differences would narrow the scope for cirve-fitting denialists to play wobblology with to likes of LOTI. And while there is going to be a lot more uncertainty with all this data pre-1950, an ENSO&Sol,&Vol model for 1880-1950 should also give a useful indication of how much work is required for the attribution of ΔT over the period.
So any chance of a 1880-1950 run of the ENSO&Sol&Vol model?
Remarkably good post-1990 fit.
To me the best way to end the ‘pause’ red herring would be a annual thirty year average graph..any chance you could whip one up?
THANK YOU Tamino. Now to bookmark this post and throw it all mathturbators that come along. Evans, Scafetta et al want to try this with their “models” do you suppose? That is a really remarkably good fit.
And, yes, happy to donate too.
As an economist, I am so, so envious
Would it be useful to apply the model to MSU and AMSU separately and then compare the two? Or the various channels separately? Different methods of finding breakpoints and/or sensor drift.
I’m a bit unhappy about the “solar” bit. As every good denialist knows, climate scientists always ignore the sun :-)
Have you run this using a constant CO2 level, as (and I apologise if this has been done elsewhere on this site) I’d be interested to see how things would look if we’d retained the CO2 level of 1960 (arbitrary I know but…)
That would be the delinearised graph in the article. CO2 is represented as simple linear trend. If you put that on actual, the fit would be terrible.
I did this to, but for the entire GISTemp LOTI interval from 1880 to 2013. I called the model CSALT
http://contextEarth.com/2015/01/30/csalt-re-analysis/
I haven’t updated the mapping for awhile but the latest ENSO excursion appears to fit like a glove.
And of course the crew over at Judith Curry’s Cimate Etc blog has their hair on fire over your model because they are probably realizing that their “Uncertainty Monster” is being tamed.