Warming Actors

This post was first written by TreizeVents (13 Winds), a French poster, on this Infoclimat forum post. With his agreement, I (Fred) just translated it roughly and posted it here.
(please feel free to suggest any translation enhancement)

This simple statistics exercise doesn't mean to be important, but rather is an exercise to evaluate how the main natural actors of the climate (Sun activity, AMO, El Nino / ENSO) act on the global temperatures evolution since 1950.

Our three basic hypotheses are as follow:
- let's set that ENSO's impact is 0,1°C per unit, with a three-months delay (we'll use the Multivariate ENSO Index, MEI) ;
- AMO also has a 0,1°C / unit influence;
- according to scientific studies, Sun's influence varies by 0,2°C between solar minimum and solar maximum. So here we'll say that a Sun with 80 spots has a 0°C impact, while 0 spots remove 0,1°C and 160 spots add 0,1°C.

When we averaging these data on a moving year, here are their respective impacts:

Let's add these actors alltogether:

This new curve shows quick and strong variations, but doesn't seem to show any warming. With our hypothesis above, these three factors can't be accountable for a global warming.

Let's now "add a (linear) warming" of +0,11°C per decade to our curve (in red below), and compare to the NOAA's real temperatures curve (in blue):

Not too bad, the correlation factor is 0.89 - but now we can simulate an exponential warming (in green):

The correlation factor is now 0.95 - and we just got this red curve by adding an exponential factor to the combined action of the three main natural factors !

These curves differ in only three points : in 1958-1964 they behave an opposite way, from 1979 to 1984 real temperatures are slightly under the simulated ones, and from 1992 to 1995 real temps are markedly under the simulation (the reason probably being the Pinatubo effect; we have no obvious explanation for the two other differences).

The following graph aims to show how each element contributes, year per year, to the global anomalies:

Here we can see that the relative global temperature stall since the 1998 El Niño peak is in no way incompatible with a continuing warming - this continuation being exponential, rather than linear. If only ENSO and solar activity were at play, we'd have a real decline since 2002 without this ongoing warming.

We also can try other simulations. In the first one (blue), I replaced the El Niño (in Pacific since mid-2009) with a moderate la Niña; in the second one (red), I pushed the solar cycle by 9 years to guestimate how a current solar maxima would impact the global anomalies (the minimum would have occured in beginning 2000, short after 1998 maximum):

El Niño's impact on the last months' anomalies is moderate - its removal doesn't lead to a strong decline. A moderate Niña would have kept the global temperatures in the 2008 range, without strong decline. Regarding the Sun, its influence is higher : if we had a maximal activity now, global anomalies would be the highest ever measured, ahead 1998 (even if NASA and other already count last months as the hottest ever recorded).

Remarks and comments are welcome...