A reader wrote me a while back and asked if I could explain how I thought the sun could be a major driver of climate when temperature and solar metrics appear to have “diverged” as in the following two charts:

In both charts, red is the solar metric (TSI in the first chart, sunspot number in the second).  The other line, either blue or green, is a global temperature metric.  In both cases, we see a sort of step change in solar output, with the first half of the century at one plateau and the second half on a higher plateau.  This chart of sunspot numbers may better illustrate this:

I had three answers for the reader:

1. In any sufficiently chaotic and complicated system, no one variable is going to consistently regress perfectly with another variable.  CO2 does not line up with temperature any better.
2. There are non-solar factors at work.  As I have said on any number of occasions, I agree that the greenhouse effect of CO2 exists and will add about 1C for each doubling of CO2.  What I disagree with is the proposition that the Earth’s climate is dominated by positive feedback that multiplies this temperature increase 3-5 or more times.  The PDO cycle is another example of a process that affects global temperatures.
3. One should not necessarily expect a linear temperature increase to be driven by a linear increase in the sun’s output.   I will illustrate this with a simplistic example, and then invite further comment.   I believe the following is a correct illustration of one heat source -> temperature phenomenon.  If so, wouldn’t we expect something similar with step-change increases in the sun’s output, and doesn’t this chart look a lot like the charts with which I began the post?