How much radiative forcing can you get from the sun?

Question

Lots of people keep saying how much more important the sun is in global warming than greenhouse gases, so prove it. Let's say solar irradiance goes up by 2 W/m^2 (a very very big change), start with the solar "constant" (about 1370 W/m^2) and given an albedo for Earth of 0.30, show how much radiative forcing you can get from that change in the sun. Now compare it to calculated anthropogenic forcings and see which is larger.

Answer 1

Wow!  You assume that the Earth's magnetic field has remained constant in the last 100 years.  That is amazing!

Answer 2

I'm sure that would make an interesting word problem in the next edition of a Physics textbook, but it has no real world application.  

Several proxy studies have concluded the Earth warms when solar activity increases and cools when solar activity decreases.  We're at a solar maximum stronger than any seen in over a thousand years.  We're experiencing record temps, too.  Cause and effect?  Maybe not...but it certainly eliminates CO2 as the leading cause.  

With such a limited understanding of such a complex system, Occam's Razor must apply.

Answer 3

Averaged over the surface of the planet, a better number for the "solar constant" is around 340 W/m^2.  So a 2 W/m^2 change in the TOA solar flux corresponds to a change in the average surface energy flux of around 0.5 W/m^2.  As you note, that is a huge change in the solar output, which varies by about 1 W/m^2 over the total solar cycle.  

Aside from the fact that there isn't any way to get enough increase in radiative forcing from the sun to account for the observed increase in global mean temperature, the time constants and phasing of the warming is all wrong.  In order to get the observed warming to be solar-forced, you have to invoke bizarre physics that suggests everything we know about ocean-atmosphere coupling is wrong.  That is not likely to happen, in my opinion.  

Occam's Razor would lead you to conclude the simpler theory fitting all the known facts is to be preferred over a more complicated theory.  Invoking solar forcing requires very complicated physics compared to the theory that radiative forcing from CO2 is responsible.

Answer 4

Let A be the albedo and R be the radius of the earth and I be the solar irradiance.  The surface area of a sphere is 4piR^2 whereas the area illuminated by the sun is piR^2.  A fraction A is reflected and 1-A is absorbed.  Therefore the effective average solar irradiance is

Ie = I*(1-A)/4 = .175*I.  

A change of 2W/m^2 in the solar constant produces a forcing of 0.35 W/m^2.  By comparison the IPCC estimate for anthropogenic forcing is 1.6 W/m^2.  For changes in TSI to match the magnitude of anthropogenic changes, the TSI would have to change by 9.1 W/m^2.  There is no evidence for such a large change in TSI in the NOAA data sets.  The TSI for all measurements fluctuates within a roughly 4 W/m^2 wide band.  Whether the long term average TSI is changing or not, the magnitude of the TSI forcing is clearly much less than the magnitude of the anthropogenic forcing.