Would the Earth Really Be 33 C colder Without Greenhouse Gases?

Thirty-three degrees C is the iconic value of the impact of greenhouse gases on Earth's climate. It is an estimate, probably not a bad estimate, but not carved in stone. CO2 does have a radiative impact on climate. Without it the world would be cooler, with more the world will be warmer, if all things stayed the same.

In the coming Ice age series, I am exploring the impact of water on climate, which is a much stronger and much more complicated Greenhouse gas. Most believe the addition CO2 in the atmosphere is over whelming the climate, but that same "most" don't feel that CO2 will cause a thermal runaway. The question to me has always been how much will CO2 do?

To estimate the impact of CO2, scientists calculate that with approximately 240 Watts/meter^2 at the top of the atmosphere (TOA) that the Earth's temperature would be 255 degrees Kelvin (K). So with the current temperature being 288K, greenhouse gases cause 33 degree K or C of warming. Based on this 33 degrees, the impact of CO2 can be calculated and about 1.2 degrees would be the impact of double CO2.

BUT, "If an ideal thermally conductive blackbody was the same distance from the Sun as the Earth is, it would have a temperature of about 5.3 °C. However, since the Earth reflects about 30%[6] (or 28%[7]) of the incoming sunlight, the planet's effective temperature (the temperature of a blackbody that would emit the same amount of radiation) is about −18 or −19 °C,[8][9] about 33°C below the actual surface temperature of about 14 °C or 15 °C.[10] The mechanism that produces this difference between the actual surface temperature and the effective temperature is due to the atmosphere and is known as the greenhouse effect.", From Wikipedia.

That reflection of about 30% is due to water vapor in the form of clouds in a large part. Liquid water which makes up most of our planet reflects only about 8 percent. Ice and snow reflect some and land some as well. Not including the reflective part of water vapor, can de-emphasize its relative impact versus CO2.

If Earth were a true blackbody, the temperature without a greenhouse gas atmosphere would be 5.3 C or 279.3 K or 9 degrees, not 33. If I estimate that water vapor accounts for 50 percent of the reflectivity, then the Earth without a greenhouse would be about 14 degrees cooler. Using the estimated 1.2 for a doubling of CO2 with this temperature, 0.51 degrees would be the estimated impact of doubled CO2.

There is nothing new here. With all things behaving properly, CO2 doubling will cause 1.2 C of warming. The difference between 1.2 and 0.51 just illustrates the uncertainty in the impact of clouds to an increase in CO2. The uncertainty with respect to clouds is nothing new either.

As if by magic, the IPCC estimated warming average is 3 degrees and the estimate based on observations is about 1.2 to 1.6 degrees. As I have mentioned before, that 3 degrees is not A estimate, but the average of two estimates. The first estimate was 2 degrees. So I think we should give a cigar to Manabe, the scientist that seems to have the better estimate.

If we take a look at the second estimate by Arrhenius, 1.6 (2.3 with water vapor) we have another estimate that is pretty close. The only fly in the ointment is Dr. James Hansen with his high estimate of 4 degrees. Well, he is nearing retirement.

Continuing: A while back I read an old post on Climate Audit, where Dr. James Annan tried to explain the estimate for climate sensitivity to a doubling of CO2.

"I noticed on your blog that you had asked for any clear reference providing a direct calculation that climate sensitivity is 3C (for a doubling of CO2). The simple answer is that there is no direct calculation to accurately prove this, which is why it remains one of the most important open questions in climate science.

We can get part of the way with simple direct calculations, though. Starting with the Stefan-Boltzmann equation,

S (1-a)/4 = s T_e^4

where S is the solar constant (1370 Wm^-2), a the planetary albedo (0.3), s (sigma) the S-B constant (5.67×10^-8) and T_e the effective emitting temperature, we can calculate T_e = 255K (from which we also get the canonical estimate of the greenhouse effect as 33C at the surface).

The change in outgoing radiation as a function of temperature is the derivative of the RHS with respect to temperature, giving 4s.T_e^3 = 3.76 . This is the extra Wm^-2 emitted per degree of warming, so if you are prepared to accept that we understand purely radiative transfer pretty well and thus the conventional value of 3.7Wm^-2 per doubling of CO2, that conveniently means a doubling of CO2 will result in a 1C warming at equilibrium, *if everything else in the atmosphere stays exactly the same*."

Before I estimated that clouds contribute about half the albedo so using Annan's equation we have 1370(1-.15)/w or 291.1 = s.T_e. So T_e = (291.1/(5.67x10^-8))^.25 = 268.9 K which is 13.9K greater than the 255K no greenhouse estimated temperature of the Earth. Instead of 33 C we could be 19.1 degrees warmer with a greenhouse atmosphere than without. Using the same derivative, the change in OUTGOING radiation required to increase the temperature 1 degree would be 5.59 Watts/meter^2 if I didn't screw up. Without going back through the derivation of the radiative impact of a doubling of CO2, I will assume 3.7 W/m^2 is correct. Then the temperature change for a doubling of CO2 would be 3.7/5.59 = 0.66 degrees C or K.

This does not mean that 5.59 W/m^2 is the radiative change in forcing required to increase the temperature one degree, just that water vapor may effect the initial estimate of 33 degrees. If the Earth was at an average temperature of 268.9 we would be in a snowball Earth, there would probably be less water vapor and more surface ice or snow so the impact of solid water with traces of water vapor could be an albedo of greater than 0.3. If the albedo of the Earth was .4, then T_e would be 205.5 and 3.4W/m^2 would equate to 1 degree change in surface temperature.

Note: This post is more of just a reminder for me. The accuracy of the ground based net infrared radiative measurements are not sufficient to confidently measure the temperature change for a small, less than one percent change in radiation. That may be changing.