By Willis Eschenbach – R$e-Blogged From WUWT

Some days I learn a lot. Today was one of them. Let me start at the start. Back in 1987 in a paper entitled ‘*The Role of Earth Radiation Budget Studies in Climate and General Circulation Research“,* a prescient climate scientist yclept Veerabhadran Ramanathan pointed out that the poorly-named “greenhouse effect” can be measured as the amount of longwave energy radiated upwards at the surface minus the upwelling longwave radiation at the top of the atmosphere, viz:

The greenhouse effect.The estimates of the outgoing longwave radiation also lead to quantitative inferences about the atmospheric greenhouse effect. At a globally averaged temperature of 15°C the surface emits about 390 W m -2, while according to satellites, the long-wave radiation escaping to space is only 237 W m -2. Thus the absorption and emission of long-wave radiation by the intervening atmospheric gases and clouds cause a net reduction of about 150 W m -2 in the radiation emitted to space. This trapping effect of radiation, referred to as the greenhouse effect, plays a dominant role in governing the temperature of the planet.

And here is what Ramanathan was talking about:

*Figure 1. All-sky (both cloudy and clear) greenhouse effect. In climate science, “upwelling” means headed for space, “downwelling” means headed for the surface, “forcing” means a change in downwelling radiation, “LW” is thermal longwave radiation, and “SW” is solar shortwave radiation. *

The best modern information about this question comes from the CERES Energy Balanced and Filled (EBAF) dataset that I used to make Figure 1. It combines a number of satellite and other measurements into a single coherent group of individual datasets. Interestingly, Ramanathan’s estimate of the size of the greenhouse effect was *“about 150 W/m2”* and modern CERES data shows a number very close to that, 158 W/m2. Well done, that man!

Today, a chance comment got me thinking about top-of-atmosphere (TOA) downwelling longwave radiation versus what happens at the surface. A doubling of CO2 is supposed to lead to a 3.7 W/m2 increase in downwelling TOA longwave radiation … but what does that do to downwelling LW at the surface?

So what I did was to calculate on a monthly basis, the change in downwelling longwave radiation at the surface for each one W/m2 change in TOA greenhouse radiation. Figure 2 shows that result.

*Figure 2. Change in downwelling radiation at the surface for each 1 W/m2 change in downwelling TOA radiation.*

Now, this is curious. On average the change at the surface is a little less than half the TOA greenhouse effect change. So an increase of 3.7 W/m2 at the TOA from a doubling of CO2 becomes a 1.8 W/m2 increase at the surface. I would note that this value of 0.46 agrees in general with the published study of Feldman et al. in Nature magazine who found (from observations, not models) that surface forcing is 0.43 times the TOA forcing, quite near to the above figure.

Next, I got to wondering about something I’d never looked at—just how large an additional energy flux in watts per square metre of energy is needed to increase the surface temperature by 1°C. This is a simple calculation using the Stefan-Boltzmann equation, but I’d never done it for the entire globe. Figure 3 shows that result.

*Figure 3. Increase in ongoing downwelling energy flux needed to increase the surface temperature by 1°C with everything else unchanged.*

In Figure 3 you can see that as Stefan-Boltzmann says, it takes more energy to raise a hot surface by 1°C than to raise a cold surface by 1°C. And for the globe, the average is about 5.5 W/m2 per degree. That was a surprise to me, I didn’t expect it to be quite that large … but then as I said, I’d never calculated it.

So here’s the summary of today’s wanderings in CERESville.

• The long-accepted value for a doubling of CO2 gives a theoretical 3.7 W/m2 increase in downwelling TOA radiation. However, because of all of the factors that affect downwelling TOA radiation (changes in clouds, temperature, water vapor, eruptions, aerosols, etc.) and the fact that the log of CO2 is essentially a straight line, it’s not possible to determine that value experimentally. Here’s the problem:

*Figure 4. Ramanathan’s greenhouse radiation, along with the change in CO2 radiation over the period. The CO2 radiation change has been set to the average of the greenhouse radiation for easy comparison.*

Using that accepted 3.7 W/m2 figure for a doubling of CO2, that would give an increase in downwelling surface radiation of 1.8 W/m2.

• This doubling of CO2, in turn, would warm the surface by:

1.8 watts per square metre CO2 surface forcing / 5.5 watts per square metre per degree C ≈ 0.3°C …

By comparison, the IPCC says that a doubling of CO2 would increase the surface temperature by 1.5°C to 4.5°C. If we take the midrange value of 3°C, this would imply that there is some mysterious feedback increasing the CO2-caused surface temperature change by a factor of about ten …

The general view seems to be that this mysterious ten-fold increase is somehow the result of feedback from water vapor and clouds. The problem with that theory is that the CERES measurements I’ve used above include all of those feedbacks. That is to say, the GHE value includes the feedback effects of clouds and water vapor, and the surface downwelling radiation also includes those feedbacks.

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