The Multiplier

Guest Post by Willis Eschenbach

This is a follow-on from my previous post entitled Greenhouse Equilibrium. If you haven’t read it, you might want to, as it introduces many of the concepts I’ll discuss in this post.

I got to thinking about the oft-repeated claim that a doubling of CO2 increases top-of-atmosphere (TOA) radiative forcing by 3.7 watts per square meter (W/m2) … and that in turn, the additional 3.7 W/m2 of TOA forcing causes a ~3° warming of the temperature. In other words, they say that ~ 1.2 W/m2 of additional radiative forcing causes one degree of warming.

What set me to thinking was the Stefan-Boltzmann equation. It relates temperature to the amount of thermal radiation emitted. It turns out that the radiation varies as the fourth power of the temperature, T4. What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree.

So how much extra energy does it take to raise the temperature of the earth (which is at about 15°C) by one degree C?

Per the S-B equation, it requires an additional ~ 5.2 W/m2 absorbed by the surface to raise the temperature of the earth by one degree C. But as discussed in my previous post, only ~ 80% of the surface absorbed energy is expressed as temperature. This means that to warm the earth by 1°C requires 5.2 / .8 = 6.5 W/m2 absorbed energy at the surface per 1° warming.

Now, recall that their claim is that 1.2 W/m2 of TOA forcing causes one degree of warming … which in turn requires 6.5 W/m2 at the surface.

Presumably, their claim is that various feedbacks amplify the change in radiative forcing. But turning 1.2 W/m2 at the TOA into 6.5 W/m2 at the surface? That’s a neat trick. I’m not seeing that happening at all.

Now, let me back up to a graphic from my previous post, along with the caption.

Figure 1. Greenhouse multiplier. The multiplier is calculated as upwelling longwave surface radiation divided by incoming solar radiation (after albedo reflections). A multiplier of 2 would mean that the surface would be radiating two W/m2 of energy for each one W/m2 of solar energy actually entering the system. This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.

Now, over the period of the CERES record, greenhouse gas forcing increased by about 0.7 W/m2.

Theoretically, this would be increased by feedback in the ratio 6.5/1.2 to the value at the surface. in this case, it converts the 0.7 TOA W/m2 to 3.8 W/m2 at the surface.

This allows us to see what the change in the greenhouse efficiency shown in Figure 1 should look like if the absorbed surface radiation increased by 3.8 W/m2. Figure 2 is the same as Figure 1, but including the expected change from the additional 3.8 W/m2 absorbed.

Figure 2. As in Figure 1, but including the trend in the multiplier that would be expected from the increase in TOA greenhouse gas forcing.

Hmmm … several points.

First, I simply don’t believe their numbers. Their claim is that a doubling of CO2 gives an additional 3.7 W/m2 at the TOA, and it results in 3°C of surface warming. That’s about 1.2 W/m2 per degree of warming.

But we know that it takes 6.5 W/m2 to raise the earth’s temperature by one degree …

I’m not seeing any physical processes by which the 1.2 W/m2 could somehow be increased to 6.5 W/m2.

Second, even if the warming were only 1°C per doubling of CO2, we still would be able to see it in the graphic. Figure 3 shows that result.

Figure 3. As in Figure 2, but with the CO2 forcing figured at one degree of warming per doubling of CO2, which is one degree per 3.7 W/m2.

But we don’t see that lesser trend in the multiplier either. Instead, the multiplier has a slight but not significant decrease, and it’s nothing like what we’d see if increasing GHGs actually were increasing the surface temperature.

However, at least that lesser trend is a bit believable since the increase from the TOA to the surface is from 3.7 W/m2 to 6.5 W/m2. Still a big reach, though … it would require strong positive feedback, and I haven’t seen that anywhere.

Now, the important thing to remember about this measurement of the efficiency of the system is that it is end-to-end. By that I mean we start with the energy entering the system (solar minus reflections) and we end up with surface temperature.

In between the sun and the surface, we have a range of emergent climate phenomen. Inter alia they include variable cloud shortwave and longwave radiation effects, changes in surface albedo and TOA albedo, massive variable advection of energy from the tropics to the poles, changes in aerosols, the La Nina/El Nino pump, variations in timing and strength of thunderstorms, variations in sensible/latent heat loss from the surface … and changes in greenhouse gases.

And what appears to be happening is that, as I’ve said for years, the changes in greenhouse gases are being counteracted by some combination of the other emergent climate variables included above.

What a marvelously complex world we inhabit!

w.

PS—As with the previous post, please stick to the topic. Claims that the greenhouse effect isn’t real or that downwelling radiation doesn’t exist have no place in the comments on this post, and they will be frowned upon from a great height. You are welcome to discuss those issues … just not on this particular post.

My Usual—I can defend my own words. I cannot defend your (mis)interpretation of my words. Please QUOTE THE EXACT WORDS you are discussing in your comments, so we can all understand who and what you are replying to.

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September 3, 2022 at 01:00PM

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