Guest Post by Willis Eschenbach

When I’m analyzing a system, I divide the variables into three categories—first-, second-, and third-order variables.

First-order variables are those variables that can change the system by more than 10%. Obviously, these must be included in any analysis of the system.

Second-order are those that can change the system by 1% to 10%. These are smaller, but still too large to overlook.

Finally, third-order variables are those than can change the system by less than 1%. These are small enough that they can be ignored in all but the most detailed analyses. To give you an idea of why we can neglect the third order variables, here’s how those three forcings would look on a graph, for an imaginary signal of say 500 W/m2.

Figure 1. Showing the relative sizes of first-, second-, and third-order variables.

Note that the series containing the third-order variable is almost invisibly different from the series where the third-order variable is left out, which is why third-order variables can be safely ignored except when you need extreme precision. So … what does this have to do with climate science?

Let’s do the same kind of analysis on the forcings of the climate system. At the TOA, the “top of atmosphere”, there is downwelling radiation from two sources: the sun, and the longwave “greenhouse” radiation from clouds and “greenhouse” gases (GHGs). The globally-averaged amount of downwelling solar radiation at the earth’s TOA (which is total incoming solar radiation less a small amount absorbed in the stratosphere) is on the order of 330 watts per square metre (W/m2). The amount of downwelling longwave radiation at the TOA, on the other hand, is about 150 W/m2.

Finally, if CO2 doubles it is supposed to change the downwelling radiation at the TOA by 3.7 W/m2 … here’s how that works out:

Figure 2. Sources of downwelling radiation at the top of the atmosphere (TOA), defined as the tropopause by the IPCC.

By that measure, CO2 doubling is clearly a third order forcing, one that we could safely ignore while we figure out what actually makes the climate run.

Or we could look at it another way. How much of the earth’s temperature is due to the sun, and how much is due to the earth’s atmosphere?

If there were no atmosphere and the earth had its current albedo (about 30%), the surface temperature would be about 33°C cooler than it currently is (see here for the calculations). Obviously, downwelling longwave radiation from the greenhouse gases is responsible for some of that warming, with DLR from clouds responsible for the rest. Cloud DLR globally averages about 30 W/m2 (see here for a discussion). So the 150 W/m2 forcing from the GHGs is responsible for on the order of 80% of the 33° temperature rise, or about 25°C.

But if 150 W/m2 of GHG forcing only warms the surface by 25°C, then the so-called “climate sensitivity” is only about 25°C warming for 150 W/m2 of TOA forcing, or a maximum about six tenths of a degree per doubling of CO2, or about 0.2% of the earth’s temperature … again, it is a third order forcing.

Now, if someone wants to claim that a change in the forcings of less than 1% is going to cause catastrophes, I have to ask … why hasn’t it done so in the past? Surely no-one thinks that the forcings have been stable to within 1% in the past hundred years … so where are the catastrophes?

Finally, most of the measurements that we can make of the climate system are imprecise, with uncertainties of up to 10% being common. Given that … how successful are we likely to be at this point in history in looking for a third-order signal that is less than 1% of the total?

w.

PS – In any natural heat engine of this type, which is running as fast as the circumstances permit, losses rise faster than the temperature. So in fact, the analyses above underestimate how small the CO2 effect really is. This is because at equilibrium, losses eat up much of any increase in forcing. So the effect of the CO2 at general climate equilibrium is less than the effect it would have at colder planetary temperatures. In other words, climate sensitivity is an inverse function of temperature.

PPS – Please don’t point out that my numbers are approximations. I know that, and they may be off a bit … but they’re not off enough to turn CO2 into a second-order forcing, much less a first-order forcing.

PPPS – What is a first-order climate variable? Clouds, clouds, clouds …

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