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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Serious question. Why is CO2 considered more important than water and sunlight when it comes to considering future temperature trends, is it a political or a scientific thing?
Para 3: These are smaller, but still to small to overlook
I suggest this should be ‘large’.
Love your work.
(From Oz)
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[REPLY: Thanks, fixed. – w.]
Brilliant and very, very succinct.
Thank you Willis.
zac – It is purely a political thing. CO2 has no significant effect on temperature as shown above.
Yet another 1st order post by Willis.
I’m sure there’ll be some 1st order and 2nd order comments and questions.
However 3rd order commentors should forget it as Willis doesn’t respond to those.
Too often folk here get over excited by possibly third-order effects – there was one last week on atmospheric CO2 concentrations not being perfectly mixed. But there is a difference between a third-order effect that varies rapidly and one that steadily increases. Ignoring the first type leaves a small amount of noise in any analysis, ignoring the second type results in an ever increasing amount of bias. Anthropogenic greenhouse gases belong to the second type.
Politically speaking, CO2 is seen as within mankind’s domain to control, depending on the doctrine being followed.
This is likely because it is about the only input into the system that we have any control over.
We can’t control the Solar input
We can’t control the water vapor feedback
We can only control the amount of G-H-G(s) we add to the system. (but not the total G-H-G input)
Hi Willis, I think you have the legend wrong in figure 1.
ok…so now is perhaps the moment to start engaging with the feedback analysis of folks such as Bart over at Climate audit. I hope so because the debates over there on this esoteric subject have been enthralling and also way over my head. But they worry the orthodoxy.
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.
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Every time I see this line of reasoning, it troubles me because it misses out a step. So here’s a serious question for you Willis….
What would the Earth’s surface temperature be if you removed the greenhouse gases, but retained all the nitrogen, oxygen and argon which comprises 99+% of its thickness? Surely that would have to be your GHG “starting point”.
What you are assuming, in effect, is that an Earth with an atmosphere comprised exclusively of nitrogen, oxygen and argon would have an identical surface temperature as an Earth with no atmosphere at all, and that doesn’t pass my “smell test”.
Hi again Willis, actually you dont have the legend wrong, its just that the colours ougth to be reversed of the +secornd order vs +secord+third order variables (IMO) to make your point better.
Because CO2 is a perfect Bogey man that can be measured, taxed, restricted etc. But almost all high tech & heavy industry produce copious amounts of so the potential revenue stream is enormous. Thus the perfect wealth redistribution from 1st world economies to qangos, ngos, & other rent seekers. Via the sticky hands of the high priests.
Every real or confected disaster can be blamed on CO2. No matter how much humanity does or does not produce.
Willis,
Do you mean this?
“Second-order are those that can change the system by 1% to 10%. These are smaller, but still to small to overlook.”
Is this a typo? should it not read:
Second-order are those that can change the system by 1% to 10%. These are smaller, but still to LARGE to overlook.
Regards…
“PPPS – What is a first-order climate variable? Clouds, clouds, clouds …”
And you talked only about radiation; CO2 doubling becomes even less important when heat transport via convection and conduction is taken into account.
CO2 is important because it can be painted as a pollutant and as a pollutant, it’s important for political purposes. Water and sunlight are obviously important to life and aren’t derived from a substance the EPA can deign to control. Early in the argument, water was not included in a listing of greenhouse gasses, partly, I believe, because it’s percentage would overwhelm that of CO2. And besides, we still cannot decide whether warming feedback from water is either plus or minus, much less the quantative impact on the MODELS.
Plain, simple, brilliant
Another point… and I am certain Lord Monckton would also agree that at < 1% the signal to noise ratios may swamp the ability to perceive response to 3rd order artifact.
This is what the Michael Manns and the rest of climate liars continually fail to point out as Lord Monckton has done so on a number of occasions.
What is the precision of the you ability to characterize the system, what is the uncertainty?
How can anyone assess a 0.01C change in climate? or a 0.1C change for that matter. particularly with all the system noise. It is BS on its face.
Zac, because CO2 can be regulated very easily. Water and Sunlight can’t. It’s a political thing.
Ok….First and foremost: The terms “first, second, and third order” are purely fictional constructs in the sense that you are using them. In real science these labels refer to the terms in a power series expansion (the linear, quadratic, and cubic terms). Your definitions are subjective and shed no new light on the underlying physics.
What you are essentially saying is that the effect of doubling CO2 is small when compared with the warming due to the sun and to the nominal effects of GHGs (minus the human contribution). *No one* would debate this point. On an absolute scale, the effects of a doubling of CO2 are small (even the IPCC predicts a change of a few degrees, compared with a baseline of somewhere around 88 degrees K…a few percent effect).
But your so-called “second-” or “third-order” effects make a HUGE difference to life on the surface of the earth. The difference between the worst ice ages and the hottest periods in our planet’s climate history is just a few percent change in heat content. By your definitions, these changes would qualify as being on the low end of “second order”. Tell that to the dinosaurs.
There are many cases in the world where small effects make a big difference. Drunkenness is due to a change in blood-alcohol that you would call “third-order”. A dangerous fever is only a few percent effect above nominal human body-temperature. In short, the effect of a small change in a physical parameter on a system can vary widely from case-to-case. You can’t simply say 1% is small…Small compared to what?
Which brings me to my question: What is your point in making these “first-“, “second-“, and “third-order” distinctions?
I think I’ve never heard so loud
The quiet message in a cloud.
=======================
Anything is possible says:
Every time I see this line of reasoning, it troubles me because it misses out a step. So here’s a serious question for you Willis….
What would the Earth’s surface temperature be if you removed the greenhouse gases, but retained all the nitrogen, oxygen and argon which comprises 99+% of its thickness? Surely that would have to be your GHG “starting point”.
What you are assuming, in effect, is that an Earth with an atmosphere comprised exclusively of nitrogen, oxygen and argon would have an identical surface temperature as an Earth with no atmosphere at all, and that doesn’t pass my “smell test”.
In fact, I believe the temperature would be warmer. How would the atmosphere get cooled without the radiating properties of GHGs? The surface heat would mostly radiate to space, but the small amount that was conducted to the air would continue to build over time.
It would be real interesting to hear the arguments of alarmists as to how this scenario would play out.
This is completely wrong. At the TOA – which is the *TOP* of the atmosphere, there is *no* downwelling LW radiation. There is only upwelling LW radiation of about the same order of magnitude as the absorbed solar. Think about it!
Along with millions of others, I’ve seen “Close Encounters of the third kind” and I know that the bigger the number the more important it is!
Argumentum ad Hollywood:
Climate changes because it is variable and can be summarised thus;
Solar is a first-order variable, Natural Greenhouse gases are second-order but (mainly) man-made CO2 is a THIRD order variable. Wow!
Extending Hynek’s scale to even higher order variables make it even worse than we first thought.
Methane eructations, cheap energy, oceanic acidification, ozone depletion and the insidious spread of Global capitalism just to mention a few may, perhaps, be even higher orders than fossil-fuelled atmospheric pollution.
We must ban everything that irritates Gaia and the sooner the better.
PS – is it sarc with a forward or a backward slash?
TOO small, not to small. Or possibly TOO large.