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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Septic,
AGW probably has a small effect, which can be disregarded for all practical purposes. But it certainly doesn’t control temperature, as we can clearly see here.
And if you study this chart for even one minute, you will be hard pressed to find any problem with the current rise in this essential trace gas. The biosphere is starved of it. More is better. And there is no evidence that the rise in CO2 has caused any global harm.
Go back to realclimate and tell them that. I would do it myself, but they have never allowed any of my posts out of moderation. Censoring bastards.
Willis says,
No…What you don’t understand is that in order to calculate the expression with feedbacks, you have to include the feedbacks AS FEEDBACKS. In using the 150 W/m^2 value, you are including the effect of water vapor as a forcing, i.e., it is part of that 150 W/m^2. So, no, you are not calculating the value of the climate sensitivity with the feedbacks.
You always have to be careful about these sorts of things. As Hansen has noted, when people calculate the temperature change between the LGM and now, they call the change in albedo due to the changes in ice a forcing. This means that they may be underestimating what will happen in the current situation where any changes in ice are considered as a feedback, not a forcing. [In fact, Hansen argued that this about doubles the climate sensitivity from ~3 to 6 C per CO2 doubling, although others have argued that this is probably not the case for temperature increases from our current largely deglaciated state and I think Hansen has, in his latest paper, backed off on this somewhat.]
If you aren’t consistent in what you consider to be a forcing and what you consider to be a feedback, you can arrive at all sorts of incorrect conclusions.
It’s difficult to discern what are first and second order variables where there are so very many third order variables, Unless you simply assume that all of the third order variables average out. The idea may work on paper, but I expect not in the real world.
Consider for example that economics may drive farmers to switch crops each year (and to different crops in different regions) with resultant changes in albedo, transpiration, cloud formation, and so on. Just one example of many.
Isn’t CO2 about the same everywhere?
Then how can it effect some places differently than others?
To clarify, if third order variables make up 90% (an extreme example), then there are no first order variables.
Willis, I understand your basic point, but “first, second, and third order effect” has a technical meaning, and that ain’t it.
Could one refer to the likes of Mann, Briffa, Hansen etc as scientists of the ‘third order’ ?
Joel Shore says:
“…Hansen argued that this about doubles the climate sensitivity from ~3 to 6 C per CO2 doubling…”
Hansen’s alarmism has been discredited by the planet itself, so which one are you gonna believe? And what do you expect from a self-serving scaremonger who pockets loot he is not entitled to receive as a government employee? The more fearmongering Hansen emits, the more payola he pockets. It’s not rocket science.
Thank you Willis for your posting, I agree with anyone who says you should collect all your postings here on WUWT , correlate them into one, – or more – books for publication and you will no doubt have best seller(s).
However, think of this one, – what we are discussing is called the “Greenhouse Effect”. Anyone who think the name Greenhouse Effect is a “misnomer” has not considered the language used in dept.
To understand what I am getting at you must consider the fact that a pot of water on the stove, a pot which has a lid on (or more extreme, a pressure cooker) will need less heat/ energy input from the stove, in order to boil, than does a pot without a lid.. (Likewise it is an observed fact that a greenhouse works because it restricts (warm) air convection.)
The “Misnomer” Greenhouse Effect” however is kept in place because the chances are that the “explanation tags” convection and radiation will be confused, or “interchanged”
– It has by now become a “norm” to talk about “Downwelling Radiation” – which, is another “misnomer” helping us to imagine that warm “air-sinks” are forms of radiation. (I am half expecting that Foehn (Chinook) winds are soon to be classed as downwelling radiation.)
Radiation is, as you should very well know, a form of energy transport
– Which whithin our discussion encompasses: Short Wave Infra Red radiation, (SWIR) which is describing a transfer of energy from a point (call it A, or the Sun) to another point (call it B or the Earth’s surface). – Or Long Wave Infra Red (LWIR) radiation which in the same way must be from B to C (C being CO2 and other “Climate Gases”), – if not – then LWIR is not radiation. – But the point is – and please take note – If IR energy is removed/ transported from B in order to subsequently be absorbed by C, then it is unlikely that B is going to experience an increased temperature even if all or 100% of B’s emitted energy is returned by C. – If B’s temperature increases, then new/extra energy must have been created as energy provided by A is considered constant. (Energy Creation and Moonshine Production are forbidden by Law).
There is, as far as I know, no evidence to prove that CO2 has ever produced extra energy which is a physical requirement for temperature increase.
If you do not agree with the physical logic that says that “an increase in temperature must be proportional to an increase in energy” then let me know the reasons why so I can consider what to do next.
If however you believe that CO2, in ever increasing density can incur an ever decreasing convection, then I must admit that maybe I shall have to think again.
I appreciate posts like these. When i was young math came easy, now not so much 🙂 I guess I don’t really look at things normal. There is a deafening scream that there is to much CO2 but just recently on scientist state that we are in a CO2 famine. I have seen more charts,graphs, models of CO2 then i really wanted to. But I have yet to see what is considered normal.
What is normal for CO2?
Is it possible to say what normal is with what we know?
With natural selection at play over the history of the Earth would looking at what average level of CO2 plants / algae thrive at be out of the question for establishing a baseline?
Ironically this week I have been writing code for a multi node temperature controller. The decision engine doesn’t stray to far from Willis’s variables graph.
Smokey says:
October 4, 2011 at 6:01 pm
Go back to realclimate and tell them that. I would do it myself, but they have never allowed any of my posts out of moderation. Censoring bastards.
=======================================================
lol, That’s ’cause in their eyes you are a blasphemer!!!!! ………….. Showing how CO2 doesn’t really correlate to temps and all……… lol!
Anything is possible says:
October 4, 2011 at 2:49 pm
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”.
This question can be answered by looking at other planets and seeing if surface temperature varies as the density of the atmosphere or the composition of the atmosphere. From what I’ve seen there is a much stronger correlation between density and temperature than there is between composition and temperature. It can be argued that this process continues past the surface of the earth to the core.
Septic Matthew says:
October 4, 2011 at 5:35 pm
Thanks, Matthew. First, the GHGs are only responsible for a maximum of about 33° of the total temperature. A doubling of CO2 increases the TOA DLR by 3.7 / 150 = 2.5%.
25% * 33°C gives us about 0.8°C of additional THEORETICAL warming, which is about three tenths of a percent warming for the earth.
This leads to the second problem. Suppose you have a car, and you wedge the gas pedal halfway to the floor on the Bonneville Salt Flats. The car speeds up until it can’t go any faster, wind and rolling resistance are equal to the power put out by the engine.
Here’s the question. If we double the amount of gas going to the engine … will we get twice the speed out of the car?
Obviously, no, we won’t. In any real heat engine doing mechanical work, losses generally increase with increasing speed. In the case of the car (or the climate) the losses go up by the square of the speed. So even neglecting increased thermal losses in the car engine, we can only get about 40% more speed by doubling the gas … and in the real world, it will be less than that. The moral of the story is that for a real machine, such as the car or the climate, the change in output is less than the change in energy input.
In fact, the climate is more so, because nature generally runs at the edge of turbulence. This makes any increases very costly energetically, due to the rapidly increasing turbulence.
So in theory you might be correct, if we were not running at thermal equilibrium at the edge of turbulence. But we are like the car in the example above, running as fast as we can given the incoming energy and the physical constraints. It took something like 150 W/m2 to raise the temperature by 33°C. But as the temperature rises, the losses (T^4, sensible, and latent heat losses) are all rising faster than the temperature, just as the example of the car.
As a result, where we are now is the place where further gains are essentially balanced by further losses. How do I know? Because if not, the system would be hotter than it is. The system is constantly adapting to maximize the entropy, which inter alia means maximize the temperature.
Remember that this system is throttled down by about 30%. That means we have nearly half again as much energy available from the sun as the system is actually using. So if it were possible for the system to run warmer, there’s heaps and heaps of energy available to raise the temperature … but the temperature hasn’t raised, it has stayed basically stable (within ± 0.5%) for the last ten thousand years or so, which is an astounding record of stability for such a seemingly chaotic and random system.
Which means that we’re running as fast as we can, that is to say, the temperature is as hot as the system can make it given the physical constraints.
And that, in turn, means that a 1% change in the forcing will have almost no effect. Oh, sure, the tropical waterwheels will turn a little faster, sensible and latent heat losses will increase, and the amount of energy pumped polewards by the Hadley circulation will increase a bit. But there will be little change in the surface temperature. To affect such a system, you need changes, not in the radiative forcings, but in the surface and cloud albedo.
So something like aerosols which change cloud reflectivity could have a long-term effect on the system. Clouds would still form at the same temperatures and conditions, but they would reflect less (or more) sunshine. As a result, the temperature would have to change slightly.
Or the Milankovich cycles could alter the surface albedo of the Northern Hemisphere summers, and ice sheets could advance as far as possible south given the physical constraints. That could reset the thermostat by a few degrees.
But changes in the other forcings? The sun has gradually gotten warmer over the last half billion years … but the Earth has not gotten gradually warmer over that time. This indicates that the setting of the planetary thermostat is not much affected by the minor forcings.
All the best,
w.
Wow!
The cloistered, self-important, inbred cadre of climate-scientists and world-dominating wannabes scored a whopping 3.8% of the vote!
Wow!
Inbreeding as a success-path would seem to indicate some promise!
.
So, if solar is 68% of the radiation, and GHG is 31%, why can we not simply make reflectors that are 3x bigger than solar reflectors and generate steam from the down-welling GHG radiation at night?
This is a fair question and one that shows the fallacy of the GHG theory. We know that glass reflects IR, so if there are these many watts/m2 raining down on the earth from GHG, then we should be able to create large glass reflectors to focus this IR at night and heat our houses or produce steam for electricity.
The problem for climate science is that if GHG is warming the earth with down-welling IR as proposed, then this same IR would solve the fossil fuel problem and provide 7×24 power, something that solar power cannot do. This sort of reliability would make the capital cost practical.
So, the million dollar question. Why can this down-welling IR from GHG not do work the way that down-welling IR from the sun can? If IR from the sun can do work and IR from GHG cannot, then the IR from GHG cannot be equivalent to IR from the sun. It is as simple as that.
Thus, any treatment of IR from the sun and GHG cannot treat them simply as watts/m2, unless and until you can show that they both can do work. So far, it has not been shown.
Wouldn’t a doubling of CO2 be 0.08%? But then, how would even a twenty fold increase in CO2, to 0.8%, cause any climate problems?
Joel Shore says:
October 4, 2011 at 6:03 pm (Edit)
Thanks, Joel, good to hear from you. Suppose there were no feedbacks. If that were the case, we wouldn’t warm up 33°, we’d warm up 35° or 30°.
So when I use the number 33°, that includes all possible feedbacks.
So how am I not including the feedbacks? My number is the number including the feedbacks. You’ll have to explain to me what I’m missing.
w.
Great stuff, very engineering back-of-envelope stuff. This might be a little off this topic but can you estimate the loss of photonic energy to photosynthesis on a planetary scale ? I looked at the climate models,and didn’t see it (perhaps I’m looking without seeing). I note much space is given to plankton turnover of CO2, but nowhere could I see calculations about the energy supplied being used to make green stuff entering the calculations. Is this a fourth (or fifth) order thing-o?
Joel Shore says:
October 4, 2011 at 5:53 pm
Depends on what timescale you are interested in. Over the last billion years, the sun has gotten stronger by something on the order of 20 W/m2. By the IPCC figures, this should have warmed the Earth by some four degrees … but that doesn’t seem to have happened.
That is totally unclear. What clouds where are “spontaneously” varying, and what are they making a difference in? When the temperature rises in the tropics, clouds form spontaneously. I have demonstrated that that spontaneous variation does indeed make a difference of hundreds of watts/m2. So your meaning isn’t clear.
I take it from two places. The first is the simplest possible model of an energetically balanced greenhouse, where absorbed equals emitted at all levels. This has to be represented as two separate, thermally separated atmospheric “shells”, since a single shell model does not concentrate enough energy to allow for the known losses. Here is that diagram:
The second is the temperature of the tropopause, which runs at about -40 to -50°C or so, or a corresponding blackbody temperature of somewhere around 150 W/m2. Since the TOA is defined by the IPCC as the tropopause, that must be the TOA radiation.
w.
Willis says:
Willis, good to talk to you as always. I don’t understand this 35° or 30° statement. What do those numbers refer to?
Willis, I suggest you read what I wrote very carefully, several times if necessary. The point is that an effect can be included as either a feedback or a forcing and you are including it as a forcing. If it is included as a forcing, then it is not part of the feedbacks; it’s part of the forcings.
Look at it this way: If the earth’s surface temperature increases by 3 C, then simply using the Stefan-Boltzmann Equation tells us that the radiation from the surface will increase by about 16.5 W/m^2. (You might be able to argue this down a little bit depending on the distribution of the temperature increases on the earth’s surface, but not by much.) Since the radiation from the TOA will still be 240 W/m^2 (at least once the earth is back in…or close to…radiative equilibrium), that means your 150 W/m^2 number will have increased to 166 W/m^2.) That is a lot larger increase than 3.7 W/m^2. So, that raises two possibilities:
(1) Your method of computing the climate sensitivity is wrong.
(2) Climate scientists, even skeptical ones like Roy Spencer or Richard Lindzen are not able to do basic math, since they haven’t made this obvious point that, if this were really all there is to it, would fatally undermine AGW.
Willis wrote;
“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.”
With respect a better terminology is more along the lines of;
A system variable that produces a system response greater than 10% of the overall system response is termed a variable with an effect within the “first order of magnitude”.
A system variable that produces a system response greater than 1% , and less than 10% of the overall system response is termed a variable with an effect within the “second order of magnitude”.
Etc.
This is easily confused with the “orders” of a polynomial equation where the “first order” is an f(x), the “second order” is an f(x*x), “third order” is an f(x*x*x) etc.
Yes indeed in the beginning of any analysis those variables that produce a “cause and effect” within the first order of magnitude are studied first. This is then followed by examination of the second order effects, etc.
However when a polynomial is involved all orders must be examined carefully since things that are squared or taken to the third power can have a huge effect. For example the effect of air drag on an automobile is a function of the third power of the speed (I could be wrong it might be a second power effect). So at 1 mph the air drag is indeed an effect of the fourth or fifth order of magnitude. But at 100 mph it becomes a first or second order of magnitude effect.
Otherwise your post is relevant to understanding the possible magnitude of the alleged warming from the “greenhouse gas effect”
Unfortunately, the “GHE” only changes the speed at which energy (variously taking the form of visible light/heat/infrared light) flows though the Sun/Earth/Atmosphere/Universe system.
UNLESS this change in the speed of energy flow amounts to a significant portion of the periodic nature of the incoming energy (i.e. sunrise/sunset) no “higher equilibrium” temperature results. That portion of the energy that flows through the system via the “GHE” only takes a few more milliseconds (estimates vary but it may be as few as 5 or maybe a few thousand) to travel through the system. Since there are about 86 million milliseconds in a day the “GHE” has no affect whatsoever on the “average” temperature of the surface of the Earth.
Increases in “Greenhouse” gases in the atmosphere of the Earth are displaced by reductions in “Non-Greenhouse” gases. Energy flows through the “Non-Greenhouse” gases at the speed of heat (aka Thermal Diffusivity). Energy flows through the “Greenhouse” gases at a speed approaching the speed of light (after accounting for multiple absorptions/re-emissions). The speed of light is quite a bit faster than the speed of heat.
Therefore increases in “Greenhouse” gases in the atmosphere only cause the gases to change temperature more quickly after changes in the energy input to the system. These changes would include; sunrise (gases heat up faster), sunset (gases cool down faster), accumulation of clouds (gases cool down faster), and the dissipation of clouds (gases warm up faster).
This effect is so small that we probably cannot afford to measure it. The historical temperature databases do not contain the necessary data.
Cheers, Kevin.
Willis wrote: The car speeds up until it can’t go any faster, wind and rolling resistance are equal to the power put out by the engine.
About climate, that is an untested assumption: that the Earth surface and lower troposphere can not warm up any more. I think that your TAO/TRITON analyses show it’s a good bet, but they are not conclusive.
In fact, the climate is more so, because nature generally runs at the edge of turbulence. This makes any increases very costly energetically, due to the rapidly increasing turbulence.
That’s empty phraseology. Quit it.
Actually, Willis, what I was trying to say is more like
“A 1% change in radiation would be ~ 0.8 C change in temperature, based simply on radiation balance.”
or
“changes of a few percent in axial tilt or semi-major axis are thought to be drivers of climate changes (Milankovitch cycles)”
Either of these would have noticeable impacts on the earth. Certainly some claims are blown out of proportion, but you don’t have to look too far to see where small changes make noticeable differences.
Smokey says:
October 4, 2011 at 6:01 pm
“Go back to realclimate and tell them that. I would do it myself, but they have never allowed any of my posts out of moderation. Censoring bastards.”
Same here and I (like many) have a degree in science to boot and the RC web-site says they are discussing real science with real scientists. Obviously RC is not really discussing science, they are lecturing (preaching), and only if you don’t ask any hard questions that might show they don’t really know what they are talking about.
RC. Just like any other Cult, you may not question the leader. Doctrine is supreme and above question.
“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”.”
Why not remove all the liquid water instead of vapor and gas states of water.
If you did that, a “second order affect” would be it’s very windy.