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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The question should be, “how much water vapour would there be without CO2 or methane?” This seems to be the elephant in the room with these discussions.
The more time that I spend at this site makes me love it more than before. And yet I despair inversely proportionally to my enjoyment.
Apart from a few hundreds (thousands) who actually cares? It’s a tiny minority in global terms.
Ok, a few Africans and some others got wiped out thanks to political aspirations inspired by globally-powered greed but is that an issue worthy of the gaze from our elected representatives?
I guess not but that is not an issue that can be held against them. Yup, they are greedy, selfish and self-seeking individuals but we voted for them. You can’t blame the scorpion for sinking the fangs in but you should hold a bit of respect back from the frog that ticked the ballot paper to put them into power!
Too many scorpions is bad but, far worse are the icky-little frogs that gave them the power to choose whom and when to sink the killer-bites into.
Forget science. ignore truth, shun honesty and come to terms with this. The scorpions have won.
Willis says:
So, which number on that diagram are you claiming corresponds to your 150 W/m^2 value? Is it the back radiation between the lowest stratosphere and the troposphere, (and the 147 W/m^2 emitted out of the lower stratosphere up into space) or is it something else?
I would not really say that the IPCC defines the tropopause as the TOA, plus I am not sure how this temperature is then relevant. To my mind, “top of the atmosphere” means you are considering the radiative balance across that boundary because you know that the only communication across that boundary is via radiation. I know that the IPCC does talk about allowing the stratosphere to adjust and thus using the tropopause instead, but I don’t think that means that the temperature at that particular point is some very important temperature, as that is not the point where most of the radiation that escapes to space is originating from.
By the way, since the last part of my previous post (i.e., where I calculated how your 150 W/m^2 number would change if the earth’s surface temperature rose by 3 C) was predicated on the notion that you were defining that 150 W/m^2 as the difference between the radiation from the surface and the radiation of the earth as seen from space (i.e., as an effective 255 K blackbody), I will withdraw my statement about knowing how your 150 W/m^2 will change until I better understand how you are deriving it. But, I still stand by my point that it is including all of the greenhouse gases (in particular, water vapor) as forcings, and hence not feedbacks.
Mann oh mann.
321 watts per square meter back radiation according to the diagraph above. So, lets all get out our glass reflectors and focus that energy just like we can with energy from the sun. It must be possible, as they are both measured in watts per square meter, and solar energy at the surface is only half as much, only 169 watts per square meter, and even a small solar reflector can burn holes through objects.
So, lets hear what happens when you place a large glass reflector out at night to try and actually use that 321 watts per square meter down-welling IR to try and heat something. Watts that you say?? It doesn’t work?? Why not, they are both watts per square meter?? Watt is it that climate science is missing??.
Septic says:
“That’s empty phraseology. Quit it.”
It seems pretty clear to me. Changes occur at the margins.
Willis,
I really like the two-layer diagram as a “first order” correction to the original. Where did you get it?
I do have one particular question. MODTRAN suggests that looking up from the tropopause (11 km) you would only see ~ 25 W/m^2 LWIR coming down, but this diagram suggests around 150 W/m^2. Perhaps the two layers should more properly be called “lower troposphere” and “upper troposphere & stratosphere”?
James Sexton says:
October 4, 2011 at 5:35 pm
What is the energy distribution towards the various frequencies of IR? For instance, does 10.5 microns put the same energy as 3.0 microns? If so, how do we know this? How does the various redundant absorption effect the energy moving towards the earth?
=====================================================================
Sigh, ok, gotta do everything myself. I love going over pre-trodden ground……..
Equation: f * λ = c
Equation: E = hc/λ
where:
f = frequency in Hertz (Hz = 1/sec)
λ = wavelength in meters (m)
c = the speed of light (299792458 m/s)
E = energy in electron Volts (eV)
h = Plank’s constant (6.626068 × 10-34 m2kg/s)
Apply this to the general CAGW discussion. Anyone care to take it from there? Look, I’m a beer drinker, and I don’t have time to focus on the minutia. Reckon this with the IGL as I mentioned earlier, and we’ll have a formula………. and it will explain why this…..http://www.theresilientearth.com/files/images/Greenhouse_Gas_Absorption-dlh-500.png , may be correct.
It is interesting that a 1% change is so dramatic. The Charney sensitivity is off by at least 33% since it is the average of two estimates, 2 and 4. DLR measurements are off by +/- 7 W/m-2 +/- 50% of the range of predicted change. Then from another perspective, a 0,1% change is 2nd order with respect to a 1% change. A couple of 3rd order changes to the system are first order PITAs for the 1% solution.
ferd berple says:
October 4, 2011 at 7:25 pm
“So, lets all get out our glass reflectors and focus that energy just like we can with energy from the sun. It must be possible …
Your statement here gives the hint as to why it will not work, if you stop to think about it. The sun’s energy comes from a very specific direction, so it can indeed be “focused”. You can reflect light and get 2 times (or 10 time or 100 times) as much energy into a small spot by cleverly placing mirrors.
On the other hand, the LWIR is diffuse. Trying to reflect in IR light from the sky will block IR from other parts of the sky, making the exercise a wash.
Or if you prefer, you can consider the 2nd law of thermodynamics: “No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature. (Wikipedia)” If we believe the 2nd law, then the process of focusing IR energy from the LWIR cannot warm the object above the temperature of the radiating object (ie the temperature of the atmosphere/clouds), ie the IR cannot transfer heat to a warmer object (Similarly, it is impossible to focus sunlight to warm an object above ~ 5800 K).
If you think ” it must be possible” to warm something with 300 W/m^s of IR from a ~ 300 K object the same way you can warm something with 300 W/m^2 of sunlight from a ~ 5800 K sun, then you think the 2nd law does not hold.
“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).”
That is true. Even the increase of temperature given by IPCC is insignificant.
The temperature increase would also be to nighttime and winter temperature. And the temperature increases would have to be in the temperate or arctic regions.
One problem is that tropical region are major element defining global temperature- remove the tropics and Earth is quite cold. Therefore to actually increase global temperature, one has to significantly increase average temperature in temperate and arctic regions. And so temperature regions would need similar to average tropical temperature.
And there is no sign of this occurring- orange trees aren’t being grown in Oregon
“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.”
Dinosaurs were probably killed by a space rock- and that affect from this space rock is far more than first order affects being discussed. It far larger affect than setting off all nuclear weapons in all human stockpile- by at least a factor 10. An example is it would cause serious earthquake on the opposite side of the planet it hit.
“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?”
Or any posion can kill you. You are itty bitty creature, the planet isn’t. The planet has major events which have happened, it’s billions of years old. Yellowstone eruption:
“The last full-scale eruption of the Yellowstone Supervolcano, the Lava Creek eruption which happened nearly 640,000 years ago, ejected approximately 240 cubic miles (1,000 km3) of rock and dust into the sky”
http://en.wikipedia.org/wiki/Yellowstone_Caldera
That is Earth getting a buzz.
Here a hiccup:
Krakatoa:
“The 1883 eruption ejected approximately 21 km3 (5.0 cu mi) of rock, ash, and pumice.”
http://en.wikipedia.org/wiki/Krakatoa#The_1883_eruption
Manabe and Strickler, Thermal Equilibrium of the Atmosphere with a convective adjustment, J Atmos Sc. Vol 21, July 1964, pp 361 – 385, has some early modeling results. They started with an Earth with no clouds, a surface albedo of 0.1 and a standard atmosphere with H2O and CO2 similar to 35N latitude in April.
A greybody calculation with no atmosphere gives an average surface T = 271 K.
With pure radiative cooling, they calculated a surface T = 332 K.
Thus, typical levels of CO2 and H2O provide greenhouse surface delta T of about 61 C. About 50 C of this is due to H2O.
With convection added, but no clouds yet, the lapse rate drops from 10 to 6.5 K/km, and the surface temperature drops to T = 300 K.
Convection provides a strong negative feedback for surface T.
Manabe also calculated surface T with a moist adiabatic lapse rate of 6.5 K/km, and found that increasing CO2 from 1 ppm to 350 ppm resulted in about 10 C of surface T increase. This gives approximately 1 C per CO2 doubling.
It was abundantly clear by 1964 that weather provides a strong negative feedback, makes the planet’s surface habitably cool, and that small changes (undetectable in existing datasets) in weather intensity (spatial coverage, frequency or duration) will have a large impact on global surface temperatures.
gbaikie says:
October 4, 2011 at 7:23 pm
“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.
And just below this comment …
Tony says:
October 4, 2011 at 7:23 pm
The question should be, “how much water vapour would there be without CO2 or methane?” This seems to be the elephant in the room with these discussions.
My response to both ..
Removing water vapor from the atmosphere, or the equally common CAGW “argument requirement” to discuss CO2 influence on the earth’s climate “from 0,0” conditions, is irrelevant.
We HAVE BOTH CO2 and water in the atmosphere.
We CANNOT remove either and make an analysis of any sort starting from those conditions.
We have an axial tilt of the earth, and that axial tilt will not change in the next 100, 500, nor 1000 years.
Solar radiation at top-of-atmosphere changes from month to month over the span of a year – a fact “approximated” in the models.
The earth rotates – a fact also not loaded in the models.
Yes, the elite physicists who want to study their ideal high-priced models in their nice air-conditioned physics classrooms for their profits and their prizes and their peer-recognition and write their peer-reviewed magazines for their friendly editors and gatekeepers can remove CO2 or remove water vapor from their approximations (er, labs) and pretend some other condition may occur in some universe.
But neither condition (no CO2 or no water vapor) will matter. Our earth has both. At best, one can only change CO2 (or methane) levels from the initial percent. And, by the way, a “sudden jump” simulated by a sudden doubling or tripling of CO2 or methane isn’t a valid analysis either.
——
By the way, if 23 different global computer models can begin with 23 different assumptions (initial conditions) and 23 different variable assignments at 23 different sites – and yet all 23 can – at best – only run hundreds of simulations to yield one average result ….. Then is that by itself not condemning the accuracy of the models?
After all, ONLY ONE initial condition (life on a tilted, rotating earth with seasons and currents and jet streams and El Nino’s and La Ninas and PDO’s and AMO’s and NAO’s) is valid. If 23 different models give one (average) result after (averaging) thousands of different computer runs, which ONE model and ONE set assumptions and ONE set of equations and ONE set of factors is correct?
When a valid finite element analysis is run on a valid computerized approximation of the real world – such as a stress strain model using boundary condition, or a neutron fluz simulation or a electro-magnetic simulation of a generator coil or a magnetic “bottle” simulation, the model doesn’t need thousands of runs – each yielding different results that have to be averaged together – to present a useable result. Each run of a valid model of a physical relationship that is correctly approximated using valid assumptions and valid “boxes” for each element yields the same results each run.
If the modeled results differ each time you run a stress-strain model, your model is wrong.
Your equations and assumptions are wrong.
Your boundary conditions are wrong.
Your initial conditions are wrong.
(You are wrong in trying to use a FEA approximation of your process …..)
Willis … I always enjoy your posts especially when the commenters go at it “tooth and nail”.
………..
Not wishing to pick a nit, but it seems to me too that the legend on Fig. 1 has an error(?).
It appears to me that the colors for First and Second Order and First, Second, and Third graphs are reversed. [Green & Purple reversed?]
Another very interesting post Willis. And yet, of course, this little “3rd order” variable, this tiny trace gas, a mere tiny fraction of our Earth’s atmosphere, is absolutely critical in preventing the Earth from becoming a snow ball planet. Amazing little molecule that CO2…
“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?”
Well a recent estimate of CO2 absorbed global per year is 150 to 175 petagrams or
10^15 grams or 150 to 175 gigatonnes. Humans emit about 30 petagrams or gigatonnes.
If converting energy you have losses, if split water with electricity, and use the H2 and O2 to make electricity you lose energy.
BUT for rough idea the amount energy you get from burning fossil fuels to that created 150 to 175 petagrams CO2 is roughly the amount energy taken from the sun by plants per year.
It gives you rough idea- and 150 to 175 petagrams is also only a rough idea.
“Tim Folkerts says:
October 4, 2011 at 7:56 pm
On the other hand, the LWIR is diffuse. Trying to reflect in IR light from the sky will block IR from other parts of the sky, making the exercise a wash.”
No, you can make a reflector that is not sensitive to direction. It is not perhaps not as efficient as point source, but it can be done.
The question remains: If watts per square meter is the measure of down welling GHG IR, then you should be able to get work from the IR, regardless of source.
As such, my original point stands. The watt is a unit of work. So, if GHG does in fact radiate watts of energy it MUST be capable of work.
We know we can get work from the watts radiated from the sun. So, where it the demonstration that you can get work from down-welling GHG IR? If it can’t do work, then it is nonsense to measure it in watts.
This is really fundamental to the problem. Where is the demonstration that GHG is capable of doing work? If it can’t do work, then why are we insisting it is somehow equivalent to watts from the sun which can do work? We might as well be talking about zero point vacuum energy heating the earth.
Anything is possible says:
October 4, 2011 at 2:49 pm
I agree with “Anything’s” point. Didn’t read all comments here, but why don’t discussions such as this examine the heat transmitted by non GHG’s? If we care about the temperature of objects near the surface, What about all the warmth from conduction via non GHG’s? It seems intuitive that this could be even the majority of the reported 33C difference on Earth vs, say, the Moon.
What would the temperature be if the earths atmosphere was 50% Co2?
Now you’re talkin’. That’s a very clear top-down explanation, much appreciated.
but —
Edit Note: that should be “effect”. “Affect” as a verb is pretty much equivalent to “originate”, not “alter”.
Apologies. I got it bass-ackwards. You’re right. “effect” it is.
Isn’t doubled CO2 .08% rather than .8%?
Jeez Louise, my typo-spewing machine is running at the borderline of turbulence.
“affect” is correct.
R. Gates says:
October 4, 2011 at 9:00 pm
“Amazing little molecule that CO2” The amazing is not the little CO2 molecule, but the brain construction of people who find the hypothesis of such a small contribution wagging the dog .
The only way that a tiny contribution can be built up over time is through resonance. There is absolutely no way that a chaotic system with the hundreds if not thousands parameters and functions entering the problem will be in a resonant state receptive to tiny changes. imo of course.
Zac, good question and goes to the heart of the AGW scam. In scientific (and engineering) equations a general principle of algebra is used to reduce the number of variables by eliminating those that don’t (seem) to change. E.g. yx^3 + vx^2 + zx = 2qx In this simple example the variable x appears many times, in algebra we simplify this equation to yx^2 + vx + z = 2q (I just did a minor one step simplification for demonstration purposes, you could manipulate the equation more for simplification)
What the AGW hoaxers are claiming regarding water vapor in the atmosphere is that it doesn’t change from year to year and therefore any changes in water vapor levels is induced by changing the amount of CO2. This is of course circular reasoning, if water vapor doesn’t change from year to year, then CO2 can’t change the amount of water vapor, you can’t have your cake and eat it too. This is one of the many slights of hand played by con artists leading a rube to believe something that is not true by glossing over the details and if you don’t look too closely you are easily misled.
However, any examination of the humidity levels from month to month quickly dispells the notion that water vapor is a constant as AGW hoaxers claim. They then talk around this inconsistency to claim it doesn’t change from year to year, thus it averages out just like thermometer errors. Again, this is a falsehood, water vapor amouts in the atmosphere does change from year to year. If it didn’t then how could you have droughts? Excess rain events? I.e. Increasing precipitation? They then talk around that inconsistency by claiming once again, claiming it’s a regional phenom IF you consider the entire planet as a whole ON AVERAGE there is no change. Yet, they claim both increasing floods and droughts as a consequence of AGW.
BTW- this is the exact same slight of hand played with the GAT (Global Average Temp), The Southern Hemisphere has shown ZERO increase in temperature for well over 30 years. They combine measurements of both Hemispheres together to create the GAT which then showed an increase from what 1980 or 79 to 2005? Aren’t averages wonderful? It is a convenient means to hide a tree in the midst of a forest. If there is no warming in the Southern Hemisphere, then logic says it can’t be global warming but Northern Hemispheric Warming. What’s their answer, water vapor in the ocean dominated Southern Hemisphere is concealing the temperature rise!!!
Policyguy:
Matt says:
October 4, 2011 at 3:08 pm
Excuse me, as mentioned in a number a posts after yours, your logic seems to have a number of serious flaws. You may want to reconsider your theoretical response to the paper. Is this peer review? Does this editor need to consider resignation??? Please guide us.
Also,
R. Gates says:
October 4, 2011 at 9:00 pm
Another very interesting post Willis. And yet, of course, this little “3rd order” variable, this tiny trace gas, a mere tiny fraction of our Earth’s atmosphere, is absolutely critical in preventing the Earth from becoming a snow ball planet. Amazing little molecule that CO2…
—–
What a ridiculous, unsupported, untrue statement, out of the blue. What are you inhaling? Try to find 4 blue (purple, red, scary orange) BB’s in a sea of 10,000 white ones. Have fun explaining the significance when you get there. Of course you could try to find 40 in a sea of 100,000 white ones, or you could really go after the big one – the 400 in a sea of 1 Million white BB’s and really understand the terror of that experience.
What a joke. Peddle it elsewhere, please.