Guest post By Ben Herman and Roger A. Pielke Sr.
During the past several months there have been various, unpublished studies circulating around the blogosphere and elsewhere claiming that the “greenhouse effect” cannot warm the Earth’s atmosphere. We would like to briefly explain the arguments that have been put forth and why they are incorrect. Two of the primary arguments that have been used are
- By virtue of the second law of Thermodynamics, heat cannot be transferred from a colder to a warmer body, and
- Since solar energy is the basic source of all energy on Earth, if we do not change the amount of solar energy absorbed, we cannot change the effective radiating temperature of the Earth.
Both of the above statements are certainly true, but as we will show, the so-called “greenhouse theory” does not violate either of these two statements. (we use quotation marks around the words “greenhouse theory” to indicate that while this terminology has been generally adopted to explain the predicted warming with the addition of absorbing gases into the atmosphere, the actual process is quite a bit different from how a greenhouse heats).
With regards to the violation of the second law, what actually happens when absorbing gases are added to the atmosphere is that the cooling is slowed down. Equilibrium with the incoming absorbed sunlight is maintained by the emission of infrared radiation to space. When absorbing gases are added to the atmosphere, more of emitted radiation from the ground is absorbed by the atmosphere. This results in increased downward radiation toward the surface, so that the rate of escape of IR radiation to space is decreased, i.e., the rate of infrared cooling is decreased. This results in warming of the lower atmosphere and thus the second law is not violated. Thus, the warming is a result of decreased cooling rates.
Going to the second statement above, it is true that in equilibrium, if the amount of solar energy absorbed is not changed, then the amount of IR energy escaping out of the top of the atmosphere also cannot change. Therefore the effective radiating temperature of the atmosphere cannot change. But, the effective radiating temperature of the atmosphere is different from the vertical profile of temperature in the atmosphere. The effective radiating temperature is that T that will give the proper value of upward IR radiation at the top of the atmosphere such that it equals the solar radiation absorbed by the Earth-atmosphere system.
In other words, it is the temperature such that 4 pi x Sigma T4 equals pi Re2 Fso, where Re is the Earth’s radius, and Fso is the solar constant. Now, when we add more CO2, the absorption per unit distance increases, and this warms the atmosphere. But the increased absorption also means that less radiation from lower, warmer levels of the atmosphere can escape to space. Thus, more of the escaping IR radiation originates from higher, cooler levels of the atmosphere. Thus, the same effective radiating temperature can exist, but the atmospheric column has warmed.
These arguments, of course, do not take into account feedbacks which will kick in as soon as a warming (or cooling) begins.
The bottom line here is that when you add IR absorbing gases to the atmosphere, you slow down the loss of energy from the ground and the ground must warm up. The rest of the processes, including convection, conduction, feedbacks, etc. are too complicated to discuss here and are not completely understood anyway. But the radiational forcing due to the addition of greenhouse gases must result in a warming contribution to the atmosphere. By itself, this will not result in a change of the effective radiation temperature of the atmosphere, but it will result in changes in the vertical profile of temperature.
The so-called “greenhouse effect” is real. The question is how much will this effect be, and this is not a simple question. There are also questions being raised as to the very sign of some of the larger feedbacks to add to the confusion. Our purpose here was to merely point out that the addition of absorbing gases into the atmosphere must result in warming, contrary to some research currently circulating that says to the contrary.
For those that might still question this conclusion, consider taking away the atmosphere from the Earth, but change nothing else, i.e., keep the solar albedo the same (the lack of clouds would of course change this), and calculate the equilibrium temperature of the Earth’s surface. If you’ve done your arithmetic correctly, you should have come up with something like 255 K. But with the atmosphere, it is about 288 K, 33 degrees warmer. This is the greenhouse effect of the atmosphere.
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Dave Dardinger says:
July 23, 2010 at 11:49 am
Robert,
the atmosphere would still affect the temperature of the planet through conduction and convection, to the point that the same radiative balance would exist at the top of the atmosphere, the surface being at a higher temperature than without an atmosphere, due to the physics of the lapse rate.
I think you’re incorrectly assuming that this atmosphere which is transparent to all radiation could still emit radiation. This is a contradiction. If it can emit LWIR then it must also absorb LWIR. Which brings up something I’ve asked about a few times without getting an answer. I assume that if molecules like O2 and N2 were to interact in a collision, there’s a small possibility they could emit IR (or absorb it). The reason that O2 and N2 don’t normally absorb or emit IR is that they’re symmetric molecules and thus can’t interact with an electromagnetic field. But while they’re in the process of collision, there will be some asymmetry set up which could lead to emission. The question is just how likely this is? My guess is that it’d be quite rare since the interaction time would be much quicker than the average time it takes for a quantum of IR to be emitted from a GHG (for instance). But the math to do the calculation is likely to be quite hairy and beyond my abilities. But surely there’s someone here who’s a wizz at QM who could solve the problem?
Such temporary dimers do exist and to do a very accurate accounting you should account for them, observed in Titan’s atmosphere if I recall correctly.
So,
Why do not Dewar (‘Thermos’) bottles contain CO2 for the excellent properties of impeding radiative heat transfer?
I’ve just filed a provisional patent on this as we speak.
I’ll remember all of you small people when I am rich beyond measure…
RR
Alex the skeptic says:
July 23, 2010 at 1:03 pm
Herman and Pielke end their dissertation with the following pragraph:
“For those that might still question this conclusion, consider taking away the atmosphere from the Earth, but change nothing else, i.e., keep the solar albedo the same (the lack of clouds would of course change this), and calculate the equilibrium temperature of the Earth’s surface. If you’ve done your arithmetic correctly, you should have come up with something like 255 K. But with the atmosphere, it is about 288 K, 33 degrees warmer. This is the greenhouse effect of the atmosphere.”
______________________________________________
Now, apart from the fact that without CO2, life as we know it would be non existent on this planet, can Ben Herman and Roger A. Pielke Sr. please tell us what the temperature would be like if we remove only the CO2 component from the atmospheric mix and keep all else unchanged? How much less the temperature of our planet would be? Wouldn’t this hypothetical removal of all CO2 be the reverse of doubling CO2, or would the logarithmic ‘diminishing returns’ characteristic come into play? If the latter is true (logarithmic diminishing return), then why the GE increase due to increase in CO2? Is it tru that the effect of increased CO2 is practically capped at 50ppm?
I m waiting with baited breath.
Assuming that the frozen oceans give the same albedo as clouds, about 260K, basically were talking about a ‘snowball’ earth. The albedo effect could lead to it being even colder than that.
George E. Smith wrote:
“Since the rate of loss of energy goes as T^4; so it is non-linear with temperature, the colder parts of the ball, are not doing their fair share of cooling, and the hotter parts are being overworked, and if we average the Temperature all over the ball surface that average will ALWAYS be hgher than the original case of an isothermal ball at 278 K all over”.
I followed your argumentation quite well until this point, but here I think you got it backwards. The average temperature will always be colder, the bigger the temperature differences in the surface, for the same total emissions. It is because of the emisivity depending on T^4. The emission gain that you get by increasing 1K the temperature is quite bigger than the emissions you lose by decreasing the temperature 1K. So in equilibrium, for the same total emissions, the bigger the temperature differences between different parts of your blackbody, the lower the average temperature will be.
Take it to the absurd. A black body with one half at 0K and another half at 100K emits the same energy as an isotermal blackbody at 84K, yet its average temperature is only 50K, considerably colder.
R Gates says
This is the worst response I’ve seen to this thread.
——————
I thank you for your comment; we can do a little more calculations; the average temperature of the atmosphere is -17°C approximately what is given by applying the Stefan law; the thermal capacity of the stratosphere is approximately 1/5 of that of the troposphere; that means that if the troposphere warms by about .7°C due to GHG effect, the stratosphere has to cool by about 3.5°C, approximately what is observed by satellites
w.r.t. to feedback, the increase of convection surely can be quantified within orders of magnitude vs. radiation. From my “Spacecraft Design” course the huge pain in heat rejection in space is the lack of convective mechanisms (even within cooling systems themselves). This leads to (plural) orders of magnitude large cooling system in space.
This would seem to indicate that pretty clearly any increase in surface temperature will alter the convective heat flow at a far higher rate than the introduced radiative forcing.
What’s the back of the envelope numbers for these?
Several commentators have expressed it more eloquently than I would have so I will not retread that ground. I would, however, say that the things that you dismiss and assume away have more effect than the CO2 and its radiation. Note that radiation is not the only mode of heat transfer. Radiation only becomes important when you are dealing with heat energy leaving the earth-atmosphere system. Remember, you are dealing with trace amounts of the substance. I would recommend some detailed study on the subject of heat and mass transfer. You might find it enlightening.
Many years ago Sapir and Whorf posited a theory, a much oversimplified statement of which would be, that language dominates thought. It never got a lot of traction in the linguistics community, though occasional efforts are still made to support versions of it. The way the climate debate has developed and proceeded suggests that maybe their work should be given more consideration.
The rather simple error of selecting a seriously flawed analogy, the greenhouse, has lead to decades of people talking past each other on this topic, mostly it would seem, because they are trying to rectify their arguments to an analogy that has no common definition and fundamentally misstates what is actually occurring. The plants inside a greenhouse enjoy a “climate” that is different from the external ambient atmosphere in which it stands. The planet with its atmosphere enjoys a climate which is different from what it would if it had no atmosphere. Other than that, none of the other efforts to extend the analogy are without serious logical flaws.
The human mind likes, perhaps even requires, analogies to attempt to process the flood of information about its external environment that it must deal with continuously. The problem this creates in discussing the planet’s climate is that for something as multifariously complex as our little blue marble the only thing that is properly analogous is the entire thing itself. As a result we end up in forums like this mostly questioning each others intelligence based on arguments that are often apples and oranges,and occasionally it seems, kumquats and water buffalo.
There is certainly a broad range of apparent intelligence among the visitors here, but as far as I can see, when it comes to the climate of the planet, what we all share along with all of humanity is incredible ignorance. From my view the only ones in this debate that can rightfully be described as “deniers” are those that will not accept that basic fact. For every press release, statement, presentation, paper, study, presentation, or off the cuff remark put forth on this topic in the last several decades there is only one response that would be almost universally applicable and that is “WE DON’T KNOW THAT”.
Forget about GHG and atmospheric processes. The mere presence of our oceans, with their large heat storage capacity, cause the earth temperature differences between night and day to be much smaller than they would be without the oceans. The mere fact of keeping temperatures stable, increases the average temperature of the planet for the same total IR emissions. And yet, I never see it mentioned when people talk about what the planet temperature should be with or without GHGs. I really wonder even if anyone has tried to calculate it. If our planet were to suffer the same temperature swings between night and day that, say, Mars suffers, its average temperature would be much colder. It is oceans that save us from that, not GHGs.
Ben Herman and Roger A. Pielke Sr.,
Great post, thanks.
In your post shouldn’t the equation be as follows:
4 x pi x Re2 x sigma x T4 = pi x Re2 x Fso
You show the equation:
4 x pi x sigma T4= pi x Re2 x Fso
Where T4 is T to the fourth power and Re2 is Re to the fourth power.
I am wondering you left out an “Re squared” in the first half of your equation?
John
Ben Herman and Roger A. Pielke Sr.,
CORRECTION : Re2 means Re squared, not “Re2 means Re to the fourth power”. I corrected in the post below. Sorry about that.
—————————
In your post shouldn’t the equation be as follows:
4 x pi x Re2 x sigma x T4 = pi x Re2 x Fso
You show the equation:
4 x pi x sigma T4= pi x Re2 x Fso
Where T4 is T to the fourth power and Re2 is Re squared.
I am wondering you left out an “Re squared” in the first half of your equation?
John
It’s not quite as simple as described in the OP.
Consider the atmosphere like insulation in your attic. It works two ways. It keeps the house warmer in the winter but it also keeps it cooler in the summer. Now consider day and night like winter and summer. The GHG insulation keeps the earth warmer at night but it also keeps it cooler during the day.
There’s an explanation why the effects don’t cancel out. To understand that one has to consider the spectrum of sunlight and the absorption bands of the GHGs.
The GHGs are largely transparent to the visible part of the spectrum. So during the day the GHGs are keeping the earth cooler that it would be otherwise as they acting as insulation against the incoming infrared radiation. But they are passing the visible spectrum straight through (discounting clouds) where some portion is absorbed by the ground and some is reflected right back out into space.
At night the visible spectrum absorbed by the ground is emitted but it is emitted as infrared radiation. Now, because the GHGs are insulators in the infrared, they are keeping surface warmer.
The GHG effect wouldn’t raise the surface temperature if the ground weren’t absorbing visible light during the day and reemitting it at night as infrared.
It’s important that be understood.
The actual mechanism of insulation is that photons in the GHG absorption bands are absorbed from a directional source (from the sun during the day and from the ground during the night) and quickly reemitted in a random direction. The net effect is that the transport of heat via infrared radiation is slowed down across the GHG insulation because, since the direction of reemission is random, some of the photons go right back in the direction they came from. One might also think of it like running through a mile of forest vs. running a mile across an open field. It takes longer to go through the forest because you have to zig zag through the trees effectively increasing the distance travelled getting from point A to point B.
stephen richards says:
July 23, 2010 at 12:15 pm
R. Gates says:
“Another of your cracked replies courtesy of the Gavin Schidt school of answers.”
“Gravity does not generate energy. Energy cannot be made or destroyed einstein.
Sure, gravity is a force which creates the conditions for the creation of stars and the nuclear energy in those stars is started by the force of gravity compressing the gases.”
As several of us discussed in a previous post, gravity is not even really a force but a condition, curvature, of space-time which occurs in the presence of mass causing everthing in its reach to move in a straight line though curved space. The source of energy represented by radioactive material in otherwise empty space would not be due to present gravity though it was originally created by gravity, previously, in the formation a large enough star to forge its properties when it exploded at the end of its life. I believe iron is the heaviest material that can be created in a “living” star that has not gone super nova. Fun stuff.
Nylo says:
July 23, 2010 at 9:01 am (Edit)
tallbloke, the GHE will by itself (i.e. without feedbacks) cause warming. However as it happens, other collateral effects may cause the warming to be increased, decreased or perhaps even reverted into cooling. Roger is only talking about the GHE, alone, without considering feedbacks.
I stand corrected – as you were Dr Pielke. I thought we’d got past that stage a few decades ago, even if we haven’t got much further since. 😉
ScienceofDoom has a great article series which is quite detailed on the subject, the first of which is called “CO2 – An Insignificant Trace Gas? Part One”
This is a great website which deals only with the science. The administrator is a true scientist and excellent teacher. In the storm of political discussion, this is a great science website to get the basics.
[url]http://scienceofdoom.com/2009/11/28/co2-an-insignificant-trace-gas-part-one/[/url]
Would someone please explain the different mechanisms of CO2 and water vapor? We know that CO2 captures and radiation and releases it randomly, so somewhat less than half of all captured radiation is sent toward Earth. What about water vapor? Does it capture radiation and than radiate it? What is the mechanism of warming?
I’m going to put this another way for you. Lets say we were talking about visible light energy rather than infra-red energy (they are, in any case, only distinct in terms of our physical perception of them rather than physical properties in any case) . What AGW proponents are saying is that we have, in CO2, a translucent panel above our heads (i.e. it absorbs light). According to AGW proponents, if we put more and more translucent panels above our heads the area beneath the translucent panels will get brighter and brighter.
Something sounds wrong with that idea doesn’t it?
What’s more, what happened to the idea that when a gas receives heat energy it causes the gas to do work which in turn results in its expansion. According to AGW theory this would happen with O2 but not with CO2 because CO2 is busily doing something else with all that heat.
Well expressed although a discussion of the lapse rate should have been included. The misunderstanding arises from many who suggest that the cooler atmosphere radiates to a warmer earth, ignoring the greater radiation from the warm earth to the cooler atmosphere.
Would someone please address the assumption that CO2 is distributed randomly throughout the atmosphere? If the assumption is correct then CO2 is the only thing in the atmosphere that is randomly distributed. Oxygen, for a handy example, is not randomly distributed. Yet this assumption underlies all so-called science by the warmist crowd. To me, the fact that this assumption is used just show that climate science has not advanced to the stage of experiment.
Thank you Ben Herman and Roger A. Pielke Sr for the tidy post, it’s resulted in the funniest thread I’ve read in ages, that kill-joy from Brenchley tried to derail it all but to no avail.
The thread is a testament to humans being rationalising rather than rational creatures.
RuhRoh says:
July 23, 2010 at 1:23 pm
So,
Why do not Dewar (‘Thermos’) bottles contain CO2 for the excellent properties of impeding radiative heat transfer?
I’ve just filed a provisional patent on this as we speak.
I’ll remember all of you small people when I am rich beyond measure…
RR
—
Just call it “CarboJug – a carbon-capture device which keeps your coffee warm!” Pre-loaded with CO2 generated from coal-fired power plants!
Put a bunch of “endorsed by the WWF, Greenpeace, and NASA/GISS” stickers on the box, get Al Gore to do the infomercials (“improve your Chakra with CarboJug”), and voila – a blockbuster product that will make you millions!
[snip- your name says it all ~mod]
From scienceofdoom.com:
“The Stefan-Bloltmann Law states:
j = εσ(T^4)
Where
j = total energy radiated per unit area per unit time
ε = emissivity, ranging from 0 to 1, where 1 is a perfect black body
σ = the Stefan Boltzmann constant, 5.67 x 10-8
σ = temperature in K
The effective temperature of the sun is 5780K, it is pretty close to a blackbody, and its radius, r = 696 x 10^6m
The area of the surface of a sphere = 4πr^2
So Total Energy, E = 5.67-8 x 57804 x π x (696 x 10^6)2 = 3.85 x 10^26 W – That’s a lot of Watts!
How much hits the earth?
Radius of the earth, re = 6.37 x 10^6 m (6,370 km)
Distance from sun to earth, ao = 1.5×10^11 m (150 million km)
Imagine a giant sphere with a radius the distance from the sun to the earth, and the earth as one tiny circle pasted onto it – that’s the proportion of the Sun’s energy that hits the earth.
The giant sphere has an area of 4πa^2 = 4π x (1.5×10^11)^2
The earth’s “circle” pasted on this giant sphere has an area = πre2 (not the whole area of the earth’s surface which would be 4πre2, just the effective 2D disc that the sun’s energy hits).
So the proportion incident on the earth’s surface = (πr^2)/ (4πa^2)
= (6.37×10^6)^2 / (4 x (1.5×10^11)^2) = 4.5 x 10^-10 -or around 1/2 billionth of the total energy
The total energy hitting the earth’s “disc” = 1.73 x 10^17 Watts
And per unit area (area = πre2) = 1,360 W/m2
First major result!
Applying the same maths to the earth – the earth’s surface also emits radiation according to the same law. This is where is starts to get tricky, but let’s consider the simple case.
Energy received from the sun = Energy emitted by the earth (if the temperature of the earth’s surface stays the same).
So we have to solve the total energy radiated out from the earth, where Te is the surface temperature of the earth:
Energy flux x total area of the earth = 1.73 x 10^17
5.67 x 10^-8 x Te^4 x (4πr^2) = 1.73 x 10^17
The result, Te = 278K = 5°C ?
Actually, not quite right. The problem is, and can easily be demonstrated by satellites measuring the energy reflected back – not all of the energy gets absorbed by the earth’s surface. Some gets reflected by clouds, the atmosphere, and some by the earths surface. On average about 30% gets reflected.
Redoing the same equation with only 70% of the energy incoming:
Adjusted Te = 254K = -19°C ?
Wow, it doesn’t feel that cold, what went wrong? Nothing went wrong, and you’re right, across the globe the “average temperature” is higher – about +16°C.
The explanation is in the (inappropriately labelled) “greenhouse gases”, which include water vapor, CO2 and methane (CH4). These gases absorb energy from wavelengths in the earth’s range, and hardly any in the sun’s range.
So the sun’s energy just passes through like they don’t exist, but when the earth emits its radiation, these gases absorb energy and then re-emit, so that the earth’s energy doesn’t just fly off into space but instead it’s absorbed and re-transmitted, some of it back down to earth.
The “greenhouse gases” heat the earth’s surface up approximately 35°C higher than it would be otherwise.”
The same website dismisses other silly myths as well. Lord Monckton’s post elegantly summarizes this.
My concern with the field in general is the magnitude of feedback / response in the natural system, continued careless use of statistical methods, missing error bars, the relative impact of CO2 vs land use, and obvious hockey team cronyism in publication including the publication of a blacklist which undermines and cheapens the entire field of study.
One of the staple arguments for a general greenhouse effect on earth is the assertion that this planet would be an overall 30-35K cooler were it not for greenhouse gases. This is based on a theoretical calculation based on the Stefan-Boltzmann law of black body radiation. Now the earth is not a black body, but the theoreticians claim they have made the necessary adjustments for this in their calculations. Of course no one can test this by removing supposed greenhouse gases from our atmosphere.
However the moon has no atmosphere. The later Apollo missions left an array of temperature sensors on the moon and recently NASA released an analysis of the results. Amazingly this shows that the moon also has an elevation of temperature (~40K) above that calculated by the theory. Does the moon then have a greenhouse‘ effect? Clearly not – it has no atmosphere. So it looks as if the calculated starting point is wrong and neither the earth nor the moon are kept warmer by any ‘greenhouse effect’.
http://climaterealists.com/attachments/database/RadiativeNonEquilbrium_BHermalyn_Final.pdf
Absorbed radiant heat incident on the surface of both is conducted downwards and is released like heat is released from any storage heater, at night.
@R.Pielke, Ben Herman, Lord Monckton,
“the cooling is slowed down.”
That’s plausible. But if it is that simple, why not laying down the equations and publish a much needed paper ?
How does this translate in terms of heat capacity, heat conductivity, thermal diffusivity, heat transfer and so on ?
What precisely means ” the cooling is slowed down” ?
Greenhouse effect is physics. Physics requires specific and precise statements, equations and numbers.
In the present state, this is just one more climatologist’s assertion.