A guest post by Leonard Weinstein. The original document is here and has more legible equations.
Leonard Weinstein
July 18, 2012
The argument is frequently made that back radiation from optically absorbing gases heats a surface more than it would be heated without back radiation, and this is the basis of the so-called Greenhouse Effect on Earth. The first thing that has to be made clear is that a suitably radiation absorbing and radiating atmosphere does radiate energy out based on its temperature, and some of this radiation does go downward, where it is absorbed by the surface (i.e., there is back radiation, and it does transfer energy to the surface). However, heat (which is the net transfer of energy, not the individual transfers) is only transferred down if the ground is cooler than the atmosphere, and this applies to all forms of heat transfer. While it is true that the atmosphere containing suitably optically absorbing gases is warmer than the local surface in some special cases, on average the surface is warmer than the integrated atmosphere effect contributing to back radiation, and so average heat transfer is from the surface up. The misunderstanding of the distinction between energy
transfer, and heat transfer (net energy transfer) seems to be the cause of much of the confusion about back radiation effects.
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Before going on with the back radiation argument, first examine a few ideal heat transfer examples, which emphasize what is trying to be shown. These include an internally uniformly heated ball with either a thermally insulated surface or a radiation-shielded surface. The ball is placed in space, with distant temperatures near absolute zero, and zero gravity. Assume all emissivity and absorption coefficients for the following examples are 1 for simplicity. The bare ball surface temperature at equilibrium is found from the balance of input energy into the ball and radiated energy to the external wall:
To=(P/σ)^0.25 (1)
Where To (oK) is absolute temperature, P (Wm-2) is input power per area of the ball, and
σ=5.67Ε−8 (Wm-2 T-4) is the Stefan-Boltzmann constant.
Now consider the same case with a relatively thin layer (compared to the size of the ball) of thermally insulating material coated directly onto the surface of the ball. Assume the insulator material is opaque to radiation, so that the only heat transfer is by conduction. The energy generated by input power heats the surface of the ball, and this energy is conducted to the external surface of the insulator, where the energy is radiated away from the surface. The assumption of a thin insulation layer implies the total surface area is about the same as the initial ball area. The temperature of the external surface then has to be the
same (=To) as the bare ball was, to balance power in and radiated energy out. However, in order to transmit the energy from the surface of the ball to the external surface of the insulator there had to be a temperature gradient through the insulation layer based on the conductivity of the insulator and thickness of the insulation layer. For the simplified case described, Fourier’s conduction law gives:
qx=-k(dT/dx) (2)
where qx (Wm-2) is the local heat transfer, k (Wm-1 T-1) is the conductivity, and x is distance outward of the insulator from the surface of the ball. The equilibrium case is a linear temperature variation, so we can substitute DT/h for dT/dx, where h is the insulator thickness, and DT is the temperature difference between outer surface of insulator and surface of ball (temperature decreasing outward). Now qx has to be the same as P, so from (2):
DT=(To-T’)=-Ph/k (3)
Where T’ is the ball surface temperature under the insulation, and thus we get:
T’=(Ph/k)+To (4)
The new ball surface temperature is now found by combining (1) + (4):
T’=(Ph/k)+(P/σ)0.25 (5)
The point to all of the above is that the surface of the ball was made hotter for the same input energy to the ball by adding the insulation layer. The increased temperature did not come from the insulation heating the surface, it came from the reduced rate of surface energy removal at the initial temperature (thermal resistance), and thus the internal surface temperature had to increase to transmit the required power. There was no added heat and no back heat transfer!
An alternate version of the insulated surface can be found by adding a thin conducting enclosing shell spaced a small distance from the wall of the ball, and filling the gap with a highly optically absorbing dense gas. Assume the gas is completely opaque to the thermal wavelengths at very short distances, so that he heat transfer would be totally dominated by diffusion (no convection, since zero gravity). The result would be exactly the same as the solid insulation case with the correct thermal conductivity, k, used (derived from the diffusion equations). It should be noted that the gas molecules have a range of speeds, even at a specific temperature (Maxwell distribution). The heat is transferred only by molecular collisions with the wall for this case. Now the variation in speed of the molecules, even at a single temperature, assures that some of the molecules hitting the ball wall will have higher energy going in that leaving the wall. Likewise, some of the molecules hitting the outer shell will have lower speeds than when they leave inward. That is, some energy is transmitted from the colder outer wall to the gas, and some energy is transmitted from the gas to the hotter ball wall. However, when all collisions are included, the net effect
is that the ball transfers heat (=P) to the outer shell, which then radiates P to space. Again, the gas layer did not result in the ball surface heating any more than for the solid insulation case. It resulted in heating due to the resistance to heat transfer at the lower temperature, and thus resulted in the temperature of the ball increasing. The fact that energy transferred both ways is not a cause of the heating.
Next we look at the bare ball, but with an enclosure of a very small thickness conductor placed a small distance above the entire surface of the ball (so the surface area of the enclosure is still essentially the same as for the bare ball), but with a high vacuum between the surface of the ball and the enclosed layer. Now only radiation heat transfer can occur in the system. The ball is heated with the same power as before, and radiates, but the enclosure layer absorbs all of the emitted radiation from the ball. The absorbed energy heats the enclosure wall up until it radiated outward the full input power P. The final temperature of the enclosure wall now is To, the same as the value in equation (1). However, it is also radiating inward at the same power P. Since the only energy absorbed by the enclosure is that radiated by the ball, the ball has to radiate 2 P to get the net transmitted power out to equal P. Since the only input power is P, the other P was absorbed energy from the enclosure. Does this mean the enclosure is heating the ball with back radiation? NO. Heat transfer is NET energy transfer, and the ball is radiating 2 P, but absorbing P, so is radiating a NET radiation heat transfer of P. This type of effect is shown in radiation equations by:
Pnet=σ (T^4hot-T^4 cold) (6)
That is, the net radiation heat transfer is determined by both the emitting and absorbing surfaces. There is radiation energy both ways, but the radiation heat transfer is one way. This is not heating by back radiation, but is commonly also considered a radiation resistance effect. There is initially a decrease in net radiation heat transfer forcing the temperature to adjust to a new level for a given power transfer level. This is directly analogous to the thermal insulation effect on the ball, where radiation is not even a factor between the ball and insulator, or the opaque gas in the enclosed layer, where there is
no radiation transfer, but some energy is transmitted both ways, and net energy (heat transfer) is only outward. The hotter surface of the ball is due to a resistance to direct radiation to space in all of these cases.
If a large number of concentric radiation enclosures were used (still assuming the total exit area is close to the same for simplicity), the ball temperature would get even hotter. In fact, each layer inward would have to radiate a net P outward to transfer the power from the ball to the external final radiator. For N layers, this means that the ball surface would have to radiate:
P’=(N+1)Po (7)
Now from (1), this means the relative ball surface temperature would increase by:
T’/To=(N+1)^0.25 (8)
Some example are shown to give an idea how the number of layers changes relative absolute temperature:
| N | T’/To |
| 1 | 1.19 |
| 10 | 1.82 |
| 100 | 3.16 |
Change in N clearly has a large effect, but the relationship is a semi-log like effect.
Planetary atmospheres are much more complex than either a simple conduction insulating layer or radiation insulation layer or multiple layers. This is due to the presence of several mechanisms to transport energy that was absorbed from the Sun, either at the surface or directly in the atmosphere, up through the atmosphere, and also due to the effect called the lapse rate. The lapse rate results from the convective mixing of the atmosphere combined with the adiabatic cooling due to expansion at decreasing pressure with increasing altitude. The lapse rate depends on the specific heat of the atmospheric gases,
gravity, and by any latent heat release, and may be affected by local temperature variations due to radiation from the surface directly to space. The simple theoretical value of that variation in a dry adiabatic atmosphere is about -9.8 C per km altitude on Earth. The effect of water evaporation and partial condensation at altitude, drops the size of this average to about -6.5 C per km, which is the called the environmental lapse rate.
The absorbed solar energy is carried up in the atmosphere by a combination of evapotransporation followed by condensation, thermal convection and radiation (including direct radiation to space, and absorbed and emitted atmospheric radiation). Eventually the conducted, convected, and radiated energy reaches high enough in the atmosphere where it radiates directly to space. This does require absorbing and radiating gases and/or clouds.
The sum of all the energy radiated to space from the different altitudes has to equal the absorbed solar energy for the equilibrium case. The key point is that the outgoing radiation average location is raised significantly above the surface. A single average altitude for outgoing radiation generally is used to replace the outgoing radiation altitude range. The temperature of the atmosphere at this average altitude then is calculated by matching the outgoing radiation to the absorbed solar radiation. The environmental lapse rate, combined with the temperature at the average altitude required to balance incoming and outgoing energy, allows the surface temperature to be then calculated. The equation for the effect is:
T’=To -GH (9)
Where To is the average surface temperature for the non-absorbing atmospheric gases case, with all radiation to space directly from the surface, G is the lapse rate (negative as shown), and H is the effective average altitude of outgoing radiation to space. The combined methods that transport energy up so that it radiated to space, are variations of energy transport resistance compared to direct radiation from the surface. In the end, the only factors that raise ground temperature to be higher than the case with no greenhouse gas is the increase in average altitude of outgoing radiation and the lapse rate. That is all
there is to the so-called greenhouse effect. If the lapse rate or albedo is changed by addition of specific gases, this is a separate effect, and is not included here.
The case of Venus is a clear example of this effect. The average altitude where radiation to space occurs is about 50 km. The average lapse rate on Venus is about 9 C per km. The surface temperature increase over the case with the same albedo and absorbed insolation but no absorbing or cloud blocking gases, would be about 450 C, so the lapse rate fully explains the increase in temperature. It is not directly due to the pressure or density alone of the atmosphere, but the resulting increase in altitude of outgoing radiation to space. Changing CO2 concentration (or other absorbing gases) might change the outgoing
altitude, but that altitude change would be the only cause of a change in surface temperature, with the lapse rate times the new altitude as the increase in temperature over the case with no absorbing gases. One point to note is that the net energy transfer (from combined radiation and other transport means) from the surface or from a location in the atmosphere where solar energy was absorbed is always exactly the same whatever the local temperature. For example, the hot surface of Venus radiated up (a very short distance) over 16 kWm-2. However, the total energy transfer up is just the order of absorbed solar energy, or about 17 Wm-2, and some of the energy carried up is by conduction and convection. Thus the net radiation heat transfer is to be almost exactly the same as radiation up. The back radiation is not heating the surface; the thermal heat transfer resistance from all causes results in the excess heating.
In the end, it does not matter what the cause of resistance to heat transfer is. Th total energy balance and thermal heat transfer resistance defines the process. For planets with enough atmosphere, the lapse rate defines the lower atmosphere temperature gradient, and if the lapse rate is not changed, the distance the location of outgoing radiation is moved up by addition of absorbing gases determines the increase in temperature effect. It should be clear the back radiation did not do the heating.
the Air Vent 
It’s not about surface heating in the first place. It’s about inhibiting cooling.
Inhibiting cooling does not increase the temperature of the earth’s surface. The insulation on your house does not increase the interior temperature. The heating source determines the interior temperature. All the insulation does is reduce the amount of energy needed to maintain a specific temperature.
Ttca;
Ya, ya, everyone nose:
Key clause bolded just in case you can’t find it.
Edit: higher energy going in that leaving the wall. → than leaving
Leonard;
An interesting way of considering the “lagged” heat in the atmosphere/surface is to consider the imagined instantaneous addition of, or alteration of, the atmosphere to the base system. The additional time it takes for input energy to make it “out” is, say, L. The total available added energy is thus L x the input rate. After dispersion throughout the system, this determines the new equilibrium temp.
The equation can be run backwards, knowing input power and observed temp change to calculate L.
However, heat (which is the net transfer of energy, not the individual transfers) is only transferred down if the ground is cooler than the atmosphere, and this applies to all forms of heat transfer
If you write this, I assume the rest of what you write is also nonsense or badly written. Frankly, I can’t be bothered ploughing through all of this to see if it makes sense or not.
I’m surprised it was published here.
This seems to me a pointless argument. There is observed back radiation, averaging 333 W/m2, and it provides that amount of heating. You can argue about whether it should be offset against the upward flux as your fancy takes you.
Yes, the surface temperature can also be derived from the level of outgoing emission combined with lapse rate. But the lapse rate is a steady gradient, not an expression of flux. So how does it heat the surface? Primarily by back radiation. Most of that 333 W/m2 came from air (GHG’s) near the surface. That air is warm (though not warmer than the surface). And why is it warm? Well, you can attribute that to the lapse rate effect if you want.
“There was no added heat and no back heat transfer!”
This is a pointless comment. In a conductor, unlike with radiant transfer, you can’t measure directional fluxes. You can only measure nett fluxes, which are upward, just as they are with radiative transfer. Whether the molecular transfer incorporates back and forward transfer is a meaningless question. With turbulent transfer in air, for example, you could in principle distinguish directions of eddy flows, and try to characterize a back flux. Of course, you could never get it exactly, because it would change depending on the scale of motions you were prepared to resolve.
“Nick Stokes said
July 21, 2012 at 6:16 am
This seems to me a pointless argument. There is observed back radiation, averaging 333 W/m2, and it provides that amount of heating”
The Arctic winter temperature is about 240K, the emissivity of ice in the near IR is close to 1.0, so that gives us 186 W/m2 back radiation during the polar night.
Now the summer peak is about 282K.
The peak solar incoming is about 500 W/m2, with a large fraction reflected off the dirty ice, call it 65%, giving about 175 W/m2. So 175 + 186 W/m2 is 360 W/m2.
This would support a summer temperature of 283K.
So why is the ‘average’ back radiation of the Earths atmosphere so much higher than it is at the North Pole?
Doc, I don’t think your numbers for Arctic Temps are correct here. It’s true that near the edge of the Arctic circle, the July temps are about 283 K, (ie the Arctic Circle roughly coincides with the 10 °C isotherm) the temps deeper in the Arctic appear to be significantly cooler. At KNMI, getting daily data of 2m temperature from the NCEP reanalysis, inputting 66.5622 to 90 North, I get the maximum daily mean temperature for the year ranging from 276.521 K to 278.0263 K. The average is about 277 degrees. Now, that is the single warmest day. The seasonal average is going to be a little lower. BTW keep in mind that there is no regional balance of radiation.
Er, more accurately, there is no regional balance between the incoming solar radiation and radiation reflected+emitted. There is of course also horizontal transfer…
I just wanted to establish the temperature at max and min. The min temperature should give the background in the Arctic.
Nick,
I tried to lay out in a logical sequence how different types of resistance to direct heat transfer, in the presence of a constant energy absorption level, resulted in the surface raising to a higher temperature. If the radiation heat transfer is a very small or zero part of the total heat transfer (the first two cases I described), it is obvious that the back radiation is not the cause of the surface heating. Please note that even in these cases the surface is also radiating. However, the back radiation from immediately above the surface exactly equals the upward radiation. By your logic, this back radiation is heating the surface also. You simply did not get the point I made that any source of heat transfer resistance results in the a fixed energy input heating the surface to a higher temperature. How is the solid insulator different from the multiple radiation barrier or a mixed conduction, convection resistance? The only heat transfer is net energy flux, and it matters not at all how this is obtained. Making a special point with radiation is no different that the back energy from the velocity distribution resulting in some energy going backwards, but net energy transfer going outward.
Sean71,
You have said exactly nothing except that you do not want to examine what was said. Please explain what about the comment is wrong.
Brian,
I have only described the average equilibrium case. How you get there is subject for another blog, but obviously there is a pumping of energy into any thermal resistance until it reaches the new balance, and the details depend on the exact problem. I did have some bold in the text I sent. Some typos are hard to avoid.
Leonard,
Take the example of a thin vacuum gap with some conducting layer on the outer side. Start with zero thickness layer. That would correspond to your N=1 shell case, and the surface would be cool. Then add more insulation. The surface warms. It warms because the insulation impedes outflow, creating a temperature gradient and differential, but the actual mechanism of warming is then increased back radiation. There is a temperature differential (so the fluxes aren’t equal), and the difference is the nett flux, which is P, the fixed power generated.
I just can’t see the point of the distinction you are making. 333 W/m2 is 333 W/m2. It’s all part of the overall temperature and heat balance.
Nick,
I think the difference between your position and mine is somewhat a semantic one, but you seem to miss the basic point that there is no difference between insulation and a radiation resistance in effect. You are reversing cause and effect. If you look at the case with insulation of a totally opaque gas (closest example is Venus, but even that is not an ideal case), the back radiation is as large as outward radiation, and yet has nothing to do with the heating (the heat transfer resistance due to the insulation or gas slows the heat transfer forcing the surface to warm to raise the level back). Heating is due to heat transfer (by definition), and the second law clearly stated it is only from hot to cold! Heat transfer resistance is not back heat transfer, and it matters not that energy flows both ways. All energy transfer is due to either radiation (photons), electrical conduction (electrons or ions), diffusion (or convection) of molecules, or transmission of local vibration in solids (phonons), moving more one way than the other. All of the methods can have energy transmitted both ways, but only the net transfer of energy matters. Any process that changes the net flux is a resistance. Back heat transfer is an mistaken concept. There is only forward heat transfer, even though energy goes both ways.
Nick,
I want to know why you do not think there is back conduction or back diffusion heating of the ball for my first two cases, but call the back radiation a direct source of heating, rather than resistance like I defined it. It is true there is energy going back, and this results in a need to be hotter to transmit the required power, but that is true also of all heat transfer types.
I noticed a few problems in the text shown here. Please go to the original text for the correct version. It can be accessed by the connection shown at the top of the post.
Nick,
Lets use something with temperature variation like Venus. Choose a ball with a small gap in vacuum, followed by an insulation layer large enough to cause a large temperature variation. The internal surface power to be radiated then conducted out is 17 W per meter square (similar to absorbed solar surface heating on Venus). The insulation layer is thick enough and low enough thermal conductivity so that the bottom of the insulation is 723K, and the outside surface is only 131.6K for no additional absorption for this case. The question is: what is the surface temperature of the ball? From my eq (6), the ball is at 723.2K. That is the radiation gap caused an increase in surface temperature of 0.2K. That is, the radiation gap only caused 0.028% of the temperature increase. This despite back radiation of nearly 16,000 W per meter sq.
Nick,
To continue from the previous, the same example with no vacuum gap would still have a ball temperature of 723K, and that is only 0.2K less than before. The vacuum gap and back radiation were not even necessary for the large heating, and adding them had very little effect.
timetochooseagain,
It is about surface heating. The inhibition of cooling AT CONSTANT POWER IN, results in the surface heating up to maintain power out.
16-The power in is in that case the source of the heating. You can say that the temperature increased due to inhibition of radiative cooling, but that inhibition is of course not a source of heat. The power out is caused by the temperature, not the other way around.
Timetochooseagain,
I am not clear what point you are trying to make. Of course the power in is the source of heating. I never said otherwise. The power in is a fixed (selected) value. The transient response would be for the decreased radiated power at the initially lower external temperature to cause the insulating surface or radiator surface for radiation to store some energy and heat up until it reached the correct temperature to radiate the input power. From then on the input power would be the radiated power, and it would be steady, with no more storage in the insulator or external radiator. What you said make no sense given what I said.
18-My point is that I don’t think it’s really controversial that “back radiation” is not a heat source, but that is not, IMAO, as significant a point as many seem to think. This is because many, quite incorrectly, think that an additional source of heat would be necessary to raise the temperature. The only thing that is necessary is that the rate of surface energy loss be reduced, such that the body accumulates energy until it’s temperature reaches the level necessary to have a zero net energy loss + gain.
Timetochooseagain,
We agree based on what you just said. I thought you were commenting on what I had said. There are still many that do say it is just the back radiation that is the cause of greenhouse gas effects. That is what I was showing was basically misrepresentation.
OK, my quote didn’t work. It seems you want to define heat in your own terms, despite a significant body of standard physics which does not use quite the same definition.
What’s wrong with accepting that heat flows from cool bodies to warm ones, and vice versa, the equilibrium condition being when all flux are equal?
You seem to be contriving a language to make possible what you want to prove – I assume therefore that it is a waste of time trying to make sense or explain. This is sky dragon stuff, I think?
If you wish to make your position clearer, try writing a concise introduction which declares what you are proving and why first, but if you are discussing the semantics of backradiation, I care not for the use of the word.
Leonard,
<i."That is, the radiation gap only caused 0.028% of the temperature increase."
Again, I think it is a pointless argument. But the fact is that the only way the inner surface is warmed is by back-radiation across the gap. That’s the only way it is affected by the presence of the insulation.
Your N=100 array of shells, if equally spaced, would if you calculate it follow something very like a Fourier law. It’s thermally almost indistinguishable from a conductor. In fact, in some porous media what appears as conductive transport is substantially radiative transfer across internal cavities.
Radiation in an near-opaque gas (cf your example) also follows a Fourier law – this is called the Rosseland limiting case. You can see it as conduction but at each point, the heat is transferred by contrary radiative fluxes that you can measure.
Nick,
I do not see how you are missing the entire point. The ONLY source of the heating is the solar radiation heating at the surface for planets, or the internally supplied heating from the ball examples. The only effect of the back radiation is to SLOW down the outward heat transfer at the initial temperature (exactly the same as pure insulation does), and thus the solar heating or internally supplied heating raises the surface temperature to rebalance outgoing to supplied. The back radiation does not heat the wall. You cannot violate the 2nd law. You are still confusing individual energy transfers with net energy transfer (which is the heat transfer). I realize some of the confusion is the different definitions we use for some of the terms, but please re-read what I said.
Nick,
How is the surface heated for a pure insulator case. Doesn’t it have to be back heat transfer conduction, based on your argument? It doesn’t matter that energy is specifically going both ways. Only net energy is heat transfer, and only heat transfer (from hot to cold) can raise the temperature.
Nick,
In the opaque gas case, molecular diffusion and collisions transport most of the energy. In the ideal insulator, distributed molecular vibration (phonons) transmit the energy at local acoustic speeds. A mix of radiation, gas conduction (and possibly convection), and solid conduction have similar effects at suitable scales, and it matters not which does what, they all are a resistance to heat transfer. In real gases, radiation may have a larger role, but it is a mix of effects, and acts just like a conductor with a particular conductivity.
Sean71,
Please google articles to find the definition of heat transfer. An example of a version of the second law of thermodynamics, which defines limitations in heat transfer, is from the German scientist Rudolf Clausius, who laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, may be stated as:
“No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.”
Hi Leonard,
Of course you are correct that back-radiation is a patent nonsense. Hold a book up to the light … how much light comes through? None. Radiation does not pass though an absorbing medium … and air is an absorbing medium for IR emissions.
However, you mis-state Clausius. What he actually said was (closely translated):
“Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.”
Consider a comet hurtling towards the earth. It is icy cold. Much colder than the surface of the earth. How much heat does it pass to the earth when it smashes into it? You could ask the people who lived around Tunguska, Siberia around 1908 if you have any doubt.
What about a ball-bearing at 0C dropped from the upper atmosphere. It is colder than the sea. It accelerates and smashes into the sea. What is the net effect?
So a cold body CAN heat a warmer body if there is also a transfer of other energy (in the first instance mainly kinetic, in the second mainly potential).
Question for Everyone: How much potential (gravitational) energy does the 10 tonnes of air (per sqm) deliver into the ground when it drops 5cm overnight? How much heat energy is transferred into potential energy per sqm when the atmosphere is raised 5cm during the day?
Bonus Question: Now where does “back-radiation” come into it?
A.
Bonus question to Andrew,
Does the dark area of the moon at minus 243F heat the Earth or cool it?
@Jeff
You ask what happens with the moon when it has its darkside toward us with a temperature of 30K? Compared to what? Compared to, say, if the moon had the same temperature as background space?
There wouldbe a net heat transfer to the moon. The net heat transfer to the moon is less than would occur to empty space, instead of sb*(T^4 – 3^4) it is sb*(T^4 – 30^T4) for that tiny portion (5.1E-6) of sky.
In order for the four main radiative layers sea/land surface, cloud layer (troposhpere), tropopause and ozone layer to radiate net as much as they did before, they would warm up. A bit. It is a very negligible effect.
I would estimate that when the moon is showing darkside we are 0.000000065C warmer than if the moon were at 3K – same as background space(assuming that is the question … I’d have to do a bit more maths to work out the impact of darkside ‘v’ brightside and a lot more maths if you wanted to compare to no moon at all).
Is this what you were looking for? Do you get the same (or similar answer)?
Why do you ask this? Is there a point you are trying to make?
Leonard,
I think I see the point – I just don’t see why it is a point. Yes, of course the sun is the only source of nett heat. But the back radiation raises the temperature to a higher level than it otherwise would be at. I call that warming.
Back to Trenberth’s numbers – 161 W/m2 insolation is absorbed. But the surface is warm enough that it emits 396 W/m2. It even loses another 97 W/m2 by other paths. How can the surface stay warm enough to do this? Because it receives 333 W/m2 in back radiation. Of course, that is just part of the emission being recycled. But if not recycled (no GHG), it would be much colder.
Back radiation cannot raise the temperature. Only heat input or work can raise the temperature. It is gravity that does work and raises the temperature. The CO2 greenhouse effect does not exist. It does not exist on Venus. It is the higher surface pressure which is about 93 times that of earth that increases the pressure. Have you never pumped up a bike tyre using a hand pump. It gets hot due to the pressure. This is physics and it is what happens in the atmosphere.
Where does the back radiation come from in Trenberth? It is energy from nowhere and it is because of the incorrect assumptions about energy balances existing. Simplify the diagram and the maths rather than any physics tells you that it is entirely wrong. I cannot add a diagram here, but imagine the energy from the sun is S and this is absorbed by the surface. The surface emits energy E to the atmosphere, where it is absorbed. The atmosphere emits energy A equally to the atmosphere and the surface. Now look at the balance (incorrect) in the atmosphere. E = 2A and since for the earth S = A then the surface is emitting twice the energy it receives from the sun. This is the utter nonsense of human caused global warming.
27-Nick, 396 W/m^2 doesn’t sound quite right. It gives a black body temperature of 289 Kelvin. Shouldn’t it be more like 390 W/m^2? That would correspond to the commonly quoted value for Earth’s surface temperature at 288 Kelvin. What am I missing here?
TTCA
“What am I missing here?”
Non-linearity. The temperature isn’t uniform, and when it’s hot, the T^4 effect means that it emits more relatively. Or as Trenberth says:
“There is widespread agreement among the other estimates that the global mean surface upward LW radiation is about 6 W m-2 higher than the values in KT97 owing to the rectification effects described in the sidebar.”
1) “333 W/m2 is 333 W/m2.”
Which cannot be captured to do work.
I mean, thats about 33% of the noon day sun in the summer and you can certainly harness the noon day sun to do something can’t you?
2) You have a desert and a jungle. Equal CO2. Vastly different water vapor. The sun goes down. Which one cools off by 30C at night?
Why doesn’t that 333 W/m2 prevent the desert from cooling off?
29-Thanks Nick. So, the original estimate of KT97 was based on a blackbody Earth and using the mean temperature: I’m guessing other work pointed out you need to weight the temperature by radiative emission before averaging? And are they still using a emissivity of 1? Because thinking about it, they really shouldn’t be doing that, as the surface emissivity can’t be exactly 1.
Nick,
I think the main difference between you and I is now just semantics. It is how we define the use of words. There is going to be a slightly revised version of my writeup at scienceofdoom’s site, with his responses, so please look for it.
Sure looks like standard textbook physics to me. To rephrase the climate model problem in terms of this discission, how does the addition of an IR absorbing gas change the “insulating properties” of the atmosphere? Since we are dealing with convection and conduction as well as radiation, does the logarithmic increase in surface temperature caused by filling out the weak CO2 spectral lines overcome the linear increase in its radiative power at the top of the atmosphere that would be aided by convection?
Paul Lindsey,
The IR absorbing is just another resistance to direct radiation to space. The conduction, convection, evapotransporation followed by condensation, and IR absorption and radiation by absorbing gases all just raise the average location of outgoing radiation (to space) above the surface. Just as an insulator on an internally heated body raises the body temperature (required to match supplied energy to removed energy), the average location of outgoing energy results in a surface temperature increase. In the case of planetary atmospheres, the presence of the lapse rate and the altitude of outgoing radiation set the level of surface temperature. Adding CO2 does add some radiation resistance, so the average outgoing altitude slightly increases, and the surface temperature increases slightly.
Assuming a fixed lapse rate, the temperature of the “characteristic emission layer” (ie one optical depth into the atmosphere as measured from space) and the temperature of the surface would increase the same amount, but it is the temperature of the characteristic emission layer which must increase sufficiently to match the temperature of the lower level before added CO2. The temperature change that must occur at the surface is ambiguous. A constant lapse rate is one way to estimate the relationship between the two-but if the lapse rate may change significantly such an estimate will not be accurate.
Timetochooseagain,
The lapse rate does not seem to be changing. In fact, the only significant way it would is a change in the water vapor condensation effect (the rest of the lapse rate term is almost all due to Cp of the gas and gravity), and this does not seem to be significant enough to change the value. Thus the only way the surface average temperature would change is the increased altitude of outgoing radiation that would result from an increase in absorbing gases.
36-I would agree that so far the lapse rate isn’t changing the way it does in models, at least if we take satellite, radiosonde, and surface temperature data seriously. Still, I wouldn’t assume that means that the lapse rate remains approximately fixed. It may be that the lapse rate changes, but not in the manner models currently have it. Or it could be some of the data are wrong (say, too much surface warming). Or, boundary layer dynamics could be responsible for the behavior of the surface temps, thus making them disconnected, to some extent, from the behavior aloft, where the atmosphere may behave as if it were following the moist adiabat at least above the boundary layer, although not within it. Klotzbach et al. for instance, suggest that various processes involving boundary layer behavior have lead to a strong surface warming at at night that is not reflective of accumulated heat per se, but redistribution of heat within the atmosphere.
Interesting analysis. There is no question that “insulation” reduces heat flux. But insulation in the presence of cyclic heating and cooling cannot make *any* difference at all to equilibrium temperature. There is still a problem with the behavior of the IR absorbing/emitting gases. The ability of a gas to absorb and emit IR at the speed of light effectively permits it to transport heat *faster* and to equilibrate *faster* that one transmitting heat energy by conduction or convection. IR absorption/emission/scattering of an input IR source has been assumed to result in thermalisation, which has not been demonstrated to be real except within IR reflective chambers used to measure radiative transfer data. Some simple physics experiments could easily settle the question.
In the real world, if we take the internally heated uniform temperature ball and add IR absorption/emission, the result will be to permit IR to escape and hence cool. Nobody I have posed this to disagrees that an isothermal earth with no sun an no ability to radiate IR would be hotter at the surface. It is a simple argument that the addition of IR absorption/emission permits radiative thermal equilibrium with space and therefore net surface cooling.
I believe the cyclic heating/cooling effects on average will be independent of all known physical parameters – molecular composition, IR absorption, etc. Anything which might heat faster in the daytime sun will cool faster in the night. Anything which might absorb more in the day will emit more at night. Anything which can heat or cool asymmetrically in the heating/cooling cycle without the addition of work must represent a perpetum mobile.
Forgot to mention – I think the notion of a lapse rate is a function of conduction and convection and not radiation. IR radiation is able to penetrate directly anywhere that is optically transparent, even if attentuated somewhat by absorption/emission/scattering. The net radiative equilibrium temperature is a result of the integrated absorption/emission through the entire thickness of atmosphere and only the slowness of conduction/convection as opposed to the instant speed of radiation over distance creates the thermal gradient.
Blouis;
there’s an interesting test of atmospheric “back-radiation” that might be done. Instead of just comparing readings looking up and down, look left and right. Those should be the same as “back-radiation” if the theory has any legs whatsoever. All that omnidirectional radiating must really make the GHGs tired! 😉
There’s talk above of a “perfect insulator”. I think a one-way perfect insulator is a version of Maxwell’s Demon, and would result in an infinitely rising enclosed temperature!
Maxwell was ahead of his time. Maxwell’s demon is the “greenhouse effect”.
Yes, assuming an internal heat source, then of course it would, until the enclosure melts. Where else would the energy go?
And why is this relevant?
Re: steveta_uk (Jul 24 06:43), No internal heat source required, just an external one, like solar radiation.
Relates to the thought experiments mentioned above. Simply makes the point that insulators do in fact conduct, but imperfectly, slowly. The time it takes for heat to move through them determines how much temperature discrepancy between source and sink they can sustain.
Brian,
The case of the ball with a thin vacuum layer and a very thin radiation absorbing enclosure, with internally supplier power, has the heat moving through at the speed of light. The temperature increase did not depend in any way on the time it took for the heat to move through. The multiple layer radiation case, where the temperature got even hotter, also did not in any way depend on the speed of the movement. The other cases, including real atmospheres in sunlight do have large energy storage terms in the gas or insulation, but that only determines the lag time to equilibrium, not the temperature difference, and different versions can have different storage capability, but come to the same temperature difference. In other words, transmission time is not a cause of the difference.
The point is this. We think there is no significant heat loss from atmosphere to space by conduction or convection in a vacuum. The only mode of heat transport to space is radiation.
An internally heated ball (earth) without ability to radiate must warm. The ability of earth to radiate IR is what makes the surface cool. So “greenhouse gases” actually are responsible for surface cooling.
Sunlight adds some temperature on top of the internally heated radiating ball, which is dependent on solar output but not on any other physical parameter.
@Blouis79, the surface of the Earth produces a radiation spectrum that is close to continuous black-body. In the absence of greenhouse gases, this outward propagating radiative energy would radiate directly into space.
So, no, that’s not quite right, though it’s an interesting “thunk” anyway.
I have still not seen any empirical evidence of thermalisation of an IR absorbing/emitting gas. Tom Vonk has argued why this is impossible from theory and his explanation makes sense to me. The fact that earth produces a near continuous blackbody spectrum means that we can see it from space and that all matter emits some IR, as any IR thermometer or photograph will show. The much touted completely accurate radiative transfer data has been measured within IR reflective chambers and so is not proof of thermalisation by interception. That all matter can emit IR doesn’t say much for us needing GHGs. That matter can absorb and emit or reflect IR as seen on IR lit IR photographs also doesn’t say much for absorbing/emitting gases.
I think it is sad that people have misinterpreted Tyndall as measuring thermalisation, which he did not. Sad to assume thermalisation of which there is no theoretical basis (if you believe Vonk and the second law and Maxwell’s demon). Fail to experimentally demonstrate thermalisation, which in an instant would prove Vonk wrong and provide experimental evidence of a “greenhouse effect”. Fail to describe a consistent physical basis for a “greenhouse effect” – backradiation vs radiative insulation vs something else. Fail to properly account for heat energy – warming from the core is always a positive surface energy input vs surface radiation is cyclic heating/cooling and I think therefore the mean temperature in the instance of cyclic heating/cooling is totally independent of any physical parameter of the surface (excepting the existence of Maxwell’s demon or a perpetuum mobile).
This from twitter:
@ScotClimate: Scottish Government found to have lied on key figure. Is the Scottish Climate Bill dead?. Will the minister resign? http://bit.ly/OwkVl1
The Scottish government lied to politicians about key financial data which was central to the argument for the bill when they passed the Scottish Climate Change Bill. The government citing Stern said that the economic cost of a 2-3°C rise would be “between 5-20% of GDP”. In fact Stern suggests there may not be any net economic harm quoting figures of 0-3%
The figures are so key to justifying the bill, that it really is difficult to see how this bill could withstand a legal challenge.
… but the scandal gets worse. The Scottish paper (The Courier) which broke this story seems to have been lent on to remove the story. Presumably by someone in government.
This is about as bad as we can get. It appears the world’s most enthusiastic government for climate change is now embroiled in lies & cover-up.
Leonard:
Thanks for taking time to prepare your interesting post.
You said “the distance the location of outgoing radiation is moved up by addition of absorbing gases determines the increase in temperature effect”. I am commenting because most of these type of discussions seem to ignore the role of the bulk of the atmosphere, the non greenhouse gases.
Now my impression is that the characteristic emission altitude is governed primarily by the bulk density of the atmosphere at that elevation. At this altitude, the atmospheric density is such that the decay time for an excited GHG molecule is less than the mean time between molecular collisions. So the excited GHG molecules preferentially radiate to space rather than lose their energy to thermalization through collision with non GHG molecules. So it would seem that an increase in concentration of a trace GHG such as CO2 would not appreciably change the bulk atmospheric density at the characteristic emission altitude and the atmosphere at that same altitude would still emit equally well to space. So would it actually be that the characteristic emission layer is slightly broadened by addition of trace GHG’s rather than being raised? It seems that the effect would be miniscule and the only way to substantially raise the altitude of emission would be to increase the mass of the atmosphere by adding substantial amounts of gases of either type, GHG or non GHG. I think the clue to this is in the atmospheres of Jupiter and Venus which despite having very different atmospheric compositions to Earth’s, have a similar lapse rate structures to Earth’s at altitudes where pressures correspond to those of the Earth’s atmosphere. And yet Venus’s characteristic emission layer is 96.5% CO2 and Earth’s is 0.039 %.
Robert,
The average lapse rate only depends on Cp of the atmosphere and gravity (all planets), with some modification if there is evaporation and condensation in the atmosphere (as on Earth). It does not depend on radiative absorption at all as long as the lapse rate is maintained by sufficient atmosphere mixing. However, it is the effective altitude of outgoing radiation times effective lapse rate that determines temperature increase over an atmosphere with no absorbing gases. However, you have to have absorbing gases (so called greenhouse gases) for this altitude to raise higher than the surface. It matters not if the transport of net energy is mainly convective or net radiation conduction, only the effective altitude where it leaves is important, and this altitude does depend on composition.
Leonard,
But is “sufficient atmosphere mixing” not primarily induced the strong convection enabled by GHG IR absorption and thermalization in the lower troposphere? It would seem that the absorption function of GHG’s in the lower troposphere is saturated and adding more trace GHG’s would not change the lapse rate as it is fixed by other parameters. So as I understand it, the proposed effect of altering atmospheric CO2 concentration on Earth’s surface temperature lies primarily in the alteration in altitude of the effective emission layer in the upper troposphere. My point was that the effective emission layer occurs where the atmospheric pressure is within a certain characteristic range and that altitude is not primarily function of the partial pressures of trace greenhouse gases. So if you were to double CO2 concentration, the effect on the altitude of effective emission would be miniscule whereas if you were to double the amount of N2 in the atmosphere, the altitude of emission to space would be raised substantially and consequently, the Earth’s surface temperature would be dramatically raised. So Earth’s climate is primarily fixed by our planets atmospheric density and the wonderful properties of that three phase greenhouse gas, water. The single phase GHG’s are simply a spent force at present concentrations. Like doping silicon to produce a semiconductor, only a trace is needed for full function.
Robert,
No. “sufficient atmosphere mixing” is not, in general, primarily induced by the strong convection enabled by GHG IR absorption and thermalization in the lower troposphere, although this does contribute some to the process. The absorption of short wave solar energy on the surface and somewhat in the atmosphere make the surface, and regions in the atmosphere, where it is absorbed, warmer than with no input. This local excess energy is transmitted to the gas by conduction (from the surface), followed by convection, and by absorbed radiation, and the warmed gas rises driven by buoyancy. In addition atmosphere over regions from day to night input variation, and over different latitudes expands and contracts and causes currents and mixing (wind). The different forces moving the gas mix it, and on average raise it through the Troposphere, maintaining (on the average) a near wet adiabatic lapse rate, and transporting energy up to an altitude where it eventually radiates to space. In addition there is some direct radiation from ground (and oceans) to space. There is also some net radiation transported up by local absorption and local radiation. However if there were no greenhouse gases present, the removal of the energy from the TOA would not occur (it would all leave directly from the ground), and there would be no relative temperature rise of the surface, but the lapse rate would still exist if there remained enough mixing. However if the mixing were not enough, the atmosphere would tend toward isothermal.
The effect of doubling the CO2 has little effect at lower altitudes (it would not change the lapse rate noticeably) but all things equal, it does slightly raise outgoing radiation level a small amount, due to the fact that partial pressure of the absorbing gas is in fact the main cause of radiation location distribution for small mass addition to an atmosphere. Saturation of some wavelengths at the lower levels is not the important factor, only the altitude where transmission to space can occur, and this does depend on partial pressures.
Doubling total atmospheric gas while maintaining the initial CO2 level would not, in fact, increase the ground temperature for the ideal case. However, there are two effects which occur, which would cause some increase. The first is pressure broadening (due to change in collision frequency), and the second is a breakdown of the ideal adiabatic calculation as we approach the Tropopause, and the Tropopause raises up to a higher altitude at large increased total mass.
I really think this kind of discussion gets sidetracked by terminology. Emission altitude, needs to be replaced as often as possible with ‘average emission altitude’. The concept of emission altitiude is ONLY related to the deltaH of the average altitude.
In addition, the argument about whether back-radiation ‘heats’ or not is dependent on whether the reader understands the engineering definition of “heat”. I find ‘heat’ to be a particularly screwed up nomenclature for energy that would not exist had science not discovered physics in the temporal order which is required.
Energy does back-radiate. It causes more warmth to exist than would exist were the radiation to have not occurred. Call it insulation or whatever but it is energy and nobody except Doug disputes that here. What seems to be the discussion is again the outdated nomenclature that is ‘heat’ when we should only use the unit ‘energy’. If we re-wrote the entire post above replacing heat with energy (or power where appropriate) using appropriate context, the whole thing would become simpler.
Carrick has made similar points many times. Physics is a cocky field. They take pride in that their units and laws have been reduced to the true basic levels. IMHO, they are right and “heat” as a discussion point should be tossed from AGW. Far too much confusions occurs.
Energy does not equal heat. Heat is a type of energy, often considered a wasted conversion of others forms, since it is a byproduct of energy usage which is unable to do the useful work of the original form.
Energy does not radiate. Energy is not electromagnetic radiation. Electromagnetic radiation may transmit energy.
What you call backradiation is not a lot different to mechanical friction or electrical resistance or any other negative vector. In Newtonian terms, backradiation being equivalent to the Newtonian reaction would have a book being propelled off the table.
The greenhouse fantasy is as real as Maxwell’s demon. A simple experiment can easily settle it.
Heat is an oddly invented concept derived from bulk properties. It leads people to a lot of confusion which the post above attempts to rectify. We all know that thermal energy transfers in all directions, cold to hot included, yet heat as an engineering definition was created from bulk properties and only flows from hot to cold.
This leads to people making all kinds of ridiculous conclusions about the meaning of the second law of thermodynamics. It also leads to poorly worded yet accurate definitions of the second law.
Second Law of Thermodynamics: It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow.
Backradiation is an actual, measurable flow of energy in the cold to hot direction which is perfectly allowable in electromagnetics. No scientist I know of disputes this. What Dr. Weinstein has written is quite accurate though in terms of the bulk property of ‘heat’ although I must admit that the causality argument he makes about what causes warming is a little confusing to me. It is like asking whether home insulation in your wall back-conducts energy or simply slows the forward transfer. In terms of heat, it slows the forward transfer, in terms of energy, it back conducts reducing the net transfer.
Talking about back-conducting by insulation is a linguistic attempt to justify mistaken back-radiation. It is nonsensical. Reflective surfaces are used as radiative insulators, not IR absorbing/emitting gases. There is still no empirical evidence I have seen to quantify thermalisation of IR by a gas, which Tom Vonk has described as inconsistent with theoretical physics of thermodynamics.
Beyond the notion of “insulation”, there is still no theoretical basis for how *any* known physical property of any material can be used to change equilibrium mean temperature when subject to alternate heating and cooling effects over day-length cycles. Even if we covered the entire earth in a proper real thermal blanket or bulk insulative or reflective or vacuum nature, the equilibrium mean temperature of the earth would be no different.
Only Maxwell’s demon can do the job.
Re: blouis79Jeff Condon (Jul 26 08:41),
The experiment was carried out over 100 years ago and no climate scientist in the debate seriously thinks the atmosphere behaves like a greenhouse. The term is just jargon hallowed by history and reflects a mistaken 19th C idea of how greenhouses worked. The question was settled before WWI. Arguing over the term is just a terminological mire that slows any progress in mutual understanding and communication between the disputants. Using the term also permits “real climate scientists” ™ to comfort themselves with the idea the “unreal climate” (c) scientists are just amateurs and don’t understand the “science” because they don’t understand the jargon. It also helps divert skeptics off down rabbit holes that are delineated largely by terminology rather than physics. AGW types can then chuckle and rub their hands, enjoying the idea that skeptics just don’t understand.
The whole battle over what “back radiation” is and what it does is the same. Jeff’s point about the use of “heat” is probably one of the sanest observations you’ll read. “Back radiation” is really shorthand for the fact that once energy is re-radiated from the surface at different a different and longer wavelength, the path outward is likely to longer than the arrival path was; some will certainly find its way “back” to the surface. The real dispute between the team and the saner disputants lies in just what the “back radiation” does for the climate while it is finding its way back off the planet.
The holes in what climatologists seem to know about how climate works are monumental. it has known since the ’90s that thunderstorms generate gamma rays. Recently both electrons and positrons – beta radiation – have also been reported! An Italian group has announced measurements of gamma rays from thunderstorm that are at energies in the mega-electron volt range, equal or greater than those emitted by solar flares. The consensus seems to be that the Italian results need confirmation, but the key take away is that there are energetic process in the atmosphere that are largely unknown, if not entirely misunderstood. When gamma rays from thunderstorms were first discovered it was thought they were generated high in the ionosphere. That is now known to be false. They come from within the clouds themselves. [You can read about this in the latest Sci Am if you bother with mag. It’s now part of Nature.]
If you assume that the energy that drives thunderstorms is still solar energy finding its way back off the planet, then the current model for how solar energy leaves the planet is not fully balanced. It appears to offer no mechanism for generating gamma ray flashes in thunderstorms. Could that be some of the “missing energy?” How to account for the beta radiation – K40 decay in the atmosphere? Does it have a role in lightening discharge, perhaps triggering the initial plasma channel? How would that affect outbound radiation levels and terrestrial energy balances?
“Backradiation” is not much different from eddy current in an electrical circuit. It may be there, it may be real, it may be measureable. It doesn’t do much. I still have not seen any experimental evidence to quantify thermalisation of IR absorption in IR absorbing/emitting/scattering gases.
That the atmospheric lapse rate can change resulting in a small change in surface temperature I have no problem with. But there is no such law as conservation of radiative equilibrium and the so-called physics isn’t beign properly treated by climate scientists, who can compute with energy, mass and specific heat capacity.
Yep pretty much agree with Jeff. Lots of bulloxed up language floating around here, don’t see much point in contributing too much, till people get their language straightened out. Leonard’s post unfortunately is full of them. In the mean time, enjoying watching http://www.facebook.com/MichaelMannScientist Getting tutelage on “how to communicate effectively with the public by calling them roaches if they don’t drool on his every word”. He’s the Master, we’re just his pupils.
Here’s some problems that I see: “Heat” doesn’t even have the right units for back radiation (radiation is measured in units of energy per unit time per unit area)
Secondly, as Jeff points out, heat’s an invented concept used to try and describe equilibrium thermodynamics before we had non-equlibrium thermodynamics (necessary to take the appropriate limit to equilibrium). It’s called a “process variable” as if that say anything, but it’s not a directly measurable quantity. (Back radiation is… the energy impinging on the ground at long wavelength IR for example might be a definition.)
Getting the units right matters. Getting the language to match that of standard radiative physics matters. Arguing over ghost definitions of back radiation is useless, describing how you would measure it in principle (and in practice) is useful.
Starting from the measurable quantities (hint: heat is not one of them) then build up a description from there is my suggestion, or at least start with a reference to a clear explanation of the measurables. Ideas like lapse rate and conduction should only be introduced if it is clear these are useful in describing the phenomena (lapse rate is useful immediately, conduction only after you’ve rederived Fourier’s Law so that it become evident that this is a useful analog).
Carrick,
I agree that getting rid of words like heat would decrease the chance for confusion by some. However, it is used, and I attempted to clear up best use if it is retained. I would like to know what parts of my writeup call for “Leonard’s post unfortunately is full of them”. I did use the terms power per m2 and call it just power some places, but I defined what I was referring to early on, so I don’t think that is the problem. Please be specific.
Leonard I’m sure you understand the concepts and in a peer reviewed paper you would be more careful in language. Switching e.g. radiative power with power or even with (more commonly) energy would not I suspect be replicated for example. It is unfortunate because it just leads to an endless string of comments by people who aren’t technically savvy enough to make the translation “oh he meant…” in their heads.
It’s important with atmospheric physics to recognize that while we are discussing equilibrium phenomena, time happens, and because it happens we must discuss rates rather than absolute amounts of heat energy exchange.
If you were to go to the literature, yes you’ll find the term “heat” used, but you’ll find it gets interchangably used in many contexts besides that of a “process variable” and other than as a process variable it is not even a physical quantity.
The fact that abused terminology gets used should not be used as a reason to continue using it. In fact the opposite holds true. (In a carefully worded article, I might have a paragraph at the end making the connection to “heat” as the process variable). In reading through your article it wasn’t clear to me at times whether you were using (the noun) “heat” in reference to the process variable or in the scrambled up way it sometimes gets used. Your phrase “No back heat transfer” comes to mind here. If “heat” is the net thermal energy exchanged between two bodies, what does “back heat transfer” even mean in the context of a body for which clearly there is a net loss of radiative heat energy (which exactly balances the average radiative heat energy absorbed from solar + internal heat energy sources)?
Carrick,
I agree with your comments. The issue I have been trying to present arises from comments made by very smart people that back radiation heats the ground, and in fact is a major source of the greenhouse effect. Heat transfer is a net energy transfer, so heat transfer to the ground implies a downward direction of net energy transfer. This is what I called back heat transfer, and is actually true in some special cases, but not in general, or on average. I think the whole issue would go away if people only used the energy transfers, and only net values.
A bit late to the party, I know, but I see this entire post as a quibble over semantics. I see nothing in it that contradicts the “mainstream” explanation of the greenhouse effect, only issues in terminology.
When the mainstream explanation says that the back-radiation from greenhouse gases “warms” the earth, it is in the sense that the presence of this back-radiation results in a higher surface temperature than would be the case if there were no such back-radiation. It is not to say that this back-radiation results in a net heat transfer from atmospheric gases to the earth’s surface.
Actually, semantics aside, I find this post a quite good standard explanation of the greenhouse effect.
Curt,
If the mainstream explanation did imply just what you said, I would exactly agree with you. However, many have exactly implied that this back-radiation results in a net heat transfer from atmospheric gases to the earth’s surface, adding to the solar input, and that this rather than the lapse rate combined with the average outgoing radiation altitude is the cause of the increased temperature. The facts are the same both ways, but it seems to me to be a confusion of cause and effect. The main problem resulting is to not acknowledge the basic role of the lapse rate, and this leads to confusion of the physics of the process.
Say I purchase an $8 item from you. I give you a $10 bill and you give me 2 $1 bills in change. If we diagram the flow, it would be perfectly valid to show $10 from me to you, and $2 from you to me. What would not be valid is to show the net $8 flow from me to you, and also the $2 “change” flow from you to me.
Similarly, it is valid to show the “back radiation” from atmosphere to earth, as long as the (on average) larger radiation from earth to the atmosphere is shown as a gross, not net, value. Obviously, the difference is the net flow. I would actually prefer an accounting that shows both gross flows of radiative energy, because both are measurable, and there are conditions in which the net flow is in the opposite direction.
Curt,
Since the absorption path decreases with concentration increase of CO2, and the lapse rate is essentially constant, the temperature difference between the back radiating layer and surface decrease inversely to concentration. Double CO2, half distance, half temperature difference. Meanwhile, the increase in surface temperature is about 1.2 C per doubling (all other things being equal). Due to the non-linear (4th power) radiation law with temperature, this implies that radiation net energy flux decreases at the same time that total energy flux is constant (solar energy in has not changed here), and surface temperature is increasing. The greater the CO2 concentration, the less the radiation heat transfer, and the more the convection and other energy transport. The end point is an opaque gas out, so no radiation heat transport, but maximum back radiation (and it is exactly like the insulation case). Yet these are exactly the condition for increased heating due to raising the outgoing radiation to space from increase greenhouse gas.
Knowing which fraction of energy transport is due to radiation and which fraction is due to convection may be useful for some purposes, but the total transport is a constant, and the net contribution due to radiation actually decreases with increase in CO2. Only the average altitude of outgoing radiation and the lapse rate matter for temperature increase.
@leonard weinstein
I can only agree with the statements in your paper.
I have been writing on the problem of a stack of semi-transparent layers, and you might appreciate my results.
Click to access IR-absorption.pdf
There is a lot in your paper, so I can’t respond offhand. However, in the end, there is such a thing as back radiation in the form of photons going that way. However, only net radiation energy transfer heats anything, and so back radiation, as a separate entity cannot heat.
While an interesting theoretical exercise, the radiation-only model or atmosphere cannot prove anything. A real model has to factor all modes of heat transfer.
Real laboratory physics experiments can simply settle the basic science behind the greenhouse fantasy, eg:
1. If IR absorbing/emitting gases can thermalise IR radiation outside of an IR reflecting measurement chamber.
2. If *any* known physical property of any material can be used to change equilibrium mean temperature when subject to alternate heating and cooling effects over day-length cycles.
3. If presence of IR absorbing/emitting gases accelerate or retard thermal mixing of gas mixtures of different temperatures.
1. Been done see CJM Simpson.
2. Been done, see any number of optical T jump experiments or pulsed IR heating experiments
3. No
This has been a service of Rabett Labs.
Any more clues to CJM Simpson?
Optical t jump or pulsed laser on wrong time scale. But still interested to see papers – any good ones you know?
Still hoping one day to find a physicist interested in real experiments.
Excellent post, Leonard!
There’s a thought experiment that I’ve found useful for explaining why it isn’t just a different emphasis on the usual back-radiation argument, and that is to study the greenhouse effect in a shallow pond of water.
Water is transparent to sunlight (close enough) but very opaque to thermal IR, absorbing it in less than a millimetre. So we consider sunlight shining through the water in a pond, being absorbed by the black bottom, and re-radiating as IR. The water now acts like a super-powerful greenhouse gas, radiating it back down.
A pond emits back-radiation massively, but no warming of the bottom results. This demonstrates that back-radiation is not synonymous with greenhouse warming. The temperature difference in a convective medium is controlled by the lapse rate and average emission altitude, which are both near zero for a pond.
The pond water is very definitely emitting hundreds of watts of back-radiation downwards to the surface, exactly balancing the hundreds of watts being emitted upwards. The net result is that in the limiting case of an infinitely intense greenhouse effect, energy transport by radiation cancels out to zero. If there were no other heat transport mechanisms at all then this would indeed cause infinite warming, but in the presence of other mechanisms it is the other mechanisms that determine the temperature. It is really just about the physics of internal radiation inside opaque materials, and one would never normally say this internal radiation “heated” the material.
I’ve tried it out a few times, and I have found that a number of intelligent people wedded to the conventional way of looking at it still have difficulty wrapping their heads around it. It’s not perfect, by any means. But I found it useful for myself.
The write-up was on why back radiation is not a source of surface heating. I think a short description of the sequence of processes show how the greenhouse effect actually takes effect is needed as a separate comment. It is briefly shown below:
The process of adding CO2 to the atmosphere occurs from the surface, and convection and mixing distribute it to the rest of the atmosphere over a finite time. However, let us consider an addition of an instantaneous well mixed quantity of CO2, small enough to not significantly affect the average CP or total mass of the atmosphere, so that the temperature level and lapse rate are also the same as before, immediately after the addition of the CO2. Also assume solar insolation is the same as before, and only consider solar energy absorption to occur at the ground. The question is: how does the surface and atmosphere heat up more from the greenhouse effect. The approximation will be used that the lapse rate, surface temperature, and solar insolation, are uniformly distributed over location and time to simplify the issue.
When the CO2 level jumps up, the effective average outgoing radiation altitude to space also instantly increases. The average altitude was about 5 km before addition, due to previous levels of water vapor, CO2, and other greenhouse gases and clouds. An increase from doubling the CO2 has been claimed to cause an eventual increase in temperature of about 1.2 C if all other effects are unchanged. For an average environmental lapse rate of -6.5 C per km, this implies the average outgoing altitude was raised by about 185 m once new equilibrium was reached.
However, the raise in outgoing altitude would occur as soon as the CO2 level increases, and is not directly tied to the temperature. It is a radiation absorption issue only. Since the temperature was 1.2 C lower at 185 m above the initial 5 km altitude, the radiation to space is initially lower from the new altitude than it was at the previous altitude. When input and output were balanced, the average temperature of the 5 km level was 255 K, and radiated 239.7 W/m2. Initially at the new altitude (5.185 km), the average temperature is 253.8 K, and radiates 235.3 W/m2 (just after the CO2 level made the step jump, the air temperature is still the same as before). However, the increased resistance to radiation heat transfer up, due to the more opaque atmosphere, results is less of the absorbed solar energy being initially removed from the ground by radiation heat transfer (which is a significant, but not necessarily dominant means of heat transfer up). Note the back radiation is not heating the ground; it is just slowing the radiation heat transfer upwards. This accumulating solar energy results in the ground heating up as the excess energy accumulates. Once the ground heats up a small amount, this increases both convective and radiation heat-transfer compared to just before the ground heated noticeably (but after the CO2 was added). However, at new equilibrium, total heat transfer out is the same as before (equals solar energy input), but the radiation heat transfer is less than before the CO2 was added, since convective heat transfer is larger. i.e., the convective heat transfer is a larger fraction of total heat transfer up at new equilibrium.
The transient increased heat transfer before a new equilibrium is obtained does not change the lapse rate at the new final equilibrium from before the CO2 was added. However, since the increased surface heating started immediately at addition of CO2, but the thermal lag of the finite mass of the atmosphere took a while to re-balance by convection and radiation, the lapse rate does increase some during the non-equilibrium stage. In the end, the energy is transmitted by conduction, convection, and radiation up through the atmosphere, driving it toward the same lapse rate as before the CO2 was added (since the higher lapse rate is unstable, and cannot be maintained), but with the entire temperature level shifted up 1.2 C for corresponding altitudes. This leads to the temperature at 5.185 km to be 255 K at the new equilibrium. At that point, the outgoing balanced incoming, and no additional heating of the surface or atmosphere occurred.
Surface heating is the crucial issue and i agree that Back-Radiation is not the real reason for surface heating.
An important clue is that the surface actually radiates more energy (117% according to Nasa) than incoming solar. The only reason it can do this is because it is being recharged by back radiation (which roughly equals incoming). When a ml of water evaporates, absorbing 540 calories from the surface, the resulting cooled surface will certainly recieve and be warmed by DLR but the flux is constant and instantaneous to the point that it becomes meaningless to attempt to ascribe the source. The point is that the flux between the surface and the atmosphere is larger than the incoming solar energy and this discrepancy is the greenhouse effect.
The important clue is that there is not agreed physical mechanism of the so called “greenhouse effect”. Climate scientists think it happens because IR absorption is a real phenomenon.
But though I keep looking and asking, there are great gaping unanswered holes in the physics.
1. Blackbody radiation is independent of molecular composition. Have not seen any experimental proof stating otherwise. So until someone can prove to me that composition does matter, it doesn’t matter what the atmosphere is made of. Excepting things that change albedo, the earth’s effective radiating temperature will only depend on solar input.
2. There is no experimental evidence of thermalization of IR by *any* so-called greenhouse gas. Emission is temperature dependent. IR absorption is real. So is temperature-dependent IR emission. Temperature of earth is determined by radiative thermal equilibrium with the sun in the day and space at night. Radiative transfer data is all measured within IR-reflective chambers – guess how much heat escapes from those?
3. There is no coherent consensus physical mechanism described for how the “atmospheric greenhouse” works. Consequently, it cannot be tested experimentally. Climate scientists claim there can be no valid experiments on our single atmosphere.
4. Measurements of earth’s temperature and CO2 levels mean nothing more than correlation.
Any of 1-4 could be easily demonstrated to be true or false in a laboratory experiment, which would “settle” the basic science. I have described numerous potential experiments on Judith Curry’s blog. All we need is some interested physicists with laboratories and some money to fund some proper experimental research. It seems beyond climate scientists to do physics research.
So, within the bounds of a more or less constant and sun-dependent earth temperature measurable from space, there are chaotic thermodynamic processes largely convection-driven within the the confines of the atmosphere and within the depths of the oceans. These complex chaotic unpredictable thermodynamic effects are responsible in large part for weather and surface temperature fluctuations. Radiative thermal equilibrium can only be a stabilizing influence.
You sound like Doug Cotton.
“1. Blackbody radiation is independent of molecular composition. ”
Blackbody is an ideal body. Blackbody approximations are often used but are not expected to match experiment. Read some books, any books at all before writing nonsense like this.
“There is no experimental evidence of thermalization of IR by *any* so-called greenhouse gas. ”
Not true at all. There is a million tons of evidence to support heating of gasses using IR. Again, you sound like Douggie!
“3. There is no coherent consensus physical mechanism described for how the “atmospheric greenhouse” works.”
There is an exact, describable process which at least guarantees a non zero warming from CO2 addition to the atmosphere. There is consensus because everyone in science would need to go back to high school to correct the fundamental physics.
” Measurements of earth’s temperature and CO2 levels mean nothing more than correlation.”
They also mean that CO2 levels are increasing and even if the isotope ratios show 50% of the CO2 increase is from fossile fuels, basic chemical fractionalizing means the primary contribution to CO2 increases is man-made.
This is not an argument which reasonable people can have. It is stupidity, misunderstanding and propaganda mixed in a bucket of ignorance and I am very tired of teaching children who won’t listen.
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Jeff, the core of the problem is experimental science, not hand-waving assertions.
Point me to a “blackbody” experiment showing a different “blackbody” material results in a different radiative equilibrium temperature.
Show be one published paper demonstrating thermalization of IR by a gas free to radiate IR to space.
Perhaps you can explain the physical process by which you think CO2 warms the atmosphere, and back it up with experimental verification of said effect in a laboratory experiment. (candidates appear to be: backradiation, radiative “insulation”, and thermalization)
Put up or be nice.
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