"According to NASA data Mars has roughly 10x as much atmospheric CO2 as Earth. The inverse square law givens energy input from the Sun at about 40% of Earth if my mental arithmetic is correct. This should mean significantly higher back radiation on Mars than Earth."

It doesn't work like that. The greenhouse effect in a convective atmosphere is caused by a combination of the adiabatic lapse rate (the change in temperature of a gas being compressed and expanded as it rises and falls in altitude; the rason the tops of mountains are colder than their bottoms) and the average altitude of emission of thermal infra red to outer space being higher up when the atmosphere contains IR-opaque gases. A fixed amount of heat enters the system per unit time, and the temperature of the whole system adjusts until exactly this amount is radiated out into space. It's the surface that radiates the radiation that converges on that temperature, which in the case of an opaque atmosphere is above the solid surface. The solid surface will then be warmer than this (this is what gets called the 'greenhouse effect') because of adiabatic compression/expansion of air convecting between those levels.

Thus, the magnitude of the greenhouse effect does not depend on the total amount of CO2, it depends on the altitude of the IR-visible 'top' of the atmosphere. On Earth it's about 5 km up, mostly because of water vapour but with clouds, CO2, and dust having an effect. On Venus, it's about 50-80 km up, and radiation is emitted mostly by the clouds rather than CO2. On Mars it's less than 1 km up, because the atmospheric pressure is so low. There's more CO2, but without nitrogen and oxygen to lift it up, it forms a very thin layer near the ground. I can't remember the numbers now, but I think it was a few degrees C.

For an even more powerful example, consider liquid water - say a shallow pool a metre deep. Water is very opaque to thermal IR, absorbing most of it within about 20 microns. Having absorbed it, it then of course re-emits it, both up and down, as does each 20 micron layer above it. Thus, in backradiation terms, water constitutes an incredibly powerful 'greenhouse'. It's a relatively simple calculation to show that considering the commonly presented 'backradiation' physics as the only heat transport mechanism, the temperature should be several thousand degrees a metre down! (Every cubic metre of water emits megawatts of backradiation internally, but virtually all of it cancels out.) If backradiation was really how it worked, the oceans would boil.

They don't, because the explanation is wrong. When Arrhenius published his estimates of the CO2 greenhouse effect based on the backradiation idea, the physicist Angstrom debunked it within a few years of publication. It wasn't until around the 1960s that the real mechanism was understood by climate scientists, based on work on stellar atmospheres by Schwarzschild (of 'black hole' fame). However, this has been known since the 60s, so why the 'backradiation' argument still persists is a mystery.

Thanks for the clear answers, it was a bit of a devils advocate question looking for confirmation of my own thoughts. Personally I think that the adiabatic lapse rate with the sun providing the major energy input explains an awful lot, and back radiation is a red herring. Particularly why Mars is relatively cold at the surface and Earth is considerably warmer. I also understand that the reason it is windier on the top of mountains (with certain caveats) is that as the moving air rises over the mountains it is prevented going higher in altitude by the layers above and has to speed up in order to move the same mass per unit time.

TBYJ
The NASA data for all planets can be found here it says Average temperature: ~210 K (-63 C) for Mars and 288 K (15 C) for Earth.

"... so why the 'backradiation' argument still persists is a mystery."

By taking a radiometer reading in one direction only, assuming that it acts as kinetic energy when in fact it acts as potential energy because of radiation oposing it. There is only one source of energy - the sun. Once that energy enters the system you can't count it more than once before it exits to space.

But some people do.

How about this, ignoring GHG theory.

Consider that our planet is a solid/liquid sphere with an outer shell of gases. These gases are concentrated at the surface due to gravity. There is a concentration gradient across the thickness of the shell, tapering to zero gas molecules at the outer surface of the shell (edge of space).

Now, consider the BB radiation emission from the planet. The earth surface radiates but this is not really the surface of the planet. There is a layer of gas molecules very close to the surface at the same temperature, more or less. Then there are more gas molecules that are just slightly cooler and so on.

If an observer in space looked at the earth where would the surface of the black body lie? Logically it would lie somewhere in the gas shell. Intuitively it would be closer to the earth surface than the edge of space, say about one third of the way through the shell.

I’m suggesting that BB temperature equates to the temperature at the effective BB surface and this is corresponds to the BB radiation emission that balances solar energy received.

Because of the gas laws and gravity, the gases below this altitude are more compressed and therefore their temperature is higher. This results in the higher temperature at the surface. This of course is the lapse rate in action.

Now, some of the gases can selectively absorb at particular IR wavelengths. They can also re-emit at these wavelengths. They do not alter the energy balance between the system under consideration and space because these interactions do not change the total energy within the system. They simply redistribute heat within the system. In this respect they are not very effective compared to convection and ocean currents which are major heat transport processes.

The balance between the earth system and space is self adjusting. If the earth gets warmer, more energy is radiated until a balance is achieved.

I’m not terribly convinced by the IR opacity argument. The concentrations of IR absorbing gases are very low. In the lower atmosphere molecular collisions are a thousand times more likely than photon emissions so excited GHG molecules just dissipate kinetic energy. In the upper atmosphere collisions are less but so are gas concentrations including GHG. IR opacity is probably negligible.

"Because of the gas laws and gravity, the gases below this altitude are more compressed and therefore their temperature is higher."

Be careful. It's not purely the gas laws and gravity - convection is required as well. Without convection, there is no rapid rise and fall of gas, and so no adiabatic compression/decompression. Without convection, you get a stratified, static atmosphere, and conduction and radiation become the only operating heat transport methods, with radiation dominant (because it's faster). If you didn't have radiation either - say the Earth was in radiative equilibrium with its uniform-temperature surroundings - then eventually conduction would equalise the temperature (over a few thousand years), and all the atmosphere would be at the same temperature top to bottom.

Temperature differences drive convection, which forces air upwards and downwards through the compress/expand cycle like the motor of a refrigerator drives the refrigerant through a similar compress/expand cycle, thus maintaining a temperature difference between one end of the cycle and the other. Maintaining a temperature difference against the second law of thermodynamics' tendency to equalise everything requires a 'power' supply (more precisely, a source of low entropy), which the temperature differences between equator and pole, day and night, sunny and cloudy supply. This mechanism only works in a convective atmosphere.

To demonstrate the effect of blocking convection, consider the example of the 'solar pond'. This is a shallow pool of water filled with salt water at the bottom and fresh water on top. This creates a density gradient that resists convection - at least until the temperature difference is high enough to overcome it - leaving conduction and radiation as the only mechanisms of heat transport. Radiation heat transport through water is also virtually non-existent - as I mentioned above - so all you've got is diffusion-based conduction. The result is that heat entering and being absorbed at the bottom runs against a large thermal resistance getting out, and the bottom of the pool heats to around 90 C in the sun. This can be used for power generation, although the efficiency is low.

Without convection, the backradiation mechanism applies. But in any convective atmosphere - which they all are - it is completely dominated by convection, which itself is limited by the adiabatic lapse rate. Backradiation no longer has any say - it is completely short-circuited. Note, there are circumstances on Earth where convection is stopped - inversion layers and the polar winters, for example - and radiative effects once again come into play. But these are not the norm.

The idea that gravity and gas laws alone explain the adiabatic lapse rate is a common error, but one there is no need to make. It doesn't concede anything to acknowledge the role of convection in this.

"In the lower atmosphere molecular collisions are a thousand times more likely than photon emissions so excited GHG molecules just dissipate kinetic energy."

Doesn't matter. What matters is the average altitude of emission to space, which is where thermal equilibrium with the Earth's surroundings occurs. You can 'see' where that is using infra-red satellite cameras, and it's definitely well above the surface.

And molecular collisions are a two-way street - they can also excite molecular vibrations as well as dissipate them, causing emission. It doesn't matter how the material is heated - whether by absorbing radiation or by being put on a hot stove - some fraction of the energy bouncing around between the different energy types gets radiated thermally. The kinetic energy of the molecule gets converted during collisions to excited electrons, which can (and do) emit. That's where thermal radiation comes from.

"In the upper atmosphere collisions are less but so are gas concentrations including GHG. IR opacity is probably negligible."

"Probably"? :-)

I should have included convection which is crucial.

The main point I was trying to make is that GHG back radiation is used to explain why the earth's black body temperature is lower than the surface temperature. I don't think this explanation is needed.

The difference in altitude between the two locations together with the lapse rate and its associated processes are sufficient to explain the differences.

GH gases absorb and emit energy and affect our system's internal energy distribution, but then so do convection, ocean currents and other variables.

My final sentence is ambiguous. I'll re-phrase it.

GH gases can alter the distribution of energy. There are other processes such as convection and ocean currents that transport energy too.

I'm simply saying that a lot more (such as the control of our climate) has been attributed to GH gases than they deserve.

"The main point I was trying to make is that GHG back radiation is used to explain why the earth's black body temperature is lower than the surface temperature. I don't think this explanation is needed."

Yes, I agree. In fact, I regard it as very misleading, and at least some of the general confusion and argument is down to their use of it.

"The difference in altitude between the two locations together with the lapse rate and its associated processes are sufficient to explain the differences."

That's a good summary.

"GH gases can alter the distribution of energy. There are other processes such as convection and ocean currents that transport energy too. I'm simply saying that a lot more (such as the control of our climate) has been attributed to GH gases than they deserve."

Indeed. There's horizontal convection, changes in humidity, storms, high and low pressure systems, evaporation, wind, rain, ice, the many effects of clouds, aerosols, the ozone layer, the interaction between troposphere and stratosphere, the meandering of the jet streams, surface albedo, bacteria releasing dimethyl sulfoxide to trigger rain, cosmic rays, ENSO, the thermohaline circulation, upwelling and downwelling, trade winds, oceanic climate oscillations (PDO, AMO, NAO, IPO, NPO etc.) and so on. There's actually a lot of really interesting physics and chemistry in climate science - the turbulent atmosphere/oceans are probably the most complicated physical system we have direct access to. But the only thing anyone ever seems to want to talk about when you bring the subject up is CO2.

But that's politics for you.

Excellent, it is so good to find someone who agrees!

Have you got any idea why most climate scientists favour the back radiation explanation? I mean technical reasons rather than funding, etc.

Radical Rodent - good discussion topic. I agree that discussions here do peel back some of the confusion and expose the basics.

I think there is a problem with the GH effect and it is not just technical. It is fashionable to accept it. To question it is to admit that you are not quite right in the head. This position is more difficult to defend when the pause demonstrates that the assumptions are flawed in some way.

Another aspect that I've noticed is that every GHG explanation I have read implies that the black body temperature and the earth surface temperature should be the same. Then the rabbit from the hat is the back radiation which explains why they are different. This back radiation is then the basis of the GH effect and the 33 degrees or whatever becomes the magnitude of the warming ability of the GHE.

When you realise that the black body radiation actually occurs high in the atmosphere, then the two different temperatures are what you would expect. They are a consequence of the lapse rate. The need for back radiation as an explanation disappears and with it the climate controlling nature of the GHG effect.

It makes me wonder how we got here, hence my question above.

I suspect it's because it's what they were taught, themselves.

There is a problem in teaching about extremely complicated systems: that you can't do it all at once. If you try, you just overwhelm with details and complications, and the student just gets lost. So most approaches tend to take it gradually. You start off with an explanation that is simple to understand, but wrong. When they understand it thoroughly, then you elaborate on a few of the biggest problems, then fill them in, or hint at how they could be filled in. Then you give them a more complicated explanation, that because they have a general map of the territory from the first explanation they can follow more easily. Make sure they understand how this is an improvement, and what it explains that the earlier explanation didn't, and then when they're confident in it, raise some more of its limitations and problems, and explain what you're approximating or simplifying that causes them. And so on.

Done well, students learn the system in stages, can cope with the complexity at each stage, but are always aware of the limits of their knowledge and what they don't know. Done badly, it can leave people with the impression they understand fully when they don't, and be left with incorrect and inconsistent beliefs - which can then make more trouble as they try to fill in the gaps in their knowledge while staying consistent with what they've been told.

I suspect the reason is historical. The backradiation argument was the original theory, which then got modified (by Manabe, Strickler, Wetherald, etc. in the 1960s) by incorporating convection, which because of the non-linear way it works completely dominates the process. Since starting with a radiation model and adding convection gives the right answer, they think of it as just a minor modification/correction of the basic backradiation process. Few pause to consider that it's actually now easier to start with convection. It's like going to the town centre via your old house, where you used to live on the other side of town, because that's the route you first learnt. (And does it matter, they might argue, if it gets you there in the end?)

There may be other reasons - I don't know. I think that when first teaching about the physics of heat flow, conduction is by far the simplest, followed by radiation, followed by convection (at least, if done in any detail). They could be starting with the non-convective mechanism because it's simpler, or more familiar from the physics of heat flow. Or maybe their point is that the adiabatic lapse rate is a limit on the gradient set up by other processes, and those other processes conceptually come first. Rather as if you were to explain the temperature of a pot of water boiling on the stove being exactly 100 C by saying it's because that's the boiling point of water, without first explaining the gas burner underneath the pot. You could argue that the basic explanation of the temperature is the burner, and that the non-linear boiling point effect is just a modification to that, that just so happens to regulate the temperature at 100 C.

That last explanation (that radiation is conceptually prior to the adiabatic limit) seemed to be ScienceOfDoom's interpretation, last time we discussed it. But that's as much information as I've got on the subject, and I really don't know why they do it.

Radical Rodent
Thanks for the original question, I remember enough from 45 years ago to understand a lot of the basics of the discussions, which have confirmed my belief that the popular current theories/hypothesis do not provide a decent explanation of anything climatic.

Just for the record, assuming a surface temperature of 15 degrees and a lapse rate of 6.4 degrees/km and the 33 degree difference, the BB radiation is from about 5km up where the temperature is -18.

And not any GHG in sight. It makes perfect sense but I still don't understand why all these climate scientists are peddling a myth. It seems unbelievable to me. The lapse rate explanation seems perfectly adequate. I just find it impossible to understand why the climate people cling to the GHG effect when they must know it isn't needed and that all the GHG articles are misleading.

"And not any GHG in sight."

The GHGs are why the emission altitude is 5 km up. More GHGs raises the altitude.

The (scientific) issue has never been the mechanism of the basic greenhouse effect. The issue has always been the feedbacks, that it is claimed triple it. The basic mechanism was, as I said, correctly determined back in the 1960s. The feedbacks are still unknown.

I'm not convinced about the atmosphere being opaque to IR at these low GHG concentrations. Water vapour will change the lapse rate but that is because of heat capacity. I don't see the need to include greenhouse gases.

I would say that the emission altitude is a consequence of the planet having a temperature gradient rather than a single surface temperature. That gradient is a consequence of the atmosphere and convection mainly. The GHG contribution is overrated I believe.

Is there a reference to the "correctly settled science" and did they have evidence? I don't believe anything that climate scientists claim.

Mr Cat

Should your approach not be to state your theory - eg the equations that underpin it - and then show how they outperform the GHG theory? Referring to words such as "lapse rate" and "heat capacity" does not really work. What predictions does your theory make and how do they differ from what is measured?

"I'm not convinced about the atmosphere being opaque to IR at these low GHG concentrations"

Isn't this shown by various measurements that have been produced in the course of this thread?

"I'm not convinced about the atmosphere being opaque to IR at these low GHG concentrations. Water vapour will change the lapse rate but that is because of heat capacity. I don't see the need to include greenhouse gases."

Fair enough. What evidence would convince you? What observations would distinguish a transparent atmosphere from a translucent/opaque one, and are they possible to make?

There are plenty of IR pictures of the water vapour band, easily available.
http://www.goes.noaa.gov/WCWV1.html
http://weather.unisys.com/satellite/sat_wv.php?inv=0&t=l12&region=us
http://www.weather.gov/satellite#wv

I take it these don't convince you?

If the atmosphere was completely transparent to thermal IR, why would the average emission altitude be 5 km? Why not zero? How can a transparent material that by definition doesn't interact with light of those frequencies emit light?

(Incidentally, water vapour changes the lapse rate primarily because of the latent heat of condensation, not its heat capacity.)

I think you're falling into the trap here of thinking the 'optical thickness' explanation somehow replaces the 'back-radiation' explanation, or the 'greenhouse' explanation. I realise dyed-in-the-woolers have a particular aversion to the GHE, and must get rid of it at any cost, but lets not throw the baby out with the bathwater.

Thought-models such as optical thickness and back-radiation are describing the same phenomenon. Like all analogies, they concentrate on one aspect at the expense of the others, as a teaching tool, to demonstrate some of what is happening.

The theory is in general terms, that having an atmosphere that is partially opaque to outgoing IR hampers the escape of heat energy from the surface to space. That is all. This means it can't cool down as fast as it would during the night time phase of the planet's rotation, which means the air is on average warmer than it would be otherwise. That is all. Everything else is just detail, some of it less helpful than others.

Back-radiation was a misguided attempt to help visualise where the 'extra heat' comes from, picturing the GH gas as some sort of flat mirror up in the sky somewhere bouncing back photons. This explanation suffers with problems of analogy, it is highly simplified and doesn't really describe the actual phenomenon, only the effects. The atmosphere acts as if it was a big long wave mirror, in as much as some long wave radiation ends up back on the surface, but that's as far as the analogy works. It's not a mirror, and the energy isn't 'back' as such - like all random heat energy it's omnidirectional. But it was a simple model answering the simple question of where the extra heat came from, it wasn't intended to describe the mechanism in detail.

Now the optical thickness argument is explaining the same phenomenon, but from a slightly different perspective. People asked, surely after a certain amount, GHG don't add any extra effect, once you've intercepted an IR photon from the surface and dissipated it as kinetic heat to other air molecules, it doesn't matter if there were 10 or 1000 other GHG molecules it might have hit. One is enough, so surely the concentration after a certain point doesn't matter. people also pointed out that convection was dominant at low altitudes, not photon exchange.

So the optical thickness explanation is there to show that increasing the concentration raises the optical ceiling, which is another mythical concept, like the IR mirror which doesn't really explain the complexity of the real system, but gives a flavour of it. IR photons in the lower atmosphere thick with GHG have no chance at all of making it out to space, most heat is exchanged kinetically - and convection is the major way that heat gets away form the surface. At a certain point - the optical depth - the concentration of GHG is low enough that photons stand a good chance of getting away to space unhindered. So in this model, the atmosphere is divided into two layers - one opaque layer where heat rises due to convection with a lapse rate, and one transparent layer, where heat escapes radiatively.

The point at which this happens is the average optical thickness, and this is the layer which is radiating to space at the same flux level as is arriving. The temperature of this layer can be calculated simply from the Stefan-Boltzmann equation linking temperature and emissions by area, since we know how much insolation is reaching the earth.. The temperature gradient of the opaque layers underneath can be calculated using the gas laws to give the temperature at the surface.

The upshot of increasing the concentration of GH molecules is to raise the ceiling - the exact changeover position between the opaque and transparent layers - which means that it is radiating from a higher position, which means the gas laws and lapse rate mean the surface temperature must be higher (so the analogy goes)

Now this explanation, whilst attractive in that it seems to be more sophisticated than the backradiation model, suffers from exactly the same problems of analogy. There is no 'point' at which IR emissions can start, there is no layer. The atmosphere is not opaque at low levels, it's a gradient from bottom to top. Also the higher the emitting layer, the larger an area it has to emit from, which lowers the temperature, which lowers the lapse rate temperature. Nothing is as simple as it would suggest.

But they are explaining the same thing. The back radiation model is showing that some of the LW radiation that leaves the surface ends up back on it again, this theory concentrates on photons to warm the surface, to make it easier to understand. The optical thickness argument explains it in terms of gas pressure, lapse rates and convection, this theory concentrates on kinetic heat transfer to warm the surface, to make it easier to understand.

The truth is neither of them are totally accurate, both make massive generalisations and ignore the contribution of the other. When you are standing outside on a summer's night, you are being warmed both by energetic air molecules warmed by convection and conduction, and also by IR photons which are bouncing around in the atmosphere between GHG molecules which happen to be aimed back down to earth. You are also being warmed by air molecules which have themselves been warmed by collision with an energetic GHG molecule which got energised by absorbing a LW photon. A LW photon which leaves your skin could quite possibly be the lucky one which escapes out to space without being intercepted. Or it might bounce around until, the quantum of energy sometimes being a photon, sometimes being a kinetic quantum being convected up to altitude, ending up in the higher more transparent layers where it escapes to space. Or equally likely, hits the grounds again and keeps it a bit warmer. It's a mixture. All of it is happening at once.

It's not one trumps the other. Both explanations simplify reality to produce an understandable model which is easier to visualise. People not trained in science may not be familiar with such dualities in physics (google wave-particle duality) but sometimes models are useful for one aspect and an apparently different model useful to calculate another. It's not one tribal group of 'backradiaters' lining up with iron bars and pitchforks against the 'optical thickers' with their wrods and shields. They are both useful.

"The theory is in general terms, that having an atmosphere that is partially opaque to outgoing IR hampers the escape of heat energy from the surface to space."

And what does that mean for the pool of water?

Nullius, your pool of water analogy was even more flawed as a description of atmosphere, for a start, it doesn't have a pressure-driven lapse rate. Secondly it doesn't have a large sink of non-participating molecules to store and transport heat non-radiatively. Thirdly, and probably most importantly, it is not heated from below, the way the atmosphere is.

Your pool gets a hotter surface layer, and that is all. Using the back-radiation analogy, half of the IR goes to the layer below, half back out to the air. The layer immediately under the top layer now gets half the energy, the layer below a quarter. Obviously half which went to the layer above, half of it comes back, so it's not purely a halving each time, but it decreases rapidly in a diminishing return. Within a cm or so, there is no heat in the water.

Your idea that the bottom of the pool would boil is not sustainable under even this simple examination.

You are falling into the trap I described that because the back-radiation model is a simplification, then it must be discarded. It's just not very useful in the case of a pool of water, because that's not what it was designed to describe.

Nullius in Verba

" say the Earth was in radiative equilibrium with its uniform-temperature surroundings - then eventually conduction would equalise the temperature (over a few thousand years), and all the atmosphere would be at the same temperature top to bottom."

Lets pick a certain value for this uniform temperature lets say 10C for instance.
The same isothermal temperature at all points of the atmosphere

Are you sure?

Remember the surface still radiates.
At the equator a maximum of around 100C is possible yet because of cosine dilution this drops to around -270C at the poles.
What about the night facing hemisphere?

Will it stay at 10C all night

Does it really matter what best describes the GE: it is not man-made. What is at issue is the effect of man-made CO2. While SoD was here a while ago it was stated that additional CO2 raised the average height of emission to space and as 'higher up is colder', those emissions dropped in magnitude. That caused an imbalance in energy flow and therefore energy was 'trapped'. This 'trapped' energy is calculated to add 1 degC for a doubling of total atmospheric CO2. All forcing calcs use this 1 degC as their starting point.

My problem with that is that trapped energy has to not reveal itself in the atmosphere because to do so would increase temperatures at ground level immediately. For me, the more likely is that as the average height of emission rises its radiation temperature travels with it and its effect is immediately apparent at the surface via the lapse rate. Therefore, no energy is trapped: incoming = outgoing at all times (24 hour average). If that is the case then the basic 1 degC starting point for feedbacks may be eroneous. This does not argue against CO2 causing surface warming but does question the adopted 1 degC starting point for the feedback arguments that follow from it.