Stephen Wilde: How conduction and convection cause a greenhouse effect arising from atmospheric mass.

This guest post from Stephen Wilde offers a descriptive theoretical and qualitative perspective on the ‘gravito-thermal’ theory. It covers the vertical profile of the atmosphere as well as the surface temperature comprehensively quantified by Nikolov and Zeller’s latest paper.

Introduction

The current scientific consensus is that Earth’s so called ‘greenhouse effect’ is caused by the presence of radiating gases in the atmosphere but many years ago, I learned what  I then understood to be the consensus view that it is actually a result of atmospheric mass such that the radiative characteristics of the atmosphere are either wholly or largely irrelevant.

The ‘greenhouse effect’ is an apt description for the mass based phenomenon because warming, descending air (which is occurring over half the planet at any given moment) will inhibit convection in the same way as does a greenhouse roof and by dissipating clouds it increases incoming sunlight through that barrier to convection just like the transparency of a greenhouse roof.

If the greenhouse effect is attributable to atmospheric mass rather than radiative characteristics then the fact that the vast bulk of Earth’s atmosphere is comprised of mass that is non-radiative is likely to mean that human emissions of radiative gases are not important as a regulator of surface temperature.

If correct, that calls into question the validity of many recent political decisions relating to global energy supplies.

I will tackle this issue in stages.

First I will briefly explain how conduction and convection within the atmosphere can raise surface temperature by 33K in the case of Earth.

I then refer to the radiative law that predicts that a body at a specific temperature must radiate at that temperature and will attempt to justify my assertion that the application of that law is not always appropriate for a surface beneath a convecting atmosphere.

I will conclude by referring to a number of problems for the theory that radiative gases cause the greenhouse effect.

1) The mass induced greenhouse effect.

1. i) Start with a rocky planet surrounded by a non-radiative atmosphere such as 100% Nitrogen with no convection.

Assume that there is no rotation to confuse matters, ignore equator to pole energy transfers and provide illumination to one side from a nearby sun.

On the illuminated side the sun heats the surface beneath the gaseous atmosphere and, since surface heating is uneven, gas density differentials arise in the horizontal plane so that warmer, less dense, Nitrogen starts to rise above colder, denser, Nitrogen that flows in beneath and convective overturning of the atmosphere has begun.

After a while, the entire illuminated side consists of less dense warm rising Nitrogen and the entire dark side consists of descending, denser and colder Nitrogen.

The Nitrogen on the illuminated side, being non-radiative, heats only by conduction from surface to air and cannot assist cooling of the surface by radiating to space.

There will be a lapse rate slope whereby the air becomes cooler with height due to expansion (via the Gas Laws) as it rises along the line of decreasing density with height. That density gradient is created by the pull of gravity on the individual molecules of the Nitrogen atmosphere.

At the top of the rising column the colder denser Nitrogen is pushed aside by the warmer more buoyant and less dense Nitrogen coming up from below and it then flows, at a high level, across to the dark side of the planet where descent occurs back towards the surface.

During the descent there is warming by compression as the Nitrogen moves back down to the surface and then the Nitrogen flows along the surface back to the base of the rising column on the illuminated side whereupon the cycle repeats.

Thus we have a very simplified climate system without radiative gases consisting of one large low pressure cell on the illuminated side and one large high pressure cell on the dark side.

1. ii) The thermal consequences of convective overturning.

On the illuminated side, conduction is absorbing energy from the surface the temperature of which as observed from space  initially appears to drop below the figure predicted by the S-B equation. Instead of being radiated straight out to space a portion of the kinetic energy at the surface is being diverted into conduction and convection. Assume sufficient insolation to give a surface temperature of 255K without an atmosphere and 33K absorbed from the surface into the atmosphere by conduction. The surface temperature appears to drop to 222K when observed from space. Those figures are illustrative only since there is dispute about the actual numbers for the scale of the so called greenhouse effect.

On the dark side the descending Nitrogen warms as it falls to the surface and when it reaches the surface the cold surface will rapidly pull some of that initially conducted energy (obtained from the illuminated side) out of the descending Nitrogen so that the surface and the Nitrogen in contact with it will become warmer than it otherwise would have been, namely by 33K.

One can see how effectively a cold, solid surface will draw heat from the atmospheric gases by noting the development of radiation fog above cold surfaces on Earth. The cold surface quickly reduces the ground level atmospheric temperature to a point below the dew point.

That less cold Nitrogen then flows via advection across the surface back to the illuminated side which is then being supplied with Nitrogen at the surface which is 33K warmer than it otherwise would have been.

That describes the first convective overturning cycle only.

The key point at that stage is that, as soon as the first cycle completes, the second convective cycle does not need to take any further energy from incoming solar radiation because the necessary energy is being advected in by winds from the unlit side. The full effect of continuing insolation can then be experienced once more.

ADDITIONALLY the air moving horizontally from the dark side to the illuminated side is 33K warmer than it otherwise would have been so the average temperature for the whole sphere actually rises to 288K

Since that 33K flowing across from the dark side goes straight up again via conduction to fuel the next convective overturning cycle and therefore does not radiate out to space, the view from space would still show a radiating temperature for the planet of 255K just as it would have done if there were no atmosphere at all.

In that scenario both sides of the planet’s surface are 33K warmer than they otherwise would have been, the view from space satisfies the S-B equation and radiation in from space equals radiation out to space. Radiative capability within the atmosphere not required.

2) The radiative ‘Problem’

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html

“The thermal energy radiated by a blackbody radiator per second per unit area is proportional to the fourth power of the absolute temperature”

known as the S-B equation.

Having set out the above conduction/convection cause of the greenhouse effect there is an immediate and substantial problem in that basic physics clearly states that a body radiates according to its temperature but I have just described a scenario whereby a planet with a non-radiative but instead a conducting and convecting atmosphere produces a surface temperature of 288k, radiates from surface to space at 255k and conducts between surface and the mass of the atmosphere at 33k.

The dominant theory of the radiative Greenhouse Effect clearly relies on that above principle of radiative physics and deals with it by proposing a surface warming effect from downward infra-red radiation (DWIR) within the atmosphere, such DWIR being the cause of the ‘extra’ 33K of kinetic energy at the surface which then raises surface temperature from the S-B prediction of 255K to the observed 288K.

I am using those numbers for convenience though I am aware that some researchers dispute them. The actual numbers make no difference here.

So is it atmospheric mass returning kinetic energy to the surface (retrieved from potential energy in descent) or is it DWIR that causes the greenhouse effect. It cannot be both.

It must be the case that a body of a specific temperature isolated from all other influences would radiate at a rate commensurate with that temperature. No issue there.

But suppose such a body with an atmosphere were subjected to a flow of externally sourced energy onto the surface and then out again AND, that during the flow of energy through the surface / atmosphere combination, other processes within the atmosphere were going on that were slower than simple radiative transmission.

Would there not be a partitioning between the radiative flow and the other slower processes with a backing up of kinetic energy within the system leading to a higher surface temperature than that explicable by radiation alone?

Conduction and convection are slower processes of energy transmission than radiation so a planet experiencing a throughput of insolation and possessing a convecting atmosphere must be an exception to the simple radiative rule of thumb. I will now go on to explain the underlying physics.

3) The reason why the S-B equation does not adequately deal with surface temperatures beneath a convecting atmosphere

The conditions that must apply for the S-B equation to apply are specific:

“The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (also known as the black-body radiant emittance or radiant exitance), j ⋆ {displaystyle j^{star }} , is directly proportional to the fourth power of the black body’s thermodynamic temperature T:”

In summary, when a planetary surface with zero reflection is subjected to insolation the surface temperature will rise to a point where energy out will match energy absorbed.

During the very first convective overturning cycle a planet with an atmosphere does not act as an ideal blackbody because the process of conduction and convection draws energy upward and away from the surface thereby converting kinetic energy (heat) at the surface into potential energy (not heat) within the body of the atmosphere.  As above, the surface temperature when measured from space appears to drop from 255K to 222K. The rate of radiative emission during the first convective cycle is less than energy received and that ‘missing’ kinetic energy has been converted to potential energy within the atmosphere which effectively removes that energy from the radiation budget altogether since potential energy is not heat and cannot be emitted.  For a period of time the planet substantially ceases to meet the blackbody approximation implicit in the requirements of the S-B equation.

Due to the time taken by convective overturning in transferring energy from the illuminated side to the dark side the lowered emissivity during the first convective cycle causes an accumulation within the atmosphere of a large amount of conducted and convected energy and so for a planet with an atmosphere the S-B equation becomes far less reliable as an indicator of surface temperature. In fact, the more massive the atmosphere the less reliable the S-B equation becomes as a guide to final surface temperature during the formation of the first convective overturning cycle.

For the thermal effect of a more massive atmosphere see here:

http://onlinelibrary.wiley.com/doi/10.1002/2016GL071279/abstract

“We find that higher atmospheric mass tends to increase the near-surface
temperature mostly due to an increase in the heat capacity of the
atmosphere, which decreases the net radiative cooling effect in the lower
layers of the atmosphere. Additionally, the vertical advection of heat by
eddies decreases with increasing atmospheric mass, resulting in further
near-surface warming.”

At the end of the first convective cycle there is no longer any energy being drawn into potential energy form from the incoming radiation because, instead, the energy required for the next convective cycle is coming via advection from the unilluminated side. At that point the planet as viewed from space reverts to acting as a blackbody once more with energy out equalling energy in.

But, the dark side is then 33K less cold than it otherwise would have been and the illuminated side is also 33K warmer than it ‘should’ be.

The S-B equation being purely radiative has failed to account for surface kinetic energy engaged in non-radiative energy exchanges between the surface and the top of the atmosphere.

The S-B equation does not deal with the scenario of ongoing recycling of kinetic and potential energy within convective overturning and the consequent effect on surface temperature, it only deals with the whole system as viewed from space so it would appear that AGW theory is applying that equation incorrectly to planets with atmospheres.

It is the incorrect application of the S-B equation that has led AGW proponents to propose a surface warming effect from DWIR (Downward Infra- Red Radiation) within the atmosphere so as to compensate for the missing non-radiative surface warming effect of descending air that is omitted from their energy budget. That is the only way they can appear to balance the budget without taking into account the separate non-radiative energy loop that is involved in conduction and convection.

DWIR exists but it has no additional surface warming effect since it emanates from any radiative  molecules in contact with or just above the surface rather than from the higher levels of the atmosphere. DWIR from those lowest molecules is a consequence of the initial conduction to those molecules from the irradiated surface and not a consequence of DWIR coming down from colder  radiative material at higher levels.

Note that the lapse rate structure of the atmosphere arises from non -radiative processes and higher, colder, radiating molecules cannot provide additional heating to the surface below.

The amount of DWIR from the atmosphere to the surface is in lockstep with the lapse rate structure which is a consequence of atmospheric mass conducting and convecting within the gravitational field. DWIR is a mere side effect of mass and gravity and not a cause of, or any sort of contributor to, the surface temperature. If radiative molecules do warm to a higher temperature than that appropriate for their position along the lapse rate slope then convective adjustments occur to neutralise the radiative imbalance in order to retain hydrostatic equilibrium.

http://www.public.asu.edu/~hhuang38/mae578_lecture_06.pdf

Thus radiative material within the mass of an atmosphere is not permitted to heat the surface. Instead, they merely cause air circulation adjustments that would be too small to discern against the background of chaotic climate variability.

4) Problems arising from the theory of the radiative greenhouse effect.

1. i) If greenhouse gases block outgoing radiation and route it back to the surface for a surface warming effect then the warmed surface sends up more radiation and those same gases send back down part of the added warmth in a never ending positive feedback. An additional positive feedback is proposed by the warming effect generating more water vapour which is also a greenhouse gas. No such positive feedback has ever been observed.
2. ii) The energy budgets that I have seen propose that convection has a net cooling effect on the surface by moving surface energy upwards ready for radiation to space from any greenhouse gases that capture it at a suitably high level. That is fine for the solely diabatic part of the process of energy transfer within the atmosphere but does not deal with the adiabatic aspect of convective overturning whereby kinetic energy taken from the surface in ascending air is returned to the surface in descending air for a zero net effect from pure (adiabatic) convection. I have heard objections that such warmed descending air cannot heat a solid surface by conduction due to the low density of air but as pointed out above a cold, solid surface draws heat from air very effectively.

iii) The concept of downward infra-red radiation (DWIR) is confused and flawed. The impression is often given that there is a discrete flow of radiation from all points of the atmosphere down to the surface but due to the lapse rate slope cooling with height that is not the case. The only location where the air radiates at 288K is where it is in contact with the surface and no additional warming effect is derived from any air above that point. If the air from which DWIR is emanating is only from the air in contact with the surface the very concept of DWIR is meaningless.

1. iv) The air temperature of 288k at the surface is a consequence of conduction from surface to air and it is such conduction that creates the entire lapse rate slope. As one moves up from the surface the molecules become spaced further apart due to the declining density gradient created by gravity so further upward conduction becomes more difficult as one goes upwards hence the cooling of the air with height in accordance with the Gas Laws. Radiative effects do intervene at various heights such as from ozone in the stratosphere but the rule holds well enough for the troposphere despite interference from the small amount of greenhouse gases of which the dominant one is water vapour. Hence the reliability of the US Standard Atmosphere used in aeronautics and rocketry.
2. v) It is correct that CO2 blocks the exit of certain energy wavelengths to space but there is good evidence for the proposition that such energy is rerouted and escapes at different wavelengths. When CO2 absorbs such energy it distorts the lapse rate slope so that convection is slowed, humidity builds up at lower levels, water vapour condenses out at a lower, warmer height and the blocked energy is emitted to space by water vapour instead. That process would prevent any surface warming from CO2.
3. vi) It is established science that for an atmosphere in hydrostatic (meaning fluid not water) equilibrium and suspended off a surface then radiative imbalances of any kind are corrected for by convective changes. That would apply to greenhouse gases which do interfere with the radiative balance.

http://www.public.asu.edu/~hhuang38/mae578_lecture_06.pdf

vii) There is evidence from other planets that the temperatures at the same pressures as for Earth are very similar after adjusting for distance from the sun despite vast differences in the radiative characteristics of the atmospheres. That tends to support the mass induced greenhouse effect rather than the radiative version.

1. ix) There is no upper troposphere ‘hot spot’ as predicted by the radiative theory.
2. x) Global temperature trends are not proceeding as anticipated.

This is not an exhaustive list.

The currently accepted ‘consensus’ of the greenhouse effect as a product of radiative gases rather than of atmospheric mass needs to be reconsidered.