David Cosserat: Atmospheric Thermal Enhancement Part I – The Great Debate Begins

My thanks to David Cosserat for the effort he has put into this guest post. It takes stamina to debate the subject matter, and while we have made progress here at the talkshop on the issues around energy in the atmosphere, it has become spread over a lot of disparate threads. Here, David pulls it all together, rationalises it and flags up the areas of agreement and disagreement between the parties. this is a thorough basis from which we can move forward to discussing the thermodynamic and gravitational aspects which will be elucidated in part 2.

Atmospheric Thermal Enhancement

Part I – The Great Debate Begins
David Cosserat – Feb 4 2013

Two threads have been running at the Talkshop recently. One was a posting on 06 Dec 2012 by Tim Folkerts. He is a mainstream supporter of the AGW theory and frequent blogger. He bravely agreed with TB to write an article entitled:  Tim Folkerts: Simple argument supporting a radiative greenhouse effect. The other thread was initiated on 14 Dec 2012 by TB himself entitled: Emissivity puzzle: energy exchange in non-vacuums.

These articles have between them generated hundreds of responses, indicating that they cover subjects of great significance to Talkshop readers. In the end the first thread ran dry in favour of the Emissivity thread but not before Tim and I and several others had engaged in a very lengthy dialogue where, surprisingly, we made quite good progress towards a common understanding on several issues relating to the ‘greenhouse effect’, particularly on things that we agreed were not part of the effect.

That discussion then continued in the Emissivity thread. Eventually the thread got so long that TB’s laptop started to groan. At this point it seemed sensible to take stock of the situation and do a re-start. This posting, which simply reviews what we discussed and where we agreed and disagreed, will establish the groundwork needed to take us forward to resolving what I believe is just one remaining significant outstanding difference of opinion.

To summarise, Tim and I (and a few others) agreed that:

• GHGs are essential for inputting short wave (SW) radiant energy from the Sun.
• GHGs are essential for outputting long wave (LW) radiant energy to space.
• The warming in the bulk of the atmosphere is due to its FIXED FUND of Kinetic Energy.
• The accompanying ‘fog’ of radiation is a consequence, not a cause of that warmth.
• Downward radiation between atmosphere and surface is not a myth. Acceptance of this fact is an essential prerequisite to a proper understanding of the thermodynamics of the atmosphere.

There were plenty of minor disagreements over terminology which we managed to paper over as being inessential to the main discussion. Tim for example doesn’t much like my emphasis of the term Kinetic Energy that I use all over the place, a practice that I am afraid he will see continued here. And Steven Wilde reminded me about the significance of Potential Energy as an additional internal energy storage mechanism. Meanwhile we both had an entertaining and friendly standoff with one commentator, Max, who repeatedly challenged our explanations about why the energy flowing through a system that includes back radiation and non-radiant flows will always obey both the 1^st law and the Stefan-Boltzmann law simultaneously. He’s still arguing, but that’s what a blog trail is all about.

And, of course, we had the statutory assertion, without which no blog trail is complete, that the atmospheric column has a larger cross-sectional area at the top than at the surface; and that this fact might just possibly completely mess up all our conclusions. Thanks, Entropic Man, for politely pointing out that the surface area at the tropopause is less than 1% larger than at the surface.  J

Although our models of energy flows and energy storage in the atmosphere turned out to be in broad scientific agreement, nevertheless I, a climate skeptic, and Tim, a mainstream warmist, have polarised views on whether or not it is the so-called greenhouse gases (GHGs) that control the temperature of the earth’s atmosphere. In the end, the anticipated disagreements melted away with the exception of  just one: although we agreed that some kind of energy flow restriction mechanism must be operating to achieve the enhancement of today’s world mean temperature of 288K (15degC) over the much lower mean surface temperature it would have if it had no atmosphere, we couldn’t agree on the exact mechanism that causes the Kinetic Energy to accumulate in the bulk of the atmosphere, thereby producing the consequential boost in atmospheric temperature:

• Tim believes that the atmosphere’s warming is caused by a controlling effect at the Top of the Atmosphere (ToA) where the GHGs convert the Kinetic Energy (KE) to radiative energy that is then output to space. He asserts that the throttling effect would increase as the concentration of GHGs increases. Consequently the Earth’s mean surface temperature would increase.I call this OUTPUT THROTTLING, a bit like screwing down the safety valve on a pressure cooker.

• I (and others) suspect that the atmosphere’s warming is caused by a throttling effect in the bulk of the atmospheric column, due to the fact that convection is a slow process that physically impedes the rate at which the Kinetic Energy can be delivered up the column to the ToA and thence to space. This mechanism would be independent of the level of GHGs in the atmosphere, assuming their concentration is already more than enough – which it is – to fulfill its two vital roles: (a) converting incoming SW radiant energy from the Sun to Kinetic Energy; and (b) converting Kinetic Energy back to LW radiant energy that is lost to space at the Top of the Atmosphere.I call this THROUGHPUT THROTTLING, a bit like the increasing restriction on the rate at which a fluid flows through a long narrow pipe as the pressure increases.

THE CHOSEN EARTH-ATMOSPHERE MODEL

Before we go into the details of energy flow, let’s briefly review what Tim and I (and some others) agreed was a suitable model of the earth-atmosphere system on which to base further discussions. Here’s the diagram:

The figures shown in square brackets are flux density values for the energy flows between space, atmosphere, and surface. These figures are taken from the Earth’s Energy Balance diagram published in the 2009 paper by Trenberth, Fasullo & Kiehl.  I do not endorse these figures as being perfectly correct but they are very helpful as an indication of the approximate proportions of the various energy flow channels. But what is important from the point of view of producing a coherent steady state model is that the input and output energy flows should balance exactly, as follows:

Earth System External Flows

In from Sun: 341Wm^-2
Out to Space: 102+199+40 = 341Wm^-2

Surface flows

Into surface: 161+ 333 = 494Wm^-2
Out of surface: 17+80+356+40 = 493Wm^-2

Atmosphere Flows

Into atmosphere: 78+17+80+356 = 531Wm^-2
Out of atmosphere: 199+333 = 532Wm^-2

Well they almost balance! Trenberth kept back 1Wm^-2 for global warming and there is also another 1Wm^-2 math error. But most of their flow estimates are subject to quite large unknown errors and so a watt or two per square metre here or there is simply ‘lost in the noise’. From our point of view that won’t matter, unless any of the Trenberth figures turn out to be grossly incorrect, which I doubt. As far as I know, nobody has come forward with any major corrections since 2009. So these are the figures that I will use below as the basis for making the discussion a little more concrete.

DOWNWELLING RADIATION

However, before we can proceed there is one thing that is essential for the credibility of the above model: agreement that long wave (LW) radiation really does flow in both directions across the surface-atmosphere interface.

Some climate skeptics use the appearance of ‘down-welling’ radiation in the Trenberth Earth’s Energy Balance diagram as a sign of the devil. They say: energy is being magically created in a loop, so how can we take these people seriously when what they are proposing is against the 1st law of thermodynamics? They ask how Trenberth’s flow of 333Wm^-2 back to the surface, and 356Wm^-2 from surface to atmosphere can be feasible if the source of energy, the incoming flow from the Sun to the earth’s surface, is only 161Wm^-2. At first glance it does look a bit like extra energy is being created from nowhere – and that would certainly be in conflict with the 1^st law.

It is a deeply engrained view that some people cannot shake off. Yet it is utterly misguided for the following reasons:

1. The temperatures of the earth’s surface and the earth’s atmosphere close to the surface are about the same. (They touch, after all!)
2. The rates at which the earth’s surface and the earth’s atmosphere near the surface radiate energy at one another, are a function of temperature  (Stefan-Boltzmann law, 1879), and so must also be about the same (varying also a little because the surface and the atmosphere have different emissivities).
3. These radiant energy flow rates are dependent on the FUNDS of Kinetic Energy stored in the atmosphere and surface. They are NOT directly related to the rate at which energy is flowing into the earth’s surface from the Sun and out again to space.

Most people have no difficulty with steps 1 and 2. After all the numbers are verified by the empirical data in the above energy diagram: 333Wm^-2 down and 356Wm^-2 up. But some people are still uncomfortable about step 3. This is because they fail to understand the distinction between the rate at which energy flows through a system and the quantity of energy stored inside that system.

A simple thought experiment may help.

Fig. 2 shows an insulated box containing two bodies X and Y separated by a vacuum. The area of their exposed  surfaces is fixed at 1m² (although this is arbitrary). The bodies are both perfect conductors of heat and both have emissivity of 1. The insulation material of the base and sides is perfect. But the insulation material of the top is slightly imperfect.

By some unspecified means, for example a small embedded electrical heating element, exactly 10 watts of power is applied continuously to the underside 1m² surface of body X. Consequently body X begins to heat up.  But as it heats up it begins to radiate towards body Y which also heats up…and begins to radiate back towards body X.

As the temperatures of body X and body Y continue to rise, the temperature differences between the inside and outside of the insulating walls increases. This results in an increasing flow of energy through the imperfectly insulated top wall to the ambient environment. The heat inside continues to build up until at some stage the heat flow through the top insulating wall reaches exactly 10 watts. When this happens the temperature of bodies X and Y will stop rising and the system will have reached steady state equilibrium. Let us suppose that at this point the steady state temperature T of body X happens to be 500K. Using the Stefan-Boltzmann equation…

I = ԑ σ T⁴

…where I [Wm^-2] is the radiative flux, ԑ=1 is the body’s emissivity and σ = 5.670373×10⁻⁸Wm⁻²K⁻⁴ is the Stefan-Boltzmann constant, we find that body X is now radiating 3544Wm^-2 towards body Y.

But at steady state, Body Y is losing exactly 10Wm^-2 through the top surface. So it must be radiating 3544 – 10 = 3534Wm^-2 back towards body X. Using the Stefan-Boltzmann equation again, we find that this corresponds to a temperature of 499.65K. And as long as the 10 watt energy flow rate continues, the temperature of each of the bodies X and Y will remain constant at 500K and 499.65K respectively.

So now we have a system where the through-flow power is a miniscule 10 watts yet the bodies inside the chamber are extremely hot and are radiating thousands of watts back and forth to each other.

It should be obvious what is going on: with a through-flow of only 10 watts, the FUND of energy held in bodies X and Y must have taken a very long time to build up to the point where those two bodies reached their equilibrium temperatures of 500K and 499.65K. This huge fund of energy wasn’t created by magic at all – it was all extracted from the 10 watt input stream as X and Y very slowly heated up. But once the bodies reached their equilibrium temperatures, they were able to maintain them forever – just so long as that small 10 watt rate of energy flow through the system was maintained, exactly making up for the 10 watts of losses through the top wall of the container.

This thought experiment incidentally also illustrates another very important point. The net flow of energy through the system creates a small downward temperature gradient in the direction of flow, exactly as the 2^nd law of thermodynamics requires. So it does not violate that law either. So no perpetual motion machines; and no possibility of building free power stations…

Hopefully this thought experiment demonstrates in a suitably dramatic way that there is no reason why a system that receives a very small amount of energy flow-through cannot reach a very high internal temperature. It all depends on the level of insulation – that is on the resistance to the flow of energy through it.

In the case of the Earth, using the figures shown in Fig. 1, the difference between the energy through-flow from the Sun to surface (161Wm^-2) and the radiation that passes between the surface and the atmosphere in both directions (356Wm^-2 up; 355Wm^-2 down) isn’t quite as dramatic as in our thought experiment. But the difference is there and it is real and it is important.

Those climate skeptics who still don’t believe that the up-and-down radiative transfers actually occur are simply not addressing the physics (or the empirical evidence) correctly.

NON-RADIATIVE ENERGY TRANSFERS

Having hopefully cleared up why Trenberth’s two-way flows of radiant energy between surface and atmosphere are essential conceptually, and are significantly larger than the Sun’s energy flowing into the earth’s surface, we can now introduce the additional complication of non-radiant energy flows that also occur between surface and atmosphere.

So how do we deal correctly with bodies that have a mix of radiant and non-radiant inputs and outputs? Well the answer is that we deal with them in exactly the same way as we have done in our thought experiment. That experiment obeys three laws (in particular) simultaneously:

• The 1^st law of thermodynamics insists that, at steady state, the energy entering the system must be exactly equal to the energy leaving the system. As an extension of that requirement, all internal flows in and out of subsystems within the system (such as each of the two bodies X and Y in our thought experiment) must of course balance as well.

• The 2^nd law of thermodynamics insists that, at steady state, there must be a temperature drop between input and output flows (or, at the very least, no temperature rise).

• The Stefan-Boltzmann law insists that if we heat a body to temperature T [K], whether by radiation or by non-radiation or by a combination of the two, it will radiate energy at a rate I [Wm^-2] as determined by the Stefan-Boltzmann equation.

Both our thought experiment and the Trenberth diagram conform to the above constraints. And it doesn’t matter that in the diagram (as in the real world) there happen to be three types of energy flow from surface to atmosphere: sensible heat, latent heat and Long Wave (LW) radiation. If the energy flows all balance and the laws are satisfied then the model is thermodynamically correct (even, if Trenberth’s empirically determined numbers may well need revision in the future as knowledge advances).

REAL WORLD THROUGH-FLOWS AND TEMPERATURE GRADIENTS

In our thought experiment the two bodies X and Y that radiate towards one another each are depicted as having homogeneous temperatures at steady state: body X at 500K and body Y at 499.65K. That is because these bodies were defined as being perfect conductors of heat, so there could be no variations in temperature within them. Yet there is necessarily a temperature gradient, of just 0.65K, between the two bodies by virtue of the 10 watt flow difference through one body and out of the other.

The real world of the earth-atmosphere system consists of physical entities such as water, land, ice, air, clouds, particulates, and so on, that are not perfect conductors and do not have emissivities of 1. So in practice there will be many internal temperature gradients. In Fig. 1 we see the surface is at Trenberth’s 289K which corresponds to a radiant outflow of 390Wm^-2 assuming emissivity ԑ = 1; and the base of the atmosphere next to the surface is shown as 287K which corresponds to a radiant flow of 333Wm^-2 assuming an emissivity ԑ = 0.86 . The 287K temperature figure is not critical to our discussion here but does conform to empirical evidence for a 2K difference between ocean surface and the atmosphere. In any case, both temperature values are close to the empirically determined 288K value commonly in use. See also the US Standard Atmosphere 1976 which specifies an atmospheric temperature at the surface of 288.15K . This is where the discussions on the second thread, Emissivity puzzle: energy exchange in non-vacuums, become important. What, exactly, is the emissivity of the atmosphere? But for the moment, we will stay with my ‘plausible’ values for the purpose of continuing the discussion of the atmospheric model without getting side-tracked into delusions of accuracy.

The atmosphere varies in temperature from 289K at the surface to around 210K at the tropopause. So it is about as far as possible from being a body with perfect ‘conductivity’ as you can get. In fact the conductivity of still air is effectively nil. Fortunately the atmosphere is able to use convection to transfer the energy in air molecules from the surface to space.

In Fig. 3, I have re-formulated the details from the Trenberth energy flow diagram of Fig. 1 to emphasise the regions where temperature gradients occur.

For discussion purposes, I have divided it into 4 regions as follows:

• SURFACE
• BASE OF THE ATMOSPHERE
• BULK OF THE ATMOSPHERE
• TOP OF THE ATMOSPHERE

As the diagram shows, of the incoming energy from the Sun, roughly 2/3 is absorbed into the SURFACE (land and ocean) and 1/3 into the BULK OF THE ATMOSPHERE. In both cases the Sun’s radiant energy is annihilated as it is converted to Kinetic Energy (heat).

In the case of the atmospheric absorption, this conversion from radiant energy is principally due to the presence of water droplets and (to a lesser extent) water vapour, mainly at cloud level in the middle heights. The molecules absorb (annihilate) photons and gain Kinetic Energy (sensible heat) accordingly. This energy is then immediately shared by kinetic molecular diffusion with the adjacent molecules (principally nitrogen and oxygen that account for about 99% of the dry atmosphere).

In the case of the surface absorption of the remaining Sun’s radiation, the surface acts like a black body, absorbing all the wavelengths of the Sun’s incoming radiation that were not absorbed on the way down through the atmosphere. The incoming photon stream is annihilated and the surface gains Kinetic Energy (heat) accordingly.

THE SURFACE AND THE BASE OF THE ATMOSPHERE

Assuming a steady-state situation, the SURFACE must lose energy at the same rate at which it receives it. It does this in three ways:

1. RADIATION: The surface, being a warm object at a temperature of 289K, radiates 396Wm^-2 of energy in the long wave infra-red according to the Stefan-Boltzmann law, thus consuming an equivalent amount of surface kinetic energy. Part of this outgoing long wave radiation (40Wm^-2) is of wavelengths that pass straight through the atmosphere to space (the so-called ‘atmospheric window’).  The remainder (356Wm^-2) is absorbed by GHGs in the BASE OF THE ATMOSPHERE. In exactly the same way as for the absorption of the Sun’s SW infrared radiation directly into the atmosphere, this energy is then immediately shared by kinetic molecular diffusion with the adjacent molecules (principally nitrogen and oxygen) all of which gain Kinetic Energy accordingly.

1. CONDUCTION/CONVECTION: Because the surface is in physical contact with the base of the atmosphere, some of its Kinetic Energy (17Wm^-2) is transferred by conduction/convection to the air molecules. Although air is intrinsically an extremely bad conductor, there are three mechanisms that improve this energy flow: (i) the horizontal flow of air across the surface due to wind; (ii) the turbulent mixing of air and water due to ocean waves; and (iii) the immediate upward transport of the warmed air by convection. These all combine to achieve an effective energy flow rate.

1. EVAPORATION: Thirdly, and most significantly, the largest fraction of the surface’s Kinetic Energy (80Wm^-2) is transferred to Latent Heat as it warms and vaporises surface water molecules, mainly ocean and other water surfaces but also moist land surfaces. The water vapour thus created rises up the atmospheric column until it cools sufficiently to condense to water droplets, forming clouds. At this point the Latent Heat (of condensation) is released and transferred to the adjacent air molecules which thereby gain Kinetic Energy accordingly.

The Kinetic Energy from the SURFACE is transferred to the BASE OF THE ATMOSPHERE within the first few centimetres by the conduction/convection and evaporation processes. Radiation from the SURFACE is also absorbed fairly quickly, certainly less than 1km (and that’s being generous – some people say the first 100 metres). This rapid absorption is assisted by the fact that the air pressure here is highest – so the probability is very high that a photon from the surface will encounter a GHG molecule within a few tens of metres and be absorbed. As we ascend the atmospheric column, the negative environmental lapse rate (to be discussed in Part II) means that the air density progressively reduces until, at the least-dense TOP OF THE ATMOPHERE (see below) exactly the opposite régime prevails and it gets more and more probable that photons emitted by GHG molecules will exit to space and be lost forever.

Consequently, the BASE OF THE ATMOSPHERE is a very thin layer, compared with the total height from surface to the tropopause. (Readers should appreciate that, for discussion purposes, its upper boundary is purely conceptual, as are the lower and upper boundaries of the TOP OF THE ATMOSPHERE. Hence all three boundaries are shown by dashed lines.)

Due to the above transfers of energy, the air at the lower boundary of the BASE OF THE ATMOSPHERE is at a temperature that is similar to, but slightly lower than, the temperature of the surface. It is similar because, just as in our thought experiment, it is in contact with the surface and net energy is flowing between them. It is lower because, again just like in our thought experiment, the direction of the net energy flow is upwards from the surface to the atmosphere.

But, like all bodies at a temperature above absolute zero, the atmosphere must radiate energy back to the surface according to the Stefan-Boltzmann law, in this case 333Wm^-2. To a large extent this balances the energy flow needed by the surface to maintain the upward radiation (390Wm^-2). So the surface only has to contribute the relatively small difference (57Wm^-2). It obtains this from the in-flowing KE derived from the Sun’s radiation absorbed at the surface.

THE BULK OF THE ATMOSPHERE

You may notice that within the BULK OF THE ATMOSPHERE the diagram shows no sign of the retention of incoming radiative energy. This is because it has all been converted either to Kinetic Energy (sensible heat) or to Latent Heat (which eventually gets converted to Kinetic Energy higher up). The point that I believe needs to be emphasised over and over and over is this:

The atmosphere has a big FUND of Kinetic Energy. And that’s what keeps it warm.

So where is all the accumulated radiation that (in some warmist mantras) ‘keeps the atmosphere heated’? Well, the bulk of the atmosphere has a temperature profile from ~282K at its base to ~223K at its upper end. Like all heated bodies, it radiates energy. And because it is a gas, as opposed to a solid or a liquid, this radiation exists everywhere within is volume. That is, individual GHG molecules that are sufficiently kinetically energised spontaneously emit photons in all directions. Each photon that is emitted by a GHG molecule results in a miniscule compensating reduction in the atmosphere’s FUND of Kinetic Energy. But this situation is very quickly reversed when the photon is absorbed by another GHG molecule in its path, which thereby returns the quantum of KE that was lost by the emitting molecule. These interactions are occurring countless billions of times per second. So the conclusion is that the photons buzzing around in the BULK OF THE ATMOSPHERE aren’t doing anything to disturb the FUND of KE held there. This is because, for every photon created, it is annihilated within an average distance of about 50 metres. This is a zero-sum game.

So we come to an inevitable conclusion:

The ‘fog’ of photons that exists in the BULK OF THE ATMOSPHERE does nothing useful at all.

In short, the radiation there is a consequence of the FUND of Kinetic Energy – not its cause – and that is why it is quite reasonably missing from my diagram. In the BULK OF THE ATMOSPHERE we need to concentrate on Kinetic Energy, the only source of sensible heat, which is the only form of energy measured as temperature.

THE TOP OF THE ATMOSPHERE

At the top, things are different. As we get further towards space the probability of an emitted photon being re-absorbed by another GHG molecule reduces, simply because the lower the density, the lower the chances of absorption. Increasingly, the Kinetic Energy that is converted to radiation is not returned to the atmospheric FUND but is instead lost to space for ever.

If you like, this is the inverse of what happens at the BASE OF THE ATMOSPHERE where radiation entering from the SURFACE gets converted to Kinetic Energy – the difference being that the BASE OF THE ATMOSPHERE radiates back towards the SURFACE, whereas the vacuum of space definitely does not radiate back towards the ToA!

TAKING STOCK

So where does this all get us?

My purpose here has simply been to help clear away a number of misconceptions that arose in the aforementioned blog trails and that I have found are also widely prevalent on both sides of the climate debate. These misconceptions introduce confusions into the important dialogue that ought to be taking place between climate warmists and climate skeptics. They hinder real progress. So what I have written above does not really break new ground. It is just an attempt to establish a few fundamental agreed principles – a common ‘communication language’ if you like – so that ongoing discussions can take place unencumbered by linguistic confusions such as “GHGs in the bulk of the atmosphere keep the atmosphere heated” (no they don’t), or “back radiation is a myth invented by the devil” (no it isn’t).

Maybe some readers will disagree with the ‘language’ or even the conclusions. Maybe worse, people will be entirely unconvinced by my whole approach, thinking that I, as a confirmed climate skeptic, should not be supping with the devil.  Maybe, conversely, Tim Folkerts, as a confirmed warmist, will be similarly admonished by his supporters for daring to enter the Tallbloke portals. But for me, and hopefully for some others, this has been an essential ‘ground clearing operation’ before (in Part II) we get on to the really serious stuff: who’s for OUTPUT THROTTLING and who’s for THROUGHPUT THROTTLING?

And what could be more exciting than that?

In the meantime I invite readers to comment on whether they think the ground rules I have attempted to establish above are helpful or not.