My Thanks to David Cosserat for this second guest post, which builds on the material covered in the strongly debated part I. Although it doesn’t cover every aspect of the elevation of the surface temperature above that of an airless planet, it neatly covers the essential issues at stake between proponents on opposing sides of the ‘greenhouse effect’ debate.
Atmospheric Thermal Enhancement
Part II – So what kind of heat flow throttling do you favour?
Our goal in these articles is really quite simple. It is to determine, exactly, the mechanism that causes the Earth’s surface (land + ocean) to have a significantly higher temperature than if it had no atmosphere at all. Is it due to the so-called radiative gases in the atmosphere such as water vapour and carbon dioxide? Or does it have some non-radiative physical cause? On this issue hangs the future of the Anthropogenic Global Warming theory.
In Part I, I discussed two possible mechanisms that might cause the temperature enhancement. One I called Throughput Throttling and the other Output Throttling. Throughput Throttling is not sensitive to radiative gas concentrations (provided those concentrations are above certain minimum levels). In contrast, Output Throttling would appear to be very sensitive to them.
Part I was intended to clear away a number of misconceptions that some skeptics have that I believe are getting in the way of a resolution of the above issue. Many skeptics tend to react against a number of ideas that appear to support the warmist cause but in reality don’t support it at all. For example they refuse to believe that:
- Greenhouse Gases (GHGs) are an essential part of the earth-atmosphere energy transfer mechanism.
- There is enhanced radiation from surface to atmosphere well above the net rate of inflow of energy from the Sun.
- There is similarly enhanced ‘back radiation’ from atmosphere to surface.
- The Trenberth energy flow model is a valuable aid to understanding the flows of energy through the earth and its atmosphere.
As long as skeptics maintain that the above propositions are false, I believe they cannot possibly engage effectively in debate with friendly warmist-inclined scientists to discuss the actual warming mechanism. This is very unfortunate because, as I hope I have demonstrated in Part I, and in the discussion trail, none of the above propositions in fact support the warmist cause anyway, even though they are believed to do so by both skeptics and warmists.
The presence of atmospheric GHGs are vital for converting a significant proportion of the Sun’s incoming radiation (78Wm-2) directly to Kinetic Energy in the atmosphere. This process, commonly referred to as thermalisation, heats the atmosphere. But the rate at which the thermalisation process occurs is NOT determined by the concentration of GHGs in the atmosphere (assuming there is a sufficient minimum concentration of GHGs to do the job). It is instead determined by the constant rate at which the Sun delivers energy in the bands that are directly absorbed.
- The earth’s surface radiates energy at an enhanced rate (356Wm-2) towards the Base of the Atmosphere. At the same time, the lowest part of the atmosphere radiates energy at an enhanced rate (333Wm-2) towards the surface. Both those figures are well above the net inflow rate from the Sun to the earth’s surface of just 161Wm-2. These enhanced flow rates more-or-less cancel one another out, the net difference being just 23Wm-2. This means that 333Wm-2 of energy circulates round and round between the two bodies (earth and atmosphere) doing no work. But this enhanced level of radiative flow is not magically produced from nowhere. It is a simple consequence of the fact that bodies at an elevated temperature radiate energy at an elevated rate (Stefan-Boltzmann law). Repeat: the enhanced radiation is a consequence of enhanced temperature levels in the surface and atmosphere and is not its cause. It does no work. Skeptics should not be afraid of that. But warmists should.
- The presence of atmospheric GHGs are vital for converting all of the Kinetic Energy (199Wm-2) that flows to the Top of the Atmosphere to radiation that is lost to space. This process cools the atmosphere. If you are a warmist who believes in Output Throttling, the concentration of GHGs in the atmosphere dictates the rate at which this ‘de-thermalisation’ process occurs. If you are a skeptic who believes instead in Throughput Throttling then the concentration of GHGs at the Top of the Atmosphere has no effect on the rate of flow of radiative energy because it acts simply as an open drain of energy to space (again assuming there is a sufficient minimum concentration of GHGs to do the job).
So, our investigation depends on the issue of whether or not so-called greenhouse gases (GHGs) such as water vapour and carbon dioxide are actually responsible for the atmospheric thermal enhancement (ATE) that leads to an elevated temperature above that of an airless planet. If they are, then adding additional CO2 to the atmosphere would cause a further temperature rise, with possibly alarming consequences for mankind. If they are not, then adding additional CO2 would not cause any further temperature rise, so attempts to limit man’s output of CO2 would be pointless.
The Controversial ‘Trenberth’ Figures
In summarising the conclusions of Part I, you will see I have used actual energy flux density figures rather than just relying on qualitative discussion. The figures are taken from the Earth’s Energy Balance diagram published in the 2009 paper by Trenberth, Fasullo & Kiehl. I said then, and I repeat now, that I do not endorse these figures as being perfectly correct. Their main use is as a helpful conversational device to fix ideas on matters of scale. But I got a barrage of criticism for using them:
- From people who thought the figures were wrong – but when challenged were unable to provide any alternative values.
- From people who thought the figures were ludicrously accurate (3 significant figures) without having read the TFK 2009 paper where it is made clear that the numbers were just best rough estimates that came out of averaging the re-analyses of several other peoples’ work.
- From people who appeared unable to appreciate that TFK 2009 might have done a fairly reasonable job on the energy flux density estimates, despite being regarded by skeptics as ‘wicked warmists’.
- From people who were anxious to provide earnest advice about how to construct a much better model than Trenberth’s containing much more additional complexity – without being sensitive to the level of detail actually required for our purposes here.
- From people who thought the model was wrong because they just hated the idea of the enhanced ‘back radiation’ loop, claiming without any proof at all that the associated upward and downward energy flow figures must be a fabrication because they violate the 1st and/or 2nd laws of thermodynamics (they don’t).
And so on, and on…
There was one other recurring concern that I found quite baffling. Several people were uncomfortable with my insistence that the TFK 2009 model was designed to represent a steady-state energy flow scenario. How, they implied, could that be appropriate for an earth system that we know constantly undergoes change over both time and space and that is subjected to increasing levels of GHGs? Well from my viewpoint that question denied the whole objective of the model: which is to smooth out all time and spatial variations so that we are left with one that exhibits a fixed energy through-flow rate and a consequential fixed mean surface temperature. I had to explain that the model was simply a necessary starting reference point for our conversation – a balanced steady-state energy flow platform from which we could move forward in our subsequent discussion. Then we could ask questions like: what happens to the surface temperature if we do something radical like doubling the concentration of atmospheric CO2?
I confess that I remain wholly unconvinced by any of the above objections. In the final analysis, they mostly seemed to me to be ‘arm waving’ conversational ploys. As I said in Part I, for over 15 years the TFK model and figures (originally published in 1997 and updated only marginally in their subsequent 2009 paper) have remained the ‘best show in town’, despite all their undoubted imperfections.
The only significant challenge to any of the Trenberth figures that I think still needs to be addressed is an important philosophical one about the ‘back radiation’ loop: whether the uni-directional ‘upwelling’ and ‘downwelling’ radiation flows exist as separate real phenomena or are just ‘virtual’ energy flows. This issue divided commentators to the point where is spawned another blog article where we all had great fun debating whether pyrgeometer instruments, (which are specifically designed to measure uni-directional radiation, and are installed all over the world at atmospheric research centres) work accurately – or even possibly are some kind of self-referential confidence trick that don’t work at all. But whichever side you take in that ongoing debate should not detain you here (please go to that blog to register your views!) because, as you will see, in this Part II we will only be using the difference between the upwelling and downwelling figures (which is accepted by most people as a small real value).
Resistances to Energy Flow
So now let us move on to unravel the remaining part of the puzzle of why the atmosphere at the surface has a temperature that is several tens of degrees C warmer than the surface of an airless earth.
In Part I, I described a Thought Experiment (Fig.2) to demonstrate that it is perfectly possible for a body that is well insulated from its surroundings to retain heat at a very high steady state temperature, whilst receiving a very small through-flow of energy. In the Thought Experiment, the resistance to flow, resulting in the high temperature, was provided simply by the near-perfect insulation of the container.
Now we have to consider which mechanism in the real atmosphere causes that resistance to flow that allows its temperature to be significantly elevated:
- Is it due to a restriction on the rate at which energy can flow up the atmospheric column?
- Is it a restriction on the rate at which energy can be converted to radiation at the Top of the Atmosphere from where it flows out of the atmosphere to space?
Of course in logic we should include other possibilities. The enhanced temperature of the atmosphere might be due to a combination of both of the above mechanisms. Or it might be due to some other entirely different cause. For the sake of clarity and simplicity, we will proceed by debating the first two ‘either/or’ possibilities, that I have dubbed Throughput Throttling and Output Throttling. We can always compromise later if we find that both effects (and/or some others) play a role.
Before considering these two contenders in more detail, we need to remember from Part I why there is an Atmospheric Thermal Enhancement effect at all (whatever mechanism proves to be correct). It has got to be due to some physical mechanism that keeps the atmosphere at a range of stable equilibrium temperatures such that the energy flowing into the earth system from the Sun exactly balances the energy flowing from the earth system out to space. This requires, as do all stable control systems, some kind of negative feedback, in this case caused by a physical resistance to energy flow.
Let us re-use our Thought Experiment apparatus from Part I, Fig. 2. But in this case we will not be considering radiation – just heat flow by conduction. This time there is no vacuum inside this new enclosure. We imagine it just contains three bodies X, Y and Z, each in contact with the next as shown in Fig. 4:
For this Thought Experiment we have no need of a top lid of ‘imperfect insulation’ to impede the outflow of energy. This is because the three bodies X, Y and Z are themselves imperfect insulators. That is, they possess varying conductivities, kx, ky and kz that are greater than zero but less than infinity.
Using a fixed 10 watts of through-flow power as in our previous Thought Experiment in Part I, body X (made of stainless steel) has the highest conductivity and therefore the lowest temperature difference between its lower and upper surfaces – just 0.5K. Body Y (made of glass) has a temperature difference of 10K. And body Z (made of plastic) has the largest temperature difference of 50K. This makes a total temperature drop up the column of 60.5K.
Now the important key question arises: if the total temperature difference up the column is 60.5K, what sets the corresponding absolute temperature values that are shown at the right of the column? Well, the temperature at the base is not fixed because the perfect insulation of the base prevents body X from being heated (or cooled) by a flow of energy through the base from (or to) the outside. Instead, you may remember, we postulated that the base is heated by some other means such as a 10 watt electrical heater. Therefore in this Thought Experiment, as in the previous one, the actual absolute temperatures in the column must be fixed relative to the temperature at the top – which in this case is simply the ambient temperature of the surroundings, 289K. Given this number, and the known temperature differences across the three bodies X, Y and Z, the other temperatures up the stack follow consequentially.
So what has a hypothetical insulated box containing three slices of differing solid materials got to do with an atmosphere? Well, it reminds us that:
- At steady state, input energy flow rate = output energy flow rate (1st law of thermodynamics)
- temperature drops are in the direction of energy flow (2nd law of thermodynamics)
- temperature drops are different for materials that have different conductivities
and most importantly of all
- external conditions dictate how those temperature differences relate to absolute temperature values (the 289K ambient temperature ‘anchor’ in our example).
Our Thought Experiment also has another important feature: it receives a constant input energy flow. This is not something we are very familiar with in everyday life where objects tend to heat up or cool down at reducing rates as they tend towards the ambient temperature of their surroundings. In contrast a constant flow source just…keeps on flowing at the same rate.
An analogy for constant energy flow that electrical engineers will understand is the case of a constant current source flowing through an electrical circuit that presents an overall constant resistance to the current flow and therefore develops a constant voltage difference across the circuit.
In the case of the earth-atmosphere system, the Sun provides the constant input energy flux. Energy flows through the atmosphere which provides resistance to heat flow. This develops an overall constant effective temperature difference between the ground and the top of the atmosphere where the energy is lost to space.
Simplified Earth-Atmosphere Energy Flow Model
Fig. 5 below is a slightly re-arranged and simplified version of Fig. 3 in Part 1. The energy flows are the standard ‘Trenberth’ numbers, as before:
Fig. 5 shows just three energy entry routes for KE arriving into the atmosphere. The first entry route is the stream of KE derived directly from the SW radiation from the Sun (78Wm-2). The second entry route is the stream of KE derived at cloud levels from Latent Heat during precipitation (80Wm-2). The third entry route is the stream of KE derived from the surface – a combination of surface conduction/convection (17Wm-2) and surface KE-to-surface LW radiation- to-atmospheric KE (23Wm-2).
Note in particular that we now no longer show the 333Wm-2 LW radiation energy flow that was cycling around continuously between surface and atmosphere in Fig. 3. This is because this continuously cycling energy does no work and so is not part of the through-flow from Sun-to-earth-to-space – which is what we now are focusing on.
However Fig. 5 can be simplified still further by making one other (and perhaps for some people unintuitive) assumption:
It doesn’t matter at what various heights the directly absorbed solar flow of radiant energy, and the latent heat of vaporisation of surface water, are converted to Kinetic Energy.
Why doesn’t it matter? It’s all because of the Environmental Lapse Rate.
The Environmental Lapse Rate
Atmospheric pressure goes down as we ascend through the atmosphere. This is simply because the pressure at any height is determined by the fixed weight of air above that point, which obviously diminishes with increasing height above the surface.
This is summed up in the US Standard atmosphere (1987), shown in a neat graphical form in Fig. 6. The vertical axis is in kilometres above the earth’s surface. Four environmental lapse rates are shown, for pressure, density, temperature and speed of sound. Up to the tropopause, all four are negative and vary monotonically with height.
As we ascend through the troposphere, the reducing pressure (green line) means that each unit volume of air contains fewer and fewer molecules. In other words, it gets less dense (orange line). Lower and lower density means the air will contain less and less stored Kinetic Energy. This in turn means it also has a lower and lower temperature (red line).
The negative temperature profile up through the troposphere to the tropopause is fixed at absolute temperature values by reference to the surface. This is at the highest temperature end of the flow because the air at the bottom of the atmospheric column is in thermal contact with the surface and the surface has a temperature that relates to the rate at which it absorbs incident radiant energy from the Sun. Note that this is the opposite of our Thought Experiment above (Fig. 4) where the absolute temperatures are all referenced to the temperature of the coolest end of the column.
Ultra-simplified Earth-Atmosphere Energy Flow Model
For diagrammatic purposes in Fig. 5, the three energy streams are shown entering the atmosphere at three specific heights. Because cloud levels vary, in the cases of directly absorbed SW radiation and of Latent Heat, there will in practice be quite a wide spread of entry heights. Even in the case of the KE flowing from the surface, the 23Wm-2 fraction (radiated from the surface and then almost immediately re-absorbed in the Base of the Atmosphere) will re-appear as KE over a (short) spread of distances from the surface. So the reality is that energy flows into the atmosphere at a multiplicity of heights.
Now consider what happens when there is a flow of Kinetic Energy into the atmosphere at any particular given height. Will that layer’s temperature be raised as it absorbs that incoming energy, thus distorting the temperature lapse rate? No, because the heated air will simply convect upwards, cooling in the process, until it reaches a height at which its temperature is in equilibrium with the air surrounding it.
Therefore, for our very specific purposes here, we do not need to concern ourselves with the varying heights at which the energy enters the atmosphere, because:
At whatever height the energy flow enters, the fixed pressure profile of the atmosphere will force the energy to be redistributed so as to maintain a fixed Kinetic Energy profile in accordance with the environmental lapse rate.
So we can simply draw our diagram as if all the energy has entered at a single arbitrary point. And what better point to choose than the surface, as shown in Fig. 7 below:
Wow! Simple or what? All that complicated climate sciencey stuff is now compressed down into one elementary diagram. Of course it won’t be a diagram that will be of much interest or use to people studying the intricacies of atmospheric sciences. (I fully expect it to generate many howls of anguish, just like before.) But for our purposes here it will do just fine.
We now have the simplest possible model of energy flow. It has factored out all the complications of the real earth-atmosphere system. Look at the complexities we have lost:
- The insertion at a range of heights of that proportion of the Sun’s incoming radiation that is directly absorbed by the atmosphere.
- The conversion of KE in the surface to Latent Heat in rising water vapour.
- The conversion of Latent Heat to KE at a range of heights relating to cloud levels.
- The conversion of KE in the surface to upward radiation which is almost immediately absorbed back to KE within the Base of the Atmosphere.
- The conversion of KE in the Base of the Atmosphere to downward radiation which is absorbed immediately back to KE within the surface, thus (predominantly) balancing the radiative element of the upward energy flow.
We have conveniently lost all the above complexities but we haven’t forgotten them. If they turn out to be important in our subsequent discussions, we can always bring them back in. In the meanwhile, let’s stay with the simplified diagram and see how well we get on with it.
And now for the $64 billion dollar question. What throttles the flow of energy through the atmosphere to space? Let me describe the two competing mechanisms as succinctly as I can:
From Fig. 7 we see that the energy lost to space through direct LW radiation (the atmospheric window) is 40Wm-2. The remainder of the energy flow, 199Wm-2, is in the form of Kinetic Energy which percolates up the atmospheric column by convection and then is lost to space at the ToA.
If convection did not exist, the atmosphere would be almost a perfect insulator. But convection does not turn the atmosphere into a perfect conductor – far from it. Convection gives the atmosphere an effective conductivity, katm, which behaves in an analogous way to the real conductivity values kx, ky and kz discussed above in Thought Experiment 2. Strictly, to take account of the lapse rate, the layers of the atmosphere should be split into a sequence of different effective conductivities, k1, k2, k3, ….kn, such that:
1/katm = 1/k1 + 1/k2 + 1/k3 + …….. + 1/kn
It is the combined effective conductivity katm that allows just sufficient energy through-flow to balance the Sun’s incoming energy flux whilst maintaining the fund of KE at one particular permanently elevated profile of temperatures.
If Throughput Throttling is the sole mechanism impeding energy flow though the atmosphere then adding GHGs to the atmosphere will have no effect – because the effective conductivity katm is due to a mechanical convective process that is not sensitive to the existence of GHG molecules.
This proposed flow control mechanism relies on the fact that the concentration of GHGs in the atmosphere affects the average height at which GHG molecules emit photons to space. If the concentration of GHGs goes up, the average emission height goes up. Why? Because the probability of photons being intercepted by other GHG molecules at the original average height is now greater due to the increased concentration of GHGs.
However, the increase in average emission height means the emission is appearing from GHGs which are at a lower temperature – so the average energy of the photons successfully emitted to space goes down. This downgrading of energy-per-photon would cause an imbalance between energy flow into the earth-atmosphere system from the Sun and energy flow outwards to space. And so atmospheric temperature rises to compensate until the energy balance is restored.
Under this scenario, therefore, adding additional quantities of GHGs to the atmosphere will cause the whole temperature profile of the atmosphere to rise in compensation. In particular, and, of particular importance to humans, the temperature of the air at the surface will therefore rise.
Let the debate begin
So which kind of throttling do you favour? Are you persuaded by the skeptical argument that says that the fund of KE in the atmosphere is kept at an elevated level by the slow rate at which convection moves KE energy up the atmospheric column, which offers an ‘effective conductance’ katm that is independent of GHG concentration? And that the conversion process to radiation at the Top of the Atmosphere offers no resistance, operating like an open drain?
Or do you prefer the warmist argument that the conversion of KE to radiation at the Top of the Atmosphere is limited in proportion to the concentration of atmospheric GHGs? The higher the concentration, the cooler is the mean height at which the release of radiation to space is achieved. This forces a compensating warming sufficient to achieve the required rate of energy throughput.
There are fierce arguments to be advanced on either side but the discussions conducted here at the Talkshop will of course be mature, polite, constructive and amicable.
Here is just one very recent dialogue on another blog to get you all going:
Steven Mosher: The greenhouse effect operates by raising the ERL [effective radiation level]. A raised ERL means an earth that radiates from a higher colder region. That means a slower rate of energy release to space and the surface cools less rapidly in response.
Konrad: No, running back to the ERL thing won’t work. The ERL game was only cooked up after it became impossible to ignore that most of the energy that radiative gases radiated to space was acquired through conduction and release of latent heat, not IR from the surface. And of course we can see cloud tops radiating strongly in IR images from space. Far hotter than the surrounding air at their altitude. The altitude of radiative gases provably does not set the temperature of much of those gases at the time they are radiating the most IR. Try again.
Let (friendly) battle begin…