## måndag 24 maj 2010

### Thermodynamics of Global Climate 2

We recall the 2nd Law of Thermodynamics for an atmosphere from the previous post:

dK + dP = W - D,          dE = - W + D + Q,

where dK, dP and dE is the rate of change of kinetic energy K, potential energy P and internal (heat) energy E, W is rate of work, D is the rate of turbulent dissipation and we added a heat source Q.

Let's put in some numbers from observations:
• Q ~ 250 Watts (per m2) from insolation
• dP ~ 0.01 x 0.65 x 10000 x g = 650 Watts
• average vertical velocity = 0.01 m/s
• average density = 0.65 kg/m3
• average thickness of troposphere = 10000 m
• dE ~ 0.01 x 0.65 x 10000 x 6 = 400 Watts
• lapse rate 6 C/km
These numbers are compatible with dP = W - D = 650 ,  dE = - W+D+Q = - 400 Watts.

With an isentropic lapse rate of 10 C/km we would have dE = -650 Watts,  and we can thus
view the input of 250 Watts as being spent on turbulent dissipation, effectively reducing the temperature drop with increasing height.

We sum up: We have formulated a basic thermodynamic model of an atmosphere acting in a cyclic thermodynamic convective process of an ascending/expanding/cooling and descending/compressing/warming flow of air, which is driven by insolation spent on
maintaining the convection under turbulent dissipation. This model is compatible with observation without any presence of socalled greenhouse gases, and thus suggests that global climate is  is mainly determined by thermodynamics and not by greenhouse gases.

For more details see the article in progress Basic Thermodynamics of the Atmosphere.

#### 25 kommentarer:

2. I would like to call your attention to three things:

1) what sets the surface temperature if the radiative properties of the atmosphere are negligible? Is the surface in radiative balance with space independently of the atmosphere? If so, what makes it 30 C warmer than the elementary calculation would indicate? After all, it is this, and not the lapse rate, that is the practical issue.

2) where does the energy that is dissipated from turbulence down to the molecular scale go; i.e. why is there a quasi-steady state at all? By quasi-steady I mean a condition where it is meaningful to have a concept of climate at all. If 250 W/m^2 is dissipated as heat, and outgoing infrared radiation is negligible, then where does this heat energy go? Why is every year not hotter than the year before? After billions of years of collecting 250 W/m^2 that can't go away, why haven't we boiled off the ocean?

3) Similarly, how can we sustain nonzero rates of change of other quantities in a quasi-stationary system?

Your thinking seems to be based on aerodynamics, where I suppose that once energy is dissipated as heat it is "not much heat" and "goes away". We aren't in that regime here. We are integrating a system over a very long time. Since the system has some empirical stability, you can't have sustained significantly nonzero values for rates of change of any globally integrated terms.

I believe your error is to accept that incoming energy can be balanced by frictional dissipation. That simply can't work. You still have that 250 watts of heat energy to account for.

The reason the system doesn't come to a boil in very short order is that energy is transferred out at (in a sufficiently long average) the same rate it comes in. (Under rapid climate change like now, there is a detectable residual imbalance going into the heat capacity of the ocean and melting/freezing ice sheets, currently on the order of about 0.5 W/m^2; but to first order we can still talk about a balance.)

The only way for the energy to get out is by radiation.

Look at it another way. There has to be longwave radiation because as seen from space the earth has a nonzero blackbody temperature. We observe the outgoing longwave radiation (OLR) from other planets as well as earth, and indeed it balances the solar input. i.e., the 250 watts goes out. What would you expect?

I think you can only severely misunderstand the system by neglecting how the energy balance is closed. You are substituting a formal approach which may be perfectly fine for mechanical systems in an environment where excess heat can be dissipated into an infinite reservoir, but which is not energetically closed at all for the purposes at hand.

3. No, heat can be transferred by convection, conduction and radiation.
Convective heat transfer seems to be the main agent in the atmosphere.
With a negative lapse rate, the surface temp is higher than on the top
of the atmosphere from where heat is radiated to space.

4. OK, you are making progress. Now what is the "top of the atmosphere" for such purposes? Could it depend on frequency?

Also, where does the 250 W come from? While a small amount is absorbed by dust in suspension, most of it hits the surface. How is that energy transferred to the atmosphere? Not convectively.

Since you are insisting it is possible to neglect radiation, you must be saying that solar energy enters the atmosphere by conduction. Now I don't know much about conduction between a solid and a gas, but it seems to me intuitively it would need a very large heat differential to amount to 250 W. On the contrary, we see the temperature of the boundary layer very close to the temperature of the surface, and at night often much cooler. So how does that energy exchange work?

5. The fact that "the top of the atmosphere" is "where heat is radiated to space" is caused by the presence of greenhouse gases in the atmosphere. That is a central component of the greenhouse effect. Without GHG's or other absorbers such as clouds, heat would be radiated directly into space from the surface (in fact, some heat still is since Earth's GHG's do not absorb the full thermal spectrum). It is only because of radiative absorption that slows down the outflow of radiation that you can have the level of convection we see, otherwise all the energy would go out radiatively from the ground.

Also note, diurnal insolation (plus GHG damping of radiative cooling) does not provide sufficient convective driving force to overturn the entire troposphere - I'm not clear on what your "cyclic thermodynamic convective process of an ascending/expanding/cooling and descending/compressing/warming flow of air" is supposed to mean, but if you meant the day/night cycle at any given location, then that is limited to the turbulent boundary layer which is much narrower than the entire troposphere (at most 3000 m thick in the day, and much less at night). If you were referring to the latitudinal convective circulation, in particular the Hadley cells and inter-tropical convergence zone etc, that of course does have the capacity to stir the entire tropopause, but it's "cyclic" only in a spatial or seasonal sense, which doesn't sound like what you're talking about.

6. Arthur, welcome to the fray. I should point out a couple of things.

1) Several of the smartest people I have ever met are collaborators of Dr. Johnson in computational fluid dynamics.

2) I very much sympathize with his and their approach to computational simulation.

Accordingly I start from a default position of admiration. So I am distressed to see his position on climate physics so off base. This is not new; consider for instance several of the articles at

http://claesjohnson.blogspot.com/2009_08_01_archive.html

7. What I try to do is to find a basic model for the action of an atmosphere
as a thermodynamic cyclic "refrigerator" driven by heat from the
Earth surface and delivering heat to the upper atmosphere from where
it radiates into space. This refrigerator works by an expanding/cooling
and compressing/warming gas (air) like a common compressor refrigerator, and cools the Earth surface by transporting away the
incoming heat from insolation. This is a basic model without many effects, but it contains turbulent heat transport by bouyancy (like in the oceans) which can be a major part of the game. Why is this so "off base"?

8. You are "off base" when you state "global climate is is mainly determined by thermodynamics and not by greenhouse gases" while simultaneously claiming that "the top of the atmosphere" is "where heat is radiated to space". The second statement is impossible without greenhouse gases.

That means, without greenhouse gases (or any other source of infrared opacity, such as clouds), in your thermodynamic "heat engine" analogy, there would be no low-temperature heat bath for the atmosphere to use as the place to dump heat and run the turbulent convection you credit with the degree of surface warming.

In fact, both convection and radiation act to *cool* the surface; the action of GHG's is to *limit* cooling via radiation, forcing more of the energy flow through other cooling routes (such as convection). GHG's are the driver here. Essentially, you have cause and effect backwards.

You will note also that you no longer need to have a turbulent dissipation of 250 W/m^2, which is a good thing because it is several orders of magnitude too high. (Most flows are limited to isobaric surfaces and so 3 D turbulence is rare outside the boundary layer.) So your theory has already changed somewhat, and for the better.

However, without examining the details of radiative transfer you will continue to have a theory which misses how energy gets into the system and how it gets out, which after all tends to matter a great deal in a heat engine.

10. The problem is to explain how heat absorbed by the Earth surface is transported to the top of the atmosphere. Can radiation account for this
transport at a lapse rate of 6 C/km? If so, show the evidence.

11. Claes, may I suggest a look at Fig 1.1 in the FAQ to the latest IPCC report?
http://www.ipcc-wg1.unibe.ch/publications/wg1-ar4/faq/wg1_faq-1.1.html
Here you find the contribution from different mechanisms of heat transport.

12. This fig is unphysical with its massive surface radiation of 350 and "back radiation" of 324. What drives this large swirl of radiation? In Nasa's fig
on my knol http://knol.google.com/k/claes-johnson/basic-thermodynamics-of-the-atmosphere/yvfu3xg7d7wt/105# this rotating radiation is not displayed, presumably because it is not there at all.

In the Nasa fig 30% of the incoming 51% to the Earth surface is transported away by convection and evaporation/condensation and 21% by radiation.

13. Claes, some figures omit certain terms for clarity, and your figure only show net transport ignoring internal heat flows. Do you really think IPCC just invented these heat flow and that no one found out in review?

Just use Stefan-Boltzmann's law to calculate the emitted energy from the ground to see how large it has to be and compare with your diagram to see it doesn't add up. (You can measure it to be sure, of course, but that takes a bit more work).

Then there there will be radiation from the atmosphere towards the ground. All non-transparent objects with finite temperature emits radiation (and greenhouse gases make the atmosphere non-transparent to IR), and half of this radiation will go downwards.

You don't need anything special to drive radiation flows like this. Just take two metal plates of the same temperature opposite each other. Since they are the same temperature there will be no *net* flow, but nevertheless each plate will emit lots of energy that is absorbed by the opposite one.

14. The conversation is going in multiple directions at once. This is always a risk in atmospheric physics. Much as we'd like things to be simple, they stubbornly refuse to be so.

Regarding the original model proposed in the article, I am afraid it is simply drastically wrong. There is no situation in which it has any utility: it does not match the actual circumstances at all. The long term average of dE, dK and dP must be zero, and the radiative term is simply ignored.

Moving on to Thomas' point (Hello Thomas! Long time no see!), we consider that we can build a budget with net terms or gross terms. In a model of economic flows between countries, we can show a net deficit, or we can show gross exchanges in both directions, wherein the net is implicit as a directional sum. Both pictures show the same thing and the effect on the chart of accounts is the same.

It is useful to think about two objects of very nearly the same temperature in this context. Suppose one is very slightly warmer than the other. The correct picture is NOT that gross energy flows only from one to the other. Because suppose some small perturbation reversed the temperature difference. How would the two objects negotiate the reversal in direction that would be called for?

No.

Objects radiate and absorb in ways determined by their temperature and composition. The concept of "temperature" simply states that if A and B are in radiative equilibrium, and B and C are as well, then so are A and C. So it is exactly to avoid energetic "swirling" that the universe is set up this way!

But this equilibrium simply means that the amount of radiative energy sent from A to B is the same as the amount sent from B to A. Both fluxes are real and measurable.

Normally, this matters very little. In the atmosphere, however, it is of first order importance. You may come to appreciate this better if you ponder what the "top of the atmosphere" means, exactly.

15. Your question indicates great confusion about the role of greenhouse gases:

"The problem is to explain how heat absorbed by the Earth surface is transported to the top of the atmosphere. Can radiation account for this
transport at a lapse rate of 6 C/km?"

The problem is not the transport of heat from Earth's surface to the top of the atmosphere, the problem is the transport of heat from the planet as a whole (or the surface where it's mainly absorbed) into space. Even with Earth's significant greenhouse effect as it is, some portion of Earth's heat flow never even touches the atmosphere, it goes directly out into space (this is partly why land cools off quickly on a clear dry night, for instance).

The effect of greenhouse gases is to greatly *reduce* the net rate of radiative heat flow from the surface - and it is a reduction in outgoing heat flow, not an increase, that leads to warming. The bigger and more significant the greenhouse effect becomes, the *lower* the portion of surface cooling that happens through radiation.

Thermal radiation in the atmosphere is usually treated ballistically, as two large total energy flows (up and down), rather than the smaller net (heat) flow. This is because within nearly transparent systems the scattering length is long and the characteristics of source and sink can be quite different (not "local" enough for local thermodynamic equilibrium or local parametrizations to apply).

But it is really the net heat flow that matters to a thermodynamic evaluation such as the one presented here. One can approximately present it as similar to conductivity (and even convection given geometry) as

Q_cond = k . (T_surf - T_trop)/l_trop
Q_conv = h_conv . (T_surf - T_trop)

(here each Q represents the rate per unit time of heat flow *out* of the surface). Q_rad0 here represents direct heat flow from surface into space, while h_rad . delta T is the heat flow from the surface caught by the atmosphere.

I.e. very roughly the total outgoing energy flow rate is represented by three contributions proportional to the surface-tropopause temperature difference, plus one that doesn't depend on that difference:

Q_out = Q_rad0 + (h_rad + h_conv + k/l_trop) (T_surf - T_trop)

The tropopause temperature is very roughly the effective radiating temperature of the planet; in any case close to fixed, so the surface temperature can be determined by balancing Q_out and Q_in:

The effect of increasing greenhouse gases is:
* reducing Q_rad0 (more radiation from the surface is captured by the atmosphere)
* reducing h_rad (the effective scattering length is reduced, the atmosphere becomes more opaque to thermal radiation)

And both of these act to increase surface temperatures. There are also secondary impacts on the convective (and conductive) components through changes in the geometry (l_trop increases, for instance).

In short, GHG's act to *reduce* heat flow by radiation from the surface, bringing about warming.

16. Nobody seems to really understand the physics of radiation, but I agree (see a previous post) that it can be viewed as a form of conduction with the net heat flow being coupled to temperature drop.

An atmosphere with only conduction would have a very large temp drop because the heat conductivity of air is small. So what is then the heat "conductivity" of radiation? Large or small?

As shown in previous posts the basic postulate of climate alarmism is dQ = 4 dT which sets the marginal radiative "conductivity" to 4 Watts/K. This sets the basis for climate alarmism with about 1 C for 4 Watts from CO2 doubling.

DT = 15 (surface - stratopause temp) we get a conductivity of about 15 Watts/K , while observations suggest 10 Watts/K. This gives instead
less than 0.5 C from CO2 doubling, and alarmism has nothing start from.

So what is then the true radiative conductivity of the atmosphere with
more or less CO2? Physics should be able to give a precise answer.

17. Claes, you seem to be putting arbitrary numbers into arbitrary equations getting whatever answer you want with no regard to whether or not it matches reality. Maybe Michael or Arthur have enough patience to continue trying to explain the subject of climate science to you, I don't.

"the basic postulate of climate alarmism is dQ = 4 dT"

is amazingly strange. I have never seen such a formula before. I can only think the factor of 4 is in reference to the 4-th power aggregate behavior of thermal radiative energy flow, but as we've already discussed here, that total upward radiative energy flow is quite different from the net surface heat flow from radiation (up minus down). In any case, that 4 is dimensionless, and the differential relationship is not dQ = 4 dT, but:

dE/E = 4 dT/T

where E is that total radiative energy flow (again, not Q, which is a difference between up and down factors).

If there were no downwelling radiation (no greenhouse effect) then E = Q, and you can plug in the numbers for a zero-greenhouse Earth (T = 255 K with E = 250 W/m^2) to see the bare ratio would be

dE = 4 * (250/255) dT . W/(m^2 K) for a factor of about 3.9 W/m^2 K rather than 4.

But that is the absolute bare response with no greenhouse gases - and note that it is a *negative* feedback on temperature. I.e. if temperature increases 1 K, then outgoing radiation from the surface increases by 3.9 W/m^2 (under these conditions) so that if incoming radiation has not changed, that increase in outgoing radiation creates an imbalance that cools the surface. Similarly a reduction in surface temperature creates a warming imbalance, so this bare radiative feedback is what makes temperatures close to stable.

A good mathematical discussion of this particular response factor (the bare "Planck" response) and how it is calculated on the real Earth is given in Appendix A of Bony et al (Journal of Climate 19:3445 (2006)) - the actual factor for Earth as it is is closer to 3.2 W/m^2 K (and quite tightly constrained).

(continued in next comment...)

19. But all that does not inform us much on the issue of radiative heat transfer under greenhouse conditions. You ask:

"what is then the heat "conductivity" of radiation?"

my previous comment mentioned a factor h_rad that is like conductivity - but don't forget there's also a Q_rad0 that completely bypasses the atmosphere. If Q_rad0 is large (and Q_rad0 = E mentioned above if there are no greenhouse gases at all) then a lot of energy escapes the planet directly into space by radiation, and warming of the surface is necessarily limited. The effect of increases in GHG's is to reduce Q_rad0 and also the conductivity-like factor h_rad - so to answer your question, the more GHGs there are, the lower the effective "heat conductivity of radiation" for the atmosphere.

And it is lower heat conductivity (in all senses of conduction, including convection etc) that causes raised temperatures - that's the principle behind all forms of insulation.

More explicitly, Q_rad depends on the frequency nu of radiation - Q_rad = Sum_nu Q_rad(nu). For frequencies that are completely absorbed by the atmosphere, there's a typical absorption length l_nu. The greater the GHG concentration, the more absorption, the shorter l_nu is. Very roughly, the radiative heat exchange from the surface then for frequency nu consists of outgoing radiation at a rate governed by the Planck function for the surface temperature, and then subtracting the Planck function for temperatures a distance l_nu above the surface.

The temperature at height l_nu is given roughly by:

T(l_nu) = T_surf + (T_surf - T_trop) * l_nu/l_trop

(assuming a constant lapse rate)

The Planck function B(T, nu) is given by

B(T, nu) = 2 h nu^3/c^2 . (1 / (e^(h nu/kT) - 1))

for relatively small temperature changes we can linearize it as
B(T, nu) = B(T0, nu) + (T - T0) B'(T0, nu)

Q_rad(nu) = B(T_surf, nu) - B(T(l_nu), nu)
= (T_surf - T_trop) . l_nu/l_trop . B'(T_surf, nu)

I.e. as GHG levels increase and l_nu decreases, Q_rad(nu) decreases for that particularly thermal frequency. This term contributes to the total effective radiative conductivity h_rad.

For frequencies nu that are not fully absorbed by the atmosphere, the absorbed fraction is a number epsilon which also governs emissions at that frequency. You then have

Q_rad(nu) = (1 - epsilon(nu)) B(T_surf, nu) + epsilon(nu) . (T_surf - T_trop) . B'(T_surf, nu)

(approximating the returning radiation as coming from the tropopause). So the epsilon(nu) term adds another contribution to h_rad (and this part increases as GHG levels increase), but the (1 - epsilon) term contributes to Q_rad0, and decreases with increasing GHG levels; the net effect of the two terms is to decrease Q_rad as GHG levels increase (higher epsilon). And as epsilon approaches 1 you get to the full absorption case where the absorption length comes into play.

All this is readily calculated for given atmosphere composition and temperature profile - but it only gives us the first-order response of the system to a change in greenhouse gases. You then have to know how that composition and temperature profile respond, and feed back on the calculation of radiative and convective behavior. Which is what climate models try to do - but there is still considerable uncertainty on those feedbacks.

20. What I ask for is the quantitative effect of doubled CO2, not qualitative which can be anyrthing from zero to infinity. This is the famous climate sensitivity predicted by IPCC to be an alarming 3 C. As far as I can see this is based on a postulate of the form dQ ~ 4 dT which gives dT = 1 C from 4 Watts/m2 radiative CO2 forcing, from which 3 C follows by ad hoc positive feedback. Do you agree with IPCC?

21. (1) I agree with Miskolczi that A_A (BOA upwelling LW IR) ~E-D (BOA downwelling LW IR)

(2) I agree with Miskolczi that the LW IR tau is 1.871 (such as it is).

(3) I agree with Miskolczi that the average ratio of S_U/OLR under greenhouse saturation conditions is ~1.666 (~5/3).

(4) I agree with Miskolczi that the planet is near greenhouse saturation BUT with the normalized greenhouse factor g only able to range (under a global heat balance condition) from ~0.378 – ~0.405 (both Ramanathan and Miskolczi wrong about the clear sky 0.333), averaging about 0.402.

(5) I contend that under clear sky conditions Miskolczi's S_T (i.e. BOA->TOA LW IR) = not only transmitted LW IR BUT ALSO an (absorbed, retransmitted, upwelling) ~37.5% fraction of sensible heat departing TOA. Mistake by FM.

(6) I contend that the planet is rarely at heat balance at any one time but is on balance over the long term due to the dictate of Maximum Entropy Production (MEP) which maximizes internal entropy, including maximizing meridional heat transfer and the production of photoautotrophic (CO2 consuming) and dark decay (CO2 generating) microorganisms.

(7) I contend that so-called paleoclimatic cases of apparent high CO2 sensitivity are mistaken and another major perturbation e.g. high TSI, asphalt and oil volcanoes (yes they do exist), must have applied at the time. There are no reliable, unambiguous proxies for high TSI.

(8) I agree 100% with Jeff Glassman that ‘greenhouse saturation’ is largely all about cloud and albedo.

http://www.rocketscientistsjournal.com/2010/03/sgw.html

Keeping on keeping on:

22. To me the crusial question is to explain why there is a temperature gradient in the first place. After all, what we learn from classical thermodynamics is that radiation, convection and conduction all cooperate to erradicate temperature gradients. It seems that the entire construction of the Greenhouse Effect relies on some heat pumping effect of the radiative transfer acting so as to maintain the temperature gradient, whilst the convective part acts in the opposite direction. This is non-standard thermodynamics and I think the proponents of the Greenhouse Effect should admit this. If we all admit that we have a problem that may need solutions outside the classical tool-box then I think we have all made progress. But that of course opens up for alternative explanations, such as gravitational effects. Who can explain the temperature gradient of Jupiter for me?

23. "Who can explain the temperature gradient of Jupiter for me?"

Vern Suomi, the father of satellite meteorology

Suomi's Paradox: The characteristic jet speed (m/s) in planetary atmospheres increases despite a decrease in thermal forcing going from Earth to Neptune.

Earth Normalized Forcing 1.0 Speed 30 m/s
Mars Normalized Forcing 0.99 Speed 80 m/s
Jupiter Normalized Forcing 0.05 Speed 100 m/s
Saturn Normalized Forcing 0.02 Speed 150 m/s
Uranus, Neptune Normalized Forcing 0.003 Speed 300 m/s

It seems likely this paradox can only be explained through consideration of the principle of MEP.

24. Thanks Steve, sounds like rocket science to me. Let me try to understand what you say. Does the jet speed relate to the temperature lapse rate of the atmosphere? Let me then ask a silly question: If we have low thermal forcing then the molecules in the atmosphere get somewhat more lazy since they do not recieve so much energy. Lazy molecules have a hard time climbing upwards due to the gravitational acceleration. Could this account for a steep lapse rate?

25. Convection acts to make an atmosphere isentropic.

Long wave radiation acts to make an atmosphere isothermal.

Shortwave radiation acts to make the surface hot and is the major input to the system.

Conduction is negligible.

This is where you start. Where you end in one dimension is how the energy escapes the system.

Then you have to move on to the zonal average. If you consider radiation as a function of latitude, you will find the tropics too cool and the poles too warm. So lateral heat exchanges by advection and phase changes of water become important and now you are off to the races. However, you still won't really close the system before you get as far as baroclinic instability, which will put you at about 1950, when von Neumann took this on as his first computational problem.

Regarding Lindzen's arguments, Lindzen has been much answered elsewhere. One point to make is that his arguments for low sensitivity seem very fragile, while arguments for the consensus sensitivity are replicated in most 3 D models but also in various streams of paleoclimate evidence.

There is little doubt that the Clausius-Clapeyron relationship is an amplifying feedback. It is conceivable that cloud cancel it out, but the evidence in that direction is problematic (generally based on short-term observations which really cannot tell the tale) and inconsistent with various streams of paleoclimate evidence.

I don't often recommend video lectures, but R Alley's presentation to AGU on this latter subject was exemplary.

http://www.agu.org/meetings/fm09/lectures/lecture_videos/A23A.shtml