the Air Vent

Because the world needs another opinion

The Power Behind Hurricanes and Tornadoes

Posted by Jeff Id on February 2, 2010

For a long time I’ve wanted to do a post on some work by Dr. Anastassia Makarieva who has in my opinion explained the driving mechanisms behind hurricanes and tornadoes. Now I’m not an expert, but as an aeronautical engineer the equations were familiar so the paper read easily. As I understand it, the mechanism she describes was previously unknown and this work is starting to gain some acceptance. If she’s right, and I think she is, the work explains far more than just hurricanes and tornadoes though, it also explains a missing driver of winds on earth as well as planets throughout the solar system – condensation.

On the validity of representing hurricanes as Carnot heat engine
A. M. Makarieva1,2, V. G. Gorshkov1,2, and B.-L. Li2

Now we’ve all been taught, warm air rises and cold air falls, to create updrafts, wind, tornadoes and this kind of thing (Carnot heat engines). Anastassia’s work demonstrates problems with the Carnot model and then looks at the forces created when a moist air column experiences condensation. The condensation itself removes water from the gas phase resulting in a pressure drop. This pressure drop powers the column of rising air in the walls of hurricanes and tornadoes. It’s really an exciting development, but as a climate outsider it seems hit you in the head obvious. Who knew this hadn’t already been figured out? Anyway, the work is very interesting and an entertaining read.

There are all kinds of things which happen when water condenses. When water condenses on a surface it creates heat on that surface. This makes sense because the molecules are closer together.

Let’s talk about that for a minute. What is temperature after all? I bet many of the readers here haven’t conceptualized what something as common as hot or cold is. I was born with an ugly obsession to need to know how everything works. Sometimes I think I should have written every article on “how it works”, except that there are a lot of people like me hanging around this blog.

Temperature is basically an amalgam of the both the number and velocity of the impact of individual particles on other particles. Think about that. It is important. The number and velocity of individual impacts. All vibrations of weird shaped molecules are taken into account, spinning, linear velocity and really about everything. In making that statement I expect someone will challenge, but the point is the concept, not the introduction of effects which create confusion.

Let’s use a sealed canister of pure gold as a surface of atoms, I like gold, it’s heavy, dense, doesn’t corrode and sounds like money. Now say the gold is 72degF temperature – room temp. Now say we have an equal temperature of hydrogen gas inside the gold can. Our gas is funny gas, normal hydrogen is H2 (two little atoms together shaped like a barbell) but ours is H1. Since the atomic weight of hydrogen is far lower than gold and the density of a gas is also far lower than a solid, an equal temperature means a couple of things:

First, our special H1 hydrogen’s spin typically would have little thermal component. In our H1 gas, it’s a single proton and electron pair. So spinning it would be entirely differnet than say an elongated octane molecule with 8 monster 6 proton carbon atoms whipping around on a powerful stiff chain with 18 hydrogen atoms stuck all around.

Second, in order to balance the vibration velocity and impact number of the surface of the gold atoms, the hydrogen gas must, on average, receive a total energy equal to that which it expends while impacting the surface of the gold.

Let’s assume temporarily that the gold atoms were perfectly stationary (absolute zero temp), after impact a fraction of a hydrogen atom’s velocity would be transferred to the gold creating a non zero temp and the hydrogen would slow down cooling off. There are some simple equations which govern this but they don’t matter to the concept.

The second law of thermodynamics is written in a variety of ways. I like this one from Wiki which recognizes the particulate nature of temperature.

Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.

Now gold in a solid is like a pile of ball bearings connected by springs. The atoms at non-zero temperature have velocity, stretching the springs between them which eventually launches them back into position. The result is incessant vibration. If the gold is the same temperature as the hydrogen, the gold’s spin, vibration and mass result in an equal transfer of velocity, spin and vibration to the hydrogen gas.

That’s it. The second law of thermo.

The point of all this is twofold; First, light particles have to hit at a much faster velocity than heavy particles of the same temperature, and second, to explain what temperature is in general.

Now that we’ve figured that out.

Let’s consider for a moment about what happens when you cram a pile of hydrogen atoms whipping around a container into a smaller container? For a moment assume the reduction in volume happens instantly. I’m not talking about a metal hammer slamming into molecules at lightspeed but rather some kind of transporter beam that instantly places all the molecules with their original velocity, spin and vibration in a smaller space.

We know the velocity of each atom didn’t increase but all but moments later, the number of impacts per unit volume inside our container have gone up. Also the number of impacts to the surface of the container per unit area has risen. The net result is a higher temperature.

Ok, so now we know higher temperatures occur when hydrogen gas particles are crammed closer together, it’s reasonably easy to expand the concept to bigger molecules. These molecules can be thousands of protons and atoms large, they bend and twist like perfect springs bouncing around and whipping in impossible complexity, yet the constant is the impacts per second, the mass of the particles and the velocity of impact. If you’ve followed this far, the second law of thermodynamics should now be hit you in the head obvious.

Of course warm temperature (average velocity and mass) transfers to cold.

So back to hurricanes, what happens when you take a bunch of H2O water gas and Vander Waals forces condense it into a liquid?

Now assume further that these microscopic drops consist of a few million water molecules. What will the average velocity of the total mass of the droplet be? Will it shoot off to the left or right at the speed of sound like an individual gas atom or will the sheer number of molecules take over and average to zero.

Zero is the answer.

Zero net velocity.


Did you know there is no such thing as suction? There isn’t, a suction is a negative pressure differential between surfaces, but the question we need to answer is the same as the one for temperature above

‘what is pressure?’

Pressure, very similarly to temperature, yet slightly different is the transfer of momentum of an impacting particle to another particle. What keeps a balloon expanded is a balance of the number and velocity of internal impacts against the stretchyness of the ballon and the number and velocity of impacts on the outside of the balloon.

More impacts per second, higher mass per impact or higher velocity per impact and the balloon is larger. Gawd it’s simple when you think of it like that isn’t it?


Now the payoff.

Say you have a column of 100% moist air right at the edge of condensation which experiences just enough pressure
change to cause a shift from gas to liquid. All of a sudden, water molecules bouncing around at the speed of sound with an equal temperature to the surrounding air, become stationary drops with a slightly warmer temperature.


Less collisions per second, there are no water molecules per second as velocity has dropped to zero for those.

Lowered pressure – big time.

Surrounding gas still having air with moisture falls, suddenly drier and lower pressure condensed air pushes past the droplets which still rise through the column of dry air now racing past in an upward direction.

What a concept. Here’s how Anastassia’s paper describes it:

Hurricanes and tornadoes could be compared to an explosion reversed and prolonged
in time. In the ordinary explosion potential energy concentrated in the explosion
center is released in a burst, making local air pressure rise sharply and causing
dynamic air 5 movement in the direction away from the explosion center. Conversely,
condensation of saturated water vapor within the column of ascending air in hurricanes
and tornadoes leads to a sharp drop of local air pressure. This further enhances the
ascending motion of yet accelerating air masses, as well as the compensating radial
fluxes of moist air incoming to the area where the process of condensation is most
10 intensive. Water vapor contained in the incoming air undergoes condensation in the
same area; this sustains the pressure difference between the hurricane center and
its environment. Hurricane could also be compared to a black hole, which sucks the
surrounding air into the center, where it partially “annihilates” due to condensation of
water vapor and its disappearance from the gas phase. Thus, hurricane is an “anti15
explosion”. While in explosion the gas phase appears from either liquid or solid phase,
in hurricanes and tornadoes, conversely, the gas phase of water vapor partially disappears
from air due to condensation.
Unlike in explosion, the velocity of air masses in hurricanes and tornadoes is significantly
lower than the velocity of thermal molecular motion. In consequence, all air
20 volumes are in thermodynamic equilibrium, so that air pressure, temperature and density
within the hurricane conform to equilibrium thermodynamics. The driving force of
all hurricane processes is a rapid release, as in compressed spring, of potential energy
previously accumulated in the form of saturated water vapor in the atmospheric column
during a prolonged period of water vapor evaporation under the action of the absorbed
25 solar radiation. Since the power of the practically instantaneous energy release in
the hurricane greatly exceeds the power of energy exchange with the environment, all
hurricane processes can be described as adiabatic. The outlined approach predicts
that high wind velocities can develop anywhere in the atmosphere (over land as well
as over the ocean), where absolute humidity is high and the process of condensation
is spatially non-homogeneous. It thus provides a unifying theoretical framework for
understanding both hurricanes and tornadoes.

For the technical readers, of which there are many, the link to the paper is here.

The whole thing is amazingly interesting to me. There is a second paper at her site too, on the same topic, which for those who enjoy math is even more entertaining. I’ll let you guys find it though, at least until I decide to have some more fun.

151 Responses to “The Power Behind Hurricanes and Tornadoes”

  1. Don said


  2. kuhnkat said

    It depends on the magnitude of the actual effect.

    Sound familiar??

  3. Tilde Guillemet said

    There are a couple of other factors in Hurricanes / Typhoons / Cyclones compared to tornadoes.

    The first three are also subject to Coriolis forces that cause the weather system to rotate strongly – different directions depending on which hemisphere. ( I’m not sure if Tornadoes have a directional preference ?)

    The rotation creates the strong surface winds increasing in velocity towards the center. At the same time there is a pressure reduction the closer you get to the center. At the center – the eye – there is almost dead calm a few kilometers across. I know this from practical experience as I have been right through the eye of a severe tropical cyclone, central pressure 942 mb

    For a cyclone (my usual term) to grow it needs a constant feed of warm water – sea surface temperatures above a certain level. Cyclones die when over land. Cyclones also die if there is excessive wind-shear at the top of the structure.

    You have lower energy but similar shape with polar lows. I’m not sure what is driving them but they pack a lot of energy. Obviously they aren’t driven by hot tropical water so perhaps other effects are also in play, not just condensation caused vacuum effects

  4. Jeff Id said

    #2 That’s the unique thing about this process. Evaporation and condensation are VERY energetic processes compared to a bit of airflow. It makes so much sense that it’s difficult to deny. This is a form of convective flow probably not included in climate models BTW and to me it seems like it may be the primary driver of winds.

  5. Jeff Id said

    #3 If you can take a moment to read the paper linked, I think you’ll find enough energy to do exactly what you experienced. How cool is that though, a once in a dozen lifetimes experience.

    The Coriolis effects are there no matter the cause of the central updraft, this is simply an explanation of what the cause was.

  6. George said

    Helps illustrate why hurricanes intensify at night, too.

  7. timetochooseagain said

    Nice find Jeff, and kudos on a well written physics lesson.

  8. CautiouslyOptimistic said

    Jeff – Great write up! You have a very natural style that makes the physics approachable and accessible.

    As a great teacher once said to me, “if you can’t expalain a concept simply, then you probably don’t know your subject as well as you think you do.”

    I’m looking forward very much to sharing your post with my 8th grade boy!

  9. Jeff, many thanks for such an easy-to-follow and at the same time comprehensive introduction to condensation-induced hydrodynamics! We have new research in progress and hope to be reporting some interesting developments in due course…

    Let me put all this into perhaps a more general perspective — why do the winds blow on Earth? Apparently, for the winds to blow there must be a gradient of air pressure.

    Air pressure of ideal gas depends on two variables, temperature and the number of molecules in a given volume. Since the Sun heats the Earth more intensely in some places and less intensely in the others, differential heating has been for centuries considered THE driver of air motion. However, despite being qualitatively appealing, this physical mechanism has not been proved from the basic physical principles to produce wind velocities of observable magnitude because of the following conceptual difficulty.

    Take a jar divided into two parts and fill the two parts with equal amounts of air, hot air in one part, and cold air in the second part. Air pressures will be different. If we remove the partition between the parts and let the air mix, there will be an air flow and finally the mixture will equilibrate at a uniform pressure and temperature. BUT, importantly, even if we DO NOT remove the partition, the system will equilibrate to equal pressure and temperature WITHOUT AIR FLOW simply via heat conductivity. This is an extreme case, but also in reality a pressure gradient associated with temperature gradient involves the problem of dissipative losses to heat conductivity. This is a very difficult theoretical problem, to determine the efficiency of such a gradient for producing kinetic energy. It has not been solved for the atmosphere, rather, people just take the observed values, put them into models and EMULATE the dynamics.

    Now let us turn to pressure differences associated with differences in the amounts of gas. Take the same jar with two parts (of the same volume) and fill the two parts with different amounts of gas of whatever temperatures. In this case it is clear that the system cannot in principle equilibrate to equal pressure and temperature without a mass flow. Until you move the access of gas from one part to another, the system will have either pressure, temperature or both different between the two parts.

    Thus, pressure differences produced by condensation which changes the amount of matter are associated with a fixed amount of potential energy that cannot be in principle lost and is fully converted to the kinetic energy. Namely for this reason the (conventionally neglected) account of mass non-conservation gradient associated with condensation allows for a straightforward determination of the resulting pressure gradients and wind velocities (provided friction is set). The atmosphere is not a heat engine with unknown efficiency. With solar energy continuously pumping vapor into the atmosphere, the atmosphere is a unique dynamic machine converting potential energy (not latent heat!!!) of vapor into the kinetic energy of wind.

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  11. hswiseman said

    Ditto the gust front and wet microburst.

  12. Sordnay said

    wouldn’t this means that with more water vapor this process will take place more easily / frecuently?

  13. Dhananjay Mardhekar said

    The basic concept used by Dr. Anastassia Makarieva in explaining the power behind the hurricanes and the tornadoes is the volumetric extinction in the condensation process. This phenomenon and the consequent generation of the pressure gradient force has already been put forth by me in the year 2005. My explanation is based on Avogadro’s Law which is the best way to explain the phenomenon. Dr. Makarieva’s work is a mere extension based on my original work.

    I have presented a paper on this at WMO’s 9th Scientific Conference on Weather Modification in the year 2007.


  14. jstults said

    Just a couple nits, otherwise pretty good ‘kinetic theory for everyone’.

    Well we know from the example above the liquid water will be warmer than the gas, simply because the particles are closer together and are colliding more often.
    I thought phase changes generally occurred at constant temperature?

    REPLY: Thanks I fixed it.

    Zero net velocity Unless there’s a bulk velocity in the gas (wind), the droplets will have roughly that velocity when they condense. It would be interesting to consider the drag effects on the droplets.

    This is a neat article, there’s a lot of delta p potential in condensation: going from ~1e-3 g/cm^3 to ~1 g/cm^3.

  15. Larry Geiger said

    Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.

    Thermal bunnies always run downhill.

  16. Re: #13 Dhananjay Mardhekar

    Pressure gradient force induced by spatially non-homogeneous condensation is an elegant physical concept. There is no doubt that it will ultimately win the minds of climate scientists. There can be little doubt either that this idea might have occurred to many people. I am delighted that Dr. Mardhekar appreciates this idea and undertakes efforts to its propagation and I have no grounds not to trust the statement that Dr. Mardhekar has come to this idea on his own.

    At the same time, at this point we know of no publications of Dr. Mardhekar where the potential energy released from condensation would be quantified and the wind velocities produced by condensation estimated.

    As for our group, the chronology of the approach we developed was as follows. In 1990 Gorshkov in the “Energetics of the Biosphere and Stability of the Environmental State”, p. 147, in Russian noted that the energetics of hurricanes and tornadoes is determined by condensation after a prolonged period of evaporation into the atmosphere, see also Gorshkov (1995) “Physical and biological bases of life stability”, p. 227. In contrast to the prevailing opinion that hurricanes take energy from the oceanic surface, Gorshkov (1990, 1995) emphasized that they operate on the basis of energy stored in the atmosphere in the form of water vapor.

    In 2002 Gorshkov, Makarieva and Pujol, see also Makarieva et al. 2003, revealed the existence of a critical lapse rate of air temperature beyond which the atmosphere is unstable to condensation. It was estimated at 1.9 K/km. This is a core statement for all the subsequent theory development by our group. If the moist adiabatic lapse rate of the atmospheric air were smaller than the critical value, no condensation would ever occur in the atmosphere — water vapor would then expand with height too quickly and depart from the state of saturation instead of undergoing condensation.

    In Preprint No. 2655 of Petersburg Nuclear Physics Institute submitted to publication 10 February 2006 Gorshkov and Makarieva first applied the concept of the non-equilibrium water vapor distribution to describe atmospheric motions. This work was later published as Makarieva and Gorshkov (2007) in the Hydrology and Earth System Sciences journal of the European Geosciences Union. The main physical scales of the problem were quantified at that time, this is a quote from the preprint:
    “The obtained theoretical estimate (16) is in good agreement with the maximum updraft velocities observed in typhoons and tornadoes (e.g., Smith (1997)).”

    We had not heard of the research of Dr. Mardhekar until summer 2009, when the Editors of Atmospheric Chemistry and Physics forwarded us a letter from Dr. Mardhekar, where he claimed the priority of putting the idea forward. We noticed that the presentation of Dr. Mardhekar made at WMO Conference in October 2007 contained but a qualitative description of the idea. By that time, our preprint with quantitative estimates of pressure gradient and wind velocities produced in hurricanes and tornadoes by water condensation has been in open access for a year and a half.

  17. Phillip Bratby said

    Sorry, I can’t resist posting the words of the song by comedy duo Falnders & Swann:

    The First Law of Thermodymamics:
    Heat is work and work is heat
    Heat is work and work is heat
    Very good!
    The Second Law of Thermodymamics:
    Heat cannot of itself pass from one body to a hotter body
    (scat music starts)
    Heat cannot of itself pass from one body to a hotter body
    Heat won’t pass from a cooler to a hotter
    Heat won’t pass from a cooler to a hotter
    You can try it if you like but you far better notter
    You can try it if you like but you far better notter
    ‘Cos the cold in the cooler will get hotter as a ruler
    ‘Cos the cold in the cooler will get hotter as a ruler
    ‘Cos the hotter body’s heat will pass to the cooler
    ‘Cos the hotter body’s heat will pass to the cooler

    First Law:
    Heat is work and work is heat and work is heat and heat is work
    Heat will pass by conduction
    Heat will pass by conduction
    Heat will pass by convection
    Heat will pass by convection
    Heat will pass by radiation
    Heat will pass by radiation
    And that’s a physical law

    Heat is work and work’s a curse
    And all the heat in the Universe
    Is gonna cooool down ‘cos it can’t increase
    Then there’ll be no more work and there’ll be perfect peace
    Yeah – that’s entropy, man!

    And all because of the Second Law of Thermodynamics, which lays down:

    That you can’t pass heat from the cooler to the hotter
    Try it if you like but you far better notter
    ‘Cos the cold in the cooler will get hotter as a ruler
    ‘Cos the hotter body’s heat will pass to the cooler
    Oh, you can’t pass heat from the cooler to the hotter
    You can try it if you like but you’ll only look a fooler
    ‘Cos the cold in the cooler will get hotter as a ruler
    That’s a physical Law!

  18. Jeff Id said

    Anastassia and Dhananjay Mardhekar,

    Thanks for coming by and explaining further. Considering I gave no warning that this post was going up, it’s impressive that two experts stopped by to discuss it.

    I agree the concept is elegant which is why the papers caught my attention. When the new research comes out, I will be interested in reading. Being non-university, papers aren’t free for me so Anastassias website was the only source of information and is very much appreciated.

  19. DeWitt Payne said

    This one’s interesting, but her paper on the fallacy of the dissipative heat engine is better. I assume that’s the other paper you mentioned.

    I’m really surprised that didn’t generate more comment at CA when she posted the link. Of course, if you don’t have a bookmark to the current Unthreaded page at CA, it’s hard to find.

  20. Sonicfrog said

    “I was born with an ugly obsession to need to know how everything works.”

    Me too, but that stupid inherited lazy gene seems to be very dominant, overriding the other.

    Anyway, Jeff this is a great post. I’m going to link to it, and, if you don’t mind the increase in traffic, I’ll forward it over to Instapundit and maybe he’ll feature it.

  21. Jeff Id said

    Here is a link to some of the published papers including the one above.

    #19, Dewitt, I can only see the abstract of this paper and I saw that at the open thread. From it, the first part of the paper discussed here sounds very similar. If you have a copy I wouldn’t mind reading, my email is on the left.

    #20, Thanks, feel free to use anything. TAV is free material for anyone to use or criticize in any way they want 😉

  22. Jeff, all papers of the Royal Society (back to the 17th century, including works of Newton, Maxwell etc.) are now in open access until 28 February 2010 (because the Society is celebrating its 350th anniversary). So you can download the Carnot paper freely, see the link at the right to the abstract.

    Thanks are due to you for opening the discussion.

  23. Jim Brock said

    I seem to recall an article in Engineering magazine in the fifties that covered the same subject, and gave the thermodynamic equations that governed hurricanes. Anyone else remember this?

  24. JAE said

    If you continue your line of reasoning about what constitutes temperature (which I concur with completely), you will “see” why the Earth’s average temperature is about 33 C higher than it “should be,” considering black-body radiation, alone. It is a function of all the kinetic and potential energy stored in the atmosphere and oceans, and has little or nothing to do with a radiative “greenhouse effect.” IMHO, of course 🙂

  25. Phillip Bratby said

    JAE: I agree, it’s just the internal energy (potential and thermal) of the atmospheric column – nothing to do with the so-called greenhouse effect.

  26. Jeff,

    Thanks for posting this. My head hurts. Maybe some other would like to participate here as well.. Lucia perhaps and DR. Curry

  27. It is not often that a new wind driver is proposed. The last time it happened, I believe, not later than 1735, when George Hadley published a note Concerning the Cause of the General Trade-Winds. (Yes, the warm air rises.) The history says his works remained neglected for about a century.

    Actually, if destined to be totally ignored for the coming decades, it is really nice to have the condensation-induced dynamics discussed in the blogosphere. What if a concept met with a resistance by the conventional meteorological paradigm will ultimately prove true via discussion in blogs before gaining the official recognition… The GCM enterprise completely ignoring the major wind driver…

    Just look at what have already happened. Meteorologists playing with heat engine concepts of the perpetuum mobile type did not allow our hurricane paper to be published in their “peer-reviewed” literature. Ok, you do not want us, we go elsewhere. Now then, the highly respectable Proceedings of the Royal Society Series A, who aim to publish “slowly burning, long lasting papers” (see the last Editorial in the journal) immediately publishes the piece. Have the meteorologists invented a physics of their own, where everything they want becomes possible? Including perpetuum mobiles sold to the public as a scientific model of hurricanes with a prestigious MIT label?

  28. Judith Curry said

    Some important stuff here. I have been closely reading Makarieva’s papers. I don’t have enough time right now to discuss the topic here, but her work deserves serious discussion, glad to see it getting some attention on this site.

  29. Dr. Judith Curry has prompted a discussion of the topic in a professional e-mail list (where many people had been already negatively influenced by the fate of our paper in ACPD, so it was not easy). She provided insightful comments and suggestions and sources of the data to our group. Most importantly for us, we met a live and competent interest, in striking contrast to our experiences elsewhere.

  30. DeWitt Payne said

    Re: Phillip Bratby (Feb 3 14:12),

    Oh, please. You must be joking or you really do deserve the term ‘denialist’. Where do you think the potential and kinetic energy comes from? Would the temperature stay the same if the Earth were teleported to intergalactic space or the sun were turned off? No, it would cool. It’s a dynamic system and the radiative properties of CO2, water vapor, methane, nitrous oxide, etc. affect the state of that system.

    If you still don’t believe that, get an IR thermometer from an auto parts or kitchen supply store (~$50, no home should be without one) and point it at the sky at night. You’ll get a reading. The reading will be higher on a cloudy night for a given temperature. Now think what the reading would be (if the thermometer went that low, which they don’t) if the atmosphere didn’t radiate in the thermal IR. I’ll give you a hint, 2.7 K or -270.6 C. Do you think it might be colder, a lot colder, if that were true?

    That’s the greenhouse effect in a nutshell.

  31. Jeff Id said

    Let’s keep the general discussion of greenhouse effect on the open thread – or maybe one of you guys can do a short but decent writeup and I’ll start a new one.

    #22 Thanks much, work is nuts today but I downloaded it and will read tonight.

  32. Tony said

    Fascinating stuff! Congratulations to all involved. Thomas Newcomen as the father of the steam engine would have been proud, as his condensing engines exploited just this principle!

    Personally I have always been fascinated by the pressure-drop caused by condensation …. and whether or not it could be of use in considering solar-powered stills of various kinds.

    And as the excellent work of Makarieva and others shows, of course the hurricane is a giant natural solar still and produces massive quantities of fresh water!

    Another point worth considering is that whilst condensation will cause a pressure-drop; a pressure-drop will cause condensation.

  33. Kenneth Fritsch said

    It is good to see that Anastassia Makarieva is obtaining some traction for her (and her coauthors) proposed mechanism for hurricane drivers. It is also good to see that Judith Curry has been instrumental in helping that process along.

    The proposed concept seems simple (to me) and Anastassia appears well-versed and articulate in explaining it. As a skeptic, and a layperson in this matter, what I require next is to hear the critiques from those with alternative theories and then, of course, replies to those critiques. Do we have any links to critiques – beyond any hand waving and of substance?

    Thanks to Jeff ID for providing a forum for this discussion at TAV.

  34. Kenneth Fritsch said

    Just look at what have already happened. Meteorologists playing with heat engine concepts of the perpetuum mobile type did not allow our hurricane paper to be published in their “peer-reviewed” literature. Ok, you do not want us, we go elsewhere. Now then, the highly respectable Proceedings of the Royal Society Series A, who aim to publish “slowly burning, long lasting papers” (see the last Editorial in the journal) immediately publishes the piece. Have the meteorologists invented a physics of their own, where everything they want becomes possible? Including perpetuum mobiles sold to the public as a scientific model of hurricanes with a prestigious MIT label?

    Anastassia, I think the blogosphere can give us insights into what goes on behind the doors of peer-review. Would that presitigious MIT label contain the name of Kerry Emanuel?

  35. Glad to see Dr. Curry show up.

    Since I’m the one who usually is most need of a nanny for my comments I’ll remind folks to be nice to the working scientists
    who show up and keep the discussion focused on the science. I’ve sent invitations to a couple other people who I can only hope will show up.
    ( not kerry, since I have no prior contact with him).

    PS. yes Kenneth.

  36. oMan said

    Thanks to Anastassia and Jeff (and commenters). I am learning so much. Some questions: is this not the kind of negative feedback mechanism that would counter the “runaway feedback” mechanism posited by the climate warmist model (where CO2 magically induces water vapor to multiply the greenhouse effect)? And if it does work to counter that mechanism, what is its magnitude? That is, if the mechanism applies (as I ignorantly suspect) to cumulonimbus weather systems as well as to hurricanes, doesn’t it move an awful lot of heat energy from sea level to upper troposphere in a big hurry?

    I seem to recall the climate warmists’ global circulation model is too coarse (and lacks modeling mechanism?) to account for heat transport by thunderstorms and the like. So maybe this is the elephant in the room?

  37. I’ve been trying to read the paper, but finding it hard to follow. Has anyone understood the proof that the Carnot engine idea violates the laws of thermo, and can explain it briefly?

    The notion of a condensation engine, as Tony said, goes back to Newcomen. He, however, injected cold water to produce the condensation. No-one is doing that in a hurricane. And that seems to be to be the weakness. Thermo does require that to run any kind of heat engine, you need a hot source and a cool sink. The intervention of a phase change does not change this – and of course, most of the thermo ideas were worked out in the context of steam engines.

    Jeff’s notion of a near-explosive condensation doesn’t work for me. Condensation liberates lots of latent heat, so it can only proceed as fast as that LH can be removed.

    I was puzzled by one of Annastassia’s early statements:
    ” This would imply heat transfer from a cooler object (oceanic surface) to a warmer object (the radiating upper atmosphere), which is impossible.”
    But no, the radiating upper atmosphere (emitting IR to space) is generally reckoned to be about 225K or so.

  38. Jeff Id said

    37, I probably should let Anastassia explain the work, my explanation was not a near-explosive one but rather was meant to explain the power of the effect. Unfortunately I used the word BOOM to represent the size of the effect, but that’s just b/c it was fun. Anastassia’s explanation was of an inverse explosion.

    Condensation passes heat to the gas phase of the atmosphere but it’s not just heat removal which creates conditions for condensation, a lowered pressure does that as well. So if the reduced pressure from gas removal is further reduced by the expansion of a warmer air, the flow will increase even more. At least that’s my guess of how the equations would work out.

    Hopefully your comment will get some further explanation from the pro’s.

  39. Tilde Guillemet said

    One piece in Jeff’s layman’s description – as compared to the original paper which I need a refresher course in Physics to read properly – puzzles me.

    “Surrounding gas still having air with moisture falls, suddenly drier and lower pressure condensed air pushes past the droplets which still rise through the column of dry air now racing past in an upward direction.”

    What happens when ordinary cumulus clouds form? You have moist buoyant air rising from the ground. At some point it hits the lifting condensation level and the cloud forms. Why does this not have the same effect? i.e. sudden drop in pressure and rapid lift taking off rapidly in the direction of space?

    I guess that this may be what happens in thunderstorms, but why doesn’t it happen for most ordinary cumulus clouds?

  40. Jeff Id said

    #39, What makes you think it doesn’t?

    Actually, the point of the paper is that with the right temperature vs pressure gradient you get a continuous action. In the case of a cloud, I don’t see anything preventing the effect. It probably is what creates some of the updrafts and billowing at the tops.

  41. MicHussey said

    WRT the Carnot model of the hurricane – in traditional engineering the Carnot model describes the amount of work an ideal engine can do as dependent on difference between the temperature of the engine and that of its environment. The problem with Hurricanes is that there isn’t a huge difference in temps beween inside and outside.

    The specific heat capacity of water as a liquid is more than double that of water vapour. And the SHC of water vapor is approx 1000 tiems that of air. This means that condensation of water vapour to water droplets requires net input of energy from somewhere.

    So condensation of water vapour doesn’t release heat – it requires a net influx of energy. One mechanism by which this can occur is that the energy is provided by the decrease in pressure (i.e. Boyles’ law). And if you want to visualize this by 1000 molecules of air running in to give up their energy to 1 molecule of water you may (but it all boils down to a pressure decrease in any case).

  42. Tilde Guillemet said


    I’m not saying it doesn’t. I am simply trying to explore the story so that even I can understand.

    My present state of knowledge about typical cumulus cloud formation is:

    Moist buoyant air parcels rise because they are less dense than surrounding dry air. As they rise they expand and cool due to the drop in ambient pressure

    At some stage when they cool enough at least some of the water in the air parcel condenses. This is the lifting condensation level.

    So you have a parcel of air with a small mount of vertical velocity that if acting alone would allow it to rise a few metres more. It contains dry air and water droplets.

    If the condensing process results in an immediate drop of pressure you would expect a very high pressure gradient at the condensing level and perhaps (?) a difference in buoyancy between the moist air below the level and the dry low pressure air above – that also contains liquid water droplets.

    There may also be a (strong ?) temperature gradient at the condensation level.

    If there is a strong pressure gradient at the condensation level, I would expect the now dry low pressure air parcel to accelerate upwards – probably leaving its water droplets behind.

    Simple observation shows that what happens in most cumulus clouds is a continued rise of the air parcel with more than just from upward momentum effects but not a ‘catastrophic’ runaway lifting. The exception being cumulo-nimbus.

    The question is what actually happens and why?

  43. MicHussey said

    Replying to myself:
    I am of course talking shite… Energy is released upon condensation.
    But the differences in SHC are perhaps interesting in a NON-Equlibrium system where water vapour and droplets exist together.

  44. curious said

    I’m probably being dim here but isn’t the point that the overall system is operating adiabatically important? Isn’t it an internal energy exchange from latent heat of vaporisation to kinetic energy of fluid (air)? My understanding of the argument is condensation is happening due to the vertical lapse rate and so the collapse of water vapour to water liquid takes place giving the very high local pressure gradient hence inducing high speed gas movement. I also think Nick in 37 has discovered a typo/translation issue as I’ve read that a couple of times and think it is the wrong way round and not consistent with the rest of the paragraph. Raises questions for me of what are the critical factors in hurricane formation and activation. Also suggest the major gas movements are taking place in the horizontal plane. Sorry if I’m completely missing it – need to read it again after doing some revision!

    PS Jeff – any news on the Steig response publication? I saw a query on this on another thread but I don’t think you picked up on it.

  45. Jeff Id said

    #41 “The specific heat capacity of water as a liquid is more than double that of water vapour. And the SHC of water vapor is approx 1000 tiems that of air. This means that condensation of water vapour to water droplets requires net input of energy from somewhere.”

    Condensation actually releases heat. That’s why when you put a flame under a moist pan a water drop will evaporate rather than condense more. It’s also the point of evaporative cooling. I’m not being cocky or anything, just pointing out a detail.


    At some stage when they cool enough at least some of the water in the air parcel condenses. This is the lifting condensation level.

    This is right to my non-expert knowledge.

    “There may also be a (strong ?) temperature gradient at the condensation level.

    My thought is that the gradient exists but is not necissarily strong. All that is required is some gradient. So if a bit of vapor condenses, other air will rise up under it and if the conditions are right, continue the condensation. The fact that it’s not always runaway, just means the conditions aren’t perfect.

  46. Jeff Id said

    #43, sorry, cross posted while watching TV.

  47. Jeff Id said

    #44 Submitted, and we’ve been asked for $$. It’s one of the most detailed papers I’ve seen. We’ll be doing a post when the time is right.

  48. I see there’s a dispute above about priority for the notion of a condensation driver. But it may be an old idea. Emanuel, in his 1991 review paper on hurricanes, says:
    “Attempts to regard the condensation heat source as external lead to the oft-repeated statement that hurricanes are driven by condensation of water vapor, a view rather analogous to that of an engineer who proclaims that elevators are driven upward by the downward acceleration of counterweights. Such a view, though energetically correct, is conceptually awkward;it is far more natural to consider the elevator and its counterweight as a single system driven by a motor.” (Emphasis mine).

    I think that’s right – there’s nothing special about condensation as a step in a heat engine. The fundamentals remain – you have to transfer heat from a hot sink to a cool source.

  49. curious said

    48 – But the argument is the hurricane is not operating as a heat engine. If I’ve understood the suggestion is that the hurricane is a physical manifestation of a transformation of the potential energy in water vapour to kinetic energy of a moving fluid. Or that’s how I read para 3 of Anastassia @ 16.

    Jeff – thanks, looking forwards to it.

  50. JAE said

    30, DeWitt: I’m only letting your nonsense go unabated because of Jeff’s plea. You are full of nonsense (or something worse), sir!

  51. Jeff Id said

    50 Seriously, write up your point in a coherent manner and send it to me by email. The blog is visited by a lot of people. Let’s leave this thread for what it is.

  52. I think the effectiveness of condensation as a power source is overrated in this discussion. Saturated air at 30C contains 4.2% wv. So after complete condensation, the volume drops by that amount. But according to Emanuel (1991), air rising in a hurricane drops by 33% in degrees K. So WV is a small factor in contraction.

    ps The comment numbering seems to have gone haywire.

  53. Re: #48 (or #25) , “hot sink to a cool source”
    I meant, of course, hot source to a cool sink.

  54. JAE said

    51, Jeff: OK, I will see what I can do. I’m a PhD chemist, not a physics guy, and I could well be on a tangent (and completely WRONG), but I have a lot of company among physicists! For sure, the addition of CO2 is not adding any heat to the planet during the last 15 years! So ????

  55. Jeff Id said

    #54, I don’t agree that CO2 doesn’t add heat but am very much looking forward to learning otherwise.

  56. R Shearer said

    As a chemist, I couldn’t get past your octane/carbon statements. Carbon is atomic # 6, therefore 6 protons (not 14). Normally the nucleus has 6 neutons also for carbon 12 or 8 for carbon 14.

  57. Jeff Id said

    #56, shoot thanks for the correction.

  58. JAE said

    55, Jeff: well, just WHERE is the heat, man? The oceans are cooling, the “global temperature” (no matter how corrupt it is) is cooling, the corals in Florida are dead, etc., etc., etc. WTF, Jeff?

  59. Jeff Id said

    #58, that is a different topic and now I’m frustrated.

  60. Many thanks to all for comments. There are indeed several issues here that might be of interest, but since all of them demand some intellectual effort to be discussed, making a mix of them may indeed result in some havoc. The issues are:

    1. Why the heat engine approach to hurricanes is incorrect.
    2. The physics of condensation and the nature of pressure gradients it produces.
    3. How the new ideas are received by the standing paradigm.

    I will briefly speak on No. 1, then concentrate on No. 2, and drop No. 3 altogether for the time being. Re #33 Kenneth, and all people interested in No. 3 can be referred to the interactive discussion here. It contains much material, so a few highlights are:

    Final Editor’s Comment by U. Poeschl

    Our Response to that comment, see Appendix 7 in the link

    Of interest is also the comment of Anonymous Referee #3 and our response.

  61. #60. cool. thx

  62. Hurricanes not a heat engine – 1

    Let we have a hot ocean at Th = 300 K and a cold atmosphere around Tc = 200 K. It is a normal situation in the tropics. Weak background wind at around several meters per second.

    Due to the temperature difference, there is a heat flux from the ocean to the atmosphere. The magnitude of this flux is roughly proportional to the temperature difference. It is a turbulent flux, so it is also proportional to eddy diffusivity, which, in turn, grows with increasing wind speed. (When I come to my countryhouse and the temperature there is below -15 deg C, I make fire in the oven and also switch on a ventilator, to let the heat spread around more rapidly. By switching the ventilator, I enhance turbulence and increase the flux of heat. The same occurs when the wind speed increases at the oceanic surface.)

    Heat flux Q from the warm ocean to the atmosphere be Q = K(V)(Th – Tc) (dimension Watts per unit area), where K(V) reflects turbulence and grows with wind speed. If Carnot efficiency is eC, the basic idea consists in the statement that the kinetic power P produced by the vortex increases with growing wind speed like P = eC Q. That is, the hurricane intensifies itself via a positive feedback between the wind speed and heat inflow. The intensification is thought to cease and the pattern become quasi-stationary, when the rate of dissipation of the appearing kinetic energy becomes equal to the rate at which it is produced by the heat engine.

    However, what is ignored completely in this approach, is that with increasing heat conductivity and increased heat flux from the heater, the cooler warms. Temperature Tc approaches Th, and the Carnot efficiency eC = (Th – Tc)/Th approaches zero. This obvious fact is otherwise well-known and discussed in detail by physicists working on finite time heat engines, see references in the Discussion section in the Proc A paper. It is also evident from common sense — when I switch the ventilator, the room warms and the temperature difference between the room and the oven decreases.

    In order to keep the temperature Tc of the cooler (in our case, the upper atmosphere) constant, one needs to take care that with the growing heat flux from the ocean, heat be removed at an equally increasing rate from the atmosphere. Now, attention, the atmosphere dispatches its heat to the outer space, and does so via thermal radiation. This heat flux, in accordance with Stephan-Boltzmann law, is set by the temperature of the radiator, i.e. is a function of Tc. IT CANNOT GROW IF Tc IS CONSTANT. It is easy to calculate (and we do that in the ACPD paper) that in order to radiate the flux of heat that is released within the hurricane, the upper atmosphere would have to have a temperature of about 400 K (see here, p. S11272). But, in this case we would have heat transfer from the ocean at 300 K to the atmosphere at 400 K, which is impossible. This is response to the concern of #37.

    Of course, in reality, the upward heat flux produced within the hurricane is transported away from the hurricane and is radiated to space from a large area. But now the problem is that we must ensure that this heat transport from the hurricane in the horizontal plane grows precisely in tune with the growing flux from the ocean, as the wind speed increases. This outward horizontal flux (never quantified in the model) remains unspecified despite being crucial for the maintenance of the vertical temperature difference. In the horizontal plane there are never temperature differences of the order of (Th – Tc) ~ 100 K, so the high Carnot efficiency employed in calculating the hurricane intensity eC ~ (Th – Tc)/Th ~ 1/3 becomes physically irrelevant.

    To put things simply, the mere presence of a temperature gradient or a heat flux somewhere does not guarantee that there is a Carnot (!) heat engine operating there and producing useful work at a maximum possible efficiency. This should be especially clear for the engineers working with real heat engines.

    This is a brief account of the problems around hurricanes as a Carnot heat engine as presented, e.g., in the work of Emanuel (1991) cited above at #48. Note also that the derivations of the concept in that work contain a physical error when the Bernoulli’s equation is integrated. This error undermines the closeness of all derivations and does not allow to get any result at all. See Section 3.1 here.

    Even people exceptionally opposing to all our studies could not help recognizing that this was an error, see, e.g., here, p. S9062, starting from the words “it was indeed a stupid error of mine”. Yet “nothing to see here, move along” is a universal trick which helps conveniently discard ANY critique.

    Perhaps for the reason that the error was ultimately spotted (although never openly admitted), in later works this particular scheme of derivations was abandoned by Kerry Emanuel in favor of a different, although related, dissipative heat engine concept. I will dwell on this in the next comment to conclude the heat engine considerations.

  63. Dhananjay Mardhekar said

    Dear Dr. Anastassia Makarieva,

    Ref. No. 16

    I have gone through your message. I have filed a Disclosure Document with the US Patent and Trademark Office on the concept of vapor volume reduction in the condensation process and its importance in hurricanes on 22nd September 2005. If required by you I can send a scanned copy of the official document of submission received from the USPTO.

    On 19th January 2006 I have also filed a patent in India on Hurricane Modification in which vapor volume reduction and its role in the suction of vapor-rich air is clearly discussed on the basis of Avogadro’s Law. The definitions used for explaining the concept are:
    1) Gram Molecular Weight: – The gram molecular weight or the gram molecule of a substance is its molecular weight expressed in grams.
    2) Gram Molecular Volume: – The gram molecular volume is the volume occupied by one gram molecule of any substance in the gaseous state or in a state of vapor is 22.4 liters at STP.

    Both the dates of the filed documents are prior to one and half year earlier than October 2007 as mentioned by you.

    When I conceived this concept, I thoroughly searched the net for about 3 months and I didn’t find anything similar to this new concept.

    I would like to send you the detailed latest description of my qualitative work. One specific figure in my write up explains convincingly and also quantitatively what exactly happens in the condensation regions in a hurricane and how a pressure gradient force is generated. You just look at the figure and it explains everything quantitatively. No other explanation is needed for the basic understanding of this new concept. It is a simple, straight forward and self explanatory figure. I agree that my work is qualitative but on this basis only quantitative work can be done.

    Therefore I propose to you that we will together go ahead in this matter as a qualitative work done by me and quantitative work done by you.

    For sending my work with figures I will require your e-mail ID which is not filtered. My e-mail ID is

  64. Hurricanes not a heat engine – 2

    The efficiency of Carnot cycle, the maximum possible one, is eC = (Th – Tc)/Th < 1. The engine cannot produce more work than there is heat received. In the dissipative heat engine the work produced is left to dissipate within the engine. This engine recirculates heat. This additional heat due to dissipation is thought to increase the heat input into the engine. In the result, the efficiency of the dissipative heat engine rises above Carnot efficiency and becomes potentially infinite (!), eD = (Th – Tc)/Tc. This is because Tc can be in principle as small as one wants. The hurricane is thus thought to intensify itself also by dissipating part of the kinetic energy it produces within itself. For Th = 300 K, Tc = 200 K, the transition from eC to eD implies an increase in the hurricane power (per unit area) by 1.5-fold, so it is not a minor numerical issue.

    In the Proc A paper, which is devoted specifically to this subject, we show that such a process cannot take place. For any heat engine, as soon as one starts dissipating work within the engine, the resulting heat warms the working body. In consequence, the heat flow from the heater decreases (because the temperature difference between the working body and the heater decreases due to the warming of the former). Even if one artificially synchronizes the timescale of work dissipation and heat flow from the heater (which by itself is a very strong stipulation never discussed in the DHE model), at best dissipating work within the engine will leave the total work produced by the engine constant. In the worst case the the engine functioning completely disintegrates due to the chaotic dissipation of work during the cycle. Dissipation of work within the engine cannot raise the engine’s performance above the Carnot efficiency.

    In reality, the hurricanes can be viewed as dynamic machines producing kinetic energy. This kinetic energy, together with latent heat, is transported away from the hurricane in the horizontal plane and dissipates there on a very large area (and not within the hurricane).

  65. Dhananjay Mardhekar said

    My abstract on Hurricane’s Secret Driving Force

    Discovering hurricane’s secret driving force
    Dhananjay Mardhekar

    The explanation of the secret driving force in hurricanes is based on Avogadro’s law. According to the law 18 grams of water when evaporated occupies 22.414 litres of vapor at standard temperature and pressure (STP). Therefore, 1.0 gram of water in the vapor form will occupy 1.245 litres. That is, 1245 ml volume of vapor at STP when condensed will form 1.0 ml volume of water. Due to the phase change that is from water vapor to liquid water, huge reduction in volume occurs. The process of condensation of vapor into liquid water from the vapor component of the vapor-rich air is continuously taking place in a hurricane particularly in the eye wall on a very large scale. The condensed water precipitates as rain or forms clouds. Each ml of the rain leaves behind a vacant space equal to 1245 ml forming a low-pressure zone and consequently a pressure gradient force is formed. Therefore, when there are continuous torrential rains in the eye wall, sometimes of the order of 500 mm in 24 hours or even more, the magnitude of the low pressure zone and the pressure gradient force forming continuously in the condensation regions of the eye wall is gigantic. At the same time the latent heat released in the condensation process is absorbed by the remaining air component, it becomes warmer and buoyant, therefore ascends and ultimately escapes from the top of the hurricane as the outflow, again forming a low pressure zone. Thus, continuous condensation and continuous ascent and escape of warm air from the top together form a continuous pressure gradient and the vapor-rich air is continuously sucked up from below, that is from above the sea surface in the region of the eye wall due to the continuously forming pressure gradient force maintaining the near sea surface convergence of the vapor rich air. The value 1245 changes with change in temperature and pressure, but it does not affect the presented concept. The formation of the low-pressure zone due to the condensation is instantaneous. The moment the condensation takes place, the low-pressure zone and the consequent pressure gradient force is formed at that instant, hence this phenomenon accelerates the fuel input process. The continuous and instantaneous pressure gradient force forming due to the continuous condensation and the volume reduction phenomenon is the secret driving force.

    Storm systems are all low pressure systems. Vapor continuously enters the hurricane system in large quantities with a very large volume and comes out of the system continuously on condensation with a very small volume in the form of rains as explained above. Therefore this phenomenon dominantly contributes in maintaining a continuous low pressure within the hurricane system.

    Thus, the vapor volume reduction in the condensation process plays an important role in the dynamics of the hurricane engine.

    An average hurricane produces 1.5 cm/day of rain inside a circle of radius 665 kilometres (Gray 1981). Area of the circle comes to 1388586.5sq.kilometres. The average rainfall is 15liters/sq.meter/day. This means 15000 m3/sq.kilometre /day. Therefore the total rainfall per day inside the circle of radius 665 kilometres is, 20828797000m3. That means 20.83 kilometre3 of rain/day. Multiplying this by 1370 (1245 value at 27.50C) comes to 28537 kilometre3. This much volume of vapor-rich air is sucked into the hurricane system per day due to the condensation and volume reduction phenomenon. This is the average value. The peak value for any hurricane must be very high and hence this new concept describes a very important phenomenon.

  66. I now proceed to the physics of condensation. Comment #65 of Dr. Mardhekar is a good start to illustrate the standard approach to condensation, which forms the basis of the prevailing idea that water vapor is insignificant in generating air motions. It also helps visualize the difference between the qualitative and the quantitative in science.

    In #65 it is calculated how much water is condensed per day, namely 28537 cubic kilometers per day. It is further suggested that this water amount is replaced by an equivalent amount of moist air “sucked into the hurricane system per day due to the condensation”. I am not checking this figure, let us just accept it for the time being.

    Let us now compare this figure with the actual amount of air that enters the hurricane area per day. We consider the hurricane area as a cylinder of height h ~ 4 km, radius r = 665 km as in #665, and radial velocity at the outskirts about u = 5 m/sec = 432 km/day. Then the sought volume of the incoming air becomes V = (2 pi r h u ) x (1 day) = 722 x 10^3 cubic kilometers. This is 252 times larger a value than the “condensation effect” calculated by Dr. Mardhekar. Or, from the other side, according to this logic, a wind velocity of 5/252 ~ 0.02 m/s would be enough to keep the hurricane in balance.

    Therefore, were the approach advanced by Dr. Mardhekar correct, one could safely neglect the 1/252th contribution of vapor imbalance to the hurricane energetics. Namely this is currently done in all models of atmospheric circulation. Why to bother about effects of the order of one hundredth of the main flow???

    Now, where is the error?

    In the above calculation of Dr. Mardhekar the value of the incoming flow was deduced from the mass balance alone. Fluid motion, however, is governed by the equations of hydrodynamics, where a pressure gradient is specified. The mass imbalance of 30000 cubic kilometers of gas per day can be replenished by any air flow moving faster than 0.02 m/s. It is not at all possible to solve the problem just considering the mass imbalance.

    I am thinking of an example… Imagine an old grandmother who drinks, say, three bottles of milk per day. This is her mass imbalance that must be replenished. She becomes ill and asks her grandson to take care of the daily milk delivery. She has a fridge for only three bottles, so the boy knows — if he brings more, she will not take it.

    We can see that there is a variety of patterns for the grandma to meet her milk demand, for example: (1) The boy can come three times a day bringing one bottle at a time. In this example, the flow of boys through the grandma’s flat is 3 boys/day. (2) The grandson can come ten times, bringing milk in only three cases, and seven times — just to ask how the grandma feels herself. Now the flow of boys through the flat increases to 10 boys/day. (3) The boy can come with a crowd of friends several times a day to ask for pocket money, boring the old lady and still bringing the same three bottles of milk for her to drink. The flow of boys through the flat can reach a very high value then.

    So, while the mass imbalance replenished by the boy flow is the same in all cases, the attractiveness of the grandma’s flat for the grandson is different. This is just ANOTHER dimension of the problem. Namely, this dimension is the horizontal pressure gradient associated with condensation. This has never been considered in the traditional accounts of atmospheric circulation.

  67. Jeff Id said

    #66 After reading this comment several times the lightbulb finally went off between your point and Dhananjay Mardhekar. The mass imbalance cannot account for the peak usage alone.

    Just because the water changed to vapor doesn’t mean it falls from the storm or doesn’t re-evaporate. After all it’s just been launched miles into the air. So since we have this condensation occurring and moist droplets being separated from hot air, there must be an evaporation of the cloud vapor going on somewhere, perhaps toward the outer edge of the storm which then re-feeds the eye and maintaining a nearly perfect saturated humidity of incoming air? Is that right?

  68. #67 If moisture re-evaporated, there could be stationary hurricanes, which eternally recycled the moisture within themselves. In reality the hurricane moisture budget is dominated by moisture convergence — i.e., it feeds on moisture that is contained in the moist air that is being sucked towards the center from the outer environment. If there is no moisture in the air surrounding the hurricane, it will be exhausted. The dominance of moisture convergence is a known fact, see, e.g., Trenberth et al. 2007 Water and energy budgets of hurricanes: Case studies of Ivan and Katrina.

    What is important is that there is always a spatial gradient of the Evaporation – Precipitation difference. This is because precipitation predominantly occurs in the rising air, while evaporation occurs both where air ascends and where it descends.

    Another basic point is that condensation is always accompanied by cooling, never rise of temperature of the local air volume where it occurs. Condensation is induced by the decrease of local temperature, as prescribed by the Clausius-Clapeyron equation.

  69. Kenneth Fritsch said

    I highly recommend that interested readers and posters here go to the link given in Post #60 by Anastassia Makarieva to the authors, reviewers and editors comment. I am about 2/3 through and find it is good reading and entertaining to boot. The authors reply to “handwaiving” by a reviewer which I now like better than the more common use of handwaving.

    What would the boy/day travel rate be to grandma’s apartment be if the delivers were vodka?

  70. M.Villeger said

    Dear Dr Makarieva,

    From the abstract of your recent paper and your comment #27 here, I figured you might be interested in this information:

    As I just finish editing the 2nd English edition of the final book by late climatologist Marcel Leroux and found this quote from his chapter on hurricanes:

    “The supply of energy
    “(…) The oft-quoted necessity for high sea temperatures (above 26°-27°C) is an example of a covariation considered as a condition. The oceanic equator, where warmer water congregates, is in fact confused with the ME, since it is air currents which displace surface water. So the cyclone is supplied by fluxes which need a long path over the ocean to store up enormous quantities of perceptible and latent heat. Latent heat is supplied in only minimal amounts by evaporation in situ, as the fluxes come already near-saturated into the vicinity of the ME. Moreover, charts of evaporation clearly show that the highest values are recorded for tropical, non-equatorial waters. Therefore, cyclones form and persist if they are fed by tropicalised fluxes which are warm and, most importantly, possessed of abundant energy (i.e. very humid). ”


    Dynamic Analysis of Weather and Climate: Atmospheric Circulation, Perturbations, Climatic Evolution, Second English Edition by Marcel Leroux, Springer- Praxis (2010) ISBN: 978-3-642-04679-7.

    I therefore thought you (and Jeff Id and Air Vent readers) might be interested in reading more about Dr. Leroux and his work as I summarized below.

    Dr. M.Villéger

    Marcel Leroux (1938-2008) was a French climatologist who demonstrated through the analysis of synoptic maps, satellite imagery, meteorological and palaeoenvironmental data over Tropical Africa that the seasonal and palaeoclimatic migration of the Meteorological Equator represents a reliable proxy of the Earth’s climate evolution [1], [5].

    This migration and the extent of the Meteorological Equator are the consequence of continuous meridional exchanges in the denser, lower layers of the atmosphere, which circulation is governed by the incessant ballet of the Mobile Polar Highs, 1.5km high, 3,000km diameter discoid, lenticular cold air-masses anticyclones originating from the poles, whose strength and frequency depends directly on the thermal polar deficit. Cooling spurns an accelerated circulation while warming will slow the general circulation and exchanges [2].

    The aerological spaces of circulation, zones of continuous circulation from the pole to the equator are bound by relief over 2,000m and the present position of continents. In light of direct observations [1], [5], Leroux’s reconstruction exposes the inconsistencies of previous general circulation models, of oscillation indexes and of frontological, dynamical, reductionist and diagnostic schools of meteorology.

    In doing so, Leroux refutes the artificial separation between Meteorology and Climatology and through the MPH concept, redefines both disciplines in a similar way Plate Tectonics revolutionized Earth Sciences in the 1960s. He reconstructed the geometry of the troposphere general circulation [2] and demonstrated that very little is owed to hazard or chaos: there is no ‘unruly climate’ but intensity shifts of the sum of weather processes that constitute the climate.

    His insightful research, particularly the evolution of atmospheric pressure along MPH trajectories, confirmed that the climatic shift observed since the 1970s corresponds to the setting of an accelerated mode of circulation, always associated with cooling during the late Quaternary palaeoclimatic evolution, and its meteorological consequences: contrasted weather, stronger mid-latitude storms, increase water vapour in the troposphere and impermanent anticyclonic stability over continents leading to vigorous cold snaps in winter and heatwaves in summer [3], [4], [7].

    In consequence, his results refute the validity of a Global Mean Temperature curve as a major climatic proxy and contradict the assumption that weather changes observed in the second half of the XX Century were the consequence of an Anthropogenic Global Warming climatic change brought by the release of greenhouse gases due to industrial and human activities [6].

    Furthermore, his work provides the meteorological mechanism for past glaciations and de-glaciations, improves meteorological prediction models and climate simulation accuracy in constraining them through the real geometry of atmospheric circulation, its discontinuities, energy exchanges and their associated clouds [7].

    Marcel Leroux was a Cartesian and his books are highly didactic yet his style borrows from the enlightenment age through Voltairian touches of irony and the luminous verve of Diderot, making them a delight to read. His final textbook summarizes his scientific findings over his entire career. The English 2nd edition of “Dynamic Analysis of Weather and Climate, Atmospheric Circulation, Perturbations, Climatic Evolution” was completed in 2008 two months before his passing and published in January 2010 [7]. It offers, I quote: “the fundamental knowledge that any climatologist worthy of the name must absolutely know before claiming to be an “expert” on climate”.

    In this post Copenhagen and “Climategate” world where IPCC findings and some of their scientists’ integrity took a beating, Leroux’s unbending honesty and luminous scientific understanding represent the fresh start the discipline of Climatology needed.

    Available at:


    · Professor of Climatology

    · PhD. 1983, WMO sponsored and distributed to all member countries.

    · Former Director of the Centre of Research in Tropical Africa Climatology, CRCTA (Dakar, Senegal)

    · Former Director of the Laboratory of Climatology-Risks-Environment, LCRE (Lyon, France), Université Jean-Moulin.


    1. Leroux M. (1983). PhD. Thesis : Le climat de l’Afrique tropicale. Ed. H. Champion/M. Slatkine, Paris/Genève, t.1. : 636 p., 349 fig., t. 2 : notice et atlas de 250 cartes.

    2. Key peer-reviewed paper: “The Mobile Polar High: a new concept explaining present mechanisms of meridional air-mass and energy exchanges and global propagation of palaeoclimatic changes” Marcel Leroux, Global and Planetary Change, 7 (1993) 69-93 Elsevier Science Publishers B V, Amsterdam

    3. Author of: “La dynamique du temps et du climat”, Editions Masson, 1996, 310pp, 1st edn; Editions Dunod, 2000, 366 pp, 2nd edn.

    4. Author of “Dynamic Analysis of Weather and Climate”, J. Wiley ed. Praxis-Wiley series in Atmospheric Physics, London, NY, 365 pp, 1998.

    5. Author of “The Meteorology and Climate of Tropical Africa”, Springer Verlag, Springer-Praxis books in Environmental Sciences, London, NY, 548 pp + CD: 300 pp, 250 charts, 2001, ISBN: 978-3-540-42636-3

    6. Author of “Global Warming: Myth or Reality? The Erring Ways of Climatology”, Springer-Praxis books in Environmental Sciences, Berlin, Heidelberg, London, New- York, 509p., 2005, ISBN: 978-3-540-23909-3

    7. Author of “Dynamic Analysis of Weather and Climate Atmospheric Circulation, Perturbations, Climatic Evolution”, Springer-Praxis books in Environmental Sciences, 2nd ed., 2010, 440p., ISBN: 978-3-642-04679-7

  71. Condensation-induced dynamics – 1

    As promised at #60, in the following two comments I will outline the major physics behind the condensation-induced atmospheric dynamics. These things take time to be digested. I am available and delighted to discuss these issues and respond to questions, if any, eight months a year. My e-mail address is elba at peterlink dot ru. I can also be contacted from here.

    1. Clausius-Clapeyron law

    … says that under terrestrial conditions saturated pressure of water vapor grows approximately two-fold per each ten degrees of temperature increase. The greater the temperature, the more water vapor can be accommodated in a unit volume.

    dp_v/p_v = (L/RT) dT/T

    Here p_v and dp_v are pressure of water vapor and its change, respectively; L ~ 45 kJ/mol is the molar heat of vaporization, R = 8.3 g/mol/K is universal gas constant, dT and T is temperature in Kelvins and its change, respectively. At T ~ 300 K p_v ~ 40 hPa.

    2. Gravity and temperature in a pure vapor atmosphere

    Let us consider an atmosphere consisting of water vapor only. We place it above an ocean, so water vapor at the surface is saturated. We consider an isothermal atmosphere, which means that vapor temperature is the same at all heights.

    We will observe that the pressure of vapor decreases with height. It does so in such a manner that vapor pressure at any height is exactly balanced by the weight of vapor in the column of unit area above that height. We have a state of hydrostatic equilibrium.

    The scale height (height at which pressure decreases e-fold) is given by h_1 = RT/(M_v g). Here M_v = 18 g/mol is molar mass of water, g = 9.8 m/s^2 is the acceleration of gravity.

    The higher the temperature of the column, the more slowly vapor pressure declines with height. The heavier the gas, the more rapidly pressure declines with height. For a mean global surface temperature T = 288 K the scale height of vapor in the isothermal atmosphere would be 13.6 km. This implies a two-fold decline per nine kilometers.

    For us here of particular interest is the fact that, as far as vapor pressure declines with height while the temperature remains the same, vapor is not saturated anywhere in the column except at the oceanic surface. No condensation takes place. The atmosphere is static.

    3. Critical lapse rate of air temperature

    We now have this duality about vapor: static pressure of vapor decreases two-fold per each nine kilometers of ascent; saturated vapor pressure decreases two-fold per each ten degrees of temperature drop.

    What happens if we start reducing temperature in the upper atmosphere, introducing a non-zero lapse rate of temperature? At first nothing happens. Temperature does decrease with height. But so does the vapor pressure due to gravity! So vapor remains unsaturated at all heights. The temperature reduces with height too slowly, no condensation occurs. The atmosphere remains static.

    When a critical value is reached – the temperature decreases two-fold per each nine kilometers – the two kings, gravity and temperature, come to a deal regarding the condensable vapor: vapor is saturated AND in hydrostatic equilibrium everywhere in the column. This situation corresponds to a critical lapse rate of 1.2 K/km.

    When the temperature lapse rate increases even further, static equilibrium becomes impossible. The upper atmosphere becomes too cold to hold enough vapor for its weight to compensate the high saturated vapor pressure at the warm surface. The excessive vapor condenses. An unbalanced vertical pressure gradient is produced. Atmospheric motion is initiated.

    The reader can entertain him/herself with an interplay between gravity and temperature and visualize the notion of the critical lapse rate here.

    4. Conclusions
    In the presence of a sufficiently large vertical lapse rate of air temperature, the vapor atmosphere cannot be static. The equilibrium state of such an atmosphere is the dynamic equilibrium, not hydrostatic equilibrium.

    Due to removal of vapor via condensation, there appears a vertical pressure gradient force directed upwards. Aiming to restore the hydrostatic equilibrium, this force accelerates the vapor from the surface upwards. But as vapor enters the upper cold atmosphere and condenses there, the equilibrium is never restored. The mass balance is closed when the condensed moisture returns back to surface as rainfall. The ascending vertical motion of vapor continues as long as there is evaporation from the oceanic surface.

    In the next comment, I will consider what happens when a non-condensable component (dry air) enters the scene. We will see how the hurricanes form.

  72. #65 Dear Dr. Mardhekar, I do not have any doubt that you filed your contribution 22 September 2005. As I noted, our preprint (which develops our ideas presented in 2002 and 2003, see #16) has an official submission date 10 February 2006. I presume your contribution has not been freely available in the Internet before that time. So, even judging from formal grounds, there can hardly be any disagreement on the point that we developed our concepts independently. The difference/similarity of these concepts and their merit are to be judged by independent observers. My e-mail is elba at peterlink dot com. We are always open for a constructive exchange of ideas. Anastassia

    #70 Dear Dr. Villeger, Many thanks for the information on the studies of Marcel Leroux. The point about hurricane moisture supply that you cited is highly relevant. I am looking forward to make myself familiar with these works. Access to books, though, might be a problem, because Russian libraries are exceptionally depauperate in science books starting from the 1990s due to financial constraints. Anastassia

    Re #71 Please note the misprint in the dimension of the universal gas constant R, which is J/mol/K.

  73. Dhananjay Mardhekar said

    #66 Dear Dr. Makarieva,

    I may be weak in mathematically evaluating the effects or importance of vapor volume reduction in the condensation process in hurricanes. But the basic concept of volumetric extinction used by you and the volume reduction in the condensation process put forth by me in trying to explain hurricane’s working is the same.

    #72 I appreciate that you have given me your e-mail ID. I am sending my conceptual paper on Discovering hurricane’s secret driving force.

  74. Dear Dr. Mardhekar and all,

    Re #72, Please note my e-mail address is elba at peterlink dot RU.


  75. Dhananjay Mardhekar said

    #73 Dear Dr. Makarieva,

    I tried to send my work on your e-mail ID
    But it is not going. Please check whether I have typed your e-mai ID correctly.

  76. Brian H said

    The relevance of this mechanism and topic to AGW is that evaporation at the surface and recondensation within clouds ‘heat pipes’ thermal energy from the lower troposphere into the tropopause and stratosphere, and thence to space.
    This constitutes a negative feedback mechanism, a huge “hole” in the GHG blanket, which prevents runaway. Venus, lacking water, has no such luck.

  77. Condensation-induced dynamics – 2

    Continued from #71

    In a pure vapor atmosphere with a large vertical lapse rate of temperature, the pressure distribution of vapor appears to be compressed compared to the hydrostatic distribution. The new, non-equilibrium scale height h_2 of vapor is inversely proportional to the lapse rate of temperature. (Lapse rate stands for the vertical gradient with minus sign, so that if temperature decreases, e.g., by 6.5 K per kilometer, the lapse rate G is positive and equal to G = 6.5 K/km).

    You should believe me that this scale height is

    h_2 = RT^2 /(LG)

    It is obtained from the the Clausius-Clapeyron equation. Putting the global mean temperature T = 288 K, L = 45 x 10^3 J/mol and mean tropospheric G = 6.5 K/km we find that h_2 = 2.4 km. This means that compared to the static distribution, vapor is compressed by h_1/h_2 = 5.6 times.

    As an aside, I can tell from my experience that almost all climate scientists know that the scale height of water vapor is indeed approximately two kilometers. But few would tell you how this can be calculated from basic physical constants, as above. We have been unable to find the above formula in any meteorological textbook we’ve read. Weaver and Ramanathan (1995) [J. Geophys. Res. D6, 100: 11585-11591] occasionally spotted this relationship and characterized it as an “incidental” finding. As far as I understand, meteorology students are not taught at classes what determines the scale height of the most important atmospheric constituent.

    Now we have this disequilibrium vertical pressure gradient of vapor, which roughly amounts to p_v/h_2, where p_v is vapor pressure at the surface. Let us imagine this strange pure water atmosphere. It rains continuously there! Moreover, the atmospheric motion is unidirectional – vapor is accelerated upwards and disappears via condensation. No horizontal wind is present.

    Now let us add dry air. What happens? The dry air molecules at the surface accelerate upwards together with vapor … and what? Where vapor disappears via condensation, dry air molecules do not have where to go — they are non-condensable. What will happen to these molecules?

    There is only one physical solution — a spontaneous symmetry breaking. In such an atmosphere convective cells will form, where moist air rises in one part of the cell and relatively dry air (depleted of moisture by condensation) descends in the other part of the cell. Apparently, there will be re-distribution of the original vertical non-equilibrium pressure gradient along the entire air streamline in the cell. In particular, a horizontal pressure gradient will appear between the regions of ascent and descent.

    Therefore, the equilibrium in such a two-component (condensable plus non-condensable) atmosphere will be a dynamic one, but with (at least) a two-dimensional motion rather than the one-dimensional vertical motion as in the pure vapor atmosphere. Adding a second, non-condensable, component results in an additional dimension for the motion!

    It would be a complex theoretical task to predict the geometry and character of such cells even on an isothermal homogenous surface, to say nothing about the real Earth surface with the many different factors playing in. But for the circulation patterns where height is much less than width (as most circulation patterns on Earth, as the atmosphere is very thin), there is an important simplifying stipulation – vertical velocity is always much smaller than horizontal velocity. This means that most part of the non-equilibrium pressure difference p_v is translated on to the horizontal dimension, so that the horizontal pressure gradient becomes of the order of p_v/L, where L is circulation horizontal size.

    The maximum air velocity U that can be developed along this pressure gradient (if friction losses are negligible) is given by the energy conservation law:

    rho U^2/2 = p_v.

    Here rho is air density. For atmospheric air at the surface, rho ~ 1 kg/m^3. Maximum vapor pressure at 30 deg C is about p_v = 4 x 10^3 Pa = 4 x 10^3 J/m^3. Note that 1 J = 1 kg m^2/s^2. Putting these figures into the above formula, we obtain air velocity 90 m/sec. This is approximately the upper ceiling to hurricane velocities ever observed. When friction is considerable (i.e., when the circulation pattern is not compact as in the hurricane but more extended, e.g., Hadley cells) the velocities produced by condensation will be much smaller.

    In a nutshell, this is how condensation drives air motions. I have simplified quite a lot of things, also in numerical terms, to concentrate on the basic physical scales of the problem. Our work is in progress. We hope to see some interest from other people as well. My apologies for these lengthy posts –- I am learning how to present these things to interested audience. Many thanks to Jeff Id for his interest in this topic.

    Re #71, it is me who needs a nanny for my posts. Instead of “the temperature decreases two-fold per each nine kilometers” there should be “the temperature decreases by ten degrees per each nine kilometers”.

  78. DeWitt Payne said

    Re: Anastassia Makarieva (Feb 5 14:01),

    We have been unable to find the above formula in any meteorological textbook we’ve read.

    That’s surprising. I found the scale height of water vapor calculated in Physical Meteorology Lecture Notes (chapter 3.12, page 62)by Rodrigo Caballero of University College Dublin and assumed it was universally known and taught.

  79. DeWitt Payne said

    Re: Anastassia Makarieva (Feb 5 03:12),

    What happens if we start reducing temperature in the upper atmosphere, introducing a non-zero lapse rate of temperature?

    I think you need to specifically include a mechanism for cooling at altitude in your explanation. The obvious candidate is, of course, radiation. In a one dimensional model, a perfectly transparent isothermal atmosphere at the same temperature as the surface is stable. Only if some component of the atmosphere is capable of emitting EM radiation at that temperature will there be cooling with altitude and initiation of convection. Water vapor does emit IR so that works.

  80. Kenneth Fritsch said

    I have finished reading the referees’ comments, the authors’ replies and the editor(s) comments and rationale for not publishing the authors’ paper. I would continue to highly recommend that interested participants at this blog read these informative exchanges.

    I personally have no credentials for judging the correctness of the authors’ applications of thermodynamics to the phenomena of hurricanes. Unfortunately on reading the technical presentations I can only reminisce about the familiar terminology used in the discussion that harkens back to my graduate and undergraduate days of long ago and recognize the equations with some general understanding of the concepts involved. It also was a reminder to how sterile my educational exposure was with regards to the application that I see in this discussion. I could perhaps with sufficient time and effort follow more completely the terms of the application, but I have major doubts about this.

    How then does the reading of these comments inform the layperson such as me and in this particular case?

    1. On observing the referees’ criticisms and the authors’ replies, I noted that the authors appear to answer all the referees’ questions/criticisms and do it in considerably more detail than the criticism were posed.
    2. Admittedly as a layperson in this matter, I judged that some of the referees’ criticisms were ill posed and uniformed while some others appeared to be gratuitous attempts to save Kerry Emanuel’s theoretical basis for his hurricane modeling without much effort in truly engaging the subject matter at hand.
    3. What I could not comprehend was the editor(s) inability to see that the critical referees did not make their cases against the papers findings. For example, one referee criticized the authors reasoning that led to their showing that the Emanuel Carnot cycle heat dissipation amounted to a physical impossibility and on the spot proposed his own mechanism of a concentrated area of production versus a larger area of dissipation. The authors defended their position with actual data and details and most notably without a counter reply by the critical referee. How does that not inform the layperson reading the exchange?

    I have one final point to be made about the exchange. It involves comments from a “friendly” referee who implied, in my view of it, that the Kerry Emanuel’s hurricane model might work reasonably well with sufficient fitting of parameters, but that the physical basis for it was flawed by the evidence presented in the authors’ paper. That being the case, it would present an interesting dilemma for the author of Storm World, Chris Mooney, who in this book categorizes climate scientists working with hurricanes as those using empiricism and those using theoretical concepts. He puts Kerry Emanuel as the exemplar of the theoreticians and makes little effort to hide his favoring that approach and combines it with a very positive portrayal of Emanuel as a person. Mooney also makes it a point of his book to note that government can impede scientific progress by not allowing the free flow of pertinent information to the public. I would be most interested to hear what Mooney might think and report on the exchange that I just read in terms of where Emanuel stands as a theoretician and the handling of the authors’ paper submittal for publication. I also propose that the handling of this paper says more about the state of this area of climate science than it does about the authors’ offerings.

  81. #78 I, too, find this highly surprising. But this is a quote from Weaver and Ramanathan (1995):

    “Incidentally, the scale height of water vapor can be roughly accounted for by differentiating the Clausius-Clapeyron relation governing H2O saturation vapor pressure (es) with respect to altitude. We find that es decreases with height with an approximate e-folding length of…”

    then the formula for h_2 in #77 follows. This is a high rank meteorological journal, Geophysical Research D.

    Even more curious was the reaction of Dr. Meesters, a learned meteorologist from Netherlands. When we asked that he indicated a published source where the vapor scale height were estimated, he replied, see p. S175, all the emphasis, including sic!, is mine:

    we were asked to provide an exact citation as to where the result was
    derived from an equation similar to Eq. (11) in MG (2007). Such a reference (with
    the Clausius-Clapeyron equation replaced by the Magnus equation—a modification to
    account for the dependency of QH2O on temperature) can be found in Von Hann (1915)
    …, where it is attributed to a still older source:
    an article by C.W. Trabert in the Encyclopaedie der mathematischen Wissenschaften.
    The result given by Von Hann is a tenfold decrease in water vapor concentration over
    a height of 5250 m, which upon conversion yields an e-fold decrease over hH2O = 2.3
    km, practically the same result as in MG (2007). We have not consulted any more
    recent texts, where such speculations (sic!) (combining the assumption of saturation with a globally-averaged profile) tend to be relatively scarce.

  82. #79

    I think you need to specifically include a mechanism for cooling at altitude in your explanation. The obvious candidate is, of course, radiation.

    True. As one can see, I concentrated on air dynamics and refrained from discussing where the temperature lapse rate comes from, just taking it as a parameter. Obviously without greenhouse substances in the atmosphere a temperature gradient is not possible. This follows from a simple observation: suppose that the upper atmosphere is colder than the lower atmosphere. Then there is necessarily a flux of heat from the surface upwards. But, in the absence of emitters/absorbers of thermal radiation in the atmosphere, where will this flux go? Nowhere, apparently, so the upper atmosphere will warm until the temperature gradient zeroes. Only if there is a sink of heat to space via radiation there can be a stationary negative gradient of air temperature. The magnitude of this gradient is a different issue.

  83. DeWitt Payne said

    Re: Anastassia Makarieva (Feb 5 16:36),

    Obviously without greenhouse substances in the atmosphere a temperature gradient is not possible.

    I’ve had a discussion with Nick Stokes about this sort of thing. What about a three dimensional system, specifically a rotating sphere exposed to sunlight with a non-radiative (perfectly transparent) atmosphere? In this case there is a horizontal temperature gradient at the surface from the equator to the poles, so there is somewhere for the heat to go. But does this lead to an adiabatic lapse rate anywhere with Hadley circulation and so forth? I don’t think so, but he does. Maybe somebody has done this and published, but I haven’t been able to find it. Maybe I’ll email Gavin Schmidt and maybe he’ll answer.

  84. #83

    What about a three dimensional system, specifically a rotating sphere exposed to sunlight with a non-radiative (perfectly transparent) atmosphere? In this case there is a horizontal temperature gradient at the surface from the equator to the poles, so there is somewhere for the heat to go.

    A global negative vertical gradient of air temperature is not possible without greenhouse substances, even if we account for the temperature difference between the equator and the pole. [Suppose air temperature decreases with height at the equator. The upward heat flux reaches the upper atmosphere and is re-directed to the pole. At the pole, there cannot be a negative vertical gradient of air temperature — here the upward heat flux has nowhere to go, because all other areas are warmer. It thus appears that the upper atmosphere of the pole represents a stationary sink of heat from the equator. But where will this heat go? Nowhere. It can only be radiated to space, but then we have an atmosphere with greenhouse substances.]

    Without greenhouse substances, it is in principle possible to have a negative vertical gradient of air temperature at the equator (e.g., by running a convective cell there), but then necessarily a positive gradient at the pole. I.e., at the pole the upper atmosphere must then be warmer than the surface. Then the heat arriving to the polar atmosphere from the equatorial atmosphere will be transported down to the surface and radiated to space therefrom. This is, of course, not what is actually observed in the atmosphere of Earth.

    But the oceanic temperature gradient associated with the thermohaline circulation is precisely of this “convective” type. The equatorial surface waters are warmer than the deep waters (which have a roughly uniform temperature worldwide at around +4 deg C), while the polar surface waters (at 0 deg C and below) are colder than the deep waters. Were that not the case, the heat flux from the warm equatorial ocean to depth would have been continuously warming the planet core…

  85. #84
    “A global negative vertical gradient of air temperature is not possible without greenhouse substances, even if we account for the temperature difference between the equator and the pole.”

    Absolutely not. This misses the while point of the dry adiabatic lapse rate. Turbulent motions combined with gravity and air compressibility pump heat downwards until something close to the dry adiabat is achieved.

    This has been known for a very long time. This classic 1946 paper (currently free from Royal Soc) discusses the mechanism. Their opening statement:
    “A necessary consequence of the classical theory of the turbulent transfer of heat in the atmosphere is that the flux of heat is in the direction from high to low potential temperature, and this normally involves the flux being from low to high actual temperature. On examination, this is shown to be consistent with the second law of thermodynamics.”

    Title: Vertical Transport of Heat by Turbulence in the Atmosphere
    Authors: Priestley, C. H. B.; Swinbank, W. C.
    Publication: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 189, Issue 1019, pp. 543-561

  86. #85

    Turbulent motions combined with gravity and air compressibility pump heat downwards until something close to the dry adiabat is achieved.

    “A necessary consequence of the classical theory of the turbulent transfer of heat in the atmosphere is that the flux of heat is in the direction from high to low potential temperature, and this normally involves the flux being from low to high actual temperature. On examination, this is shown to be consistent with the second law of thermodynamics.”

    The second law of thermodynamics prohibits heat flow from cold to hot bodies. Heat always flows from the hot to the cold. In the paper of Priestly and Swinbank (1947) heat and mechanical energy are confused.

    The flux given by their formula (3) and called “total flux” (“the flux” in the the above citation) is obtained by summing the fluxes of “mechanical energy” and heat. This is because “Professor Taylor and Professor Cowling”, as the authors admit on p. 545, reminded the authors that there also exists a flux of potential energy convertable to the mechanical energy, which is associated with the expansion/compression of the gas.

    Originally, the authors wanted to call “heat flux” the quantity c_vdT (1). However, in accordance with the first law of thermodynamics, HEAT dQ = c_vdT + pdV. The authors forgot about the second term. After they were reminded about that by those two Professors, the authors changed to c_pdT. Using RdT = pdV + Vdp for ideal gas and noting that c_p = c_v + R, they had c_pdT = dQ + Vdp. But c_pdT is not HEAT either. HEAT is dQ. For flux c_pdT there are no stipulations coming from the second law of thermodynamics. The authors created and discussed a controversy that does not exist.

    Whilst HEAT must flow from the hot to the cold (and, hence, the heat flux is always directed upwards in an atmosphere where temperature diminishes with height), the potential and mechanical energy can go anywhere. Heat is energy, not every energy is heat. This is where the authors got confused. A global negative gradient of air temperature is impossible without greenhouse substances because of the HEAT disposal problems outlined in #84.

  87. RB said

    “But the oceanic temperature gradient associated with the thermohaline circulation is precisely of this “convective” type. ”

    Interesting .. I’ve been toying with understanding the greenhouse effect by means of electrical analogs through correspondence with Ohm’s Law and Kirchhoff’s law for current. Here, the sun corresponds to a pulse train current source driving Earth’s capacitor where the atmosphere is equivalent to a resistive path. It seems to me that the convective processes represent an equivalent inductance that provides a ‘back-EMF’ opposing the rise in surface temperatures. In this context, it seems to me that Trenberth is justified in hypothesizing that lack of deep ocean monitoring may be the cause of the gap in the energy budget since the energy stored in the ‘inductor’ may not be fully captured with existing observation systems.

  88. #86
    “The second law of thermodynamics prohibits heat flow from cold to hot bodies. Heat always flows from the hot to the cold. “
    Again just not true. Refrigerators work. And that’s what you’re missing. Turbulent ke does work to pump heat downwards. That’s the process Priestley/Swinbank are describing. They didn’t invent it. It was then, and is now, standard atmospheric physics.

  89. RB said

    Hmm… it looks like exploring the correspondence between convection and inductance is worth some exploration.

  90. DeWitt Payne said

    Re: Nick Stokes (Feb 8 16:12),

    Refrigerators do work. They are heat pumps. But pumps don’t work by themselves. They require a source of energy to function. And they work in a limited area. The only way you transfer heat from cold to hot locally is to transfer even more heat from hot to cold somewhere else. Turbulence is mechanical energy. Where is that going to come from? What generates the turbulence? You can’t just wave your arms and say it happens. Turbulence is a dissipative process and needs a constant source of energy. Without that, any local turbulence will die out. Radiative heat loss from the atmosphere at altitude drives upward convection at the equator. A radiative atmosphere always becomes unstable because heat comes in at the surface and goes away at altitude. The loss from radiation is always more than the input from radiation, absent an absorption of incoming radiation at short enough wavelength that emission can be neglected (oxygen and ozone in the Earth’s atmosphere). That’s what starts the whole atmospheric circulation process. That was Hadley’s contribution to atmospheric science. With no radiative cooling to drive convection locally there is no upward movement. Heat comes in and leaves at the surface only. There is no permanent driver of vertical energy flow in the atmosphere so there is no reason for the atmosphere to approach the adiabatic lapse rate. In fact, it’s probably the other way around. A non-radiative atmosphere will want to be isothermal locally and conduction rather than convection will dominate.

  91. JamesGardiner said

    I’m with Nick here. In turbulent chaotic systems the 2nd law can be broken easily enough. It’s only a statistical law after all:
    “In 1900, at the age of 42, Planck achieved this, but in the process he had to abandon one of his greatest beliefs – that the second law of thermodynamics was an absolute law of nature. He was forced to accept Ludwig Boltzmann’s statistical explanation for the second law.”

    I’m with Planck and Boltzmann too 🙂

  92. DeWitt Payne said

    Re: JamesGardiner (Feb 8 21:00),

    In turbulent chaotic systems the 2nd law can be broken easily enough

    Begging the question. Assuming that a non-radiative atmosphere would be turbulent is assuming the result. Also, please cite an example.

  93. #90 deWitt
    “The only way you transfer heat from cold to hot locally is to transfer even more heat from hot to cold somewhere else.”
    Exactly, and that happens. 235 W/m2 can do a lot of pumping.

    A thought about Hadley Cells – why are they so long and narrow? If they are just working between the tropical surface and TOA they should be more or less circular or less. The reason they stretch so far is that the main cool sink is the temperate surface. In fact they would stretch further but for that R-B instability, which produces the Ferrer cell.

    I’m working on a post which may try to quantify the amount of heat that has to be pumped to maintain the lapse rate. I think it will not be large.

  94. DeWitt Payne said

    Re: Nick Stokes (Feb 8 23:06),

    But you’re not pumping heat through a non-radiative atmosphere. It goes into the surface and leaves from the surface. The only possible interaction of the atmosphere is with the surface by conduction. I still don’t see a mechanism for your refrigerator. If I’m correct, then any temperature profile with less than the adiabatic lapse rate cannot have vertical convection and will require no energy at all to maintain. In fact, it will evolve to an isothermal system by conduction, which can’t be neglected when it isn’t dominated by convection and radiation. This is absolutely true for a one dimensional system.

  95. I recall a lecture from my Thermodynamics class back in the 1980s. It covered the reason for updrafts in thunderclouds, in a qualitative fashion.

    Water vapor is lighter than air anyway, so humid air, all things being equal, humid air will tend to rise.

    As air rises, the pressure drops and the air expands.

    As the air expands, it cools.

    As it cools, it may reach the dew point. If so, subsequent cooling will result in water condensation.

    AS water condenses into droplets, it dumps heat into the surrounding air.

    This heats the surrounding air, causing it to expand, causing it to become less dense.

    Less dense air rises.


    Eventually, you run out of water vapor, which limits how much extra heat can be dumped into a volume of air.

    I’m thinking the main difference is that someone went through and provided the numbers.

  96. #94
    Consider an absorption refrigerator. Nothing mechanical, just add heat. The inhomogeneous heating is sufficient to make it work.

    The atmospheric heat pump at sub-adiabat lapse rate doesn’t need to be efficient – there’s 235 W/m2 to play with. All it needs is surface inhomogeneity – latitudinal is the big one, but there’s all the local kinds. As long as there’s free energy from a temp difference, some motion will ensue.

    The maximum entropy enthusiasts (I’m not really one) would put it like this. A temp difference represents a state whose entropy could be raised by heat transfer. Conduction would do it, but fluid motion will maximise the rate.

  97. DeWitt Payne said

    An absorption refrigerator is nothing like an atmosphere of, say, pure argon. You have two or three components, in the system, ammonia, water and possibly hydrogen gas as well. There are phase changes from liquid to gas and then from gas to solution and then back again. The density of the solution of ammonia is different from pure water. The size and shape of the various pieces of tubing in the circuit are critical and so is it’s orientation. There’s a reason besides not falling out of bed that you make an RV with an absorption refrigerator as level as possible. Water circulation is necessary as well, but its driven by the bubbles of ammonia that are forced out of solution by the heat source. Those bubbles are less dense than the liquid around them so they rise. The diameter of the tubing is carefully sized so as the bubbles rise, they carry water with them. In the atmosphere you need vertical density differences to drive circulation as well. That only happens if the lapse rate exceeds the critical value. But you can’t get there from here. A horizontal temperature gradient has density differences, but at constant pressure and gravitational potential energy, there’s no force acting to cause circulation in any direction. You’ll get conduction, not convection or advection.

  98. In my opinion, it is physically misleading to think of refrigerators as of “heat pumps”. This causes all the confusion. There is a heat flux from the warm room to the refrigerator. If nothing is done, this heat flux will warm the fridge and the meal will spoil. To prevent this, there is a flux of “heat plus potential/mechanical energy” from the fridge to the room, as explained in #86.

    Two things are important — (1) The source of potential/mechanical energy is located in the fridge (motor). (2) This backward flux of energy is larger than the heat flux from the room to the fridge. So the fridge warms the room at a rate equal to the electric power of its motor (nothing to do with heat fluxes governed by temperature).

    Let we have an atmosphere without greenhouse substances, but with a negative temperature gradient due to convection. There is a heat flux H from the warm Earth surface to the cold atmosphere. As in the fridge, we want to counteract this heat flux by a “heat plus potential/mechanical energy” flux from the upper atmosphere to the surface, to obviate the need for the atmosphere to radiate.

    To do so, let us collect the incoming solar energy Es at the top of the atmosphere and convert it to potential/mechanical energy (e.g., using solar batteries).[This can be done at an efficiency close to unity due to the difference in the temperatures of solar (6000 K) versus thermal (300 K) photons.] We now use this work, almost equal to Es, to counteract the heat flux H coming from the surface. Note that thermodynamics strictly confines the magnitude of H that can be counteracted with help of work Es. When the temperature difference between the surface and the atmosphere is large, Es must be much greater than H.

    The incoming flux of energy to the surface is now equal to H + Es. Es is then radiated to space from the surface as thermal radiation. In total, the surface loses Es to space, loses H to the upper atmosphere along the temperature gradient and receives H+Es from above by convection to close the balance. Surface is the only sink for heat.

    In this situation, we do have some negative temperature gradient in the atmosphere. But it is not that the surface has warmed compared to the absence of convection. The surface radiates Es and its temperature remains -18 deg C, as the value of Es prescribes. Instead, it is the upper atmosphere that has cooled. This happened due to the fact that some part of energy is now present in the form of mechanical energy of air motion rather than in the form of internal energy. It is not possible to warm the Earth “pumping heat” by convection and elevate surface temperature above the value which it has when convection is absent.

    It is easy to see that nothing is changed if a horizontal temperature difference is included. The mean global surface temperature remains -18 deg C, not +15 deg C, irrespective of the presence/absence of convection.

  99. curious said

    98 – Anastassia- I do not recognise that as the generally taught version of a mechanically powered refridgerator. My recollection is, as DeWitt described, a heat pump and the power of the motor/compressor is related to the heat throughput of the pump by the coefficient of performance:

    The inside of the fridge (except when the door is open!) is a hermtically sealed space within the room. I do not see how there is a mechanical element to the heat exchange from the internal space to the evaporator.

    I do agree however that the net additional heat flux to the room within which the refridgerator is located is the power of the motor which is simply being used to move heat from inside the fridge to the room. The power flow to the motor is arriving via the electric flex connecting it to the suppply. In the absorbtion fridge this power flow to the fridge is the (say) gas flow to the flame.

  100. #99


    the net additional heat flux to the room within which the refridgerator is located is the power of the motor which is simply being used to move heat from inside the fridge to the room.

    In the stationary case, the power of the motor is the only heat flux to the room, not an additional one. Apart from the motor power, the fridge does not produce any energy (no perpetuum mobile inside). A statement that the room receives a heat flux equal to the motor power plus something else conflicts with the energy conservation law.

    There is a flux of heat from the room to the fridge (irrespective of whether the door is open or close), which goes from the warm to the cold, and a backward flux of “the same heat plus motor power” to the room. (For this reason, whether there is a fridge with a motor in the room, or just a motor, it is one and the same for the room in terms of energy budget.) The fridge as a heat engine is necessitated precisely by the existence of the heat flux from the warm room to the cold camera.

    I think this is a good discussion. It is my pleasure to participate.

  101. JamesGardiner said

    De Witt

    Some examples here, with a nice discussion of the limitations of thermodynamics:
    Full text of which is here:

    The 2nd law refers to a bulk effect. The only alternative to turbulent flow is laminar flow. It’s only a minor point, but you should be aware when you invoke a law that it has limitations and assumptions. One size doesn’t fit all. It’s the same with the Kirchhoff law, which only applies to the atmosphere if you make gross assumptions.

  102. DeWitt Payne said

    Re: JamesGardiner (Feb 9 08:08),

    Where in that article does it actually say that the Second Law can be violated in anything more than in a very small volume for a very short time? Boltzmann said that the Second Law was not absolute indeed, but the probability of a violation decreases very rapidly as the number of particles in the system increases. We’re talking about 1 chance in something like 10E60 here for any sort of bulk system.

    As far as Kirchhoff’s Law, show me where in the troposphere conditions exist that make it inapplicable, or even inaccurate enough to be significant.

    Newton’s laws of motion are not perfect either, but they’re good enough for most applications.

  103. DeWitt Payne said

    Re: Nick Stokes (Feb 9 00:09),

    The latitudinal temperature gradient is tiny compared to what you see vertically in a radiative atmosphere. Lets say worst case, temperature at the equator is 400 K and temperature at the poles is 2.7 K. The diameter of the Earth is 6371 km so the distance from the equator to the pole is 10,000 km. That’s a gradient of 0.04 degrees per kilometer. The value of the dry adiabat for air is 10 degrees per kilometer or more than two orders of magnitude different. The average vertical velocity in the ITCZ is on the order of a few centimeters per second and that’s for a situation where the work required to lift a kilogram of air to altitude is small because the temperature gradient is close to the adiabat. That low velocity does create much higher velocity winds along the surface, but there has to be vertical convection first.

    If convection can impose a positive lapse rate on an initially isothermal atmosphere, then why does convection essentially stop at the tropopause?

  104. DeWitt Payne said


    Have you ever flown over the Los Angeles area on a really smoggy day? the upper boundary of the smog is quite distinct. Why? There’s a temperature inversion.

  105. Re: DeWitt Payne (Feb 9 19:21),
    The low horizontal gradient is not relevant, because heat there is transported by an organised structure (a cell). When the wind carries heat, the flux isn’t proportional to temp gradient.

    “If convection can impose a positive lapse rate on an initially isothermal atmosphere, then why does convection essentially stop at the tropopause?”
    I don’t see the connection. But it’s true that convection (turbulent KE) diminishes with height, and when it is insufficient to force a positive lapse (cooling with altitude), then the lapse lapses, with better convective stability (positive feedback) and a fairly sudden change.

    But there’s something else going on. Close to the troposphere IR transport is more important (thinner air), and that also acts against the adiabatic heat pump (it amounts to leakage).

    I don’t see the relevance of the temp inversion either. Actually temp grad=0 isn’t very significant; convective stability increases as the lapse decreases from 9.8 K/km, so a negative value is even more stable, but there’s no sudden change at 0.

  106. Re: JamesGardiner (Feb 8 21:00)
    Actually, my argument is that there is no breach of the Second Law

  107. DeWitt Payne said

    Re: Nick Stokes (Feb 10 05:11),

    You continue to beg the question. You also don’t appear to understand the origin of the tropopause and the stratosphere. There would be no tropopause if there were no oxygen in the atmosphere. In an isothermal atmosphere, the equivalent of the tropopause will be at or near the surface, depending on the surface heat capacity and time of day.

    As near as I can tell, you say that there will be vertical and horizontal air flow because there will be vertical and horizontal air flow. That’s assuming the conclusion in your premise or begging the question. I’m saying that any local flows will damp out because there is insufficient driving force horizontally for any local flow to accelerate and become widespread. In an isothermal atmosphere, not only is there no driving force, there are very strong forces buoyancy forces acting against vertical flow. If there is no large scale vertical flow, there will be no large scale horizontal flow either. The diurnal cycle will only result in expansion and contraction of the planetary boundary layer. Unless the surface has high heat capacity, it will get very cold at night and the lapse rate near the surface will be negative. At peak temperature during the day, there might be sufficient heating to create some vertical motion. But that would only result in the expansion of the boundary layer, not deep convection. If the surface heat capacity is high, there won’t be much temperature change at all.

    Your argument that air circulation alone will cause the lapse rate to be close to the adiabatic rate remains unconvincing absent a detailed mechanism, including how the air flow will start and spread. All I’ve seen so far is an assertion that it will.

  108. Kenneth Fritsch said

    Anastassia at Post #60 said:

    How the new ideas are received by the standing paradigm.

    and followed that this part of the discussion might be held in abeyance for the time being. I am wondering if you, Anastassia, judge the time is right to discuss this issue. I can certainly understand a decision to let your replies to the open discussion stand and not rile the waters while you are looking for support in this area of the climate science community.

    I have enjoyed the discussion currently holding sway here and greatly enjoyed the online open discussion of your paper. A small part of that might be that it reveals others who like me do not fully comprehend and appreciate the applications of thermodynamics to the workings of the atmosphere. It also brings forth the issue of how a layperson without full understanding of the science at hand can attempt to judge who knows what they are talking about and who does not, or alternatively that discussion does not resolve or lead to a resolution of the issue at hand.

  109. #107

    My reading of this issue is somewhat different. I can see two separate problems associated with what Nick Stokes is saying:

    1. If there is circulation in the atmosphere (of some nature), can it maintain a negative vertical gradient of air temperature in the absence of greenhouse substances? E.g., we can switch a very powerful ventilator and mix the air in the gravity field. Will a vertical temperature gradient form, if the atmosphere does not radiate?

    2. If a temperature gradient CAN be formed, then how much power it will demand to be sustained? This issue too splits into two issues.

    2a. Given the sensible heat flux of the order of one tenth of solar power, is the observed mechanical power of the Earth’s circulation enough to maintain the observed global mean lapse rate of 6.5 K/km without involving radiative processes?

    2b. Can the observed horizontal temperature gradients drive a circulation of sufficient power to maintain the observed lapse rate? More generally, what drives the circulation of Earth?

  110. #108

    Kenneth, the matter is that I feel very strongly about how our work is received. I am now doing my very first steps in blog commenting, so I am trying to be cautious and avoid topics where I can say something that I will later regret. Moreover, our top priority is to win interest and cooperation for the new physics rather than to perpetuate the opposition.

    But, speaking generally, I think that our story is an interesting one to follow. A lot depends on whether we are right or wrong. If we are wrong, nothing special has happened (an incorrect paper was rejected). Now suppose we are right in proposing a novel circulation driver. Should this involve some responsibility for those who were unable to understand the new physics and prevented publication of our studies instead of promoting them?

    Imagine a doctor who put a wrong diagnosis and the patient died. Even neglecting whether the doctor did that consciously (homicide) or not, the issue is about his professional competence. Suppose the patient did not die, but suffered a lot, and then recovered after changing the doctor. Does this circumstance free the bad doctor from the responsibility? Can he be left to continue his practice, which threatens the health of other patients?

    Absolutely the same questions pertain to the duty of Editors of scientific journals. Currently there is some responsibility imposed on the Editors about publishing an incorrect paper. This is, however, just a very minor harm that can be made to science. Wrong papers are (quickly) exposed and the scientific thought moves further. The major harm consists in NOT publishing a CORRECT paper with novel ideas. Currently the Editors are absolutely free of any responsibility regarding such major professional errors. Moreover, as they are afraid of publishing wrong stuff, they are inclined not to publish a doubtful paper, to spare themselves of possible troubles.

    This pathological situation is rooted in the worship of the peer-reviewed literature. People tend to consider publications in mainstream journals as the ultimate truth rather than a debatable state-of-the-arts in the considered discipline. This makes the Editors highly resistant to the publication of studies potentially undermining the standing paradigm. Peer-reviewed literature, this bible of science, should not contradict itself. Only priests of the highest rank (or groups of such priests) can sometimes be involved in discussing possible varying interpretations of the sacred texts or even dispute a little bit among themselves. People from the street and non-meteorologists are not qualified.

    There are many other issues involved. For example, if a scientist is approached by somebody proposing a novel thing in his discipline, is it his duty or option to take notice? For example, suppose we have a state-funded scientific climatic center, where the scientists are paid by the country to perform climate research of top quality. Suppose a professor in that center is contacted from outside about a novel driver of atmospheric circulation. This conflicts with his paradigm, he is irritated and does not want to look further into that. Then some time passes, and the approach is demonstrated to be correct, and other people in other countries start doing relevant research. Will the tax-payers who support the professor’s existence be happy about his position towards the novel research? The position which ultimately made the national climate center lag behind exciting developments?

  111. Kenneth Fritsch said

    Anastassia @ Post #110:

    Without going back to the online discussion of your paper, I recollect that some of the editors’ comments appeared to be attempting to cover the issue of an eventuality of a novel and new approach to understanding the atmosphere being overlooked by not publishing your paper. They seemed to cover their collective behinds by noting that the discussion of the paper was at least made public by the process and at least given that backdoor publicity. Of course, the more credence they give to putting the public review process on a level with a published peer-review paper, the more they downplay the importance of peer review (relative to other modern methods of disseminating ideas).

    I did not understand at all the editors’ decisions not to publish in light of the exchanges all ending with comments from the papers authors that would appear to have addressed the critical referees’ criticisms in detail and without further comments from the referees.

  112. #112, Kenneth, re: publishing/non publishing novel things

    This ACPD discussion contains a remarkable self-diagnosis of the meteorological community voiced by the Editor-in-Chief who explicitly reflected the consolidated position of the Editorial Board:

    “If the criticisms and concepts presented by the authors were valid, they could and would most likely be pursued by other members of the scientific community on the basis of the discussion paper and the accompanying comments published in ACPD, regardless of whether or not a revised manuscript achieves publication in ACP. If, however, the referees’ and editors’ concerns are valid, final publication in ACP might mislead other scientists and authors to erroneously build upon and cite the work as a generally accepted scientific theory.”, p. 12410

    The message should not be underestimated. It contains lots of information, in particular:

    (1) there are hopefully some thinking members in the community who are able to pay attention to a good idea, even if it is rejected from a peer-reviewed journal and just available in the Internet.

    (2) if a paper is published in the ACP, a peer-reviewed journal with high impact factor, no one in the community is inclined to exercise critical thinking on its evaluation. Any theory published in ACP is perceived “as a generally accepted scientific theory”. Nobody looks into fundamentals, people just “build upon”. The community is explicitly depicted as a thoughtless crowd governed by peer-reviewed texts. Publishing an unconventional text is dangerous, because the crowd will be misguided. Nobody inside will be able to see the fault by themselves.

    From combined consideration of (1) and (2) it is clear that thinking individuals represent a negligible proportion of the community. It is not my point. It is a self-portrait. If a science works like this, no results can be trusted.

    (3) while some concern is expressed about the fate of the ideas, the authors as personalities can die — nobody cares. That the authors might face an undeserved blow which may kill their creativity, is not even mentioned. This is a minor point, but one reflecting the moral standards of the community.

  113. #109 Anastassia
    Will a vertical temperature gradient form, if the atmosphere does not radiate?
    Yes. This is the standard theory of the dry adiabat. The gradient is g/c_p; no radiative properties mentioned there. Just g and the specific heat of air.

    Given the sensible heat flux of the order of one tenth of solar power, is the observed mechanical power of the Earth’s circulation enough to maintain the observed global mean lapse rate of 6.5 K/km without involving radiative processes?
    Yes. It’s like the question, how much power do you need to keep a refrigerator cold? It just depends on the amount of leakage. In the air, leakage consists of all the processes that conduct heat down a temp gradient. Conduction, radiation, mostly via the Rosseland paradigm. Not convection – that is what is involved in the adiabatic heat pump process. The leakage isn’t so much.

    Can the observed horizontal temperature gradients drive a circulation of sufficient power to maintain the observed lapse rate? More generally, what drives the circulation of Earth?
    You can put this the other way around. What would be required to maintain temperate latitudes at the same temp as tropical? As long as they are not, there is a temp difference that can maintain a heat engine. And it will only fail if the temperate latitudes to come close to tropical temperatures.

  114. #107 deWitt
    There would be no tropopause if there were no oxygen in the atmosphere.
    Is this a reference to the role of ozone in absorbing UV? That’s a rather different issue. And the notion of a tropopause in an isothermal atmosphere is rather artificial.

    In an isothermal atmosphere, not only is there no driving force, there are very strong forces buoyancy forces acting against vertical flow.
    You won’t have a truly isothermal atmosphere without GHG. If poles and tropics are to be at the same temp, you would need strong lateral transport.
    If you have horizontal motion, there will always be vertical motion. This follows from viscous torque applied to the fluid, especially at the surface. Torque creates rotation, eddies, turbulence, which diffuses upward from the surface.
    But it also is required from mass conservation. Any convergence of a horizontal flow requires that the fluid gets out of that plane, up or down.

    Starting an air circulation is not really an issue. Over millions of years, there will be major volcanoes, meteor impacts etc. I’m not suggesting that is how they do start – just saying that they would act as starters if nothing else did. The only question is whether there is enough energy to maintain circulation.

  115. DeWitt Payne said

    Re: Anastassia Makarieva (Feb 10 12:17),

    The problem I see with a ventilator is that it isn’t adiabatic, which seems to me to violate a basic assumption of Physical Meteorology. Then there’s the problem(?) that on average, the temperature of the air just above the surface must be warmer than the surface, possibly a lot warmer, in order to transfer the heat to the surface so it can be radiated away. Maybe the difference won’t be very large at the critical lapse rate, but it will be huge starting from an isothermal atmosphere. How can that even happen? It seems prima facie to be a violation of the Second Law. Think about the size and power of the ventilator needed to mix a 10,000 kilogram column of air above just one square meter. You couldn’t do it with just one at the surface. You’d need a fan every few meters for ten or twenty kilometers.

    So let’s say we don’t mix, but transfer. We’ll pump the air up at the equator and pump it back down further north (or south). If I’ve done my sums correctly, it takes 10,000 watts to move a 10,000 column of air vertically at a rate of 1 m/sec. Clearly we don’t have that much to play with. For 24 Watts you get a vertical velocity of 0.0024 m/sec or 2.4 mm/sec if you neglect any other source of dissipation. That’s in the ballpark of the peak vertical flow rate at the equator of 0.2 Pa/sec at 500 hPa, again if I did my sums correctly. If you run the pump long enough, the column of air will have the adiabatic lapse rate. But now the air has to come down somewhere. And the somewhere has to be north or south of the equator or there will be no net heat flow. Also, the 24 W/m2 has to come out of the local energy budget so the surface temperature will drop by enough to balance power in and out again. For the Earth as it exists now, the radiation surplus at the equator is about 75 W/m2, but the Earth has ocean circulation as well as air circulation. Since the atmosphere cannot lose heat by radiation, when you push it back down again, and it will be pushing because the air moving down will be warmer and so less dense than the air around it, it will have the same temperature and lapse rate as the column of air at the equator. The rate of heat transfer will depend on the temperature at the point where the air reaches the surface again. This is getting too complicated to do in my head. I’ll have to think about this some more.

    The thing is, though, if the diurnal temperature cycle can’t break a temperature inversion in the Los Angeles Basin (and I’ve lived there before the clean air laws were passed and it can’t), how can it do so anywhere else?

  116. Re: DeWitt Payne (Feb 10 16:39),
    “If I’ve done my sums correctly, it takes 10,000 watts to move a 10,000 column of air vertically at a rate of 1 m/sec. “
    Absolutely not. The air is more or less neutrally buoyant. There’s no work done in rearranging air, as such.

    The drag on the system comes from this adiabatic, or near-adiabatic, effect. If the lapse rate < 9.8 K/km, then the air as you raise it becomes cooler than the surrounding air. Then you do work, but nothing like that much. And you do work when it descends too. That’s where the heat pump takes in energy.

  117. DeWitt Payne said

    Re: Nick Stokes (Feb 10 16:00),

    And the notion of a tropopause in an isothermal atmosphere is rather artificial.

    You’re missing the point again. The point was that convection in the Earth’s atmosphere stops at the tropopause because there’s a temperature inversion there, not the other way around. Smog is trapped in the LA basin because there’s a temperature inversion and the diurnal temperature cycle doesn’t break that inversion. In a locally isothermal atmosphere, the temperature inversion starts at the surface.

    The only question is whether there is enough energy to maintain circulation.

    Which is, of course, the question you have yet to answer. In a non-radiative atmosphere, you could have temporary local flows, but they will die out by dissipation, not accelerate and spread, IMO.

    If poles and tropics are to be at the same temp, you would need strong lateral transport.

    A three dimensional, non-radiative atmosphere need only be isothermal vertically and longitudinally, not meridionally. The temperature of the air column will be the average temperature at the surface. The local meridional heat flow will then be controlled by conduction, not convection, and there won’t be much conduction because the temperature gradient is small. The only exception is for very close to the poles for a polar orientation perpendicular to the orbital plane. It would look something like this in the absence of any conduction. The thermal conductivity of air is 0.0243 W/mK at 273 K. With a temperature gradient of 0.04 K/km (an overestimate for most of the surface), energy transfer would be ~1 microwatt/m2

  118. DeWitt Payne said

    Re: Nick Stokes (Feb 10 17:17),

    Absolutely not. The air is more or less neutrally buoyant. There’s no work done in rearranging air, as such.

    Begging the question again. The air is only neutrally buoyant with altitude if the lapse rate is identical to the adiabatic rate, which is definitely not true for a locally isothermal atmosphere. Even rearranging a neutrally buoyant column cannot be done in a finite amount of time without an energy input. Your initial premise, IIRC, is that an isothermal atmosphere will evolve to an adiabatic atmosphere. You have to do a lot of work to get from one to the other. And more to the point, the only source of energy to do the work is the temperature difference from equator to pole. So you do indeed have to lift the column so air will flow away from the equator at the top and flow toward the equator at the bottom.

  119. Kenneth Fritsch said

    Anastassia @ post# 112:

    You have taken the analysis of the editors’ comments deeper than I had considered and I would have to say that I agree with your assessments and would reconsider my comment that the editors’ comments were made primarily to cover their rear ends. I guess I was taken aback by the editors being that philosophical about their decisions to reject the paper. I suppose that kind of response from editors was precipitated by the paper’s thesis presenting a totally new approach and dismissing the theoretical basis of the currently accepted one.

    You need not reply to my query here, but I was wondering whether you and your coauthors were aware of the high esteem that Kerry Emanuel is held by those in the climate science community who tend to favor what they see as his pioneering work in turning the “hurricane” science away from the empirical approach (Grey, Landsea and others) to the theoretical. Chris Mooney’s book published the book, entitled Storm World, a couple of years ago that purports to explain this battle.

    Your paper would appear to reproach that pioneering Emanuel work in putting hurricane science on a theoretical plane. Could that part of your paper been the sticking point for the critical referees and the editors and more so than publishing your new approach?

  120. DeWitt Payne said


    Let’s look at this another way. How does meridional circulation transfer heat from the equator to the poles? Guess what, it’s not by sensible heat transfer from warmer air to the surface. It’s the greenhouse effect. The warmer air radiates more and so the surface cools less. That’s not possible for a non-radiative atmosphere. If you look at the charts of sensible and latent heat transfer to the atmosphere in this reference, you never see negative numbers. If heat transfer can only be by sensible transfer to the surface, you’ll get many orders of magnitude less. For the Earth, average meridional heat transfer peaks at 5E15 watts at about 40N and 40S latitude. That’s an average of about 58 W/m2 for every square meter above latitude 40. You can get that sort of transfer rate in the other direction when surface temperature is tens of degrees higher than the air above it. Good luck doing it by convection in the other direction, not to mention the truly massive temperature inversion that implies.

  121. Re: DeWitt Payne (Feb 10 17:23),
    The number that counts for the onset of convection, and formation of cells, is the Rayleigh number. For air, it is (g L^3 ΔT)/(ανT), α=thermal diffusivity, ν = kinematic viscosity, and L a characteristic length. Consider a 10km cube of air. The lateral temp difference may only be 0.4K, say, but α and ν are each about 10^-3, and L=10^4, so overall, it’s about 10^16. Which is huge. Such a situation cannot be stationary.

  122. DeWitt Payne said

    Re: Nick Stokes (Feb 10 20:20),

    I seriously question your use of a characteristic length of 10 km, especially when the temperature gradient is smooth and the location of the vertical plane is arbitrary. Why not pick 100 or 1,000 km while you’re at it? Not to mention that the acceleration due to gravity in the horizontal direction is zero so the Rayleigh number, no matter what the characteristic length, is still zero. In the vertical direction, the change in potential temperature for a lapse rate less than the critical rate is negative. We don’t have an actual plate with a temperature warmer than the gas temperature creating a boundary layer (with dimension a lot smaller than 10 km) that is more buoyant than the bulk.

  123. Re: DeWitt Payne (Feb 10 21:47), Why not pick 100 or 1,000 km while you’re at it?
    I chose 10km related to the height of the atmosphere. The Rayleigh number is used for buoyant convection calculations in full knowledge that g is vertical only.

    There’s a good 2006 review of general circulation, incl Hadley cells, by Schneider, here. There’s very little mention of GHG’s.

  124. DeWitt Payne said

    Re: Nick Stokes (Feb 10 21:56),

    You will get horizontal circulation that increases with altitude because the temperature gradient from the equator to the poles causes a density difference an thus a decrease of pressure as you go from the equator to the pole at constant altitude. So there’s a pressure gradient from the equator to the poles which increases with altitude. Coriolis force will turn the wind parallel to the isobars. Whether you get a jet stream without a tropopause is another question. Whether that helps your issue is yet another question because it’s still horizontal flow, not vertical.

    You can read through Caballero’s lecture notes on Physical Meteorology without much mention of radiation except at the surface. However, meteorologists seem to me to accept the existence of a near critical lapse rate in the troposphere as a given. But a one dimensional radiative/convective model will produce something very close to the observed lapse rate regardless of starting conditions. I don’t see how you can ignore that.

  125. M.Villeger said

    If I can interject into this conversation:

    #93, #120
    may I point out that observations do not support the existence of Ferrel cells in tropospheric circulation and that only a portion of Hadley cells have been observed (the descending air doesn’t reach the surface due to the Trade Inversion discontinuity) and direct you to the following references:

    [Marcel Leroux, “The Mobile Polar High: a new concept explaining present mechanisms of meridional air-mass and energy exchanges and global propagation of palaeoclimatic changes” Global and Planetary Change, 7 (1993) 69-93 Elsevier Science Publishers B V, Amsterdam] AND [cf. Chapter 5 in “Dynamic Analysis of Weather and Climate Atmospheric Circulation, Perturbations, Climatic Evolution”, Springer-Praxis books in Environmental Sciences, 2nd ed., 2010, 440p., ISBN: 978-3-642-04679-7]

    If I may presume of her answer, I do not think Dr. Makarieva is reproaching “turning the “hurricane” science away from the empirical approach (Grey, Landsea and others) to the theoretical” since she works herself in a Theoretical Physics Division… on the contrary but my take here is that she wishes to ensure mathematics apply to the right description of the studied object.

    So the problem is not that one should not move to theoretical work or that empirical work is always obsolete but that a sound naturalistic approach should underlie the theoretical quest. The accepted but not observed “Ferrel” cells are an example of the danger of taking old stuff at face value. That means that cursory observations are not enough: it is not enough to suggest barocline perturbations “look like” what’s happening in the lower atmosphere just because one knows how to calculate and solve fluid mechanic equations. The question is “does it effectively, really work this way in the troposphere?” And that answer requires measures, field observations and knowledge often dismissed as empirical by elegant theorists…

    On this subject FASTEX “Fronts and Atlantic Storms Track Experiment” was a lesson for all involved: a multi nation experiment was supposed to demonstrate how a storm –cyclone- in the North Atlantic was being created first in altitude and was later developing in the lower layers as a consequence. The manifesto that won financial backing for this unprecedented campaign of measures and data acquisition, monitoring a storm through airplanes, satellites, ships etc. was explicit about the result the meteorological brass was expecting [reference : Chalon et Joly (1996). FASTEX : un programme d’étude des tempêtes atlantiques et des systèmes nuageux associés. La Météorologie, No. 16, p. 41-47]. Data were acquired in January-February 1997. The first analysis came in November and was later published [reference : Arbogast et Joly (1997) Identification des précurseurs d’une cyclogenèse, C.R. Acad. Sciences, Paris. 1998, 326, p. 227-230] showing the « unexpected role of a precursor located in the lower layers » !

    Incidentally this result was the only one expected by Leroux. I really encourage you guys to learn about the reality of tropospheric circulation not its Schneider approximation.

  126. deWitt.

    the only part I vaguely understand is the smog in LA part.

  127. #119 Kenneth, # 125 M. Villeger, re: theory in climate research

    Kenneth, you raise your provocative question for the second time. I have not read the book of Chris Mooney, but I would agree wholeheartedly that there is hardly a scientific discipline in a more desperate need for a physical theory than modern meteorology. Let me outline my personal perspective.

    As I noted in #9, the basic physical idea behind atmospheric motions in modern meteorology is differential heating. As Nick Stokes put it in #96, “as long as there’s free energy from a temp difference, some motion will ensue.” But the fundamental question is how much is that “some” compared to the motions actually observed. Playing more than two centuries’ with the idea that the warm air rises, it has not been possible to prove that the differential heating is able to produce observable air velocities. As DeWitt Payne #97 put it, “a horizontal temperature gradient has density differences, but at constant pressure and gravitational potential energy, there’s no force acting to cause circulation in any direction”.

    In the first half of the 20th century climate physicists still recognized this major problem and openly admitted it. Brunt (1944), as cited by Lewis (1998), wrote:

    “It has been pointed out by many writers that it is impossible to derive a theory of the general circulation based on the known value of the solar constant, the constitution of the atmosphere, and the distribution of land and sea . . . It is only possible to begin by assuming the known temperature distribution, then deriving the corresponding pressure distribution, and finally the corresponding wind circulation.”

    A dozen of years after Brunt (1944) went desperate over the physical theory of climate, the world witnessed the birth of numerical climate modeling. The research emphasis readily shifted from the trouble-making physics to the rewarding procedure of collecting as much empirical data as possible, feeding them to computers and replicating circulation in models. But why the circulation is such as it is? That this question does not have an answer coming from the basic physical principles — only few scientists now remembered.

    The majority of meteorology students were now brought up on climate models, which displayed nice pictures of high resemblance to the reality as if “the science were settled”. One can often hear that, because the models employ the Navier-Stokes equations, there is a solid physical theory behind them. Such a remarkable statement reveals a critical misunderstanding by the modellers (they should not be confused with theorists) of the information contained in the Navier-Stokes equations. These equations can tell you what the air velocity will be, if you know the air pressure gradient, and vice versa. They do not give you a slightest hint on what should be the pressure gradient on Earth. This must be found from independent considerations. That are lacking.

    The last fifty years of numerical climate modelling have undoubtedly become the Dark Ages of climate physical theory. Global circulation models that are unaware of the physical principles driving the circulation do not have any predictive power. It is just an outlet where scientists in late 50s turned in despair over the theoretical problems summarized by Brunt (1944). But, as for an ostrich hiding his head in sand, this is a way to nowhere.

    As we now understand, there are a few people in the modern climate community who do remember the problems. They do know that no physical explanation for the hurricanes exist. They do know that Hadley circulation cannot be understood in quantitative terms based on differential heating. They do know that, whilst widely used for precipitation predictions, the GCMs err severalfold in describing the Amazon water cycle. But this negative knowledge is rarely discussed with the public. The public is let to pay for the models.

    In this situation Kerry Emanuel, starting from his works in late 1980s, attempted to describe hurricanes from the basic physical principles. His were theoretical works, and he is undoubtedly a theorist. The very existence of his works signals to the rest of the climate community, ready to sink completely in modelling, that there ARE physical problems that must be solved. It is not enough to make a numerical statistical model with a thousand parameters to emulate the hurricanes that happened in the past. It is necessary to understand the physics behind them, to be able to make responsible quantitative predictions in a world where the climate is supposed to change. In this perspective the significance of Emanuel’s works should not be underestimated.

    Let us also note that in the modern modelling-focused world the culture of physical theory has been largely lost and continues to erode. Most physicists in the second part of the 20th century were busy making bombs. Climate science was not perceived as either globally important or prestigious. Kerry Emanuel has been practically alone in his efforts. I doubt he could meaningfully discuss his ideas with more than a half per cent of the total number of scientists who are currently paid for performing climate research.

    The only problem is that the theory of Kerry Emanuel is incorrect. Objectively, there is nothing terrible about that. The positive outcome of the analysis of this theory is a convincing proof that hurricanes cannot be explained as heat engines. It is now necessary to analyze the newly available evidence and move further. The condensation-induced dynamics has all the potential to provoke a Renaissance in the physical theory of atmospheric circulation. Its fundamental physics immediately yields the characteristic magnitudes of pressure gradients observable on Earth.

  128. DeWitt Payne said

    How much work you can get out of a real engine, as opposed to a reversible Carnot cycle, depends not only on the temperature difference, but also on how fast you can transfer the heat into and out of the working fluid. In the tropics over water, that’s fairly fast. You have direct heating by absorption of incoming sunlight in the near IR, heating by absorption of LWIR from the surface and, over the ocean or anywhere there is high surface water content, by latent heat transfer from evaporation of water and the resulting increase in specific humidity. At high latitude or altitude, the radiative transfer of heat to space is also fast. None of those things are true for a non-radiative atmosphere. Heat transfer can only happen at the surface. For heat transfer to be rapid there must be not only a high temperature difference between the surface and the air above it, but also high winds to keep the diffusion layer thin. The surface must also have high heat capacity and high thermal conductivity or heat transfer will stop at night because the temperature difference goes away. I still don’t see any way the surface winds can develop to accomplish this.

  129. #128 DeWitt Payne

    You made a point earlier that the fact that a non-radiating atmosphere with a negative temperature gradient caused by mixing is warmer than the surface does not conform to the Second Law. It is an interesting point and I’ve been thinking on that, but so far I have been unable to see why this is so, i.e., why it does not conform. Not sure, but I am a slow and hesitating thinker. It now looks to me like it is in principle possible to get a gradient by mechanical mixing. The Earth will not be warmed, of course, but the upper atmosphere will be colder.

    The next question is whether the actual circulation could support the actual gradient in the absence of greenhouse substances. My estimate is like this: the minimum amount of work W needed to counteract heat leakage H between reservoirs with temperatures Th (hot) and Tc (cold) is found from consideration of the reverse Carnot cycle and is equal to W = eps H/(1-eps), where eps = (Th – Tc)/Th is Carnot efficiency. In the atmosphere taking Th = 300 K, Tc = 240 K, we have eps = 0.2. Sensible heat flux is H ~ 0.1 F, where F is solar power. We thus have W = 0.025 F. (If I am not mistaken). Incidentally, this value is of the order of the observed mechanical power of atmospheric circulation.

    Could this power be produced by a heat engine working between the equator and the pole? Suppose for simplicity these areas are equal in size (not the case). Let we have a mean 30 deg C temperature difference, then eps ~ 0.1. The difference in solar radiation between the equator and the pole is about 75 W/m^2. We thus have maximum work about several Watts per square meter, which is of comparable magnitude to the W value obtained above.

    These estimates show that the gradient could only be maintained based on two perfect Carnot cycles in the atmosphere. Physically, this is not realistic.

  130. Kenneth Fritsch said

    Anastassia @ Post #127:

    Thanks much for the historical perspective on the empirical and theoretical approach to understanding atmospheric circulation and hurricanes. Who says you cannot ask naive (Ok, maybe dumb) questions and get informative answers?

    With regards to what I think M. Villeger is implying here in Post #125 , I would agree. My take is that Anastassia agrees that a theoretical approach is required but that that approach needs to be tied to the correct science. Chris Mooney’s separation of the hurricane scientists between the camp of Grey and Landsea and that camp that includes Emanuel does not deal with the perspective that Anastassia is providing here. Grey, especially, would appear to hold the more theoretical models for hurricanes in lower regards than those he derives from historical TC data. I do not necessarily think that that camp, depicted as empiricists by Mooney, out of hand disgard theoretical models and approaches – just those that either do not use good science or do not hold up in light of empirical data.

    Unfortunately part of this divide that Mooney makes is based on where the scientists come down on the issue of increasing SST and its influence on TC frequency and intensity.

  131. Re: Anastassia Makarieva (Feb 11 12:48),
    My calculation of the work needed to maintain the lapse rate L goes like this. Suppose the effective conductivity of the air is k. That’s not just molecular conductivity (small) but includes latent heat of water and radiative transfer, thought of as Rosseland conduction. Then the leakage flux is kL, and the power needed per unit altitude is kL*L/T or kL^2/T.

    It’s fairly easy to estimate the radiative part of k; the latent heat is best estimated from rainfall.

  132. Re: DeWitt Payne (Feb 11 11:57)
    The heat engine only takes a small part of the total power in sunlight. And from the calc in #131, the conductivity k, and hence the power draw, goes way down without GHG.

  133. DeWitt Payne said

    Re: Nick Stokes (Feb 11 15:23),

    The leakage goes down, but so does the available power. The fraction of sunlight that can be transferred to the atmosphere in the absence of radiative coupling goes down a lot. You still need to show that it doesn’t go down by more than the conductivity decreases. Also, what fraction of the total present energy flow through the atmosphere, 195 W/m2 in the Kiehl and Trenberth energy balance diagram, is the conductivity along the temperature gradient? My guess is vanishingly small.

    Re: Anastassia Makarieva (Feb 11 12:48),

    Absorbed insolation at the equator is about 330 W/m2 on average and is about 50 W/m2 at the South Pole and 80 W/m2 at the North Pole so the difference is over 250 W/m2. In the absence of heat transfer, that would be, averaging to 65 W/m2, surface temperatures of 276 K at the equator and 184 K at the poles, or a difference of 92 K compared to a difference of something like 70 K for our planet. The maximum Carnot cycle power should be more than sufficient to transfer a lot of heat. My question, though, is how much of that power is actually available in a realistic cycle in the absence of radiative and latent heat transfer to and from the working fluid. The heat transfer at high latitude on our planet is radiative, not sensible or latent. Without that, the lapse rate due to transfer of heat from the equator may increase the lapse rate at the equator but it will also decrease the lapse rate at the poles. The combined effect will necessarily decrease the pressure gradient and the driving force for meridional circulation.

  134. Nick Stokes said

    3133 deWitt
    Also, what fraction of the total present energy flow through the atmosphere, 195 W/m2 in the Kiehl and Trenberth energy balance diagram, is the conductivity along the temperature gradient?
    Latent heat – 78 W/m2 (generally said to reduce the lapse rate to the “moist adiabat”)
    Radiative in Rosseland mode – at least most of the 165 W/m2 emitted upward by the atmosphere
    plus a part of the remainder of the 350 W/m2 which travels through part of the atmosphere
    The point of the Rosseland view is that it is explicitly proportional to temp grad. But even where that approx does not apply very well, there is still a movement of heat down the said temp grad.

  135. DeWitt Payne said

    I still can’t figure out why you are bothering with the Rosseland model. As near as I can tell it’s an approximation you use when you can’t do a more exact solution and the optical density for much of the thermal spectrum isn’t high enough for it to be accurate. Maybe you’d use something like that in a GCM when you’re pressed for CPU cycles and can’t use a more accurate band model. But if you can use a band model like MODTRAN, why wouldn’t you?

  136. #133 DeWitte Payne
    My knowledge is that the annual absorbed solar flux at the equator is slightly above 200 W/m2, e.g., Hatzianastassiou et al. 2005 and falls down to 20 W/m2 at the poles. But direct comparison of these values makes no sense, if we want to know what happens in the horizontal direction. We have to account for the difference in the area of these regions. One cannot transfer all heat formed at the equator to a single point of zero area at the pole. The same pertains to temperature differences. Perhaps my estimates of 30 deg C and ~75 W/m2 difference as the mean horizontal differences for the flux and temp are too low, but my guess is that not by much.

    #131 Nick Stokes
    Let for a unit height your lapse rate L be equal to Th-Tc (high – low temp). Then you estimate your work as W = H(Th-Tc)/Th = eps H, where H is the leakage flux of heat and eps is Carnot efficiency. This means your work is always smaller than leakage.

    In reality W = eps H/(1-eps), i.e., at sufficiently large temperature differences the work needed to reverse a heat flow is much larger than the heat flow itself. This formula follows from the consideration of the reverse Carnot cycle. Work W is introduced to the working body at the colder isotherm together with flux H that must be reversed. Total flux “returned” to the heater is thus H+W. So we have W = eps(H+W) and W = eps H /(1-eps).

  137. Re: DeWitt Payne (Feb 12 01:50),
    The reason why I turn to the Rosselande model is that it describes the relation of the IR energy flux to the air temp gradient – it’s linear like conduction in appropriate (high OD) bands. That’s hard to figure out any other way (most people don’t try). So it’s the only way I can think of for expressing the relation between IR and the lapse rate. It doesn’t matter if it gets rough with low OD – the nature of the dependence doesn’t change that much.

    Re: Anastassia Makarieva (Feb 12 02:20),
    This means your work is always smaller than leakage.
    Well, they’re hard to compare. On my calc, if the leakage is 150 W/m2.say, that’s kL; and L=10, T=250, say, so the power needed per m2 per m altitude is 6 Pa (J/m^3). I’m not sure whether that’s high or low.

  138. #133, #136 Accounting for the one third absorption by the atmosphere, the fluxes increase proportionally for the equator and the pole, hence the difference in our estimates. If we account for the high albedo of the pole, the difference in insolation that is solely due to geometry becomes much smaller.

    In my estimate in #129 I only accounted for the “reversal” of sensible heat. Taking the global mean flux of latent heat to be about half of absorbed solar radiation at the surface (150 W/m2), the minimum mechanical work W needed to reverse this heat flow becomes W = eps/(1-eps) H = 0.2/0.8 * 0.5 Fs = 19 W/m2. Lorenz (1967) estimated the mechanical power of general circulation to be around 1% of total solar power (225 W/m2), i.e. around 2 W/m2. This shows that, whatever is the source of mechanical power for the observed circulation, this power is by far insufficient to sustain the observed temperature lapse rate in the absence of an additional sink for heat in the atmosphere, which is radiation by greenhouse substances.

  139. Re: Nick Stokes (Feb 12 02:55),
    A mistake there. The lapse rate L is of course not 10 but 0.01K/m in SI units, making the power per m altitude 0.006 W/m3 (or Pa/s) to maintain a lapse rate L. That is 6 W/m2/km altitude, which sounds too high relative to that Lorenz power of circulation. Maybe my estimate of 150 W/m2 is too high.

    But I don’t see how an extra heat sink helps (#138).

  140. #139 Nick Stokes

    This is link to Lorenz’ works including books, I once found it very helpful.

    You estimate your work as W = eps Fs taking Fs as the total flux of energy at the surface. For 10 km you have 60 W/m2. I count this as an overestimate, because here one needs to bother about latent heat only, which is H = 0.5 Fs. The formula is not W = eps * H, but W = eps/(1-eps)H. This would give 37.5 W/m2. The actual gradient is 6.5 K/km, not 10 K/km. This reduces this estimate to 24 W/m2, which is essentially close to my estimate (I took a smaller height than 10 km) but in any case much higher than the circulation power.

    The extra sink in the atmosphere takes away all the heat flux that would otherwise warm the upper atmosphere and destroy the lapse rate. No problem of “pumping heat” downwards in this case. So, while the actual value of the lapse rate is set by convection (6.5 K/km is an approximate mean of the dry and moist adiabatic rate), this lapse rate is maintained by transfer of thermal radiation in the atmosphere.


  141. Re: Nick Stokes (Feb 12 07:02)
    #140 OK now I do see how the extra heat sink comes in, and that my use of 150 W/m2 was mis-conceived, and my answer #134 was wrong. The 150W/m2 figure is not the right one to use, because that is a steady flow through the system, exiting, not heat that has to be pumped back.

    My formula in #131 is the same as Anastassia’s #136, except that I’m doing it per unit height. Th-Tc = (dT/dx) dx = L dx.

    To try to bring things together, I think this is where we’ve got to:
    1. I’ve been paying insufficient attention to the role of radiative TOA cooling in creating a steady flux through the air, which would create a lapse rate. I need to deal with that better
    2. deWitt needs to fit the role of the dry adiabat, which definitely does need an associated heat pump, into his way of thinking about maintaining the lapse rate
    It’s late here, and I now can’t think how to quantify that.

  142. #141 Nick

    For me, so far an important gain has been to appreciate the possibility that convection alone could indeed make a lapse rate even if the greenhouse substances were absent. In #84 and earlier I started from a complete denial of such a possibility.

  143. DeWitt Payne said


    I learned about thermal winds and that a meridional temperature gradient will cause a pressure gradient and induce circulation even in a perfectly transparent atmosphere. That will increase the lapse rate at the equator and decrease the lapse rate at the poles. Whether the decrease in lapse rate at the equator will go all the way to the adiabatic lapse rate, though, is still to be determined. I still think it won’t because the heat flow will be limited by how fast you can transfer heat downward at high latitudes, and you can’t do that by convection. Or at least that’s what I think right now.

    Chapter 6 in Caballero’s Physical Meteorology Lecture Notes is about turbulence and heat transfer in the boundary layer. The math is a little beyond me at the moment.

  144. Re: DeWitt Payne (Feb 12 14:13),
    A key part from Chap 6 is:
    “Under statically unstable conditions (e.g. when there is strong solar warming of the surface), there will be an extra source of kinetic energy for the turbulence, and the turbulent fluxes should be correspondingly stronger. When the mean flow is stable (e.g. due to nighttime cooling of the surface), air parcels will have to do work to move up or down, so turbulence will be weaker (another way of putting it is that some of the kinetic energy derived from shear instability will be converted to potential energy of the mean stratification).”
    That’s the switch between heat pump and heat engine that I have been talking through, as the lapse rate passes through 9.8 K/km. The Richardson number does seem to be important. It’s a pity the notes fade just when it was getting interesting.

  145. DeWitt Payne said

    Re: Nick Stokes (Feb 12 17:50),

    That’s the switch between heat pump and heat engine that I have been talking through, as the lapse rate passes through 9.8 K/km.

    Yes, but only if the overall lapse rate is close to critical anyway, which will be true for a radiative atmosphere like the Earth, but has yet to be established for a transparent atmosphere. If the lapse rate at altitude is far less than critical, the boundary layer will expand during the day and contract at night with little effect on the lapse rate at higher altitude where there is much, much less turbulence. Note that it does this to a considerable extent even on the Earth. The only deep convection is moist convection, and that’s mainly in the Tropics. That’s also one of the main points of contention that Gerald Browning has against computer climate models. The grid size is too coarse to resolve that sort of thing so the temperature and moisture profile of the entire grid box is rearranged whenever unstable conditions are detected.

  146. DeWitt Payne said

    Re: Nick Stokes (Feb 12 17:50),

    It’s a pity the notes fade just when it was getting interesting.

    It seems to be a work in progress. When I first discovered it a year or two ago, there was a lot less, basically just the first three chapters. And parts of those were pretty rough. I should go back and look at it more often to see when there are changes. There’s probably some automated way to do that.

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  150. ghl said

    You appear to confuse temperature ( molecular KE ) and pressure ( momentum transfer ). If you magically shrunk ( compressed ) the gas while retaining the same molecular velocity (temperature ) you would have the gas at the same temperature but twice the pressure. Isothermal compression. Basics. You are confusing yourself with a flurry of words.

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