the Air Vent

Because the world needs another opinion

Where do winds come from?

Posted by Jeff Id on October 15, 2010

Discussion continued at this post:

Again, some very important (and simple) confirmation of condensation driven winds.  When you see the top of clouds forming or evaporating, it should make you think.  The paper is open for scientific commentary there and blog commentary here.


Anastassia Makarieva
Where do winds come from? A new theory on how water vapor condensation influences atmospheric pressure and dynamics

Makarieva A.M., Gorshkov V.G., Sheil D., Nobre A.D., Li B.-L.

now up for public discussion at ACPD:

According to the Economist , the biotic pump theory stating that natural forests drive winds to sustain the water cycle on land has caused “a stir” in Western academia. Indeed, last time it was in the end of the 17th century (see Halley 1686) that a physical driver of winds was proposed. That time it was differential heating (the statement that the warm air rises being lighter than cold air). It formed the basis of a consensus regarding the causes of atmospheric motion, a consensus that is now over three hundred years old. However, this consensus had formed long before the kinetic theory of gases was formulated. This fundamental theory revealed that gas pressure depends not only on temperature, but also on the number of gas molecules in a unit volume. Phase transitions of water (condensation and evaporation) namely change this number. Thus, spatial gradients of the intensity of condensation/evaporation are to be associated with air pressure gradients that cause the air to move. (By consequence, natural forests known for their high evaporation potential become a major player in atmospheric circulation .)

Remarkably, the effects of condensation/evaporation on air pressure via removal/addition of vapor molecules have managed to escape wide attention for a very long time. This to such a degree that, as documented in our paper, there is now a confusion among scientists as to whether condensation increases or reduces moist air pressure. In other words, even the sign of the effect remains unclear to many meteorologists, let alone its quantitative magnitude. This is despite the recognition that namely the lack of theoretical concepts to treat moist effects is a major obstacle for the development of the atmospheric circulation theory (Schneider 2006 p. 682).

In the above paper just made available for public discussion at the Atmospheric Chemistry and Physics Discussions journal of the European Geosciences Union (EGU), we review the recently available knowledge on the dynamic effects of the phase transitions of water on air circulation and advance the physical foundations of the biotic pump theory in all its integrity. We want the new theory to be scrutinized openly and as widely and deeply as possible, and we are ready to invest efforts to clarify and defend our findings in public in the coming weeks. We hope that the EGU platform will be a guarantee that the discussion, including criticisms, will be constructive and of essence.

Please, feel free to join the commentators or to encourage to comment those scientists who you believe might be interested in the topic. The discussion is open until 10 December 2010 during which time the authors will be available to share their insights, for what they are worth, into this really exciting question: Where do winds come from?

Yours sincerely,
Anastassia Makarieva

158 Responses to “Where do winds come from?”

  1. mrpkw said

    “We” think we can control the climate and “we” don’t even know how wind is made??

  2. Jeff Id said


    I think that is one of the big lessons here but in addition this appears to me to be the likely primary driver in weather. If it were included in forecast models, we might see a substantial improvement in results. The climate models are too crude to benefit much though, at least from what I (a serious novice) can tell.

  3. vivendi said

    In the above paper just made available for public discussion …
    Isn’t this phrase remarkable for its humility? It’s not “science is settled, the debate is over” but rather an invitation for others to join the round table and weigh in with their arguments, pro or con.

  4. Brian H said

    Oh, I’m sure the parameter-pluckers on the Team can come up with a scattershot of modified models that will bracket the truth somehow or other. Then they just have to take an average of the models, right?

  5. mrpkw said

    # 2
    I was being very,very,very factitious !!

  6. Tony Hansen said

    Having quickly read the Trenberth 2003 paper they cite, of most interest is the number of times uncertainty crops up.

  7. Tony Hansen said

    From Trenberth 2003:
    “Models can typically simulate some but not all of the diurnal cycle pattern, but some models are wrong everywhere”.

    As you say in #2 Jeff -‘If it were included in forecast models, we might see a substantial improvement in results’

    Any improvement to those that “are wrong everywhere” would rate as substantial 🙂

  8. Jeff Id said

    This is what makes wind folks. The equations are right there. I’m regularly amazed that so many technical people are too focused on minutiae of Wegman when faced with obvious world-changing science.

  9. 8
    Jeff, it seems very like standard hurricane theory to me. That’s the trouble with unreviewed publishing – you get a cloud of equations and a claim that it is all new. Citation standards are low – she relies a lot on Poschl 2009, which turns out to be a web comment someone wrote on one of her previous papers. That’s the source, for example, of the eyebrow raising claim that “there is doubt as to whether condensation leads to reduced or to increased atmospheric pressure”.

    I don’t believe that there’s any physics here that is not included in GCM’s. Anyway, we might get to hear what Judith Curry thinks.

  10. I’ve lodged a query about how Eq 34 follows from 32 and 33. I’m not sure if I’ve mastered the system – it isn’t showing yet. If anyone here can see it, I’d be grateful.

  11. Anastassia Makarieva said

    #9 A clarification on the citation of Poeschl 2009:

    Rather than being just a someone, Dr. Poeschl is the Editor-in-Chief of the Atmospheric Chemistry and Physics journal. Poeschl (2009) [ ] is a list of review assessments of our previous work on hurricanes, where another well-respected scientist, Dr. Daniel Rosenfeld [ ], claims that condensation increases air pressure. This statement, as clarified by Dr. Poeschl (see here: ], was endorsed by the entire ACP executive committee [ ], a body composed of distinguished meteorologists.

    Note that the statement was not a side or casual issue, but a major argument against our work on hurricanes, where we claimed that condensation lowers air pressure.

  12. Jeff Id said


    Since some in meteorology doesn’t see the sign in eq 13 as correct, I think it is time for an experimental demonstration.

    How about a single chamber which contains humid air or dry air. Its size approximates adiabatic conditions. A single window in the side is used to observe condensation. RH, temp and pressure are monitored. Air is drawn from the chamber by a vacuum pump of some kind at a controlled rate until condensation occurs. The experiment could be repeated for both dry and moist air, the difference would be the adiabatic pressure change caused by condensation.

  13. Dan Hughes said

    Removing mass from the chamber will confound the situation; the pressure will decrease.

    How about a cloud chamber?

  14. Jeff Id said

    #13, Dan, The pressure will decrease at differential rates with moist and dry air. The difference being created by the condensation.

  15. Jeff Id said

    #10 Nick,

    If you substitute N = Nv + Nd to combine eq #32 and #33 it looks like it might work. I’ve got another project at the moment but will attempt later.

  16. Jeff Id said


    How about two chambers of equal size one pumped to a vacuum. High humidity vapor in one test and dry air is in another. A valve is opened between the chambers to suddenly double the volume. The pressure change should cause condensation in the moist air version and the final pressure won’t follow ideal gas law.

  17. #10, #15

    Eq. 34 (condensation rate) cannot be derived from Eqs. 32 and 33 (continuity equation) in any way. It is an independent equation. This is discussed in detail on lines 7-29 on page 24034.

    Regarding experiments, an essential thing to take into account is that we are talking about gas in the gravity field. Its pressure at the surface, if there is approximate hydrostatic equilibrium, is simply equal to the weight of all molecules in the column of unit area. Whether we warm the column or make it colder, provided the gas molecules are all there, surface pressure will not change. But if we remove some gas (by condensation or by a chemical reaction, does not matter) from the column, surface pressure will go down.

    Section 2 of the paper, including Eq. (13), is aimed to demonstrate a different point: if one has a certain amount of moist air, whatever one does with this air — if condensation occurs, the pressure falls.

  18. Jeff Id said


    If I recall, the argument that pressure would go up was based on temperature change created from the phase change of water. You have addressed that with the equations, however a physical demonstration is hard for detractors to disagree with.

    If an experiment were to drop pressure until condensation occurred and compare to a pure ideal gas situation, you would have the aspects of heat incorporated in your experiment. The phase change would cause additional pressure drop according to eq 13, were the arguments about heat correct the equations would be wrong (although it is difficult to imagine how) and pressure would drop less than an ideal gas.

    What am I missing?

  19. John F. Pittman said

    Re: Jeff Id (Oct 16 09:19), there are several problems with this approach. The sudden opening will mean it will not be adiabatic expansion. “”Sudden”” will also besides introducing PVn in the gas equation, it will also induce mechanical energy and entropy factors. The air column is a boundary value problem.

  20. Jeff Id said

    I see you have sent me some reading material also, thank you.

  21. John F. Pittman said

    Damn my superscript n on PVn disappeared.

  22. Jeff Id said


    I agree that you have identified a source of error in the experiment, but it sounds small to me. Certianly, if the air were to switch over in say 10 seconds, that would be pretty sudden and the heating caused by mechanical motion would be fairly minor in comparison to the flow. But even if it were wrong, you would be comparing identical situation to a dry gas and looking at the difference with both experiments having similar errors.

  23. John F. Pittman said

    Re: Jeff Id (Oct 16 10:48), Well, that is the nature of an experiment, to determine if you have set it up so the god of physics can actually speak intelligibly.

  24. kim said

    Hmm, water sucks, wind blows, and you need a weatherman to tell which way.

  25. kim said

    Ooh, heck, that should be ‘Water sucks, heat blows, and you need a weatherman to tell which way the wind blows’.

  26. Paul linsay said

    #11. Condensation decreases air pressure. This happens all the time when cooking. I made a pot of stew this week and left the cover on while the pot cooled down. The water vapor condensed making it nearly impossible to pull the top off. This also happens when steaming vegetables in the microwave. If I take the top off the steamer and put it on the marble counter, it seals to the counter after it’s cooled off.

    Yes, it’s not a closed system, but it’s hard to understand how it would be opposite sign in an open system.

  27. #18 Jeff,

    1. If I get you right, in your experiment you wish to know how moist air pressure will change upon condensation compared to pressure of dry air under similar conditions. The result will depend on what you call similar conditions. If you cool both moist and dry gases (with equal initial temperature) by 10 degrees Celsius (the same temperature change), the resulting pressure of moist air will be always lower if condensation has occured. If you take one and the same amount of energy away from both gases (either in the form of heat or in the form of work the gas performs in the course of adiabatic expansion), then the resulting pressure difference between the gases will depend on how much moisture condensed and how much latent heat was released. But, once again, upon condensation pressure of moist air will be lower than it was.

    2. There is a different question — can condensation be accompanied by a rise of moist air pressure? Here comparisons with dry air (pure ideal gas) are not relevant, because there is no condensation in moist air. This is what our section 2 is about and our answer is no.

    3. A different and most relevant statement for condensation-driven winds is that irrespective of whether heat is released or absorbed upon processes leading to gas mass removal, under conditions of hydrostatic equilibrium the mass removal associated with condensation reduces pressure in the lower atmosphere.

    Rather than lack of experimental data, the confusion we are discussing in the paper can be due to incorrect posing of questions 1-3 and mismatching questions and answers.

  28. Jeff Id said


    I already believe what will happen but as I understand it, your detractors say that due to temp change during condensation the pressure will rise. Therefore it is better (more clear) to construct the experiment by adjusting pressure rather than temp. Another concept I had worked by temp which is also a proof, but I deleted before posting for this reason.

    If I’m misunderstanding the critics it doesn’t matter. I’m not claiming you are or even may be wrong, they are. It would require me to rework my entire physical understanding of fluids if you are wrong which would take considerable effort for an aeronautical engineer.

    I just was considering a simple very low cost experiment so those who don’t understand the physics behind the math would be convinced. Twenty years ago in my university days, I probably could have built the thing in a week from stuff already in the building.

    Those who work in math often don’t like to experiment but if the detractors don’t work well in math sometimes it is good to show them.

  29. DeWitt Payne said

    The temperature of a volume of moist gas won’t go up as the water condenses unless it was super cooled. Saying that is like saying the temperature of a well stirred slurry of ice and water goes down as the ice melts. When you have a system where there is a phase change, the temperature is very nearly constant. This is used for temperature calibration routinely. There’s the triple point of water, the freezing point of zinc, etc. If I can find my old P.Chem. Lab book, there was an experiment in it on determining the phase diagram of a condensible gas. IIRC, it involved a lot of mercury used to change the pressure and volume of a container while watching for a film to form on the mercury surface.

  30. Richard111 said

    When I took my PPL back in 1971 I was taught to avoid cumulus cloud as condensing water vapour inside the cloud caused strong updraughts due do to reduced pressure. This could be a danger to my aircraft. I never tested this. 🙂

  31. Jeff Id said


    My experiments were taken from reading the critiques in comment #11 link 1 which included things like this:


    It follows that for one g/kg of condensed water vapor (qsat = −10−3kgkg−1) the rise
    of Twet − Tdry is 2.5 K, so Twet/Tdry rises by 8.3 x 10−3 . On the other hand, with
    10−3 of the mass condensed, the fraction of disappeared molecules is 10−3/0.622 (accounting
    for the lower mass of the water molecules compared to dry air) so Nwet/Ndry
    falls by about 1.6 x 10−3.
    It is seen from this somewhat cumbersome exercise that the rise of Twet/Tdry goes
    faster than the fall of Nwet/Ndry. So pV becomes larger for the wet than for the dry parcel.
    Hence, either the pressure p or the volume V or both must be higher for wet air than
    for dry air (for the same lifting). And this shows that the effect of condensation, by latent
    heat release, has more the form of an “explosion” than of an “anti-explosion”. This is
    qualitatively again the same result as what was already found from the closed-vessel
    calculation, where some artificial constraints were made just to lower the number of
    varying parameters.
    As you wrote, even the sign was questioned. I have read all of the critiques which were of varying quality and came to the idea that a simple experiment could at least address this stuff.

  32. Anna #15,
    I find your treatment of Eq 34 very odd. It sure looks like it’s meant to follow from 32 and 33, and then a couple of pages later you have a long explanation about how lots of people think that and they are wrong. Well, OK, I thought that too, but why not say something at the point where 34 is introduced?

    But more importantly, how is 34 derived? You’ve said a lot about it later, but I still can’t see where it comes from. And it looks wrong. 32 and 33 are standard continuity, and allow for both horizontal and vertical velocities and gradients. 34 has only z-components, and doesn’t even include the velocity gradient.

    OK, I see a little bit more at the bottom of p 24030, which is hard to understand. You really should give a proper derivation at the point where you introduce it.

  33. HaroldW said

    #26 Paul linsay:

    I’ve noticed the same effect, but I believe that it’s the cooling of the air above your stew which is the principal cause of the reduction in pressure. Just the old “pV=nRT” equation, with the volume fixed and the lid acting as a seal to keep n constant as well.

    There is definitely condensation as well; whether the condensation augments, or detracts from, the thermal effect upon pressure I can’t say from observation.

  34. Brian H said

    Re: mrpkw (Oct 15 18:01),
    Just blowing hot air? 😉

  35. DeWitt Payne said

    Re: HaroldW (Oct 16 17:22),

    I believe that it’s the cooling of the air above your stew which is the principal cause of the reduction in pressure.

    Nope. If the water is boiling, i.e. the vapor pressure of water is equal to atmospheric pressure inside the pot, when the pot cools the pressure inside the pot will be equal to the vapor pressure of water at the lower temperature, i.e. very small. Here’s an example complete with video using a soda can.

  36. cementafriend said

    I suppose it should not surprise me that there are people who latch onto a bit of physics (which they do not understand when put in various contexts) to support beliefs they hold from misinformation. I know that engineers, at least, in English speaking countries have lost public respect (say compared to Isambard K Brunel)because there are engine drivers and mechanics who call themselves engineers. It is a pity all Professional Engineers do not use a registered title such as the French Ingineur.
    Professional Engineers who have some competency in thermodynamics and understand refrigeration and air conditioning would not find the information in the paper by Markarieva et al exceptional. It has been suggested to Anastassia that she should contact engineering researchers who are studying boundary layers in specially instrumented wind tunnels to obtain some data. It is also suggested that she reads some engineering text books on heat transfer and fluid dynamics. Perry’s Chemical Engineering Handbook could be a good initial reference. From my reading of textbook’s and articles on so-called Climate (or atmospheric) science there seems to be no real understanding of even the basics.

  37. Brian H said

    But, doncha unnerstand, that’s all just specialist carping about Big Issues that only the enlightened Climate Generalists at CRU are privileged to comprehend in their complex wholeness?

    Or SLT.

  38. Jeff Id said


    That is a perfect demonstration of the effect. There is no way that a non-mathematical meteorologist can watch a can be crushed and not realize the effect is far greater than any thermal expansion.

  39. HaroldW said

    #35 DeWitt,
    I appreciate the correction. My reading of the original post did not lead me to believe that the stew was boiling. But even at 80 C — and I’m just guessing about that — it turns out that the vapor pressure is about half an atmosphere, much higher than I would have guessed.

    The video you posted was quite amazing. I had never seen that demonstrated before. Thanks again.

  40. Carrick said

    NIck Stokes:

    OK, I see a little bit more at the bottom of p 24030, which is hard to understand. You really should give a proper derivation at the point where you introduce it.

    I agree with Nick… this part of the paper could use a serious rework.

  41. Brian H said

    condensation releases latent heat energy. Where does it go?

  42. DeWitt Payne said

    Re: Brian H (Oct 17 03:21),

    Freezing water releases latent energy. Does the water heat up as it freezes? If it did heat up, it wouldn’t be freezing any more. As heat is removed from the system, enough water freezes to keep the temperature nearly constant. The same is true with condensation. As heat is removed from the system, enough water condenses to keep the temperature nearly constant. You can have a supercooled system where for lack of nucleation there is no crystallization or condensation and the temperature is lower than it would be at equilibrium. See this article for example. Throw in a seed crystal or, for water vapor, zap it with an alpha particle or other ionizing radiation and you get a phase change and a temperature increase. But that’s only true if there are no ice crystals or water droplets present.

    Cloud and bubble chambers for observing the tracks of charged particles work on similar principles. In the case of a bubble chamber, the working fluid is superheated above the boiling point rather than cooled below the condensation point.

    If you cool water very, very fast, you can actually make a glass rather than crystalline ice.

  43. #32, #40 Nick, Carrick

    The whole of section 4.2 is devoted to the question of why Eq. 34 is as it is. It is an important equation and your attention is welcome. I encourage you to give Section 4.2 a careful read. I would also suggest one to contrast what one will have read in our Section 4.2 with Section 4.4 of Gill (1982), in particular, paying attention to formulae 4.4.9 and 4.4.10. If you feel Eq. 34 is wrong, I am keen to know why you think so and what, in your opinion, the correct equation should be.

    My training as a physicist was harsh in some ways. I recall one day I was disappointed with what a senior colleague was proposing, irritated and felt he was wrong. But I could not properly express myself scientifically, just emotional dissatisfaction. Then I was told the following story. A leading physicist was giving a lecture reporting novel and controversial findings. When the lecture was over, he asked for questions. A very-well-respected-scientist stood up with a smirk and started, in a slow and apparently mocking manner — I DO NOT UNDERSTAND HOW YOU COULD… But the lecturer, immediately knowing his attitude, interrupted — “My apologies, but this is a statement, not a question. Next question, please!” The lesson was well taken. Today I believe I have learnt to be specific in my comments and know that “I do not understand” is 99% my problem, not that of the author.

    #32 Nick
    Anastassia and Anna are as different names as are Nick and Bob. I would not mind being called by my own name here.

  44. I agree that the video linked to in #35 is impressive. There are several other examples of mechanical movement caused by pressure difference due to phase transitions of water. One of them is the drinking bird (not all of their types but some). BTW more precisely it would be to say that condensation occurs when energy is removed from the gas. It does not necessarily have to be heat. When the air ascends and expands adiabatically, energy is taken away from the air in the form of work it performs. This leads to cooling and condensation.

    Another peculiar example from daily life of how gas mass removal lowers air pressure is fire cupping in medicine. The idea is that a chemical reaction and condensation that occur during burning within the jar reduce concentrations of gases such that total pressure falls despite the gas is warmed. In the result, patient’s skin is sucked into the jar where the pressure has lowered. The funny thing is that you must know what to burn to have the effect. (I am not sure people here know well what cupping is, but in my country it used to be a common way of treating cold, for example. I remember as a girl having all back in bruises left by these jars.)

    An interesting thing about condensation-driven atmospheric movement is that, if we look at a stationary or quasi-stationary circulation pattern as a whole, we can see that while there is intense condensation in some part of the circulation, there is no temperature change. That is, of course each individual air parcel that rises does cool, but the circulation pattern as a whole has a stationary temperature distribution.

  45. Anastassia,
    My apologies for my error with your name. I had recently been in dialogue with another commenter called Anna on another blog – it was just absent-mindedness.

    I will read Sec 4.2. However, I think you should have a pointer to it at the time you introduce Eq 34.

  46. 45 Anastassia,
    I now see where 34 comes from. It is, approx, derived from 32 and 33 – if you replace Nd in eq 33 by N, which is a reasonable approx, and assume horizontal uniformity, so the first terms can be dropped. Then if you use the product rule on the z-derivatives, and eliminate dw/dz, you get 34.
    32: d(N w)/dz = N dw/dz + w dN/dz = 0
    33: d(Nv w)/dz = Nv dw/dz + w dNv/dz = S
    so N w dNv/dz – Nv w dN/dz = N S
    and so
    34: S = w dNv/dz – w Nv/N dN/dz

    But the assumption of horizontal uniformity won’t work. It’s a steady flow, so in one dimension, conserving mass, w=0, since it is w=0 at the ground.

    So I think 34 is wrong.

    If you think there is a different derivation, you need to state it.

  47. #46 Nick,

    What you show is that Eq. 34 cannot be derived from Eqs. 32 and 33. This is indeed so for the physical reasons outlined in the end of Section 4.2: the continuity equation does not know whether condensation/evaporation occurs or not.

    Equation 34 is not “derived”, but, in the considered problem, is as an independent equation. It is written based on what we know about the process of gas mass removal. If the process of gas mass removal had the form of a chemical reaction, then Eq. 34 would be specifying the rate of that reaction. If there were a beast of Maxwell’s demon kin who would be eating vapor molecules at a certain rate somewhere in the atmosphere — then Eq. 34 would be reflecting the demon’s appetite. And so on. As we know that gas molecules are removed due to condensation during adiabatic ascent, we specify the condensation rate accordingly.

    By the way, the approximation N \approx  N_d that you suggest is not valid in the considered problem, because all the effect is proportional to water vapor concentration, Nv. So in spite of N_v \ll N_d, Nv cannot be discarded. Free manipulation with replacements of N for Nd in the meteorological literature is one of the reasons of why what we are now talking about has been overlooked.

  48. Anastassia,
    34 has to be derived from some physical laws via mathematics. But OK, if you want it to be independent, then the algebra can be run backwards.
    32: ∇.(Nd v)= Nd ∇.v + v.∇ Nd = 0 using vector notation v=(u,0,w) etc
    33: ∇.(Nv v)= Nv ∇.v + v.∇ Nv = S
    Take Nd*33-Nv*32
    v.(Nd ∇ Nv – Nv ∇ Nd) = Nd * S
    by 34
    v.(Nd ∇ Nv – Nv ∇ Nd) = Nd/N N*S = Nd/N w (Nd dNv/dz – Nv dNd/dz)
    But in components
    v.(Nd ∇ Nv – Nv ∇ Nd) = u (Nd dNv/dx – Nv dNd/dx) + w (Nd dNv/dz – Nv dNd/dz)
    u (Nd dNv/dx – Nv dNd/dx) = (Nd/N – 1) * w (Nd dNv/dz – Nv dNd/dz)
    Now (Nd/N – 1) is very small, which means u is very small.

    So from 32, d(Nd w)/dz = – d(Nd u)/dz is also small
    But at the ground, Nd w = 0
    so Nd w is very small everywhere
    ie w is very small
    and from 34, so is S.

    Now OK, you may not believe all this. But what you do have to do is provide a proof of 34, or a demonstration. Not just waffly talk about it.

  49. Carrick said


    Today I believe I have learnt to be specific in my comments and know that “I do not understand” is 99% my problem, not that of the author

    You’re assuming that I don’t understand, I never said that. What I’m saying is the manuscript needs reworking to improve its readability.

    What amounts to poor organization of a manuscript is a fault with the author, not the reader. We’re suggesting reworking the text so that the derivation of Eq. 34 is linked in some way to the following description. And like Nick some form of rigorous justification for the equation is needed.

  50. [removed by request – copied in full below]

  51. [removed by request – copied in full below]

  52. [removed by request – copied in full below]

  53. Am I banned from posting or just doing something wrong? I cannot post text with formulae.

  54. OK, now I see it is something in my text. So I try to change:

    #48 Nick,

    u (Nd dNv/dx – Nv dNd/dx) = (Nd/N – 1) * w (Nd dNv/dz – Nv dNd/dz)
    Now (Nd/N – 1) is very small, which means u is very small.

    This statement is incorrect as well as the argument that follows.
    (N_d/N - 1) = -N_v/N \ll -1 is small. But since dN_v/dx = 0 on the isothermal surface considered, the main term in the left-hand side at u is N_v dN_d/dx. If you divide both sides by this term, you will see that there is a large term
    N_d/N_v \gg 1 at w at the right hand side. So there is a small term times a large term, no conclusion can be drawn on the magnitude of u.

    I warn you once again about discarding ‘small terms’ of the order of N_v/N. In the considered problem it is the main term. Also, when you say that something is small, it is a must to indicate compared to what. Hurricanes, for example, are characterized by pressure drop of 50 hPa, which is a meager five per cent of total atmospheric pressure.

    So I still do not have any physical argument against validity of S (Eq. 34) except the statement that the background physics on adiabatic condensation is a waffly talk. But not to lose the bigger picture for the future, let us suppose that S (Eq. 34) is wrong. And let us recall that, according to Nick’s #9, all condensation physics is included into GCMs. Then it should be easy to point me to a correct equation for S.

  55. Jeff Id said


    Nobody has ever been banned here and I haven’t snipped a comment in nearly a year now. I don’t have much control over the spam filter though because it’s a free blog.

    WordPress has options to let me in to approve the automatically identified spam comments. I get about 150 spams/day here.

  56. #49 Carrick,

    This takes us a bit off-topic but anyway. I did not presume that you do not understand (btw, if you do understand, means that paper is organized satisfactorily). I meant that “I do not understand” or other general statements that “the paper should be better organized” should not count in a scientific discussion. In my opinion. I would never allow myself to recommend the authors whose paper I review to better organize themselves. This would show very little respect to the authors, who have been working a lot and thought a lot on the findings that I may be staring at for the first time in my life. Perhaps they know better what is better? Perhaps they aim to publish a slow-burning, long-lasting paper, not easy reading for readers who just scan across pages rather than think over? How can I take the responsibility to point them what to do with their novel results? How can I know that the paper structure that is optimal for a first reading will be the same optimal for a subsequent deeper study? We are not talking of literature, we are talking of science here.

  57. DeWitt Payne said

    Re: Anastassia Makarieva (Oct 17 05:42),

    BTW more precisely it would be to say that condensation occurs when energy is removed from the gas. It does not necessarily have to be heat. When the air ascends and expands adiabatically, energy is taken away from the air in the form of work it performs. This leads to cooling and condensation.

    Indeed. After I posted last night I realized I should have used adiabatic expansion for the example of condensation in a moist gas. In adiabatic expansion, the temperature of a moist gas decreases at a slower rate as the pressure decreases than for a dry gas. One can still have supercooling where the temperature initially follows the dry adiabat. When condensation finally begins, the temperature (at constant pressure) will increase, but it will never exceed the equilibrium moist adiabatic temperature. A more complete discussion of the thermodynamics of moist air from a meteorological perspective can be found in Chapter 3 of R. Caballero’s Physical Meteorology Lecture Notes (30 MB pdf).

  58. kim said

    Though the man’s language was incomprehensible, the bruises on his back pointed pathognomonically to the diagnosis: Pneumonia.

  59. Jeff Id said


    I didn’t guess correctly where the equation came from either so an extra clue would have been helpful. Had you not replied, I would have traveled the same path as Nick. The criticism is minor and reasonable unlike some of the open reviews for your hurricane paper which I just reread again almost in their entirety. The meteorologists simply don’t/didn’t understand the basics of gasses in most of the cases. I should mention also that unlike myself with a bachelors and part of a masters in aeronautical and mechanical engineering, Carrick’s qualifications match your own.

    As far as understanding what is going on, the detail of eq 34 changes nothing. I am absolutely convinced that you have correctly identified the sources of most winds on earth including the driving forces behind hurricanes. It has always bothered me that warm air was enough to create some of the bigger winds experienced. The pressure change of condensation absolutely dwarfs any temperature differences. I spent a lot of time wondering how temperature change could be enough to drive a tornado. Condensation explains so much about weather we experience it is annoying that the effect is not part of standard texts all the way down to 4th grade. Any slight updraft from warm moist air turns into a powerhouse of energy release, cloud tops billow upward, ever seen a day with cumulus clouds and no wind — me neither.

    I expect this to become the standard in meteorology in the future and am still surprised to be told it is not.

  60. Jeff,

    I am enjoying the discussion, and I like the way Nick is attacking our stuff. I cannot say that the criticism is meant to be minor though, as it is claimed that Eq. 34 is incorrect because our talks are waffly. So I do expect Nick to come up with his own correct version of Eq. 34, which is included into all (or at least one) GCMs.

    There must be an explanation for the fact that condensation-driven dynamics has not yet become the standard. And Nick’s wanderings help explain why it has not. There is a fundamental confusion in the literature about Eqs. 32, 33, 34. So it would be helpful to disentangle it logically and in public.

    I am passionate about all this, so if I am sometimes carried away in my talks, I ask for apologies in advance. Sometimes you just press “submit” earlier than you should have done that.

  61. Jeff Id said

    #60 You don’t need to apologize for anything. Sometimes discussions get heated. The nice thing about science blogging is that people get to take their time before posting. Conversations which face to face take minutes and lead nowhere turn into thoughtful discussions that have records. I’m sure Nick is considering this with whatever free time he has to spend. I have little time today because I spent all day yesterday reading papers. 😉

  62. Anastassia,
    I have pretty much given the correct version above, but I’ll do it more completely. The thing is, though, it’s your revolutionary theory, and you need a derivation.

    Eq 32 and 33 correctly describe mass conservation, and that is all you can get there. If you insist 34 is independent, it must be based on some other physics. You never say what that is.

    The logical candidate is thermal expansion – adiabatics. But if that is being invoked, there will be specific heats in your formula, as the ratio You don’t have that.

    So, OK, you can use 32 and 33 to eliminate the velocity gradient, if that’s what you want.

    So working from my previous comment:
    v.(Nd ∇ Nv – Nv ∇ Nd) = Nd * S
    S = v.( ∇ Nv – Nv/Nd ∇ Nd)
    It’s not too unlike 34, but with Nd instead of N, and with the horizontal components necessarily included. Writing out in components:

    S = u.( d Nv/dx – Nv/Nd d Nd/dx) + w.( d Nv/dz – Nv/Nd d Nd/dz)

    But you can’t get rid of the horizontal components without running into the problem I mentioned. With just vertical velocity and conservation of mass, nothing can happen, because w=0 at the ground.

    ps – where I am it is now early morning.

  63. Brian H said

    Not responsive, and not correct. That the water does not change temperature during phase change is irrelevant. Freezing water dumps heat to its environment. Condensing water vapour dumps heat to its environment. Melting water draws heat from its environment. Evaporating water draws heat from its environment (hence the efficacy of sweat).

    Do you serious dispute any of the above?

  64. Brian H said

    typo: “seriously”, not “serious”.

  65. cementafriend said

    Jeff @59 well said.
    However, this maybe all new to physicists (and so called climate scientists) who have limited ideas about thermodynamics, heat transfer (including phase change), mass transfer and fluid dynamics.
    One of the reference books in my universities study was “Transport Phenomena” by R. Byron bird, Warren E Stewart & Edwin N Lightfoot (John Wiley 1962). In the preface they write “Herein we present the subjects of momentum transport (vicious flow, energy transport (heat conduction, convection, and radiation), and mass transport (diffusion). ——-Our thought has been that the subject of transport phenomena should rank with thermodynamics, mechanics, and electromagnetism as one of the key “engineering sciences”.” It is a pity that atmospheric studies has not been conducted by engineers who have some competency in the basic “engineering sciences” but I suppose being practical people they have looked for bigger and better rewards in industry.
    Please, Anastassia read some engineering texts, make some reference to Nusselt, Prantdl, and Reynolds numbers and make a contribution that will overturn the narrow thinking of those studying climate.

  66. Paul Linsay said

    #63, #42, #41. Just guessing here, but, presumably what happens during condensation is that a water molecule in the gas forms a chemical bond with the water molecules on the surface of the liquid water. Forming the bond releases a photon.

    Following this guess further to estimate the energy of the photon: the latent heat of vaporization/condensation of water is 2257 kJ/kg. The mass of a water molecule is 18 amu = 3e-26 kg. Hence the energy released per molecule condensing on the surface is 6.74e-20 J. The wavelength of the equivalent photon is 3 um. This is to be compared to the peak wavelength of the Plank spectrum of boiling water of 8 um.


  67. #62 Nick,

    In our work we speak of horizontal pressure gradients produced by condensation. We say that if there is a process removing gas from the atmosphere, the area where this process occurs will be characterized by low surface pressure (irrespective of whether heat is released or absorbed during such a process). More specifically, we say that this process is condensation caused by the fact that when the moist saturated air ascends, it cools. We say that the rate of condensation caused by adiabatic ascent is given by Eq. 34. From this we derive the associated pressure gradients.

    You say that Eq. 34 is wrong. Instead, the correct equation for condensation rate is (I quote you)

    S = u.( d Nv/dx – Nv/Nd d Nd/dx) + w.( d Nv/dz – Nv/Nd d Nd/dz) [1]

    You are not aware of any other equation for condensation rate that you think could be used in GCMs to account for the effects we are describing.

    Is it a correct reflection of your attitude? To be honest, I am now asking not to let you retreat by sideways afterwards, so you might wish to give it a second thought.

    What surprises me then is that having such a great equation for condensation rate as [1] above, you bother about “a logical candidate is thermal expansion – adiabatics”. Is it really needed?

  68. Anastassia,
    GCM’s don’t have or need a special equation like 34 for condensation. The equations for conservation of mass (32,33) are part of the Navier-Stokes equations which they solve in 3 dimensions. They don’t need to manipulate to cover special cases.

    Equation 34, in any of these versions, doesn’t determine the rate of condensation. It doesn’t incorporate vapor pressure information. All it does is tell you the relation between the rate of condensation and the density gradiemts.

    I don’t think it’s a “great equation”. It’s just a minor manipulation of the laws for conservation of mass of the species.

    And there’s nothing “adiabatic” about your Eq 34. If there was, it would have to include specific heats. There should indeed be an equation to cover conservation of energy, specifically thermal. That would be best treated using potential temperature.

    You still haven’t said what physical principle your Eq 34 was based on.

  69. #68 Nick,

    GCM’s don’t have or need a special equation like 34 for condensation. The equations for conservation of mass (32,33) are part of the Navier-Stokes equations which they solve in 3 dimensions. They don’t need to manipulate to cover special cases.

    This is a great point. We will remember it for the future. But right now this is just a note someone made on a blog discussing our work. The discussion in ACPD is open until 10 December 2010. I would like to see what the reviewers will have to say. If a similar opinion is expressed by a reviewer, it would be an official opinion of a respected member of the meteorological community, to be added to the historical statement that condensation cannot reduce air pressure because of warming associated with latent heat release. Then I will officially respond in ACPD (with a copy here).

    Conservation of energy, as you certainly know, is included into the set of equations that are solved in GCMs; it is accounted for in any problem in hydrodynamics. In our work we are talking about pressure gradients caused by mass non-conservation of vapor. This relates to the continuity equation (mass conservation), not to the conservation of energy equation.

    To sum up, as far as in your opinion no specific expression for condensation rate is needed to account for the effects of mass removal, there is no logic in continuing the discussion of our Eq. 34. Whatever its nature might be, this equation is useless.

    If you do not have any other points to make, I will wait for the reviewers to express their opinions and then make a return to your above statement. If, in the meantime, it occurs to you that an equation for condensation rate might be helpful, please, let me know and I will immediately resume the discussion.

  70. […] Lo que han hecho es publicar sus trabajos y ponerlos en la red, pidiendo a otros científicos que discutan el planteamiento y las fórmulas. Un ejemplo bien interesante de discusión con Makarieva está ocurriendo en The Air Vent [–>]. […]

  71. DeWitt Payne said

    Re: Brian H (Oct 17 20:38),

    Freezing water dumps heat to its environment. Condensing water vapour dumps heat to its environment.

    You have cause and effect reversed. Water freezes because heat is removed and ice melts because heat is added. Unless the system is supercooled or superheated water does not freeze nor ice melt spontaneously. The same goes for the vapor/liquid phase change.

  72. I’m one of the authors. I wanted to just jump in and say that we WELCOME feedback on clarity! We want it and we need it.

    Science works through critical scrutiny so we must welcome that. But we need to ensure misreadings and assumptions dont get in the way. We need clarity and understanding and we need to put time and effort into that. So any comments and inputs showing areas where we can improve are VERY WELCOME. So thanks Carrick and co.!!! Please keep it coming

    Best wishes

  73. Brian H said

    A distinction without a difference. The process of heat transfer is all that I was pointing out. When water freezes, its environment is warmed, etc. Supercooled or superheated water are nice demonstrations of the transport of energy involved, though. “Spontaneity” is irrelevant, unless you want to get really philosophical about causality. 😉 Is causality spontaneous? Is spontaneity caused or causal? Is causality caused by spontaneity? And so on. ;-D

  74. Brian H said

    “Just be-cause,” said Tom spontaneously. 😀

  75. Jeff Id said


    “GCM’s don’t have or need a special equation like 34 for condensation. The equations for conservation of mass (32,33) are part of the Navier-Stokes equations which they solve in 3 dimensions. They don’t need to manipulate to cover special cases.”

    I’m going to disagree with you this time, Navier-Stokes is in no way designed to handle condensation physics. The paper discusses pressure changes created by phase change (eq13) which is going to leave me considering today how that affects an otherwise continuous fluid field in NS. It’s going to be another busy day at work though so I’m not sure where the time is coming from.

  76. Jeff Id said

    In aeronautical engineering we looked at NS to cover very simple problems like 2d vortices and other things. It never occurred to me that it might be used to cover all the physics of GCM’s having never taken the time to seek out code for a GCM or look into how they are solved. The linearized viscosity terms at the cube boundry of a finite element model would be 1d. So FEA analysis and basic pressure eqtn’s should fairly simply produce the condensation associated pressure drop with this theory, it is a surprise to find that they don’t.

    I wonder if anyone has looked at the additional drag and lift created by condensation effects.

  77. As it is indicated in the article such movement is a static one, and often singles out other factors and one dimensional (horizontal)in nature. What would be interesting is when updraft and downdraft movements are incorporated (still triggered by different pressure but surface heating should be the dominant cause).

  78. DeWitt Payne said

    Re: Brian H (Oct 18 07:49),

    A distinction without a difference. The process of heat transfer is all that I was pointing out. When water freezes, its environment is warmed, etc.

    Hardly. Your statement requires a violation of the Second Law, mine doesn’t.

  79. Jeff,
    I didn’t say that the Navier-Stokes equations will handle condensation physics. Eq 34 doesn’t handle condensation physics either. All it does, whether in AM’s form or mine, is tell you the relation between rate of condensation and density gradients. In a GCM, that would come out of the Navier-Stokes solution.

    Of course a GCM would have an energy equation, in which the latent heat of condensation would appear. And there would be an actual condensation model to account for effects of nucleation etc.

    But GCM’s are based primarily on Navier-Stokes with turbulence modelling for force balance and continuity. So is almost all aero modelling.

    Here is a 15 year old example of 3D modelling which is entirely NS-based (I know that, ‘cos I wrote the code).

    I should add that continuity, as in 32,33, is for species mass balance (wv, dry air etc). The NS equations as you normally see them for a homogeneous fluid have only one continuity equation.

    Condensation effects on lift and drag are taken into account in aero calculations. Here is just one example, (again 15 y.o.).

  80. Jeff Id said

    “I didn’t say that the Navier-Stokes equations will handle condensation physics. ”

    Sorry, I misunderstood your point. Neat NS flow model. The paper only has part of the intro.

    I’m going to take a crack at eq 34 myself. On reading again, it makes physical sense to me but I haven’t reviewed your differences yet. No time to play now.

  81. Dr T G Watkins said

    Very enjoyable read. I enter the discussion with some trepidation having little proper physics or maths!
    I follow the discussion well but I’m amazed that some think that in an ‘open’ system the rise in temp from condensation can cause the pressure to rise.
    Surely, the now more energetic ‘air’ molecules will disperse increasing the volume of that particular packet (tranche) as it is not constrained thus it’s pressure will fall.
    Dewitt’s tin can example should be familiar to anyone who did ‘high school’ physics in the ’60s and Anastassia’s blood suckers are examples of pressure, volume, temp in closed containers. (My kids were always amused by a piece of paper preventing an inverted glass bottle full of water from emptying.)
    I’m probably missing something (brains) as usual.

  82. Jeff Id said


    I’m going to let people down. No time for me. Family and running a business are becoming quite time consuming.

  83. Brian H said

    #78; DeWitt;
    An environment at below freezing temps will be somewhat less below freezing after the water freezes. Do tell how this violates the Second Law!

  84. Brian H said

    Examine the heat flows through the ice-making equipment and ice surface in a skating or curling rink some time. Massive amounts of heat are drawn away from the surface to make new or re-surfaced ice. Not by violating the Second Law, atall, atall.

  85. Brian H said

    Another interesting example is the practice of citrus growers of misting their fruit in an unseasonal freeze to coat them with ice. The process of freezing the water dumps heat into the fruit and keeps it from solidifying!

  86. Jeff Id said


    DeWitt is right. Consider that in order for the heat to continue to be transferred as the freezing process continues the environment will cool. Were the environment to warm from heat release, the freezing would stop. If cooling continued to absorb the extra energy, the freezing would continue. So your argument basically boils down to slowed freezing and no increase in temp.

    Certainly your point that were the water not present the environment would be cooler is right but the point DeWitt makes is one that meteorologists have missed and that is that the bulk atmosphere cannot warm (or cool) from condensation, the ‘bulk property’ environment likewise cannot warm from freezing. Anastassia has said she will wait for what the reviewers have to say, from reading the hurricane reviews she received, I think she’s already seen the best comments.

    A derivation/explanation of 34 would be helpful but not having time myself to explore more tonight, the equation makes basic physical sense when I read it. Term by term it’s hard to argue with. I’ve not studied Nick’s results though and have spent less than 5 minutes in blogland tonight.

    Nick deserves more than that from me.

  87. Brian H said

    The water loses “latent heat” when it freezes. Thatt warms the environment, since there is nowhere else for it to go.

    From the 2008 Columbia Encyclopedia:
    “The latent heat of fusion for ice is 80 calories per gram. This amount of heat is absorbed by each gram of ice in melting or is given up by each gram of water in freezing.”

  88. Brian H said

    “Consider that in order for the heat to continue to be transferred as the freezing process continues the environment will cool. Were the environment to warm from heat release, the freezing would stop. If cooling continued to absorb the extra energy, the freezing would continue.”
    Come again? That first sentence makes no sense. Heat

    from the freezing water warms the environment. Period. If the environment temp is very close to greezing, the freezing may only be partial (Slushy or soft ice, etc. The bane of backyard skating rink makers everywhere.)

    I think Anastassia is right. The “bulk atmosphere” term is bogus; we are not talking about changing the entire planet simultaneously, just the local, in-contact atmosphere, and it certainly can swing widely in temperature due to phase-change effects.

  89. Brian H said

    P.S. Cloud phase-change warming is made even more drastic by the fact that in most cases during precipitation water vapor ‘de-sublimates’ directly onto ice crystals, providing a twofer. YCLIU

  90. Brian H said

    Sorry about the typos. Something is putting a 3-10 second lag into my keyboard.

  91. #86 On the contrary, Jeff, I am permanently interested in what is being said. Perhaps the most interesting comments are still to come. Moreover, it would be a great pleasure for me to discuss in detail the physics of Eq. 34. Still I wanted first to emphasize, using Nick’s comments, how critical it is to have a special equation for condensation. Here I can see some evolution.

    At #68 Nick says

    GCM’s don’t have or need a special equation like 34 for condensation.

    but at #79 it becomes

    And there would be an actual condensation model to account for effects of nucleation etc.


    But GCM’s are based primarily on Navier-Stokes with turbulence modelling for force balance and continuity.

    I do not want to lose the bigger picture. Suppose we have a standard closed set of equations to describe a non-condensable gas: the NS equations, the continuity (mass conservation) equation, the conservation of energy equation and the equation of state (ideal gas). The number of equations is such that they are sufficient to determine the dependence of velocity, pressure and density on spatial coordinates.

    Now let us make the following observation. The standard continuity (conservation of mass) equation has zero (0) in the right-hand part like Eq. 32. Zero is a constant.

    OK, we have described our non-condensable gas. Now suppose that the gas is condensable. This means that, instead of zero, we now have “S” (condensation rate) in the right-hand part of the continuity equation. S is not a constant. We have got a new variable. Thus, we are in need of a new equation. This equation must specify the process which causes the non-conservation of the gas.

    Without such a new equation that reflects that process (condensation, evaporation, annihilation etc.) we can no longer solve the problem.

    Remember that each of the initial equations is based on fundamental physical laws. “A model” will not suffice for S when the basic physics is discussed. We must base our specification of S on some solid physics.

    Another important point that we cannot derive this equation for S from the initial ones.

    This is just to illustrate the point that one cannot nod to GCMs as having “everything included” having no idea about what the extra equation for S should look like.

  92. Anastassia,
    A couple of misconceptions there. A proper conservation of species mass, or continuity equation will always include sources. It relates the mass being created in a region with the mass being convected out of it. Sometimes a diffusion term will be included too.

    GCM’s don’t have or need a special equation like 34 for condensation. Eq 34 relates the source to the density gradients; in a GCM that is done by the species mass equations. Of course, the actual source S needs to be defined by some equation taking account of temperature, vapor pressure curves, nucleation etc. Eq 34 is not such an equation.

    Before being sure about what is or isn’t in a GCM, you should look to see. CCSM3 is one that is well documented. Check out Sec 4.2 and Sec 4.3 to see if you think the treatment of water vapor is inadequate. 4.4 and 4.5 are useful too.

  93. #92 Nick,

    Of course, the actual source S needs to be defined by some equation taking account of temperature, vapor pressure curves, nucleation etc.

    Good. I am glad you do not think that it can be derived from NS.

    Eq 34 is not such an equation.

    So far you have not presented any arguments to support this conclusion. You are welcome to do so.

    Before being sure about what is or isn’t in a GCM, you should look to see.

    GCMs do not spring from nowhere, Nick. Normally they should be based on science that has been discussed in the literature. So if we are talking of basic principles, they should not be sought for in a GCM, but in the relevant literature.

    But regarding the model, I did have a look. With one exception, there does not seem to be any essential physics there pertinent to condensation dynamics that we have not discussed in our paper. First of all, see Section 4.2 to note that in this GCM the rainfall is parameterized using a one-dimenisonal vertical scheme. This is what we are talking about all the way: condensation rate caused by adiabatic ascent depends on vertical movement (i.e., movement along the temperature gradient in our horizontally isothermal case) only.

    In particular, pay attention to Eq. (4.89), where the rate of liquid water generation is described. This rate is proportional to the vertical flux of matter multiplied by a function of the vertical change of vapor mixing ratio q. If you compare this to Eq. (34), this may give you a hint on the underlying physics of the latter, note especially the symbol $\latex \gamma $ in Eq. 34.

    Second, I have repeatedly pointed out (and this is discussed in the paper) that the magnitude of horizontal pressure gradients associated with condensation are very sensitive to small terms of the order of Nv/N ~ q ~ gamma. Because if Nv = 0, they obviously disappear. For example, replacing N for Nd in Eq. 34 corresponds to a radical change in the processes that are described. Instead you are talking of a numerical parameterization of rainfall that has several external input parameters. In other words, this model could be tuned to be 95% accurate in describing the rainfall rate, but would err 100% in predicting the associated horizontal pressure gradients.

    No theoretical derivation can be made using such a parameterization. You must get all the essential physics in beforehand. This is done in our Eq. 34 and discussed in detail in Section 4.2.

  94. “So far you have not presented any arguments to support this conclusion. You are welcome to do so.”
    Let me say it again, with expansion. Eq 34 is not an equation that takes account of temperature, wvapor pressure curves, nucleation etc. Nothing about those properties is there. Instead it just relates S to density gradients, which is just what a mass conservation or continuity equation does.
    Conversely, CAM’s eq 4.89 says nothing about the gradient of anything, but does, as expanded by 4.90,4.91 etc tell you about the effect of humidity, latent heat etc.

    This is where the Navier-Stokes equations come in. You don’t need anything special to convert condensation-induced vertical updrafts etc into horizontal pressure gradients and motion. The mass continuity equation in the N-S equations ensures that that happens.

  95. #94 Nick,

    Eq 34 is not an equation that takes account of temperature, wvapor pressure curves, nucleation etc.

    This is incorrect. Please, read the paper to find out how \gamma depends on z.

    Conversely, CAM’s eq 4.89 says nothing about the gradient of anything, but does, as expanded by 4.90,4.91 etc tell you about the effect of humidity, latent heat etc.

    This is incorrect. If you understand the physical content of Eq. 4.89, I would be interested in your reading. In reality Eq. 4.89 describes the vertical change in vapor mixing ratio q associated with condensation. It is the basic equation for all the parameterization there. Remove that equation, and you will have nothing.

    I would also like to mention the expression “nucleation etc.” Before turning to etc., it is necessary to figure out the main process. The main process is that when moist saturated air rises, it cools. Eq. 4.89 namely attempts to describe this.

    The nucleation processes are microphysical processes that influence such large-scale parameters as the absolute value of saturated concentration of vapor and for the large-scale circulation can be taken into account by specifying the value of the latter.

    This is where the Navier-Stokes equations come in. You don’t need anything special to convert condensation-induced vertical updrafts etc into horizontal pressure gradients and motion. The mass continuity equation in the N-S equations ensures that that happens.

    I repeat: in order that the horizontal pressure gradients caused by condensation were reproduced by a GCM, you must have a physically sound value of condensation rate (or rainfall rate).

    As I explained in #91, as soon as we have not a zero, but a variable (S) in the right hand side of the continuity equation, we must have a basic physical equation for S relating it to some of those variables and functions that we already have (velocity, pressure, density, coordinates, temperature). If we do not have such an equation, we cannot solve the problem.

    So far you have not been able to point me to such an equation for S in a GCM. You believe it is somewhere there. Yes, it is there. I tell you that it is Eq. 4.89 and I explained why it did not help.

  96. #94 Nick

    Instead it just relates S to density gradients, which is just what a mass conservation or continuity equation does.

    Equation z(x,y) = x+y relates z to x and y. Equation z(x,y) = x^2 + y^2 also relates z to x and y, but in a different way. For this reason, these equations can be combined to gather some meaningful information about the relationship between x and y. This is how things work.

  97. Russ said

    Hey Brian H, Doesn’t Nick Stokes sound allot like cmb?

  98. Russ said

    And Jeff Id, Be carefull Of DeWitt Payne, he is a twisty charector and as smart as he appears, sooner or later it will catch up with him, and I have already caught him doing that here!

  99. Anastassia,
    Eq 34 simply relates S to density gradients. It’s plain as can be, on the page. You may be able to later introduce new physics to combine with the equation, but that is what it says.

    Conversely, Eq 4.89 contains no gradients. There are no derivatives.

    There’s no point in keeping going around in circles. You need to produce that derivation of your eq 34.

  100. #99 Nick,

    A hint: the fact that there are no formal sign of derivatives in Eq. 4.89 does not mean that they are not there. Remember we are talking about discrete parameterization with several horizontal layers. Just think physics, not algebra.

    You claim to have a knowledge of GCMs: I tell you that if you understand where Eq. 4.89 comes from (and share this knowledge with us), you should be able to understand Eq. 34. If you do not understand where Eq. 4.89 comes from, you cannot claim that the GCM has every effect of condensation included or that you understand how it works.

    I do not know who is keeping around in circles here.

  101. Jeff Id said

    Anastasia and Nick, I have to thank you both. This past hour has been my first experience reading a climate model and it is very exciting what has been pointed out. The model does not appear to incorporate condensation pressure loss. Mass in = mass out yes, but pressure isn’t recalculated for condensation.

    Nick’s point that the horizontal pressure gradient is created throuh NS is perfectly fine but Anastassia’s point that without the proper pressure drop, you get the wrong answer is also true.

    Wow, unless someone can show us where the proper calculations are done this is a huge deal for climate science.

  102. #101 Jeff,

    unless someone can show us where the proper calculations are done

    There, there! Just show us a nice theoretical paper in the meteorological mainstream where the basic physics underlying condensation rate S were discussed before being included into a GCM and an equation for S proposed. Currently, from the literature review we’ve done (see the paper), condensation rate is at best just taken from the black box of model parameterizations (like the one Nick referred to) and then put into NS equations to produce nearly nothing. But there are even worse cases… pertaining textbooks… I believe I will have time to tell about them.

  103. Jeff Id said

    Anastassia, I’m moving this to the top again for a bit and since it is 5 am here now and I’m totally wound up, it looks like I’ll have some time.

  104. Russ said

    Jeff Id, Thats the problem here, It’s a climate model, they try to mimic real life, but it is their best understanding of how things work! It should never be trusted as it don’t work, because there are too many unknowns. Computer modles work when there are knowns to work with, and that is the extent of it. But they flont it as if it is what will happen in weather to being the climate they forsee as doom! Yet it never happens, Why is that? That is a question to ask here?????

  105. Russ said

    It’s quite here all of a sudden?

  106. Jeff,
    That’s my point about the N-S equations; they take care of that. It goes like this:
    mass loss goes into the mass conservation equation, and forces a change in div(v) – basically a converging flow.
    That affects the coupled momentum equation, of which the relevant terms are ρ Dv/Dt = -∇P
    P=pressure. Taking divergence of both sides (there’s a minor issue doing this through D/Dt, but we’ll do it for now):
    ∇^2 P = – ρ D div(v)/Dt
    That’s the Pressure Poisson Equation that comes out of the N-S eqns, and is a common computational device. The converging flow, forced through the mass continuity equation, acts as a source (negative here) in the pressure equation. You don’t need a special pressure treatment.

    That’s basically why fluids flow the way they do – take some out, and fluid fills the gap. It’s all in the N-S equations, which are all about the interaction of pressure and velocity.

  107. Russ said

    And when that doesn’t work out in the real world, What then Nick?

  108. Russ said

    What excuse will it be?

  109. Jeff Id said


    I don’t see where the delta P from condensation is calculated. It looks to be parametrized out of the physics. The mass equations on the page you linked, don’t take into accout any gas volume loss due to condensation that I can see.

    We are talking about eq 13 in this case not 34

  110. Jeff Id said

    Russ, It’s good to be skeptical but it is better to follow the reasons.

  111. Russ, the planes you fly in are designed by people who calculate using Navier-Stokes equations. Better hope it works!

  112. Russ said

    It is better to follow the reasons is why we are here in the first place.
    there are engineers out ther that use computer modles effictively, and then there are pretenders, and they are educated people that twist the numbers to suit their needs. Hows that for putting this bluntly, or in laymans terms if you do not want to.

  113. Russ said

    And Nick Stokes, as I said earlier, if you weren’t paying attention. Computer modles work when there are knowns to work with, and that is the extent of it. So what part of that you didn’t understand from the rest in #104?

  114. Jeff Id said

    Russ, I sent you an email but got an error.

  115. Russ said

    What was in that email you sent?

  116. Jeff Id said

    you have mine send me yours

    jeffid1 at gmail dot com

  117. Re #106
    I should have included the gravity term among the relevant terms for the N-S momentum eq:
    ρ (g+Dv/Dt) = -∇P
    It’s complicated in Chap 4 of the CAM3 text, because they use potential temperature (a good idea), and it’s mixed up with the discretisation. They have also done a spectral transformation. Chap 3 may be easier.
    In short, I haven’t located yet where the condensation volume deficit is passed into the N-S mass equation. But I’m sure it is there.

    Unfortunately, I’m at the other end of the day – it’s now 11 pm here. Hopefully you’ll all have it figured by the morning 🙂

  118. Jeff Id said

    In short, I haven’t located yet where the condensation volume deficit is passed into the N-S mass equation. But I’m sure it is there.”

    I’m fairly certain it is not. If you look at the methods in general, they have skipped it.


  119. Russ said

    [snip – first one in almost a year]

  120. Jeff Id said

    Russ, your email isn’t working, send me one plz.

  121. kim said

    The pony is in there.
    I know it has to be there.
    Now I’ll dream it up.

  122. Russ said

    Exactly, Kim!

    And “snip – first one in almost a year”, Jeff that is actually the Forth One now, as you deleted the other Three snips of my post and left the Forth one.

  123. Jeff Id said

    I’m trying to help you out but you won’t email. Feel free to re-post anything you like on the open thread. You are on to something which looks bigger than climategate and commenting like it is something fun. If you want me to summarize all the technical commentary you left for our readers.

    Russ thinks models stink!

    there you go.

    You’re welcome!

  124. Carrick said

    This contains a description of how you treat condensation in fluid mechanics.

    It’s certainly not part of the Navier-Stokes equation, though of course it can be treated correctly within the framework of fluid mechanics.

    See Eq. (2) for how it’s treated in the continuity equation.

  125. Jeff Id said


    I see condensation but no pressure calcs.

  126. Jeff Id said

    Nope I’m wrong, it is in there.

  127. […] Comments Steve Fitzpatrick on Denying the CatastropheJeff Id on Where do winds come from?Steve Fitzpatrick on Denying the CatastropheCarrick on Denying the Catastrophekim on […]

  128. Carrick said

    Jeff ID, my interest is in the infrasound generated by meteorological phenomena. I would have been seriously bummed out if he didn’t compute the pressure generated by it!

    here’s a book on storm and cloud dynamics. It’s a bit dated, but Chapter 2 is online, which includes a detailed discussion of the thermodynamics.

  129. #77 Daniel,

    I apparently overlooked your concise comment, but fortunately Douglas alerted us to it. Welcome to the discussion!

    I am sorry I must be off-line for the next 12-16 hours, but as a quick response — we DO consider vertical motion! In particular, the resulting formula for horizontal pressure gradient, Eq. 27, is directly proportional to vertical velocity. I hope to be able to be more detailed tomorrow.

    As we have never communicated before, let me use this opportunity to thank you for the effort you and Douglas undertook to generate discussion of forest-driven winds! Whatever it ultimately leads to, I am certain the science will benefit.

  130. Re #129, should be Eq. 37, not Eq. 27.

  131. RuhRoh said

    @72 a minor point of potential disambiguation;

    At line 3,4 of page 24025, I’m confused about the reference to “the warmer column” and “the colder column”. Are these implicitly the moist and dry columns of the prior paragraph?

    Also, does a column of moist air ‘weigh’ more than a column of dry air?
    I realize that these are elementary issues compared to the weighty matter of the exsanguination of the GCM numerology, but it is where I got stuck before falling asleep last night.
    I guess anyone who can potentially actually make it through sections 3 and 4 would not be confused by the material in section 2, but, on the other hand, apparently a lot of practicing atmospherists are indeed also confused about the concepts in section 2. So, I am only pointing out a place where some readers will fall off the intended path.

    I was once a smart feller, but now I just know to roll down the windows whenever I hear rumbling…

    I did have the great privilege of a few (trivial) interactions with RP Feynman.
    I think he would greatly enjoy the interchanges happening here.
    Listen again to his ‘Los Alamos from Below’ talk at UCSB (as I recall), particularly the section about how the Niehls Bohr’s son recruited RPF for a private thrashing-out-the-BS section before going public.

    Excellent work by you all.

  132. RuhRoh said

    What the heck is a ‘dry adiabatic lapse rate adjustment’ (section 4.6)?
    And why do they have to ‘adjust the temperature’ and average the humidity ?
    Is this a situation where their faulty implementation of the physics leads to unphysical model predictions, and thus they have to explicitly ‘plaster over’ the cracks?

    Does the word ‘moist’ in this context mean ‘saturated’ 100% RH air?

    I thought that ‘enthalpy’ of air went up with more included water vapor, but I haven’t used ‘enthalpy’ in a sentence for several decades…

  133. Charlie A said

    @Anastassia Makarieva — I’m barely able to follow the details of this discussion, but one thing that is striking is your evasiveness on the source/derivation of equation 34 (condensation rate).

    Could you review that a bit.


    You and Nick Stokes seem to be going in circles, not quite understanding each other’s point. I’m pretty sure that spending the time it takes to understand precisely his points would be worth your while.

    Even if he is wrong, his particular view and set of misunderstandings are likely to be common among climate modelers.

  134. Jeff Id said

    I figured it out last night Charlie. The equation is very simple form, my partial derrivatives will be lower case d. There is no derrivation provided because the equation is basically derived from simple mass flow.

    S = w d Nv/dz – w Nv/N dN/dz

    N’s are all molar density or the molecules/volume. Nv is vapor N is vapor plus dry Nd. The second term (after the plus) is w(vertcial velocity) times the Nv/N ratio times the change in density per vertical distance dN/dz. This means that the ratio Nv/N isn’t changing in this term. IOW this is the part which stays in vapor form even though density decreases with an updraft. The first term simply is the rate that vapor is lost to dNv/dz condensation in an updraft times velocity w. Add em together and thatssit, no big thing required, although it wasn’t immediately obvious to me.

  135. Jeff Id said

    S represents the vapor lost to condensation. We can ignore any horizontal u or v direction velocity because the assumption is that the ground layer is fully saturated so dNv/du =0.

  136. #133 Charlie,

    Let us look in greater detail on where Eq. 34 is derived and what its physics is. We will do it in the context of my comment #91. There I said that if we have a gas which mass either disappears or is produced, we must specify the rate of this process to solve the problem. We must do so without introducing new variables — because each new variable introduced to a closed set of equations will demand one more equation etc. So, we have to express condensation rate in terms of density, velocity, temperature and/or spatial coordinates.

    What such an equation for non-conservation could look like? It could take any form. As I said above at #47, we could place small demons in the atmosphere who would be eating vapor molecules as they pass by. Then Eq. 34 would be reflecting the rate at which the demons do so. This is to emphasize that Eq. 34, logically, does not have ANY relation to the continuity equation. It is a specific equation describing a specific process.

    The process we are considering here is condensation. We want to keep the picture simple: we have a horizontally isothermal surface where, in the absence of condensation, there would be no pressure gradients altogether. We can imagine that the air circulates at vanishingly small vertical w and horizontal u velocities.

    Why should condensation occur at all? We know that it occurs because the air ascends (and cools). This is a fundamental process: when the air ascends in the gravitational field, it cools and, if it is saturated, vapor condenses.

    The air does not condense because of being replaced along a horizontal surface at velocity u. There is no such law. The air does not condense because it accelerates — there is no such law. So, re: Jeff’s #135, we do not ignore the horizontal u,v components of velocity and/or velocity gradients: they just have nothing to do with the condensation process. While the vertical velocity is key.

    So far we have concluded that S is proportional to w. Next we know the following. All the non-condensable gases (oxygen, nitrogen) have a scale height of around 8 km (that is, their pressure falls e-times at 8 km above the sea level), water vapor is strikingly different. It has a scale height of around 2 km. As we wrote extensively in our previous works, this is because air at a certain height becomes too cold to contain the surface amount of moisture, such that the excessive moisture condenses.

    We thus feel that the vertical gradient dNv/dz < 0 of vapor density should carry the information about how much vapor has condensed in a small volume of height dz. Had it not been for the gravitational expansion, we could stop here and write S = wdNv/dz, meaning that the decrease of vapor density along the direction of decreasing temperature reflects its mass removal by condensation.

    However, we feel that there is a complication. Indeed, density of other gases decreases with height as well, but they do not condense. Their density decreases due to the gravitational expansion, a process that has a control over vapor as well. We thus need to substract the effect of gravitational expansion (which has nothing to do with condensation) from the overall vertical change of vapor density.

    We need some reference. Suppose we had a pure vapor atmosphere — what would be substract then from dNv/dz? We would substract the equilibrium density gradient calculated for a non-condensable gas of the same mass. The scale height for such a gas is denoted by low index n in Fig. 1a in the paper. That is, we would imagine an atmosphere in hydrostatic equilibrium composed of the same gas but if it were non-condensable, calculated its density gradient (dNv/dz)n and had S = w[dNv/dz – (dNv/dz)n].

    But in the real atmosphere we do have another reference. We know (and presume) that moist air as a whole is very close to hydrostatic equilibrium. That is, it behaves as if no condensation took place, with an excess of dry air replacing shortage of vapor caused by condensation. Therefore, dN/dz at any height gives us information how the density of gases would decrease in the absence of condensation. We thus take the water vapor share of this effect, (Nv/N)dN/dz, and finally obtain Eq. 34:

    S = w[dNv/dz – (Nv/N)dN/dz]

    This equation contains the important information about hydrostatic equilibrium, as discussed in Section 4.2. Namely this fact is the cause of the horizontal pressure gradient that we arrive at in Eq. 37: some part of dry air has gone upwards from the surface to compensate for the shortage of condensation-affected vapor aloft. If we keep dry air indifferent to what is going on with vapor, then it will be Nd, not N, that should be used as a reference, such that the modified equation would be Sd = w[dNv/dz – (Nv/Nd)dNd/dz]. It is easy to see that in this case dp/dx is obviously zero.

    That is, just replace N Nd = N - N_v \approx N and the horizontal gradient disappears. I repeat that my reading of the meteorological literature is such that people operate freely and without giving much thought replacing N by Nd, as they think that N_v/N << 1 and Nv can be neglected. True, it can be neglected somewhere (see Section 4.3), but here it is key.

    To find a numerical answer to the problem, we need to know dNv/dz. This is done by standard procedure considering the moist adiabatic equation together with hydrostatic equilibrium. Details of these calculations are given in Section 3.2.

  137. curryja said

    Wow, what a great discussion. I am a fan of Anastassia’s work, I look forward to digging into this paper in detail.

  138. Brian H said

    Judith! Welcome in!

    Anastassia; just an English spelling note: “substract” is not a word; use “subtract”. 😉

  139. Note that the discussion continues in Jeff’s post here:

  140. Note that the discussion continues in Jeff’s post here:

  141. #138

    Thank you, Brian! I very much appreciate language corrections, learning all the time.

  142. #134
    Jeff, I missed this earlier. You’ve given a cons mass argument, which makes it pretty much what I got in #46. The thing is, you already have cons mass in 32,33, so it is not an extra principle. It just ignores the horiz derivatives.

    But you can’t have 32,33 and 34 together. It’s double counting in terms of principles. What that means is that you can eliminate S between them and get a relation between densities and their gradients, which is pretty much that the horiz terms are zero. But that’s spurious – generally they aren’t.

  143. #142 Nick,

    1) Eq. 34 cannot be derived from Eqs. 32 and 33. In #46 you attempted to do so by putting u = 0 and Nv = 0 (Nd = N), none of which is true.

    2) Horizontal derivatives cannot be ignored in the continuity equations 32, 33 and they are not.

    3) Horizontal derivatives do not enter the expression for adiabatic condensation caused by the ascent of moist saturated air, for physical reasons explained in #136. This fact is taken into account in model parameterizations of condensation as well, see, e.g., Eq. 4.89 in CAM3. Here mc is the vertical matter flux. If you know of an equation for condensation rate that would carry horizontal components, I would be interested to see it.

  144. 143
    Jeff’s argument is based on conservation of mass. You still won’t say what your argument is based on.

    My expression for S was derived by simple algebra from 32,33. If your 34 is also true, then the two expressions for S can be equated. If you do that, you’ll find that the horizontal derivatives are very small.

    You’re right, they can’t be. Contradiction. 34 is neither independent nor correct.

  145. #144 Nick,

    You say that “My expression for S was derived by simple algebra from 32,33.”

    This is incorrect. Your expression was derived not by simple algebra, but by making unrealistic assumptions, namely Nv=0 and u = 0, so it just has no physical sense. Thus, equating our expression for S with yours is meaningless and no conclusion can be driven from this regarding the magnitude of horizontal gradients. Here I mean your derivation of S in #46,

    Your attempt to conclude that horizontal gradients are small in #48 contain a mathematical error, which I describe at #54.

    I did say all we have to say concerning the physics of Eq. 34, both in the paper and in #136 above, where I also dwelt on the issue of why it does not carry horizontal components. Simply because moving an air parcel in an isothermal horizontal plane does not lead to condensation. In my view, this is as clear as it could be.

    From your side, you have not so far given any reference to a competing equation for determining condensation rate in a GCM or described how it could be derived. Even a basic physical consideration would be valuable.

  146. Brian H said

    From the “Tips” page, a ref to an article about another way in which plants control the atmosphere: Winds!

    More biomass = slower surface winds.

  147. #146 Brian,

    Thank you for posting this question. I know of this paper.

    Indeed, on a windy day there is more wind on bare land than inside a forest. So if you have your house on a bare field, then plant some apple trees and keep record of surface wind in your garden, I promise you will see a slow-down as the trees grow.

    In our work on biotic pump we are talking of continental scale wind patterns. It is calm under the forest canopy, but moist winds are blowing above it. Remove forests, and wind will blow in a different direction. Besids providing land with moisture, a key function of forest cover consists in stabilizing the air flow. There are no hurricanes above the Amazon.

    So of interest would be a record of wind pattern fluctuations, i.e. if there is a net change in directions of winds over time and net change in the frequency of winds of various intensity. Of course measurements should not be made on the surface, but above the characteristic roughness scale.

  148. tallbloke said

    “it was in the end of the 17th century (see Halley 1686) that a physical driver of winds was proposed. That time it was differential heating (the statement that the warm air rises being lighter than cold air). It formed the basis of a consensus regarding the causes of atmospheric motion, a consensus that is now over three hundred years old.”

    Shows how long memes can hang around for in our scientific institutions. let’s hope co2 driven climate theory doesn’t last that long!

  149. Brian H said

    Re: tallbloke (Oct 28 06:39),
    And sometimes the old and discredited is new again! Leeches are great for draining swellings and bruises, etc. And the right kind of maggots do a very neat job of clearing dead tissue and bacteria from gangrene etc.

  150. E O'Connor said


    Re your comment on fire cupping. This brought back memories of my father and grandfather. They were ‘Donauschwabens’ from Banat, now divided between Hungary, Serbia and Romania. Both were barbers and provided the service of making incisions and cupping on the upper back to relieve high blood pressure.

  151. BlueIce2HotSea said

    Mark T

    The ongoing discussion that Jeff has initiated here with Anastassia Makarieva was preceeded by about one year in dialogs between Curry and Makarieva.

    Her reaction could have been, “This is preposterous. The temperature-differential paradigm for wind generation in hurricanes has been replaced with condensation… crackpot outsiders!”

    But instead she tried to find a reason other than prejudice to reject the research and was drawn in. She gets high marks from me for curiosity and civility. I like that in a scientist.

    And now that my defense of Dr. Curry has become borderline pathological, I had probably better back off for awhile. You may have the last word.


  152. BlueIce2HotSea said

    Oops. Meant to post here:

  153. Gary P said

    I was thinking about this post while admiring one of the weather maps from the recent record low pressure storm that blew across N. America. I suspect the one place where the loss of volume due to condensation is going to have the most effect is in the large cyclonic systems that blow across the mid-latitudes. The time scale for these are in days and across 500-1000 km. The latent heat of condensation will be quickly be lost to space due to the rapid vertical motion in the condensing storms. The time scale for this is hours. Thus the arguments about the air expanding due to the latent heat fail on the time scale of the large cyclones. The low pressure zones have to be intensified by the condensation that continues until they run low on water vapor.

  154. anna v said

    I came to the thread to get the link for the comments at ACPD , and cannot resist the following answer to the question:”where do winds come from”

    When I and my siblings were very young we lived in a house that had a huge eucalyptus tree next to the stone wall separating our house from the neighbor. One day my father started discussing cutting down the tree because it might bring down the stone wall.
    “And how will the winds blow if you cut the tree” piped up my little brother !
    The tree made enormous noise in strong wind, and like many people, cause and effect were confused in his three year old brain.

  155. Doug Proctor said

    Heck, I’d like to know where the COLD WEATHER comes from. In the US, they say it comes from Canada. In southern Canada, we say it comes from the Arctic. In the Arctic it is sometimes warmer than in southern Alberta, and then gets really, really, really, cold. But there is nowhere left to go for colder air masses than down south …

    Back in the ’70s we used to say that everything, ultimately, came from American supermarkets. Perhaps cold weather, ultimately, comes these days from Walmart freezers …

  156. […] Discussion of our propositions secured over a thousand comments in the blogosphere within four weeks of publication indicating wide interest. Among the ACPD discussion participants two are active bloggers. Does blog culture outcompete formal peer review in evaluating novel concepts? It’s an open question. But let’s take a moment to focus on science. […]

  157. Some of the readers may still be interested the fate of our draft paper “Where do winds come from?” and our condensation theory as originally highlighted on The Air Vent here. A second referee was appointed –- many thanks to all of those that helped with that. Now we wait for their judgements. In the meantime, several substantive comments and replies have been posted. We believe that responding to these comments has clarified our presentation and helped identify and address some misunderstandings. Again we are grateful to all those who have contributed. The open discussion was extended until at least April 7th, 2011 (from the original deadline of December 10th, 2010).

    We are glad to be part of this new way of assessing and refining science and invite you to join! We welcome comments, criticisms and suggestions. How can we be more convincing? (Additional developments on this topic can also be found here.)

  158. […] Where do winds come from? […]

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: