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Earth's air conditioner

  1. Oct 11, 2009 #1
    In some threads in the past I hinted vaguely that one feedback mechanism in climate is not really mentioned extensively, that's the latent heat energy transport, from evaporation at the Earth surface to condensation in the higher levels, forming clouds and altering the dynamic radiation balance, especially as feedback on changing radiation and heat budget, for instance with changing concentrations of radiative gasses. (or more bluntly global warming).

    The only thing I encounter is the assumption that relative humidity remains more or less constant as the earth warms due to the increase of greenhouse gasses, causing a dominant positive feedback effect of more greenhouse effect of the extra water vapor.

    But the main question here is, as asked several times before, how much energy is required to evaporate that excess water to keep relative humidity constant under constant temperatures? And indirectly, how does that relate to the increased energy available due to increased greenhouse effect?

    It has been suggested that in a closed box construction that would not need to be much, however the atmosphere is full of conveyor belts (convection, advection), transporting energy (heat and latent energy) from the Earth surface to higher levels, (as said) changing the radiation balance.

    So let's try some numbers to quantify this. Of course, there is no way to model this and come up with three digits behind the decimal, but we could do some back of the envellope calculations to get an idea of the order of magnitude. This would give an idea if it can be ignored in the modelling of the atmosphere (as seems to be the case right now, if I have understood it correctly) or if it's a factor of importance of the feedbacks in total.

    So how much evaporation is going on in the first place?

    That will be in the next post
    Last edited: Oct 11, 2009
  2. jcsd
  3. Oct 11, 2009 #2
    http://www.britannica.com/EBchecked/topic-art/121560/46275/Global-distribution-of-mean-annual-evaporation [Broken]:


    According to the caption that's in centimeters per year. Obviously the order of magnitude of the evaporation is about one meter per year, which we could use as a tentative working unit. How does this translate to watt/m2, the usual unit for the radiation energy?
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  4. Oct 11, 2009 #3
    One meter of water per square meter per year is obviously 1,000,000 ml per 31,536,000 seconds or 0,032 ml/sec.

    The latent heat (Lc), or energy needed to evaporate one gram (is one ml) of water is about 2500 joules =(watt/sec).

    So the evaporation energy of one meter water per year is 2500*0.032 = 80 w/m2. Not a value to neglect and nobody does that but it would be interesting to see what the delta evaporation would have to be if the temperature increases 1 or 2 or 4 degrees or something like that, to maintain the assumed constant relative humidity.
    Last edited: Oct 11, 2009
  5. Oct 11, 2009 #4


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    Andre, you've had an answer already several times to that question, or to that claim.

    A large part of the heat transport in the troposphere is due to convection, and a part of the "convected" heat is in the form of latent heat of evaporation. There is no need to increase any "heat input" to have a higher absolute humidity. With the same amount or even less evaporation, you can, in principle, also have a higher absolute humidity if at the same time, the velocity of convection diminishes - which is entirely possible, as it will compensate exactly to get the lapse rate right.

    There is a difference between the DENSITY of something, and the FLUX of something. You can have a higher density of something, while at the same time having a smaller flux, if the velocity of convection diminishes.

    If the absolute humidity of the air is larger, that means that the heat transport of convection is more efficient (at least, between the point of evaporation, and the point of condensation and precipitation where the heat is again released). As such, the upward velocity will be lower.

    The total amount of heat transported will always be the same, and this flux will be distributed over radiative transport, some conduction, and convection (containing "heat capacity" and containing "latent heat"), in such a way that the lapse rate will be respected. This can be done with just any amount of humidity in the air. Convection will adapt to it.
  6. Oct 11, 2009 #5
    I wasn't ready yet, but I can't recall to have seen quantitative answers to my question, which is what we are looking for in this thread. And of course those aren't answers but merely confines of orders of magnitudes. So what the rate of convection does, is certainly decisive.

    But it would be hard to argue that when the surface temperature increases that convection rates are not affected likewise.
  7. Oct 11, 2009 #6
    So with the evaporation rates we were looking at absolute values water evaporating.

    Climatology talks about relative humidity assumed being constant in the climate sensitivity modelling. Therefore the next step would be to investigate how absolute humidity and relative humidity behave under different temperatures.

    Not comparing anything yet, no apples and oranges, just looking at the incremental changes in absolute humitidy per degree of temperature rise.

    Using the http://www.humidity-calculator.com/index.php [Broken] I used these settings:


    using 50% RH in the "FROM" cell and 70% respectively for the two series, setting the "gas temperature" in the center from 15-20 degrees and noting the absolute humidity output in the "TO" cell in g/m3.

    This is the result:


    This shows that for every degree temperature increase, there must be some 6% more water vapor per unit of volume to maintain relative humidity, in usual climate temperature ranges.
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  8. Oct 11, 2009 #7


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    Yes, Andre, the "absolute humidity" is the partial pressure of water vapor. There is a well-known relationship between the partial pressure of water vapor in equilibrium with water at a given temperature: the Clausius-Clapeyron equation. (see http://en.wikipedia.org/wiki/Vapor_pressure for a short description). It is in fact the pressure of water vapor in an otherwise empty closed bottle in which there is also liquid water.
    This partial pressure is totally independent of the other gas components in fact (as long as we can consider them as ideal gas). In the atmosphere, the *relative* humidity is the ratio of the actual partial pressure of H2O wrt the equilibrium partial pressure one would have in equilibrium with water at the same pressure. It is rarely more than 100%, because if you have more than 100%, the thermodynamic equilibrium would want part of this vapor to condense into water, which is exactly what you have with precipitation. In order to have more than 100% humidity, you need to have a metastable state.

    It is also difficult to have much less than 100% if there is water everywhere, like for instance when it is raining because there's enough possibility for evaporation.

    To have a lower relative humidity than 100% means that you had "equilibrium" vapor, and then you heated it without having warmer water in the neighbourhood, or you mixed it with dryer air.

    Having warmer water will automatically give rise to higher partial pressures of water vapor just above the water surface. After that, it will depend what will happen to that "saturated" air: how it will change temperature, how it will mix with dryer air and so on.

    In principle, if you have a higher water temperature, you will have a higher partial pressure.

    The error in your idea that you need much more power to evaporate all that water lies in your tacit assumption that convection will "pump the same or harder". There's no reason for that, on the contrary. Convection wants to restore the lapse rate, and if the "carrier" has more heat in it, it can do so with less "effort".
    (that said, the fact itself that humidity is different can change, by itself, also the lapse rate, complicating the issue - and going indeed in the sense of a smaller temperature difference, but normally that's already taken into account).
  9. Oct 11, 2009 #8
    But that's not what Lindzen et al 2009 find.
  10. Oct 11, 2009 #9
    Now let's have yet another look at the hadley cell cross section from north to south as depicted in principle here:


    This is a big conveyer belt comprising from 30N to 30 about half of the earth surface and getting about 60% of the solar radiation when looking at the basic black body model.

    The circulation cell picks up moisture at leg#4 in the tradewinds when moving to the equator. The convection takes place at leg#1, where the air expands, cools adiabatically and loses much moisture again. Then close to the tropopause and hence at very low temperatures (and hence very low absolute humidities) the air moves out from the equator again and at leg #3 it descends, heats up adiabatically and since there is no moisture source aloft, it becomes very dry (low relative humidity), the desert lattitudes.

    So if this is in equilibrium, what would happen if we would increase the surface temperature with one degree celsius due to greenhouse effect and we would also want to increase the (average) absolute moisture of all the air with 6% average to maintain roughly the same relative humidity?

    What would happen to the rate of the Hadley cell conveyer belt? And what would happen to the rate of evaporation at leg 4?

    Another premisse is that in leg #2a/2b, the closest to the tropopause, the increased greenhouse effect is not warming but cooling, as both modelled and observed, due to an increased out radiation of IR. That means that the absolute humidity at the tropopause would not tend to increase, hence the absolute humidity at the transition between legs #3 and #4 the absolutely humidity did not change either. So it looks that evaporation at leg #4 has to increase to make that 6% overal, assuming that the circulation rate of the hadley cell does not change.
    Last edited: Oct 11, 2009
  11. Oct 11, 2009 #10
    So we have a lot of variables here and as Vanesch contends, it all depends if the convection cells speed up or slow down due to increased greenhouse effect.

    If it slows down, the air at leg #4 stays in contact with the water for a longer time and will take up more water vapor, this could satisfy the requirement for maintaining relative humidity at higher temperatures.

    If the pace of the hadley cell would be unchanged then it would seem logical that enroute on leg #4 the air has to pick up more water vapor with increased greenhouse effect. It would seem logical that a limit for that effect would be 6% per degree surface warming as calculated earlier, but the higher levels at lower temperatures would require less absolute humidity to maintain relatice humidity. So it would be an educated guess how much that would be, but certainly not zero.

    The hadley cell however, has two engines in the vertical legs #1 and #3 its power determined by the density differences (bouyancy) of the air in the column in relation to the environment.

    Leg #1 is even a two stage engine, as the light most air rises it cools dry adiabatically first. It can only keep rising when this cooling does not make the air colder as the environment (lapse rate). However when the dew point temperature is reached, the condensing water vapor releases its latent heat and the adiabatic cooling is significantly less now, the second stage. This is keeping the temperature of the air above ambient temperature more easily so the air keeps rising much more easily.

    The other engine, the subsidence in leg #3 is again dependent on the cooling aloft due to out radiation and the surface temperature.

    So what is the greenhouse effect on this engine, with warmer and moister surface air at the leg #1 to #4 transition? Obviously it is lighter now at a higher temperature, due to the greenhouse effect but so is the environment. The additional water vapor however with a lower molecular weight makes it a tad lighter -buoyant- than the ambient air, so it appears that there is no reason to assume that the initial convection is slower now. However with a higher absolute humidity, the dew point will be reached earlier at a higher temperature and the second stage engine, -the moist adiabatic cooling- will ignite earlier. Hence there are reasons to assume that the convection engine under more greenhouse effect with constant relative humidity would be getting stronger.

    Next as the tropopause under more greenhouse cools more, the air aloft is getting more dense and would tend to subsidize more rapidly also adding more power to the Hadley cell.

    But if the Hadley cell circulation rate increases under more greenhouse effect, the contact time between ocean and air is shorter and more evaporation would need to take place to satisfy the constant relative humidity assumption.

    There are reasons to believe that the evaporation rate would have to increase, under higher surface temperatures, while maintaining roughly constant humidity on the average.

    An upper level could be 6% per degree warming, likely less but not a whole lot due to the increased pace of the hadley cell circulation.

    On the evaporation unit of one meter per year, equaling 80 w/m2, a 6% increase would hence require an additional 5 w/m2. Maybe only in the order of magnitude of half of that, but there is an assumption that doubling CO2 would increase temperatures with ...oh... some 2-4 degrees so it is likely that we are still talking about order of magnitude 10 w/m2 energy required for the additional condensation.

    But I seem to recall that there was only an extra 3.7 w/m2 available for doubling CO2 but the required energy for more evaporation could exceed that, making it quite hard to maintain absolute humidity. So could it be that the latent heat cycle at the equator imposes a considerable negative feedback on variations in radiative gasses in the atmosphere?

    Maybe this could explain what Lindzen and Choi 2009 observed:

    Last edited: Oct 11, 2009
  12. Oct 12, 2009 #11
  13. Oct 13, 2009 #12


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    Yes. So one cannot conclude much about the humidity on the basis of power alone, as the velocity plays of course an essential role.

    What I wanted to point out, is that the "regulation variable" in the control loop is exactly that velocity of convection, which will adapt so that the to be regulated value is ok again, and the to be regulated value is the lapse rate. So the hypothesis of constant velocity is not justified.

    Convection is driven, as you say, by the boyancy relationship (together with the adiabatic expansion law of the gas - including condensation).

    No, as the pace of the cell is the "regulation variable": the one that will adapt.

    Indeed, so convection will speed up if the actual lapse rate is higher than the "adiabatic" lapse rate (as a larger actual lapse rate will imply that temperature drops faster than "zero boyancy" and hence that more dense layers are higher up, increasing the drive (the pace) of convection) ; if the actual lapse rate is lower than the adiabatic lapse rate, then convection will come to a halt (kind of stratospheric situation) until it heats up below and changes this again. So the pace of the Hadley cell will be such that the lapse rate will be restored, which will come down to requiring a certain power transport through convection (namely the "missing" part that was not transported through radiation and conduction). Now, if there is more latent heat (more humidity) in the air, the same power transport will be possible with a LOWER pace. Hence, with higher humidity, the pace of the cell will slow down.

    (ok, there's one extra point: the humidity itself also changes the adiabatic lapse rate by itself, so it is somewhat more involved than this)

    Yes, but the air that has lost (through precipitation) the vapor will be denser (water vapor is lighter than air), so it will be at same "boyancy" for a higher temperature. But all this is calculated into the adiabatic lapse rate (the caveat at the end of my preceding paragraph).

    Again, you can conclude nothing about the humidity by the power of the forcing itself.
  14. Oct 13, 2009 #13
    That's the essential point of discussion it seems.
    But why would there be a mechanism that would want to relugate power transport. There is no regulator, all there is, as said are two engines driving the Hadley Cell at a certain pace, and that pace is regulated by dynamically changing bouyance differences. Note that the humidity is also changed by precipitation changes in leg #1

    Interesting thought however more moist air at the same temp and pressure contains less air molecules, so condensation will decrease it's pressure, or rather if we look at the ascend, where the air expands adiabatically. Maintaining pressure equal to the ambient pressure, less molecules will have to expand less to accomplish that, and hence the adiabatic temperature drop will also be less, keeping the bouyancy up. So indeed there is a lot more to it.

    However there are some fundamental issues perhaps. Not the least that the proof is in the pudding, as cited before, Lindzen et al 2009 a finding distinctive negative feedback signal on short wave refection (higher albedo - more clouds), and the dominance of negative feedback (anti persistency) is confirmed by the several publications of Olavi Karner.

    Furthermore, are there valid comparable physical processes, maybe? How about a boiling pot with water, with a lot of convection. The rate of boiling however is directly related with the excess energy at the bottom of the pot. The more energy, the more vigourous the boiling

    Bottom line is that the dynamic changes of enery in the latent heat cycle appear to be in the same order of magnitude as the energy changes due to climate sensitivity, yet I can't seem to find any scientific study about it, observing modelling predicting and testing the conduct of the latent heat cycle in climate changes.
  15. Oct 13, 2009 #14
    This is not a comparable physical process. Water evaporates at 100C The more molecules that reach 100C in a given period of time will determine how vigorously the water boils.

    Appears to be?

    How is that possible?

    If they were the same, then temperature would not fluctuate, just like the water in the pot remains at 100C no matter how high the flame. Since temperature does fluctuate, your hypothesis cannot be correct.
  16. Oct 15, 2009 #15


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    There is a "regulator", it is boyancy, which, by itself, drives convection. So convection will go "as hard" or "as slow" as is needed so that any bit of air, at any altitude, will have the same boyancy as any other (at least, as long as we are in tropospheric conditions), and this will be the case when the lapse rate is given by the adiabatic lapse rate (including the condensation and hence precipitation of water).

    In other words, we have a temperature dependent on altitude T(z), and a pressure dependent on altitude p(z) which are determined by a rather simple set of equations:

    The first is the adiabatic relationship, which gives you temperature as a function of pressure: it is the temperature that a gas will have when you change (lower) its pressure. For an ideal gas, that's pretty easy ; for a gas containing vapor, we have to include the latent heat of condensation and remove the condensate. But in any case, this gives us:

    T = f(p,T0)

    We can also calculate the fraction of the condensated vapor for a given pressure (and hence temperature), and hence the new composition of the gas phase.

    The other relationship is the vertical hydrostatic equilibrium:

    dp/dz = - m p g / R T where m is the average molecular weight of the gas (note that this may change as a function of p and T (but again of p) due to the condensation of part of the watervapor).

    These equations determine normally entirely the temperature profile, the pressure profile and the composition. The only caveat is of course clouds, which are of course condensed vapor, but which didn't yet precipitate. In the above approach, one assumes immediate precipitation of any form of condensate.

    But apart from that, we have T(z) and p(z) fixed.

    Well, convection will "convect" enough, and not more, to establish this. Why ? Because if it is "not enough" then lighter air will be lower lying than denser air, and boyancy will drive convection. And if it is "too much", then lower lying air will be denser, and there will not be any boyancy deficit that would drive convection.

    So the convection velocity will ADAPT so as to instore those dependencies.

    This has the advantage that we don't have to break our heads over how much convection there will be, because we know what will be the *result* of it. Once we have the result, we could calculate backwards how much convection is actually needed to obtain it.

    This is half correct. Condensation will of course not decrease the pressure (which is set by the "environment" ; by the hydrostatic equation), but it will decrease in VOLUME. However, you are correct that the "wet" adiabat, with condensation, gives us a *smaller* lapse rate than would be a dryer adiabat. A smaller lapse rate is equivalent to a cooler surface to obtain the same temperature at the "last black layer" which is needed for the emission of heat flux as radiation into space.

    So it is true that adding a condensible substance, by itself, will lower the lapse rate, and hence cool the surface. This comes about because the transport of latent heat doesn't require a "temperature drop" upon expansion. This is maybe the effect you were talking about in the beginning: yes, adding a condensible vapor to the air will give rise to a cooler surface if you need to reach a given temperature at a certain altitude.

    However, with water vapor, this is offset by another effect: the fact that water vapor is ALSO a greenhouse gas (and will hence "push" the "last black layer" to a higher altitude).

    But all these effects are taken into account already when one considers the correct lapse rate (except for cloud formation).
  17. Oct 15, 2009 #16
  18. Oct 15, 2009 #17


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    I explained myself maybe badly, because the relationship "has the same boyancy as another " is probably not clearly defined. What is understood by that is:

    two "bubbles" of air, A and B, have "the same boyancy" if:

    suppose that bubble A has a lower altitude than bubble B,
    when we transport bubble A to the altitude of bubble B and allow it to expand adiabatically and condense out all that has to be condensed out, then the density of bubble A, transported, will be the same as the density of bubble B.

    If it turns out that the density of bubble A, transported, will be LOWER than that of B, this means that A has a relative higher boyancy, and will be transported quickly by convection. If bubble A has higher density, then it will remain in place. Only when it has the same density, it will be indifferent wrt to convection.
  19. Oct 15, 2009 #18
    I see what you are saying now. Convection 'tries' to make it 'so that any bit of air, at any altitude, will have the same buoyancy as any other' but of course it can never completely succeed or there would be no force left to power the convection itself. the only way it could succeed is if the convection were infinitely fast
  20. Oct 15, 2009 #19


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    Yes. There needs to remain a small gradient to keep convection going and "power the losses", true.

    But the important point is that convection, as you say, "tries" to attain a certain equilibrium, namely the "buoyancy equilibrium", and succeeds more or less well in establishing this. As such, we do not need to look in a very detailed way into this (unless you want to look into details such as the small remaining gradient): we KNOW that if there is convection, this equilibrium will be largely realized. The variable of "adjustment" is the intensity of convection, the cycling speed of a hadley cell. The more power that needs to be transported by convection (to keep the buoyancy equilibrium while there's "heating" at the surface), the faster the cycle will go, and the more heat that can be transported by unit of air volume (for instance, containing more vapor, and hence more latent heat), the slower the cycle will turn. (*)

    And this is where part of Andre's argument goes wrong: you cannot have "not enough power" to evaporate water "fast enough" (meaning, convection with humid air would "take too much power - more than is available"). Because if that's so, convection will simply slow down. He holds fixed the "variable of adjustment" which is the hadley turnover velocity, but that's not what should be done as it is the variable of adjustment in this system.

    (*) however, careful, because if there's more vapor, the buoyancy equilibrium - given by the lapse rate - will be different too.
    Last edited: Oct 15, 2009
  21. Oct 16, 2009 #20
    Hmmm I'm not seeing back what I intended to argue, so obviously I failed to make that clear. So maybe there is hope and perhaps we try again with shorter steps and each of them documented.

    Do we agree that rate convection is primarely a function of actual lapse rate or environmental lapse rate (ELR), after reading http://data.piercecollege.edu/weather/stability.html [Broken] are related. The steeper the Environmental Lapse Rate, the more instable the air mass and the stronger the convection.

    Next step: increased greenhouse effect is assumed to have two distinct effects on atmospheric temperature, an increase at ground level but a decrease at the middle and upper atmosphere.

    Next step, Now if the lower atmosphere is warmer and the upper is cooler, do we agree that this makes the Environmental lapse rate steeper? And hence the atmosphere more unstable and hence causes an increase in convection rate?
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