Understanding the Role of Latent Heat Energy Transport in Climate Change

[Andre]

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

 

[Andre]

http://www.britannica.com/EBchecked/topic-art/121560/46275/Global-distribution-of-mean-annual-evaporation :

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?

 

[Andre]

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 (L_c), or energy needed to evaporate one gram (is one ml) of water is about http://www.usatoday.com/weather/wlatent.htm.

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.

 

[vanesch]

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.

 

[Andre]

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.

 

[Andre]

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 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.

 

[vanesch]

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).

 

[Andre]

But that's not what Lindzen et al 2009 find.

 

[Andre]

Now let's have yet another look at the http://www.meteohistory.org/2006historyofmeteorology3/2persson_hadley.pdf 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 modeled 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.

 

[Andre]

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.

Concluding
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:

http://www.agu.org/contents/journals/ViewPapersInPress.do?journalCode=GL

Full paper http://www.leif.org/EOS/2009GL039628-pip.pdf

 

[granpa]

looks like the capacity of the air for water vapor doubles for every 20 degrees celcius

http://en.wikipedia.org/wiki/Vapor_pressure

 

[vanesch]

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.

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).

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.

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

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.

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)

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.

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.

 

[Andre]

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)

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

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.

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 energy 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.

 

[Skyhunter]

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

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.

Bottom line is that the dynamic changes of energy 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.

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.

 

[vanesch]

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

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.

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.

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).

 

[granpa]

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

huh?

 

[vanesch]

huh?

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.

 

[granpa]

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

 

[vanesch]

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

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.

 

[Andre]

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.

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 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?

 

[vanesch]

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.

Ok, although the documentation is not necessary for elementary steps, you know.

Do we agree that rate convection is primarely a function of actual lapse rate or environmental lapse rate (ELR),

No, we don't. I don't see where you get this out of your source. Could you indicate an exact quote ?

What we have is that convection gives rise to a certain adiabatic (equilibrium) lapse rate. But nowhere we see anything about a relationship between the RATE of convection, and the lapse rate (= change of temperature with altitude) itself.

So I bug already here...

What is true however, is that the further the actual state of the atmosphere is from its stable state (with the adiabatic lapse rate), the more instable the atmosphere is and the more intense the convection will be, to restore the lapse rate again. But these are meteorological deviations that can happen. We are talking of an atmosphere which is already in a stable state (has already a correct lapse rate), and about the convection in this stable state. We're not talking about momentarily and potentially large deviations from that state (which cannot last very long).

 

[Andre]

What I intended to say was:

The strength of convection depends on the (in)stability of the air column

http://space.hsv.usra.edu/TRESTE/te.../ess_lab_exercise_resources/19._stability.doc shows on page 3 the relation between lapse rate and stability.

Sorry it seemed nearly axiomatic to me.

So if you heat the base and cool the top, you make the environmental lapse rate steeper and the atmosphere more unstable. and the more unstable the atmosphere, the stronger the convection.

 

[vanesch]

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.

The cooling happens mainly in the tropopause and in the stratosphere, where there is no significant convection anymore, and no adiabatic lapse rate is instored. So there's no influence here. In fact, this cooling doesn't play much of an active role in the greenhouse effect, because what counts is the "last black layer" of emission, which for most frequencies in the IR is situated in the troposphere.
The stratosphere is already "too hot" to be part of a convective cell, that's why it is a stratosphere in the first place. If this cools somewhat, this doesn't change much concerning any convection (it might be that the tropopause will rise somewhat, to allow for a continuity in the temperature profile). The actual lapse rate of the stratosphere is far below the adiabatic lapse rate, and hence there is no drive for convection.

The heating happens in the troposphere, where there is a shift of the adiabat (similar lapse rate, but "shifted" towards higher temperatures). The reason for this is that due to greenhouse gasses, the "last black layer of emission" lies higher up in this troposphere, and in order for it to emit the same amount of radiation, and hence to be on average on the same temperature the whole temperature profile has to shift "upward".

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?

Not at all, because the "cooler" part is already in the stratosphere, where the "adiabatic link" is lost.

 

[vanesch]

Okay the step was too large?

What I intended to say was:



http://space.hsv.usra.edu/TRESTE/te.../ess_lab_exercise_resources/19._stability.doc shows on page 3 the relation between lapse rate and stability.

Sorry it seemed nearly axiomatic to me.

Yes, this can well be, but we're not talking about momentary deviations from the "right" lapse rate (as can happen in meteorological situations).

We're talking about an atmosphere that is at about the right lapse rate, and where this is maintained by a constant convection. Not *deviations* from this stationary situation. Of course in the case of strong deviations from the equilibrium situation, you will have a stronger "correction" towards the "right" lapse rate.

 

[Andre]

No we are talking about a permanent change due to increased greenhouse effect.

 

[vanesch]

No we are talking about a permanent change due to increased greenhouse effect.

I see what you want to say. You say: you heat more "below", you cool more "on top", so evidently, you will get a stronger convection! If that were the case, then that would indeed be right. You would constantly be pulling the atmospheric temperature profile AWAY from its "natural state" which is the adiabatic lapse rate. So of course, if you do that, you get stronger convection. No discussion here.

The problem is again that there is a confusion of what is cause, and what is effect. We don't "heat more" below, and we don't "cool more" on top, within the troposphere.

The effect of the greenhouse gasses is that the average height of emission of the black body radiation increases, simply because the "black layers" are now more numerous and thinner (they are of course strongly function of frequency through the absorption profile of CO2). As the same amount of radiation has to be emitted into space, this radiation is now on average emitted from a higher place, and it turns out that for most important frequencies, this happens to be somewhere in the troposphere.

Now, if nothing would happen, it would mean that on average these layers are now higher, and so also colder, and hence, would emit less radiation than they used to be. The only way for them to emit the same radiation as before, is that they become somewhat hotter.

Now, if these layers remain within the troposphere, and we consider an atmosphere in equilibrium, then the whole temperature profile has to shift, because the CHANGE in temperature with altitude is fixed by the lapse rate, and this means that the WHOLE troposphere will shift upward in temperature.

So the whole troposphere becomes warmer, just to allow these layers to be at the right temperature to emit the right amount of IR radiation.

In the stratosphere, the air is already hotter than it would have been if it were still part of the troposphere, so it doesn't take part in any convection. The reason is that this stratosphere has its own heating, directly from the sun (mainly due to ozone I believe). The stratosphere doesn't do much to the greenhouse effect, and it is above the "last black layer", so most of the IR radiation emitted from the troposphere goes right through it, into space. SOME of it will be absorbed by CO2, but not much, as it is not a "black layer". However, CO2 also allows the stratosphere to EMIT more radiation, because it becomes a bit "darker" nevertheless (a higher emissivity). Turns out (don't know the details) that the balance of somewhat more absorption of IR, and somewhat more emissivity allows the stratosphere to cool somewhat. It can visibly get rid somewhat easier of its own heat with some more CO2 than without, even though it will also absorb some IR from below.

So predictions are that the stratosphere should cool somewhat, or rather, heat somewhat less. But this has nothing to do with what was happening below, in the troposphere. It will STILL be too hot to become part of the troposphere and take part in any convection.
By the time we are in the stratosphere, we do not follow the adiabat anymore, for long.

 

[granpa]

the overall convection of the Earth is due to the average pressure at the equator and he average pressure farther north. thunderstorms are of course low pressure areas. the pressure under a storm depends on the weight of air above it. if the air carries more water vapor then more latent heat is released and therefore the lighter the air becomes. (and I would guess the higher the air can rise before running out of 'steam'). the result is lower pressure and more convection. the most significant thing to my thinking is the surprising effect temperature has on the amount of water vapor the air can carry. for every 20 degrees Celsius increase the amount of water vapor it can carry doubles. that's a lot. so even a modest increase in temperature should result in much more convection and therefore much more cooling. Earth's temperature should therefore be, in a larger sense, relatively stable.

despite ice ages the world hasnt yet frozen solid like Mars and despite huge flood basalts the worlds oceans haven't boiled away like venus

 

[Skyhunter]

the most significant thing to my thinking is the surprising effect temperature has on the amount of water vapor the air can carry. for every 20 degrees Celsius increase the amount of water vapor it can carry doubles. that's a lot. so even a modest increase in temperature should result in much more convection and therefore much more cooling. Earth's temperature should therefore be, in a larger sense, relatively stable.

Do you not see the internal contradiction in this logic?

Essentially what you are arguing is that the Earth cannot warm because warming causes cooling. The fact that temperature trends exist demonstrate this hypothesis to be incorrect.

As the air warms it holds more water vapor, more heat does not automatically mean more evaporation, that is why there is a temperature index that takes into account humidity. 100F in the desert with low humidity feels much cooler than 100F in a humid swamp. The reason is that evaporation slows as the atmosphere reaches saturation.

There is no one for one balance, warmer temperatures lead to a positive water vapor feedback as specific humidity increases. More precipitation will lead to more latent heat being released higher in the troposphere as sensible heat, but it is still the troposphere, and the energy must still be emitted into space before any actual cooling takes place in the climate system. Evaporation is just a different form of storing energy, the cooling does not take place until the energy is released into space.

Scientists are not overlooking some obvious mechanism that forces the climate to maintain a constant temperature like a boiling pot of water.

Although if the oceans warm enough to boil, the boiling will prevent the oceans from further warming, but until that temperature is reached the Earth's climate system can continue to warm as the atmosphere becomes optically thicker.

 

[granpa]

I certainly did not say that warming results in net cooling.

I said that modest warming greatly increases the amount of water vapor in the air which increases the rate at which warm moist air at ground level is lifted up to the upper troposphere where it is above most of the Earth's 'blanket' of greenhouse gases and so can cool quickly by radiating its heat to space. the world still warms up but not by much.

 

[vanesch]

BTW, it is interesting to see why there can be a stratosphere. There is a relatively large heat flux upward from the surface (and there's also some absorption of solar heat in the air itself), and in the lower troposphere, the radiative transport part of this heat flux is relatively small: a large part of the heat transport in the troposphere is done by convection. Now, convection needs the lapse rate to be *at least" equal to the adiabatic lapse rate, and will try to restore this adiabatic lapse rate. Now, something seems weird at first sight: if the temperature is dropping with altitude in the troposphere (the lapse rate) and if even such a gradient doesn't allow the system to transport heat enough just by radiation, then how come that in the stratosphere, where there is even an inverse temperature gradient, all of a sudden, there's no convection anymore ? Where did this heat flux "stop" ??

The answer is of course that by the time we reach the stratosphere, heat transport outward (net heat transport outward) has been taken care off more and more by radiation and once we're past "the last black layer" (which is, I repeat, strongly frequency-dependent: some "last layers" are the surface, and others are high up), most of the heat transport is now radiation. Hence no *NEED* anymore for convection, and hence a stratosphere, and hence, no more adiabat to follow.

So the net heat transport outward increases of course slightly (there's a large part due to the surface, and then each layer has itself to get rid of absorbed radiation), but the mode of transport of that heat, which is dominantly convection in the lower troposphere, will switch more and more to net radiative transport when we go higher and higher (and have less and less 'dark layers' above us, and space becomes "visible" for more and more frequencies) and at a certain point, radiative transport is sufficient not to "block" heat from below so much that the adiabatic lapse rate is crossed, and hence, there's no drive for convection anymore.

 

[vanesch]

so even a modest increase in temperature should result in much more convection and therefore much more cooling. Earth's temperature should therefore be, in a larger sense, relatively stable.

What you are describing is actually the capacity of convection to have the temperature profile "stick to" the adiabatic lapse rate. It is also what Andre (correctly) described: an "unstable" atmosphere (one that has an actual lapse rate that is bigger than the adiabatic one) will give rise to very strong convection, which will quickly try to restore the adiabatic lapse rate. All that is correct. But this is about *deviations* from the steady-state situation we are considering. Mostly meteorological phenomena. What people are considering are the changes in the steady-state situation itself.

The point is that a greenhouse gas *shifts* the temperature profile, while keeping the same lapse rate (well, humidity itself will change this lapse rate by itself, make it softer, and this effect will also result in a relative cooling, that is to say, a less strong heating than if the lapse rate were kept constant). This shift comes about simply because the final radiating layers are now higher-up, and need to be at a similar temperature as before in order to be able to radiate as much as before.

 

[Andre]

It seems that we have made considerable progress. But the question remains if convection (especially in the hadley cell) is merely a mechanism that restores the lapse rate and dies out once established; or is it a continuous motoring engine of the Earth's air conditioner that transports surface heat (via evaporation in the form latent energy) to higher levels for easier out radiation.

Back later.

 

[vanesch]

It seems that we have made considerable progress. But the question remains if convection (especially in the hadley cell) is merely a mechanism that restores the lapse rate and dies out once established; or is it a continuous motoring engine of the Earth's air conditioner that transports surface heat (via evaporation in the form latent energy) to higher levels for easier out radiation.
.

Of course it is an "air conditioner" that works continuously and it DOES cool the Earth significantly (as I said, a LARGE part of the heat transport in the lower troposphere is on the account of convection).

I didn't say that "once the lapse rate is established, convection dies out" either, as there is a continuous drive (the heating of the surface) that tries to pull the lapse rate to higher values than the adiabatic lapse rate. As I said also to granpa, it is correct that this implies that there is a continuous small deviation from the adiabatic lapse rate to "drive" the convection. There will be a steady state situation where the deviation from the adiabatic lapse rate is just enough to give you the right amount of convection to transport all the heat it has to transport. But this deviation can be supposed to be small, so we can say that the steady state situation is "essentially" given by the adiabatic lapse rate.

What is important, however, is to see that this deviation (and hence the strength of the convection) is auto-regulated in such a way that the heat transport is OK. Indeed, if there wouldn't be "enough" heat transport, then it would get "hotter below" and the actual lapse rate would deviate more from the adiabat, hence increasing the convection rate. If there would be "too much" heat transport, it would get cooler below, and hence the deviation from the adiabat would get smaller (or would even reverse sign), which would slow down the convection rate (or even bring it to a stop).

So convection will regulate itself (together with the small deviation from the adiabat) such that heat transport is what it has to be to get "steady state". Of course, this is "on average". Locally, and temporarily, you can get strong deviations from this "average steady state", that's meteorology.

And, on average again, the lapse rate will be (close to) the adiabat.

But yes, it has an important cooling effect, and is in fact the main transportation of heat at low altitudes. However, this is already taken care off when considering the lapse rate.

And now back to "how much power do you need to get the air wet through evaporation". Well, GIVEN that convection will ADAPT to transport whatever power is to be transported, whether the air is humid or dry, this doesn't matter. ANY amount of power can be transported by convection, with humid OR with dry air. With humid air, as the transport is more efficient (and does, indeed, require evaporation as part of the heat transport process), the convection will "slow down" to adapt itself to it. With dry air, as the heat transport is somewhat less efficient (no evaporation, no latent heat), convection will need to speed up to transport the same amount of heat.

But the power, by itself, doesn't determine the humidity of the air by itself. If things are such that the air is humid, then convection will HAVE TO slow down.

This, up to the caveat that the adiabatic lapse rate is ALSO altered with humid air, so this complicates matters somewhat.

 

[vanesch]

Of course it is an "air conditioner" that works continuously and it DOES cool the Earth significantly (as I said, a LARGE part of the heat transport in the lower troposphere is on the account of convection).

[ ... ]

And, on average again, the lapse rate will be (close to) the adiabat.

But yes, it has an important cooling effect, and is in fact the main transportation of heat at low altitudes. However, this is already taken care off when considering the lapse rate.

To add to this: in fact, if there wouldn't be any convection, and only radiative heat transport, then the lapse rate would be WAY HIGHER as, in the lower troposphere, radiative transport is a much less efficient heat transport mechanism. Convection sets into REDUCE this lapse rate to the adiabatic one (up to our small deviation) because convection cannot reduce it any more (if the lapse rate is SMALLER than the adiabatic lapse rate, the atmosphere would be in buoyancy equilibrium - it would be a stratosphere).

With a "fixed" temperature at the "last black layer" which has to radiate heat into space, the smaller the lapse rate, the cooler it is at the surface. So without convection - and hence a very large lapse rate - it would be very very hot at the surface, and convection reduces this (works - as you say - as a air conditioner) to the extend that it can, by bringing the lapse rate to its minimum possible value that is still compatible with convection, namely the adiabatic lapse rate.

So it is true that humid air would "cool" the surface somewhat more than dry air, because the wet adiabat is less steep than the dry adiabat. Having a condensible vapor in the air does "cool" the surface more.
(however, in the case of water, it is ALSO a strong greenhouse gas, so this sets off the cooling by heating through increasing the average height of emission by the "last black layer").

 

[Skyhunter]

I certainly did not say that warming results in net cooling.

I said that modest warming greatly increases the amount of water vapor in the air which increases the rate at which warm moist air at ground level is lifted up to the upper troposphere where it is above most of the Earth's 'blanket' of greenhouse gases and so can cool quickly by radiating its heat to space. the world still warms up but not by much.

Thank you for the clarification.

I am not suggesting that latent heat transport is minor, just that it is not being excluded from the equation. As Vanesch has pointed out in this thread, it is an integral component of the adiabat.