In How the “Greenhouse” Effect Works – A Guest Post and Discussion there was considerable discussion about the temperature profile in the atmosphere and how it might change with more “greenhouse” gases. The temperature profile is also known as the lapse rate.
The lapse rate has already been covered in Potential Temperature and for those new to the subject Density, Stability and Motion in Fluids is also worth a read.
Some Basics
Let’s take a look at a stable (dry) atmospheric temperature profile:
Figure 1 – Just Stable
The graph on the left is the potential temperature, θ, and on the right the “real temperature”, T. The temperature declines by 10°C per km (and this value is not affected by any “greenhouse” gases). The potential temperature is constant. Remember that for stable atmospheres the potential temperature cannot reduce with height.
A quick recap from Potential Temperature:
- “potential temperature” stays constant when a parcel of air is displaced “quickly” to a new height (note 1)
- potential temperature is the actual temperature of a parcel of air once it is moved “quickly” to the ground
- in dry atmospheres the actual temperature change is about 10°C per km
Now an unstable atmosphere:
Figure 2 – Unstable
Because the temperature at a given altitude is “too cold”, when any air is displaced from the surface it will of course cool, but finish warmer at 1km and 2km than the environment and so keep rising. This situation is unstable - leading to convection until the stable situation in figure 1 is reached.
We can also see that the potential temperature decreases with altitude, which is another way of conveying the same information.
The important comparison between the first two graphs is to understand that figure 2 can never be stable. The atmosphere will always correct this via convection. Exactly how long it takes to revert to figure 1 depends on dynamic considerations.
Let’s look at another scenario:
Figure 3 – Very Stable
Now the temperature reduces with height, but not sufficiently to induce convection. So a parcel of air displaced from the surface ends up colder than the surrounding air and sinks back down.
And we can even get temperature inversions, very popular in polar winter and nighttime in many locations:
Figure 4 – Very very stable
So how do figures 3 & 4 come undone? Surely once the atmosphere is stable to convection then it becomes static and heat can only move radiatively from the surface into the atmosphere?
The basic principle of heat movement in the climate is that the sun warms the surface (because the atmosphere is mostly transparent to solar radiation) and so the atmosphere is continually warmed from underneath.
Figure 5 – Atmospheric temperature changes as surface warms
As the surface warms the atmospheric temperature profiles move from a → d. This is a result of convection. But where does all this heat go that was convected from the surface into the atmosphere.
Here is a graphic reproduced from Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Eleven – Heating Rates:
From Petty (2006)
Figure 6 – Radiative Cooling of the Atmosphere
This illustrates that the atmosphere is always cooling via radiation to space – and cooling at all altitudes.
So the atmosphere cools via radiation, the surface warms from solar radiation and when the lapse rate reaches a critical value convection is initiated which moves heat from the surface back into the atmosphere.
As a minor question, how does a temperature inversion ever get created? It’s a temporary thing. In the case of nighttime, the surface can lose heat via radiation more quickly than the atmosphere. The surface is a more effective radiator than the atmosphere. In the case of the polar winter, the same effect takes place over a longer timescale. But eventually, when the sun comes up, the surface gets reheated.
Where Convection Stops – The Tropopause
Actually there are a few different definitions for the tropopause. But let’s save that for another day. There is a point at which convection stops. Why?
Suppose there was no convection, only radiation. If we consider heat transfer via radiation then there is a change as the atmosphere thins out.
Let’s take a massively over-simplistic approach to help newcomers. Suppose a photon of a given wavelength has to normally travel 100 molecules before getting absorbed. In this case, as the atmosphere thins out from 1000 mbar (surface) to 200 mbar (typical tropopause), the same photon would have to travel 400 molecules before getting absorbed. This means that the temperature change vs height reduces the more the atmosphere thins out. As a way of thinking, it’s like the resistance to temperature change reduces as the atmosphere thins out.
A simple example of radiative equilibrium for gray atmospheres (note 2) is given in Vanishing Nets:
Figure 7 – Radiative Equilibrium
See how the temperature change with height (the lapse rate) reduces the higher we go. So at a certain point the potential temperature always increases with height, making the atmosphere resistant to convection.
The point at which the radiative lapse rate is less than the adiabatic lapse rate is where the atmosphere stops convecting. However, this is not technically the tropopause (note 3).
Another way to think about this for newcomers is that the temperature reduction caused by lifting a parcel of (dry) air 1km is always about 10°C. So if the temperature reduction due to radiative heat transfer is 5°C then the lifted parcel is always cooler than the surrounding air and so sinks back = no convection.
Now the atmosphere is not gray so this is not a simple problem, but it can be solved using the radiative transfer equations with numerical methods.
We can see the real (averaged) climate in this graphic of potential temperature:
From Marshall & Plumb (2008)
Figure 8
In the tropics the (moist) potential temperature is close to constant with altitude until about 200 mbar. And at other latitudes the potential temperature increases with height very strongly once we get above about 300 mbar. This shows that the atmosphere is stratified above certain altitudes.
Increasing CO2 – The Simple Aspects
Let’s consider the simple aspects of more CO2. These got a lot of discussion in How the “Greenhouse” Effect Works – A Guest Post and Discussion.
We increase the amount of CO2 in the atmosphere but at the surface the change in downwards longwave radiation (DLR) from the atmosphere is pretty small, perhaps insignificant.
By comparison, at the top of atmosphere (TOA) the radiative effect is significant. The atmosphere becomes more opaque, so the flux from each level to space is reduced by the intervening atmosphere. Therefore, the emission of radiation moves upwards, and “moving upwards” means from a colder part of the atmosphere. Colder atmospheres radiate less brightly and so the TOA flux is reduced.
This reduces the cooling to space and so warms the top of the troposphere. Therefore, there will be less convective flux from the surface into this part of the atmosphere.
As a result the surface warms.
Increasing CO2 – The Complex Aspects
The real world environmental lapse rate is more complex than might be inferred from the earlier descriptions. This is because the large scale circulation of the atmosphere results in environmental temperature profiles that are different from the adiabatic lapse rates.
The environment can never end up with a greater lapse rate than the adiabatic lapse rate but it can easily end up with a smaller one.
More on this in another article. But as a taster, here are some monthly averaged environmental lapse rates:
From Stone & Carlson (1979)
Figure 9
From Stone & Carlson (1979)
Figure 10
And of course, one of the biggest questions in an atmosphere with more CO2 is how water vapor concentration changes in response to surface temperature change. Changes in water vapor have multiple effects, but the one for consideration here is the change to the lapse rate. The dry adiabatic lapse rate is 9.8 °C/km, while the moist adiabatic lapse rate varies from 4 °C/km in the tropics near the surface (where the water vapor concentration is highest).
Consider an atmosphere where the temperature reduces by 15 °C in 2km. Dry air moving upwards reduces in temperature by 20 °C – which is colder than the surrounding air – and so it sinks back. Very moist air moving upwards reduces in temperature by about 10 °C – which is warmer than the surrounding air – and so it keeps rising.
So more moisture reduces the lapse rate, effectively making the atmosphere more prone to convection – moving heat into the upper troposphere more effectively. (Cue tropical hotspot discussion).
References
Atmospheric Lapse Rates and Their Parameterization, Stone & Carlson, Journal of the Atmospheric Sciences (1979) – Free paper
Notes
Note 1: A parcel of air displaced “quickly” to a new height is written for ease of understanding. Technically, potential temperature stays constant if a parcel of air is displaced “adiabatically” – which means no exchange of heat with the surrounding atmosphere.
Note 2: A gray atmosphere is one where the absorption vs wavelength is constant. More technically, this is usually a “semi-gray” atmosphere because the atmosphere is transparent to solar radiation but absorbs terrestrial radiation.
Note 3: The tropopause is usually defined where the lapse rate is at a minimum. In radiative equilibrium the temperature would continue to decrease with height even after the point where convection stops. It is only the presence of radiative gases (ozone) that absorb solar radiation that cause the stratospheric temperatures to increase.
A few questions, and points of disagreement:
1. Why have GHGs no effect on the dry lapse rate?
2. What would be the effect of increased GHGs on figure 6?
3. The atmosphere is not “mostly transparent to solar radiation”. See eg _http://telstar.ote.cmu.edu/environ/m3/s2/04solarad.shtml (you might have oversimplified it there)
4. Under “Increasing CO2 – The Simple Aspects” why don’t you just state that a temperature increase at TOA obviously means a temperature increase at the surface, due to the lapse rate? (analogously, an increase in atmospheric mass would move TOA upwards, once again warming the surface)
5. “more moisture reduces the lapse rate”…but H2O is also a GHG. So what is the actual (total) contribution of water vapor to tropospheric temperature?
6. Not sure what are the basis for Note 3. Stratospheric temperatures increase somewhat on Jupiter for example _http://telstar.ote.cmu.edu/environ/m3/s2/04solarad.shtml and Saturn _http://astronomy.nmsu.edu/tharriso/ast105/Saturn.html – not to mention Venus, Uranus, Neptune. Positive tropospheric lapse rates and negative stratospheric lapse rates appear to be a characteristic of every planetary atmosphere, independent of composition.
As usual, there is no polemics in the above. I have always found this site considerably of a higher quality than most as it just shows what the IPCC could have been if rent-seekers and primadonnas had been isolated from the start
BTW…an old obsession of mine…it shouldn’t be called TOA but TOT=Top of the Troposphere.
The tropopause as level of relevant radiative forcing is apt because the stability means convective transfer of heat can be neglected.
Or can it? There is a certain amount of troposphere/stratosphere exchange each year which remains unquantified. But with that exchange, there is surely energy exchange as well.
Further problems with the tropopause as significant level is that for much of the winter polar regions, no level meets the standard definition and in the tropics, there may be multiple levels meeting the standard def.
It does also raise the question about the significance of upper level radiance.
Omnologos,
1. Because the equations which relate energy conservation and expansion result in a formula: lapse rate, Γ = -cp/g, where cp = heat capacity of air under constant pressure and g = gravitational acceleration.
2. See figure 4 in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Eleven – Heating Rates
3. It is a handy approximation in providing conceptual understanding.
4. Because it is not obvious to everyone.
5. This is a complex subject which can only be answered with GCMs. The intent of this article is to help readers understand the lapse rate cause and effect better.
6. The basis for note 3 is that the lapse rate minimum is not the same point as where convection ceases.
Omnologos,
More on point 6..
The reason that stratospheric temperatures increase with height above the convective region is due to the absorption in the stratosphere of solar radiation. If there was no absorption of solar radiation in the stratosphere then temperatures would continue to decline with height.
thanks!
SoD,
I think what increases the lapse rate toward the DALR (10 C/km) is interesting, and there’s more to it than you say.
The atmosphere, with GHG, does cool by radiation. But it’s also warmed from below. The more it emits (via GHG conc), the more it absorbs. The nett result is a separate thermal gradient. With radiative transfer in general this is hard to calculate, but in the case of a fairly opaque atmosphere, it follows the Rosseland model. This gives an explicit temperature gradient that incorporates the effect of cooling from above that you describe (for a given upward IR flux). It’s a grey gas model, and not fully accurate for the relatively transparent air, but it’s still useful.
The point is that you can quantify the effect, and I believe it is not enough to bring the lapse rate up to observed values.
There is another effect, described here, which I believe is dominant. You have described how when the DALR is exceeded, convective instability transports heat upward, and brings the LR back down. That effect is proportional to the amount by which the DALR is exceeded. The excess creates a heat engine; the upward transport, from hot to cold, transfers kinetic energy to the gas.
Below the DALR, this runs in reverse. Vertical motion is forced by the wind. Downward moving air becomes warmer than ambient, transporting heat down, and taking energy from the flow to counter buoyancy. Upward moving also takes energy, and “transfers cold” up – ie heat down. The nett result is a heat pump, with energy from wind maintaining the lapse rate. This incidentally works without GHG.
I’ve quantified this for Venus in this post, which also discusses Rosseland.
SoD,
First two comments.
Although I believe that I know what you are talking about the inserted paragraph of massively over-simplistic approach seems difficult to understand. Also the numbers 100, 1000, 200 and 400 appear to conflict (should the last be 500, I’m not sure as I don’t understand the paragraph fully).
The Figure 8 is based on equivalent potential temperature, but is it really relevant at higher latitudes and does the Figure justify fully the conclusion
“.. the potential temperature increases with height very strongly once we get above about 300 mbar. This shows that the atmosphere is stratified above certain altitudes.”
as the equivalent potential temperature is perhaps not the right variable to use for discussing stratification, when the air is far from saturation.
Pekka Pirilä,
The problem with “massively over-simplistic” approaches is that people who understand the subject wonder whether it makes sense.
With any attempt to explain complex stuff to newcomers I may well have missed the mark and any who don’t understand it please throw in a comment. There is no “right answer” when trying to make hard subjects easy..
At 1000 mbar the density is about 1.3 kg/m3 but at 200 mbar the density is about 0.3 kg/m3. I just did the calculation.
Equivalent potential temperature is just like potential temperature but with moisture taken into account. So if there is no moisture Equivalent potential temperature = potential temperature.
θe = θ exp(Lq/cpT)
where q = water vapor, L = latent heat of vaporization, cp = specific heat capacity, T = temperature, θe = equivalent potential temperature and θ = (dry) potential temperature
So if the air is dry, θe → θ as q → 0.
My point on the equivalent potential temperature is that it changes when the moisture level changes at values far from saturation but these changes do not affect the buoyancy. Thus considerations of equivalent potential temperature do not reflect always the local stability conditions.
SoD,
Your link for the Stone – Carlson paper didn’t work for me, but a Google search with “Stone Carlson lapse” gave a link directly to the AMS journal that worked.
Thanks, I updated the article with the correct link.
Pekka Pirilä
“..but these changes do not affect the buoyancy..” ?
The buoyancy consideration is simply the temperature of the parcel of air moved to that altitude vs the surrounding (environmental) air temperature at that altitude.
Maybe I misunderstand your point. Can you explain in a little more detail, perhaps with an example?
SoD,
When the moisture is less than 100% the stability is controlled by dry lapse rate and by the differences in (non-equivalent) potential temperature. If all air that needs to be considered has the same absolute moisture and the moisture remains less than 100% the equivalent potential temperature and the potential temperature have different values but change in unison.
If we must, however, consider air of varying moisture this is not true but the two potential temperatures are not related in such a simple way. This is true when horizontal air motion is taken into account. There may also be problems when temporal averages are considered as the averages do not necessarily follow the same laws at values used in calculation of averages, because the laws may have variable coefficients.
Pekka Pirilä,
So if I understand you, the fact that relative humidity is generally less than 100% in the free troposphere means that moist (aka equivalent) potential temperature should not be used?
For reference for other readers here is the average relative humidity field:
SoD,
I don’t say that it should not be used, but rather than none of available variables does a perfect job. As long as we are guaranteed that relative humidity remains below 100% the standard potential temperature is fine. When the air is everywhere saturated the equivalent potential temperature works well and it works well also in some other cases when it gives the same results as the standard potential temperature. Thus it’s certainly useful in a wide range of situations, but not perfect always.
My understanding is that the equivalent potential temperature may give rather misleading results when winds lead to the situation where the moisture content varies significantly with altitude at relative humidities well below 100%. Similarly calculating averages at locations where the relative humidity varies essentially in time may lead to misleading results.
The plots that you have shown are interesting and informative but not as straightforward to interpret as you wrote. Thus the text should perhaps be reformulated but I’m not expert enough to propose what would be the best formulation. I’m a physicist but not an expert on atmosphere and my comments are based on general knowledge of physics and some simple reasoning.
Pekka Pirilä,
Not really.
(Dry) potential temperature, θ, is conserved in adiabatic processes for dry air and for moist air where no condensation or vaporization occurs.
Equivalent (aka “Moist”) potential temperature, θe, is conserved in adiabatic processes for both dry and moist air.
θe = θ exp(Lq/cpT)
where θe = equivalent (aka “Moist”) potential temperature
θ = (dry) potential temperature
L = latent heat of vaporization
q = specific humidity
cp = specific heat at constant pressure
T = temperature in K
If no condensation (or vaporization) occurs then q is constant.
Note that equivalent potential temperature is a different concept from the saturated adiabatic lapse rate.
So if we take the example of a parcel of moist air moving up from the surface it will follow a dry adiabat until condensation occurs (at the LCL = lifting condensation level), after which it follows the saturated adiabatic lapse rate. [Of course, if it mixes with dry or unsaturated air at any stage this changes things].
But for the entire (adiabatic) raising of this parcel of air, equivalent potential temperature is conserved.
And for reference here is the annual mean dry potential temperature:
c.f. Figure 8, we can see that in the upper troposphere and the stratosphere dry and equivalent potential temperatures are very similar.
SoD,
I don’t understand what you mean by “not really” as nothing in what you write further contradicts my statement.
The equivalent potential temperature is fine when we can follow one particular parcel or air and compare it only with other air that has gone trough the identical history, but it’s not valid when air of differing histories and consequently different moisture levels meet. All the derivations that you refer to are based on the single common history.
My second comment on the problems that we meet in applying the concepts to annual averages are true for all choices of temperature variable. In most regions the temperature profile follows closely either dry or moist adiabat over some altitude range during some periods but not the same adiabat or any adiabat always and not over the same range of altitudes. When that’s the case as it’s at high latitudes and less strongly at mid latitudes the annual average is nothing more than annual average of a variable that is determined by many different processes at different times. Only the tropics can be described fairly well by one approach.
Concerning the similarity of the two plots in the upper troposphere.
The plots must be similar in that region because the saturation absolute moisture is already so low that the energy released in condensation is rather small in comparison with heat capacity of dry air.
Pekka Pirilä,
Earlier you said:
Yet your latest comment (9:17pm) appears to agree that the figure does show it – due to the fact that both dry and equivalent potential temperature are almost the same for the upper troposphere.
SoD,
There must be some misunderstanding between us. In the upper troposphere where temperatures are low and absolute moisture also always low the dry and moist adiabat are almost identical and the potential temperatures also change in unison.
The differences occur in middle and low troposphere where we face as an example the situation that dry downcoming air warms rapidly and has a rather high lapse rate reduced by dissipative processes from the dry adiabat. That goes on until the warm air hits moister air of higher potential temperature near to the surface and cannot continue the downwards motion. This results in very low lapse rate and might result even in temperature inversion. Such situations are not equal over all seasons which leads to all kind of apparent effects in annual averages.
I think I share your concern for SoD’s explanation Pekka Pirila, there just aren’t enough variables in the formula offered. All ‘parcels’ of air are not equal for buoyancy! Without a connection between ‘q’ and the gravity constant, or at least ‘density’, a parcel finds ‘density equilibrium’ at an indeterminate ‘final altitude’ and ‘final temperature’ along the lapse rate curve.
Though, this is a complex problem that SoD may not want to include in this thread, as altitude and decompression also alters the relative humidity and the latent heat of condensation within the parcel.
Best regards, Ray Dart.
I failed the login test yet again.
Ray Dart, AKA suricat.
Ray.
The following is the sequence in an ideal model of how the increased CO2 heats the ground and atmosphere.
The process of adding CO2 to the atmosphere occurs from the surface, and convection and mixing distribute it to the rest of the atmosphere over a finite time. However, let us image an addition of an instantaneous well mixed quantity of CO2, small enough to not significantly affect the average CP or total mass of the atmosphere, so that the temperature level and lapse rate are also the same as before, immediately after the addition of the CO2. Also assume solar insolation is the same as before, and only consider solar energy absorption to occur at the ground. The question is: how does the surface and atmosphere heat up more from the greenhouse effect. The approximation will be used that the lapse rate, surface temperature, and solar insolation, are uniformly distributed over location and time to simplify the issue, and clouds and feedback are ignored.
When the CO2 level jumps up, the effective average outgoing radiation altitude to space also instantly increases. The average altitude was about 5 km before addition, due to previous levels of water vapor, CO2, and other greenhouse gases and clouds. An increase from doubling the CO2 has been claimed to cause an eventual increase in temperature of about 1.2 C if all other effects are unchanged. For an average environmental lapse rate of -6.5 C per km, this implies the average outgoing level was raised by about 185 m once new equilibrium was reached.
However, the raise in outgoing level would occur as soon as the CO2 level increases, and is not directly tied to the temperature. It is a radiation absorption issue only. Since the temperature was initially 1.2 C lower at 185 m above the initial 5 km level, the radiation to space is initially lower from the new level. When input and output were balanced, the average temperature of the 5 km level was 255 K, and radiated 239.7 W/m2. Initially at the new altitude (5.185 km), the average temperature is 253.8 K, and radiates 235.3 W/m2. Initially, just after the CO2 level made the step jump, the air temperature is the same as before. However, the increased resistance to radiation heat transfer up, due to the more opaque atmosphere, results is less of the absorbed solar energy being initially removed from the ground by radiation heat transfer (which is a significant, but not necessarily dominant means of heat transfer up). Note the back radiation is not heating the ground; it is just slowing the net radiation heat transfer up. This accumulating solar energy results in the ground heating up, as the excess energy accumulates. Once the ground heats up a small amount, this increases both convective and radiation heat-transfer, compared to just before the ground heated noticeably (but after the CO2 was added). However, at new equilibrium, total heat transfer out is the same as before (equals solar energy input), the convective heat transfer is a larger fraction of total heat transfer up at new equilibrium.
The increased heat transfer does not change the lapse rate at the new final equilibrium from before the CO2 was added. However, since the increased surface heating started immediately at addition of CO2, but the thermal lag of the finite mass of the atmosphere took a while to rebalance by convection and radiation, the lapse rate does increase some during the non-equilibrium stage. In the end, the energy is transmitted by conduction, convection, and radiation up through the atmosphere, driving it toward the same lapse rate as before the CO2 was added, but with the entire temperature level shifted up 1.2 C at final new equilibrium, for corresponding altitudes. This leads to the temperature at 5.185 km to be driven up to 255 K at the new equilibrium. At that point, the outgoing balanced incoming, and no additional heating of the surface or atmosphere occurred.
Leonard,
That’s one of the self-consistent ways of simplifying the description. My main complaint is that the heat capacity of the atmosphere is very small in comparison with the mixed surface layer of oceans. Therefore the adjustment of the atmospheric temperature is essentially instantaneous and the main source of delay is in oceans. Land areas are both smaller and faster to warm up.
Another point that’s not a complaint in the same sense is that I don’t like the emphasis given to the “average radiation level” as that’s not a physical entity but only a numerical value obtained from certain calculations. This is, however, more a matter of taste than disagreement on deeper level.
Pekka,
I agree with your points, but simplification makes the understanding of process easier to discuss. As far as the ocean accumulation, there are currents lasting hundreds to thousands of years, and just tracking a few years at a limited number of sites is by no means clear indication of what is happening.
[...] 2012/08/12: TSoD: Temperature Profile in the Atmosphere – The Lapse Rate [...]
SOD,
I have a question that this topic brings to mind.
The average atmosphere has a greenhouse radiative forcing which leads to an auto-convective atmosphere ( as seen in Manabe and Strickler):
http://www.drroyspencer.com/wp-content/uploads/Manabe-Strickler-1964-fig.4.png
Because this is unstable, convection restores the atmosphere to a more stable lapse rate, and in so doing, negates some portion of the radiative imbalance.
By adding additional CO2, presumably the radiative forcing alone leads to an even steeper lapse rate, but convection again opposes.
The Myhre paper indicates what the radiative forcing for a doubling of CO2 should be ( 3.7W/m^2). Much of the analysis assumes this level.
But that is before convection.
Isn’t the forcing overstated because it will be reversed by convection?
Couldn’t ALL of the radiative forcing be reversed by convective motion?
No, that’s after convection. All relevant scientific papers since Manabe and Strickler at least, if not for even longer, are based on an atmosphere whose temperature profile is restricted by convection. That’s always one central starting point.
The Myhre paper I was referring to regards forcing. The IPCC definition of RF does not include convection. The GCMs then model an atmosphere incorporating the RF as a climatic response.
This may be valid for all I know, but it is an asynchronous numerical solution to concurrent physical processes.
The Myhre paper is based on an atmosphere with convection but it needs not consider it explicitly. The calculation of forcing as is done in the Myhre paper assumes that the troposphere is unchanged in all other respects expect CO2 concentration. That affects radiation immediately but changes the temperatures as well as convection with delay. The IPCC definition of forcing refers to the moment before any temperatures have changed and before convection starts to change.
The changes in the temperatures and convection enter the analysis when the consequences of the forcing are considered, not in the forcing as defined by IPCC.
In the above replace “expect” by “except”.
Climate Weenie,
There are competing feedback effects. The forcing is easy to calculate but the feedbacks are the tricky bits.
From a simple perspective the lapse rate doesn’t change due to convection. When the atmosphere becomes more opaque the upper troposphere warms, and this reduces convection. Which is what warms the surface.
If you grasp this important principle then you can start to think about second order effects – the feedbacks.
There are other papers which express this better but as I had just used this graphic in an earlier article, here are the respective feedback effects as calculated by some GCMs from Soden:
As you can see the lapse rate feedback is a negative feedback. But this feedback is usually the increased radiation to space as a result of a warmer atmosphere.
I see what yer sayin’ – the GCMs determine convective response in the from of lapse rate feedback.
Worthwhile for me to re-read Manabe and Soden papers a number of times.
“From a simple perspective the lapse rate doesn’t change due to convection. When the atmosphere becomes more opaque the upper troposphere warms, and this reduces convection. Which is what warms the surface.”
You may wish to revisit this paragraph. Manabe demonstrates that convection warms the upper troposphere and cools the lower troposphere,
opposing the unstable atmosphere that radiation alone causes, which restores stability.
Climate Weenie,
The Manabe & Strickler 1964 paper (recommended to everyone) has a number of topics and the one which I think you are referring to is how the temperature profile under radiative-convective equilibrium differs from that under a solely radiative equilibrium.
In this case, of course the temperature cools more slowly (higher lapse rate) under radiative equilibrium and so convection (by comparison) results in a warmer upper troposphere.
This is a different topic from the mechanism of temperature change in the atmospheric/surface temperature profile due to an instantaneous change in CO2 concentration -which Manabe & Strickler don’t actually cover.
The Myhre paper calculates a net absorption increase of 3.7 W/m^2 per CO2 doubling (i.e an instantaneous reduction in direct surface radiation to space). This entire amount is then arbitrarily applied to the IPCC’s definition of ‘radiative forcing’, for which I argue is not only incorrect, but a rookie or freshman mistake. I maitain there is absolutely no physical or logical basis for which the atmosphere would downward re-emit this entire amount as it is applied to the IPCC’s definition of RF.
Also, despite what apparently most people think, RT simulations, such as what Myhre has done, do not actually calculate the IPCC’s defintion of RF. They calculate net changes in direct surface radiation to space for changes in GHG concentration, such as when CO2 is doubled.
RW,
You have not understood the Myhre paper (by that I refer to the 1998 GRL paper, but his earlier 1997 JGR paper explains some issues better). Myhre uses in his calculation several alternative models which all take as starting point the observed temperature profiles at three latitudes, that this is enough was demonstrated in the 1997 paper. The 1997 paper contains also more discussion on the models used.
The radiative transfer models calculate absorption and emission at all altitudes and are in this dependent on the temperature profiles. They indicate clearly that their calculation is not based on calculating only the net changes in direct surface radiation to space.
All your claims about deficiencies in the calculation are erroneous and must be caused on your ignorance of what was really done.
Pekka,
I’ve sought direct clarification on this specific point from Myhre himself. The physical meaning of the 3.7 W/m^2 is the instantaneous reduction in direct surface radiation to space. That is, when CO2 is doubled the atmosphere absorbs an additional 3.7 W/m^2 of surface radiative power that was previously passing directly from the surface into space the same as if the atmosphere wasn’t even there. Now of course the absorption occurs all the way up at different amounts at different altitudes, but the 3.7 W/m^2 is the total net absorption increase through to the TOA because it includes a stratosphere adjustment (which is very small anyway).
My point is that what is being calculated in RT says and implies absolutely nothing about what happens after absorption, and has been arbitrarily assumed to be all downward directed upon re-emission by the atmosphere via the IPCC’s definition of RF, for which there is no physical or logical basis.
There must have been a misunderstanding between you and Myhre.
Pekka,
email me and I’ll forward you the entire exchange I had with Myhre.
wetmorer @hotmail.com
Pekka,
In other words, what I’m saying is the RT simulations calculate the net absorption increase for changes in GHG concentrations. They do not calculate the IPCC’s definition of RF, i.e. change in net (down minus up) irradiance (solar plus long-wave; in Wm-2).
Click my name and check last lines of “About me” for email address.
Found it and forwarded…
Perhaps a better way to put this is the physical meaning of the 3.7 W/m^2 per CO2 doubling is just plain ‘minus up’.
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scienceofdoom,
You appear to not have read my comment Aug 12 at 7:45 pm. The main energy going into the atmosphere comes from the solar heated surface, and direct atmospheric absorption of solar energy by clouds. However increased CO2 does not directly increasing cloud effects. The initial response to increasing CO2 is to make the atmosphere slightly more opaque to long wave radiation, with little effect on incoming solar energy, and raise the average altitude of outgoing long wave radiation. This does not initially result in heating of the upper Troposphere and reduced convection. It reduces surface radiation heat transfer up and increases surface convection, due to the surface heating more from the reduced radiation heat transfer. Total heat transfer up is initially increased over the level before addition of CO2 (with all of the increase due to convection effects, not radiation), but once the entire atmosphere is heated to the new level (with lag due to thermal capacity), due to the raising of the altitude of outgoing radiation, the total heat transfer up is the same as before (and equals absorbed solar energy). At the new level, the radiation heat transfer up is less than before, but convection up increases.
My last sentence is for heat transfer from the surface. Obviously at the outgoing altitude, all escaping energy is radiation, and at equilibrium, equals absorbed solar energy.
Leonard,
I don’t think I agree with you. Finally, we might have a real disagreement!
A more opaque atmosphere will radiate less to space from the mid to upper troposphere which cools it = radiative cooling. Let’s call this Δu.
The surface will experience a much less significant change, an increase in DLR = radiative heating. Let’s call this Δd.
I believe that Δu > Δd.
Agree or disagree? (before I go further)
I disagree with your contention. The convection continually adjusts to maintain the lapse rate (locally warm spots are more buoyant so quickly rise to mix and restore the local environmental lapse rate), so variations in radiation heat transfer does not significantly change the average temperature profile in the atmosphere even at fairly short time scales. However, the increased opaqueness would immediately cut radiation heat transfer from the surface, so it would heat up. There is a significant lag to transfer to the air, especially from the oceans (note most of the energy absorbed in the oceans is at significant depths).
scienceofdoom,
To specifically respond to your question, keep in mind that atmospheric omnidirectional radiation fluxes occur based on local absolute concentration of absorbing and radiating gases and local average temperatures. The outgoing radiation to space occurs from a range of altitudes, but on average is from about 5 km. At this altitude, both lower radiating gas concentrations and significantly lower average atmospheric temperature occurs than from near the surface. Thus the downward amount of atmospheric radiation near the ground, (delta d) is > than (delta u), the radiation upward to space (or upward from any altitude higher than a lower portion of atmosphere). There is no steady state condition that this is not so for real atmospheres. Even for transient conditions, there would not be a hot spot since the convection and reduced radiation flux up from lower levels does not increase local energy concentration faster than the lapse rate at whatever level it as the entire profile shifted up to the slightly warmer temperature at corresponding altitudes.
SOD,
One more comment. The large increase in DLR is due to the greater opaqueness of the atmosphere resulting in DLR coming from location closer to the ground, which are warmer than from the initial higher locations. Since net radiation flux is the difference of the ground up minus the absorbed air down, the net flux up decreases, and solar energy accumulates on the surface but added convection removes it.
Leonard,
To clarify, d > u (that is, the DLR at the surface is greater than the emission to space from the atmosphere)
But I expect that under this dynamic condition Δd < Δu (Scenario A)
The reasons for this can’t be determined “by inspection” because it is a very non-linear problem. I haven’t proven it, I expect it. The reason is primarily about the DLR from water vapor at the surface.
And I could be wrong. I can test it without water vapor because I have built a line by line MATLAB model. But to include water vapor properly I need a continuum model which is especially important for water vapor near the surface because there is a (specific humidity)2 relationship.
In any case, if it turns out that Δd > Δu (Scenario B) then in that case the dynamic description would be a little more complicated but we would come to the same conclusion about the new steady state condition (we have already agreed about the steady state condition).
Under Scenario A, the description should be correct – do you agree? (I realize you don’t accept Scenario A at the moment).
Under Scenario B:
- the surface warms up due to the increased DLR
- the upper atmosphere warms up (but less) due to a reduction in radiative cooling
- what happens next exactly depends on the profile of warming in the atmosphere due to less CO2 radiative cooling:
SOD and others: When I look at the Moist Potential Temperature Plot (latitude vs altitude, Figure 8) and the Relative Humidity Plot, I try to picture them superimposed with the Hadley and other cells. If I understand the situation correctly, parcels of air can move along lines of equal moist potential temperature without any work being done by or on the parcel. The fact that these plots are annual means and zonal averages complicates things.
a) The dark green band from 20S to 20N is obviously associated with the ascending branch of the Hadley circulation which appears to be rising adiabatically since it is all the same potential temperature (340 degK). The plot doesn’t actually tell us if the air is rising or falling, just that it appears to be well-mixed adiabatically from the surface to 200 mb.
b) The descending branch of the Hadley circulation comes down with a potential temperature of 320-330, probably after radiatively cooling at 200 mb. Cooling would require about 5-10 days according to Figure 6. The slight tilt to the lines suggests that the air doesn’t descent perfectly vertically or adiabatically.
c) However, the relative humidity plot shows us that the Hadley circulation is not an adiabatic process. As the Hadley circulation descends from 700 mb to 900 mb, relative humidity nearly doubles despite the rising temperature. Is there some sort of turbulent boundary layer mixing at these altitudes (that brings in moisture from the ocean, but not over land)? Likewise, there is some reduction in the relative humidity of the ascending branch, where one might anticipate 100% relative humidity during adiabatic movement.
d) I can’t really see any signs of the polar or Ferrel cells, suggesting that they may move slowly enough that mixing or radiation make these significantly non-adiabatic circulations.
e) The constant potential temperature at all latitudes just above 200 mb is consistent with, but does not require, the existence of meridional circulation at this altitude. Is there an explanation for the constant potential energy at this altitude? What radiative equilibrium (Figure 7) would look like on a moist potential temperature plot?
Frank,
Good questions. I will be writing some articles about global atmospheric circulation and we can try and address these points along the way.
Leonard,
Is there a way to directly email you?
RW,
You can mail me at the National Institute of Aerospace, where I am currently employed. My e-mail (which could be found on the web for that location) is:
leonard.weinstein@nianet.org
Thanks. I have emailed you.
FWIW, while the lapse rate is independent of temperature, the temperature at any point in the atmosphere depends on the temperature at the surface and THAT depends on the greenhouse effect. The simplest way of visualizing this is that the greenhouse effect shifts the line in Fig1, moving the intercept
Eli,
Who or what are you responding to. Both SOD and I both agree that is true. No one I know said otherwise. If one of my statements made you think I indicated otherwise, then my text was not clear enough, but I don’t know where.
As usual there was lots of the usual triumphant back and forth about how the lapse rate is independent of the greenhouse effect, which is true, but Eli merely pointed out that the greenhouse effect is the major determinant of the actual temperature at all tropospheric altitudes. Otherwise it would be a hell of a lot more like Antarctica in the tropics. Was not directed specifically at thee at all.
Eli Rabett says….. without the greenhouse effect…..
” Otherwise it would be a hell of a lot more like Antarctica in the tropics”
Solar isolation producing a maximum of 123C at the equator .
Underwater volcanic activity keeping some parts of Oceans from freezing up.
These two facts alone should remove any cause for alarm on that score.
Oh right, those mysterious underwater volcanoes. As Fermi said about aliens where are they. OTOH, Eli reads blogs.
Eli,
Again, what are you responding to. I have stated often that the lapse rate is temperature independent, but the level is determined by the solar insolation combined with greenhouse effect (altitude of outgoing radiation).
Leonard – to be picky: the temperature at any point in the troposphere depends (mainly, but not only) on the temperature at TOA (actually, at the top of the troposphere), and that depends (also) on the greenhouse effect.
The surface is not magically changing the temperature at TOA, it’s the other way around.
“the greenhouse effect is the major determinant of the actual temperature at all tropospheric altitudes. Otherwise it would be a hell of a lot more like Antarctica in the tropics”
That is backwards, of course.
Were radiative forcing not countered by convection, the surface would be much hotter than it actually is.
The tropics would be not a hell of a lot more like Antarctica, but a hell of a lot more like hell.
SOD,
All of my comments assumed the water vapor did not increase significantly when the CO2 jumped, so it is not a player at the start of the transition. It would eventually increase with time (it has to significantly heat at the surface, surface water evaporate, and be convected partially up), but then the entire system would go to the new equilibrium probably as fast. There may be some intermediate state where water vapor would allow a hot spot, but not at the start, or at the new equilibrium. Obviously the real world is much more complicated (even the lapse rate is not really short term constant, and day to night and other variations make any transition too complex to realistically model well).
The basic point I want to make is that even though the outgoing radiation flux is decreased at the beginning of the transition, so is the upward radiation net heat transfer feeding the middle and upper atmosphere. i.e, the radiation heat transfer is everywhere (except right at the surface) reduced at first, and convection controls the lapse rate. Please note that radiation heat transfer is smallest at the surface (due to the added component of convective heat transfer), and largest at the altitudes where it goes to space (since convective heat transfer approaches zero there).
Leonard,
I was also assuming no instantaneous change in water vapor.
If we took a dry atmosphere then I agree with your reasoning. My understanding, which I am happy to be proven wrong about, is that in the lower troposphere water vapor radiation is so strong that CO2 concentration changes have less effect than would be expected. I.e., if the atmosphere is already radiating strongly at a certain wavelength then more CO2 has little effect.
It is probably of curiosity value only..
Within limits. At the surface concentrations of CO2 can vary strongly, as can concentrations of H2O and, at least in the CO2 bend region there is not so much overlap (try it with SpectralCalc. Of course, there is also the issue of aerosols.
SOD,
If somehow scenario A ( Δd < Δu) were true for a transient condition, then there could be a transient hot spot. I do not see how it is likely for the reasons I stated. I think we both agree on the final equilibrium state.
SOD,
Keep in mind that in the real world, CO2 presently increases about 2 ppm per YEAR. Atmospheric mixing and shifting elevation is very slow, so no real chance of scenario A seems possible, since the atmospheric lapse rate adjustments would occur much faster than in a year, and the result would be essentially continuous essentially equilibrium states.
Given that you can see the annual cycle in the various CO2 mixing ratio records, it is not so slow. FWIW, in general it takes about 5 years to push a gas molecule from the surface up to the tropopause, so mixing at 1 or 2 km would be just a matter of months. Mixing across the equator would be at about the same order or a bit faster (look at the lags in the CFC mixing ratio measurements.)
Warmer sea surface increases moisture at low latitudes. That’s expected to result in a reduced lapse rate and larger warming at fixed altitude than at the surface. The moisture content of the atmosphere is close to the saturation value and thus determined by the local temperature. At the same temperature the moisture is as high after the warming as it was before. That means further that the emission directly to space from water vapor is close to the same after the warming as it was before.
Considering the situation as was done above we see that there is very little feedback from low altitude water vapor changes. More detailed analysis would certainly find some effect, but from the above we can understand why the water vapor feedback and lapse rate feedback cancel largely at low latitudes. The well known observation that their sum is known more accurately than they are separately has a clear physical reason in the fact that the moisture level is controlled by the local temperature of the air.
Similar considerations do not apply in situations where the moisture is not near saturation as it is guaranteed to be in the raising air over tropical ocean.
Leonard Weinstein writes: “An increase from doubling the CO2 has been claimed to cause an eventual increase in temperature of about 1.2 C if all other effects are unchanged. For an average environmental lapse rate of -6.5 C per km, this implies the average outgoing level was raised by about 185 m once new equilibrium was reached.”
All this makes sense if the lapse rate itself doesn’t react to the increased radiative forcing. But of course we know it must do because any increase in surface temperature leads to enhanced evaporation from the oceans thus reducing the lapse rate. How else did is it possible that life on Earth survived for the last 3 billion years ?
What about CO2 ? The basic argument for the enhanced greenhouse effect depends on a raising of the effective height of the free path length for IR photons of CO2 to colder levels thus reducing heat loss to space. If simultaneously enhanced CO2 forcing leads to an adjustment of the lapse rate caused by induced evaporation from 70% coverage of global oceans then there is negative feedback.
What I tried to explain is that the negative lapse rate feedback that you describe is always and unavoidably linked with an equal positive water vapor feedback that cancels its effect locally. Elsewhere the water vapor feedback is stronger and therefore the net effect of these feedbacks is positive.
Clive,
Your second comment discusses an additional point that leads to a negative feedback of some strength. That brings, however, up the questionable value of the concept of average altitude of emission to space. It must be understood that this value is never calculated as an average of some distribution of altitudes but it’s determined by calculating first the the total emission, determining then the temperature of a black body that emits as much and checking then what is the altitude of that temperature in an averaged atmosphere. Thus any change in atmosphere that influences the outgoing radiation influences also this “average altitude”. Calling it the “average altitude” is really misleading, “effective radiative altitude” might correspond better to the meaning of this value.
With increasing temperature of the tropical ocean and reduced lapse rate the convection reaches higher altitudes and the tropopause is pushed up. The temperature of the tropopause is not likely to change much as the net effect of all changes, what changes more is its altitude as far as I understand. Both before and after the change we’ll have around tropopause a range of altitudes from uppermost troposphere to low stratosphere of a temperature close to the minimum. The change in the CO2 concentration is not the only reason for the apparent change in the altitude of emission at wavelengths dominated by CO2, the change in the temperature profile has also a significant effect. There will always be more CO2 near to the temperature of the tropopause than near the somewhat higher temperatures of the upper troposphere because the thickness of such a layer is inversely proportional to the local lapse rate. That gives always a special importance for the layers around the tropopause. That means further that all mechanisms that raise the altitude of the tropopause are important for the radiative balance, not only the change in CO2 concentration.
I don’t claim that I understand all the details but I’m pretty sure that most of the commonly presented descriptions are significantly incomplete.
SoD,
I’m wondering why my comments end very often in the state of awaiting moderation (as one comment did again a while ago). Not nearly every time but perhaps every third time or so. Do you have any idea of the reason for that?
Pekka,
It must be frustrating. A lot of Frank’s comments end up in moderation for reasons I have never been able to work out.
I’m using hosted WordPress and it comes with a lot of under the hood stuff that I can’t change (and wouldn’t want to try). If it decides there is something not right it puts it into moderation. If it is more sure there is something not right it puts it into spam. Some of the WordPress algorithms are determined by what is happening on other blogs.
Not a perfect world and sorry to all those who get comments held up for a long time.
For anyone who gets a comment disappearing please email me at scienceofdoom – you know what goes here – gmail.com. For comments that say “In moderation” I already will have a WordPress email waiting for me.
Clive Best,
As far as I can tell from the published data, there is a modest increase in very low altitude absolute water vapor level, but not in relative humidity, which is the major cause of change of lapse rate. At higher altitudes, the absolute water vapor level does not show significant change, and relative humidity actually decreases. The net effect of all seems to be no obvious change in average lapse rate.
Clive Best,
“What about CO2 ? The basic argument for the enhanced greenhouse effect depends on a raising of the effective height of the free path length for IR photons of CO2 to colder levels thus reducing heat loss to space. If simultaneously enhanced CO2 forcing leads to an adjustment of the lapse rate caused by induced evaporation from 70% coverage of global oceans then there is negative feedback.”
What do you mean by ‘enhanced greenhouse effect’ in this context? Also, negative feedback in what way? Increased cooling of the surface via increased heat removed from the surface as the latent heat of evaporation? Or something else?
@RW @ Leonard I am referring to AGW (enhanced greenhouse effect) caused by human emissions of CO2. An induced change in energy flux through the atmosphere must surely also be reflected by a change in the lapse rate. Changes in water vapor is one obvious source for this. However I suspect that CO2 has also a role here.
I think the lapse rate will change increases in CO2 because more IR photons emitted from the surface will now be absorbed by CO2 molecules than before. Part of this energy will be transfered to nearby N2 and O2 molecules, and the rest re-emitted as photons randomly. This essentially causes a gradient heat flow through the atmosphere.
If anthropogenic increases in CO2 itself changes the lapse rate by thermalising absorbed IR with adjacent air throughout the atmosphere, then it too would provide negative feedback by reducing the lapse rate. In other words the effective radiation altitude where the CO2 fog clears is now slightly warmer than it was before (due now just to CO2). Perhaps this thermalising effect is already included in radiative transfer models, but I have never seen this stated explicitly.
Pekka Pirilä argued that the H2O negative feedback from the lapse rate is almost exactly balanced by the positive feedback from extra H2O greenhouse effect. If the same turned out to be the case for CO2 then we can all go home !
OK, so by ‘enhanced greenhouse effect’, you are not referring to claimed net positive feedback. That’s what I was asking. You won’t get any argument from me that the case for net positive feedback, let alone net positive feedback of 300% or more coming from the two most dynamic components of the whole atmosphere (clouds and water vapor), is spectacularly flawed.
What I discussed applies to water vapour because water condesates when the temperature drops and very little water is left when the tropopause is reached. Nothing comparable occurs with CO2.
CO2 has very little direct influence on lapse rate because it has little effect on the thermodynamic properties of air at the present or foreseeable concentrations and because the lapse rate is determined by these properties rather than changes in radiative energy transfer as long as we are in troposphere.
Clive Best,
And this is a helpful comment because it shows that you have no idea about the subject at all.
What is an adiabatic process?
Have a read of Potential Temperature.
Those who have not understood physics basics are doomed to perpetual mixing up of the basics.
Have you wondered why not a single atmospheric physics text book agrees with you? Do you even know that not a single atmospheric physics text book agrees with you?
SoD: Lets try and keep the abuse to a minimum! Adiabatic means no heat input into the system. I am simply trying to better understand myself what drives the lapse rate. I am not trying to preach some dogma! If I am wrong then I will simply accept my mistake – for me it is not a problem. A perfect M-B gas without any greenhouse gases – i.e.no H2O or CO2 will result in a DALR – however you derive it. Such a planet will radiate freely to space from the surface but will also loose a small amount of kinetic energy, and IR radiation from ionised gas into space . Some energy balance will eventually be reached maximising entropy. Gravity and Cp(bulk heat transfer) determine the lapse rate.
Adding H2O and CO2 causes IR energy(heat) to be absorbed differentially throughout the atmosphere. H2O has 2 phase transitions at Earth temperatures resulting rapid heat flux responses. CO2 also effects the lapse rate by diffusing heat from up the surface. Any change in either water vapor or CO2 concentration must therefore change the lapse rate.
Punto Basta.
Clive,
Some greenhouse gases are needed to create a convective atmosphere. Without any absorption and emission of radiation the atmosphere would be essentially isothermal and relatively warm in comparison with most of surface, because it would lack all strong mechanisms that could cool it.
As soon as we have convection the lapse rate is determined by it. More CO2 will increase a little the heigth of the troposphere but not the lapse rate within it.
Clive Best (August 20, 2012 at 9:32 pm)
I apologize.
So many people keep confidently disputing physics 101 that I find it difficult to always stay calm.
Clive,
Thermalising absorbed radiation does not affect the lapse rate. Convection adjusts it. The increase in CO2 is far too small alone to affect the average Cp, and thus lapse rate.
Leonard,
Thanks for the clear statement ! Although I still need to think about it !
cheers
Clive
Should read : I think the lapse rate will change as a consequence of increases in CO2
@Pekka Pirilä .
I think you have hit the nail on the head…..
“Some greenhouse gases are needed to create a convective atmosphere. Without any absorption and emission of radiation the atmosphere would be essentially isothermal and relatively warm in comparison with most of surface, because it would lack all strong mechanisms that could cool it.”
If the atmosphere consisted only of nitrogen – would there be a lapse rate ?
Please convince me !
The greenhouse gases emit radiation from the top of atmosphere making it colder than the surface. That’s the reason for any lapse rate. Pure nitrogen emits extremely little and would not have any lapse rate or actually it might be warmer at the top as it absorbs some UV from sun.
With enough greenhouse gases the lapse rate would be higher than is stable. That leads to convection that brings the lapse rate to the limit of stability. This limit is the adiabatic lapse rate. It’s value depends on density and specific heat of the gas and also on moisture and heat of condesation in case of air saturated by water vapor.
Doesn’t gravity comes in here somewhere as well ? Nitrogen molecules must still loose energy rising to the top of the atmosphere. With a fixed surface temperature of ~ 288K and ~ 3K temperature for outer space surely there must still be a temperature gradient even without greenhouse gases ?
I have my umbrella open for more abuse !
Gravity has always one effect: It makes the density of the atmosphere smaller at higher altitudes. There are less molecules that have high velocities and there are less molecules at high altitudes, but the average velocity does not depend on the altitude in an atmosphere where convection is excluded.
Each individual molecule slows down when going up, but that’s exactly canceled by the effect that originally faster molecules are more likely to go up than slow ones. The exact cancellation applies to a atmosphere that totally insulated in all other aspects except that it’s in contact with a surface of constant temperature at bottom. Even nitrogen has some interaction, only extremely weak, and the Earth surface is not at constant temperature. These factors change the situation a little, but even so an atmosphere of pure nitrogen would be close to isothermal. There would be a thin layer of inversion near surface when the atmosphere is warmer. That stops effectively the cooling influence of cold surface, Higher up conduction would win over very long periods and bring the atmosphere close to isothermal. The conduction is a very weak process but even so it would probably be the strongest one.
All the above is of little relevance for understanding the troposphere but it’s closer to what happens in stratosphere of the real Earth atmosphere.
The adiabatic lapse rate is the temperature change (K/km) that a parcel of air has if it is vertically displaced adiabatically.
This means, if you move a parcel of air 1km upwards how much does its temperature change if there is no transfer of energy in or out of the parcel of air.
The temperature changes because the pressure reduces with altitude and so the parcel of air expands. This is doing work against its environment and the first law of thermodynamics says that this energy must come from somewhere. It comes from internal energy of the parcel of air, thus reducing its temperature.
The reason this is a useful concept is because conduction and radiation move heat relatively slowly compared with atmospheric motion (the wind).
We can see that this is a useful concept because the theoretically calculated adiabatic lapse rate matches the actual environment where convection is common.
If the environment creates a temperature drop with altitude which is greater than the adiabatic lapse rate then convection will take place, as explained in Density, Stability and Motion in Fluids.
Regardless of whether any significant convection ever occurs in practice, if you displace a parcel of air adiabatically by 1km it will reduce in temperature by an amount determined by the adiabatic lapse rate.
All of which has been explained in previous articles.
And it doesn’t mean that the atmosphere does not absorb and emit radiation. It is one very small part of the jigsaw puzzle called climate.
This discussion has been very useful for me at any rate, because it has cleared up in my mind what is the basic driver for the lapse rate.
Without any greenhouse gases in air there would be no IR loss to space from the top of the atmosphere. The Earth would then radiate directly from the surface and the average temperature would be -18C. The atmopsphere would become approximately isothermal also with a temperature of ~ -18C
Hydrostatic change of pressure with height remains the same.
There would be no lapse rate and essentially no convection in the atmosphere.
Now we add greenhouse gases so the atmosphere itself absorbs and radiates energy to space. Loosing energy from the top of the atmosphere sets up a temperature gradient. Convection then drives the lapse rate towards the DALR. Nick Stokes has given an analogy with a heat pump where work is expended to maintain the lapse rate, which I think is rather nice.
“The heat pump is provided by vertical air movements (the energy comes from the KE lost). Heat is pumped down, balancing the conduction upward, and this is the mechanism pushing the lapse rate toward the DALR. Pump efficiency is proportional to the deviation from the DALR. So the actual lapse rate settles to a point below the DALR where the heat pump balances the conductive losses (including IR transport). Adding GHGs pushes that balance point further below.”
Clive,
All known atmospheres contain some “greenhouse gases”, even if in relatively small concentration. Since thermal conductivity in the absence of convection is incredibly slow (it would take from many thousands to millions of years to conduct energy from the ground to the top of the atmosphere in the absence of convection), even a small amount of convection would totally dominate the mixed state of any atmosphere. Except for conditions where radiation cooling make the ground cooler than the air above it (night or comparable), the mixing due to wind from day/night variation and different latitude temperatures, and buoyancy of ground heated air would tend to maintain a lapse rate close to adiabatic (with possible modification due to evaporation and condensation). The adiabatic lapse rate is only dependent on specific heat of the air and level of gravity. The actual level of temperature in the profile is only dependent on absorbed solar energy, lapse rate, and average altitude of outgoing long wave radiation. Even with very little absorbing gas, so that the outgoing altitude is near the ground, the lapse rate will establish as near the “wet adiabatic level”. The condition for an average isothermal atmosphere is not realistic with real atmospheres.
Leonard,
I like to think in the way Clive presented the logic. That the one alternative is purely theoretical does not take anything off from the value it has in understanding what’s going on.
Furthermore the case of only a little greenhouse gases would not be so different from that in the sense that the troposphere with it’s adiabatic lapse rate would then be only a small part of the atmosphere. The tropopause would be at much lower altitude and most of the atmosphere would be in stratosphere even by air mass.
Clive,
If the absorbing gases were very small (say no water vapor or methane, and CO2 at only 10 ppm) so that the level of outgoing radiation was very near the ground, and assuming the same absorbed solar insolation, the ground would only be slightly above 255 K, but the atmosphere would have a lapse rate close to 10 K per km.
Yes, the lapse rate would be the same but extend only to very low altitudes.
Pekka,
Heating in the Stratosphere is due to UV dissociation of O2 and formation of Ozone, which absorbs solar energy to heat. Reducing greenhouse gases would not lower the altitude this occurs at. While a much lower average altitude of outgoing radiation from ground absorbed radiation would result in much lower mixing at higher altitude (but still some from spill over from lower level winds), conductivity is still a MUCH lower speed process, so even the small residual spill over mixing combined with the small amount of thermal conduction downward, and small residual radiation (some CO2 would exist all the way up) would not reduce the location of the Tropopause as much as you seem to indicate, even though it would lower some. The result would likely be a slow deviation from lapse rate over a large distance, and a much broader Tropopause. The devil is in the details.
Leonard,
I admit my error.
The absolute temperature of the tropopause is 16% lower than the surface temperature in case of an atmosphere with very weak absorption and emission of all radiation as long as there’s enough radiative heat transfer to dominate over conduction. Only when the radiative heat transfer is so extremely weak that conduction gets important the temperature of the tropopause gets close to the surface and it’s altitude correspondingly low.
Nitrogen does absorb far ultraviolet and that has also some lowering influence on the altitude of tropopause, but the solar radiation has very little energy at those wavelengths. Thus the effect is rather weak.
I have to make a further correction.
The value of 16% that I mention above is derived in Pierrehumbert’s book on Planetary Climates for a atmosphere that’s gray over the LWIR range of wavelengths and transparent for incoming solar radiation. Furthermore an emittivity of 100% is assumed for the surface. It’s based on the following simple argument:
When absorptivity/emissivity is very small practically all LW radiation absorbed by the atmospheric gases originates at the surface. The gas emits equal amounts downwards and upwards but the radiation from the surface is only the upwards radiation. For radiative balance that is the signature of the tropopause the upwards radiation from the gas must be one half of the radiation it absorbs from that coming from the surface. For gray gas the Stefan-Boltzmann formula is valid and radiation is proportional to the fourth power of the temperature. Fourth root of 0.5 is 0.84 or 16% less than 1.0. This is the 16% I mentioned.
If the only significant GHG is CO2, the 15 um band dominates both absorption and emission. Thus we must determine the temperature from the requirement that Planck’s law gives a emittive power of one half for the radiation at that particular wavelength in comparison to that obtained at the temperature of the surface. Taking for the surface temperature the value of 278K the corresponding temperature is 232K. As another example choosing 254K as the surface temperature the temperature of the tropopause turns out to be 215K. Temperature ratios are for these cases 0.83 and 0.85. Thus the value of 0.84 is a good approximation for the 15um band of CO2 but the result would be quite different if the only important wavelength would be 5um as an example (ratios 0.94 and 0.94). Here we see that the temperature dependence at a single wavelength may differ strongly from that of a gray or black body.
SOD and LW
I must be missing something; for this and the previous article and comment all seem more complicated than need be.
The slope of the dry adiabat (the lapse rate) varies inversely with specific heat at constant pressure. H2O has a higher specific heat than dry air and the moist lapse rate is steeper than the dry one. CO2 has a lower specific heat than dry air and moves the adiabat back towards its original slope. Neither change in the slope of the adiabat affects the surface temperature. Why, then, do we expect increasing quantities of CO2 in the atmosphere to warm the surface?
A warmer surface requires an outwards shift of the adiabat. Adding CO2, the heaviest of the atmospheric gases, would do this. By contrast, adding the lighter-than-air H2O gas would shift the adiabat inwards and reduce surface temperature.
But change in atmospheric density is not among the explanations usually given for a warming surface. One of these is that adding CO2 forces atmospheric radiation to space higher and weaker resulting in the atmosphere losing energy to space at a lesser rate. Supplied with energy from below at an unchanged rate, the atmosphere thus stores energy and warms. A warmer atmosphere relative to the surface steepens the adiabat (reduces the lapse rate). It doesn’t outward shift the adiabat and warm the surface, as Leonard Weinstein’s explanation implies. The warming of the atmosphere carries a self-regulating negative feedback – its rate of energy loss to space increases and stored energy and temperature reduce. With reference to the adiabat, the addition of CO2 moves the radiating co-ordinate up the adiabat and rotates the adiabat clockwise about its origin at the surface; while the negative feedback reverses these movements. But wherever the adiabat and the radiating co-ordinate on it settle at the new equilibrium, the surface temperature remains unchanged.
Another explanation involves the warmer atmosphere radiating to the surface at greater intensity causing it to warm. This is the contentious “back- radiation” which follows Prevost’s theory of radiative exchanges (1792) but contravenes Clausius’s 2LoT (which forbids energy transport from colder to warmer regions- 1850). SOD explains away the apparent theoretical conflict with his credulity-stretching “imaginary vs real 2LoT”. LW on the other hand, though recognising back-radiation, disallows its direct surface warming quality, instead attributing to it a quality of resisting energy loss from the surface which translates, via an ill-defined mechanism, to a warming surface due to storage of solar energy.
Hoping that my interpretations of these analyses are reasonable, evidently both can’t be right and, I would submit, both are flawed. The models employed by both analysts ignore the ubiquitous presence of radiation and direct interaction with bodies it surrounds. Absorption and emission of radiation involving the surface or atmospheric GHGs would then result in changes in the energy density of the surrounding radiation medium, absorption reducing it, emission increasing it. This would obviate the general need for complicating view factors between bodies mutually exchanging radiation and for atmospheric back-radiation specifically. It would also obviate the cognitive disjunct between K&T’s assessment of the relative energy supply to the surface from the atmosphere and from the sun, 2:1 in favour of the atmosphere, and everyday experience.
SOD, if I might be so bold as to venture to suggest a theme for a future article it would be: Experimental provenance of mutually exclusive theories: radiative exchanges which prescribes atmospheric back-radiation and 2LoT which proscribes it.
John..
..Comment moved to the The Amazing Case of “Back-Radiation” article..
John Millett,
The moist adiabat is steeper than the dry one not because of the specific heat capacity of water vapor vs dry air. The moist adiabat is steeper because the latent heat term appears in the conservation of energy equation that is used to derive the lapse rate.
Do the calculation for yourself of the difference in heat capacity of dry air vs moist air at 15g/kg and report back with the answer. Likewise for dry air with CO2 at 280ppm vs 560ppm.
Perhaps a reformulation on the role of latent heat release is helpful for some people. (There’s nothing new in this except in the formulation.)
When a parcel of air moves up it expands, which means that it pushes surrounding air outwards. In that it uses it’s internal thermal energy to do work. That means that the air cools. How much it cools is determined by the temperature change that is needed to release the required amount of energy.
In dry air the ratio of energy released and temperature change is the specific heat. When the air is saturated by water vapor the decrease in temperature leads to condensation of part of the moisture because the saturation value of absolute moisture decreases rapidly with decreasing temperature. This adds to the the energy released when the temperature decreases and has an effect similar to an addition to the specific heat to create a higher “effective specific heat”. The moist adiabat is obtained when the calculation is determined using this “effective specific heat”.
There are some additional effects related to the expansion and to the reduction in the number of molecules in gas phase, but these effects are much smaller under atmospheric conditions and they are taken into account when the calculation is actually done.
In lower and middle troposphere the release of latent heat is a very significant effect. In highest troposphere it a small effect because the saturation moisture is so small at lowest tropospheric temperatures that further reductions in moisture cannot release much energy any more. The influence of the specific heat of CO2 is always negligible and that of water vapor is also small but not totally negligible in the warm moist air of lower troposphere at low latitudes where around 5% of air is water vapor.
One further difference is that the above is presented for the upwards motion of the air parcel. For the downwards motion the adiabat is typically the dry adiabat as the water droplets or ice particles may have fallen down or reached large enough size to prevent the rapid evaporation that would be needed to maintain saturation in warming air.
Pekka Pirila
That was useful, thankyou. A couple of points:
“When a parcel of air moves up it expands, which means that it pushes surrounding air outwards. In that it uses it’s internal thermal energy to do work. That means that the air cools. How much it cools is determined by the temperature change that is needed to release the required amount of energy”.
Why does the air parcel move upwards?
It is common knowledge that “hot air rises”. However, a hot air balloon rises, not proximately because the air inside it is hot, rather because the resultant higher energy density raises the pressure inside above that outside; and the outside pressure is lower at the top than at the bottom. I think the same mechanism applies in the natural air parcel, resulting in a vertical elongation of the parcel as observed in cloud formation.
The phrase “release the required amount of energy” asks “released to where?”. It can’t be to the surroundings, it can only be internally. I find it more satisfactory to think in terms of reducing energy density which occurs as volume increases as the higher internal pressure pushes the parcel boundary outwards (mainly upwards). The specific heat quantifies the relationship between changes in energy density and temperature. Moist air’s higher specific heat explains its steeper adiabat.
John Millet,
The energy released is used to do the work inherent in the expansion of the volume of the parcel, i.e. in pushing the rest of the atmosphere out of the extra volume taken by the parcel when it expands.
The reason for the rising motion of a parcel is often in its temperature being higher than the surrounding atmosphere has at the same altitude. Going further back to the reason of this temperature difference the reason is typically in the temperature of the surface at that location. There might, e.g., be a dark spot that absorbs more solar radiation and gets hotter than the surrounding areas. Another common reason for the rising movement is in larger scale air flows that may force the parcel to go up while its temperature is not different from the surrounding air at the same altitude.
Scienceofdoom
“The moist adiabat is steeper because the latent heat term appears in the conservation of energy equation that is used to derive the lapse rate”.
I take your point: insignificant GHGs can have only minuscule effects on the lapse rate through variations in either specific heat or density. Something else is needed to explain the large difference between dry and moist lapse rates. I think I see the link between lapse rate (an atmospheric temperature profile) and atmospheric energy balance (the time rate of change of atmospheric energy content). An increase in the latter implies the atmosphere cooling faster relative to the surface, that is, an increase in the lapse rate, a flattening of the adiabat.
John Millett,
I will copy your comment to the The Amazing Case of “Back-Radiation” article and you can discuss your amazing theories there. Readers please respond on the topic of back radiation in that article. John Millett has already explained his theory in the comments there.
Thanks, Pekka. Your description is clearer to me when I mentally substitute the words “expend” or “consume” for the word “release”.
John Millett,
Air is heated by conduction and convection from the solar heated ground. As air heats at constant pressure it expands to lower density (pv=RT). Buoyancy then lifts the lower density hotter air up where it expands and cools as has been previously stated. It also mixes with and carries some surrounding air up. There is also cooled air in the upper Troposphere (cooled by radiation to space) that falls back downward, since it is now more dense than surrounding air that has not yet lost as much energy by radiation. Thus there are continual up and down currents carrying the heated ground energy to radiate to space, as well as some direct radiated energy from the ground, and some radiation heat transfer due to local absorption and radiation.
Got it, though ” mixes with and carries some surrounding air up” looks at odds with the assumed adiabatic process.
The bit in your explanation of the greenhouse effect that I don’t get is how raising the radiating altitude translates into a warmer surface, implying an outward shift of the adiabat. Rather, the additional surface energy stored in the atmosphere, that increasing the mass of the absorber induces, creates a temperature gradient between the atmosphere and the surface, implying a rotation, not a shift, of the adiabat.
Leonard Weinstein
Two equations presented by two authorities relating surface and effective radiating temperatures perplex me greatly:
Hartmann……….Ts = (n+1)^0.25 * Te where “n” is the number of atmospheric slices.
Pierrehumbert……..Ts = (Ps/Prad)^(R/Cp) * Trad
Recognising that radiative equilibrium is not a sound basis for determining the relationship between effective radiating temperature and actual surface temperature, nevertheless, how reliable is a theory (radiative transfer) in which the value of the objective variable (surface temperature) depends on the arbitrary choice of the number of atmospheric slices which pass on radiation from one to the next?
The choice is not without constraint: the layer must not be so thick as to contravene the isothermal assumption nor so thin as to inhibit the molecular collision that supports that assumption and the accompanying blackbody assumption. If, for current purposes, half a degree gradient within the layer is assumed to approximate local thermal equilibrium, 13 layers per km would be necessary in an atmosphere with a lapse rate of 6.5 degrees per km or 200 layers in total. These numbers would imply a surface temperature 3.76 times the effective radiating temperature compared with the actual 1.13 times. They also imply that the non-radiative fluxes cool the surface by an incredible 700 degrees C. Alternatively, obviously no fewer than one slice, or the whole atmosphere, may be chosen, in which case the non-radiative fluxes cool the surface by 15 degrees. Two slices is the popular choice (forget the constraining assumptions) whence non-radiative fluxes cool the surface by about 50 degrees.
Hartman, using the 2-layer model, shows DLR at 89% of pre-albedo solar flux (compared with 50% absorbed by the surface directly) proclaiming it to be the key to our benign climate. Without it, he maintains, not only would the surface be much colder on average but also the diurnal range would widen owing to both colder minima and (surely illogically) hotter maxima.
Pierrehumbert provides this formula linking surface and effective radiating temperatures:
Ts = (Ps/Prad)^(R/Cp) * Trad
A similar eqn could be written, with the variables primed, for an atmosphere with a higher concentration of CO2 which raises the radiating altitude. That is, T’rad and P’rad less than Trad and Prad, respectively. The ratio of the two eqns would be:
(T’s/Ts) = (P’rad/Prad)^(R/Cp) * (T’rad/Trad)
Unless my rusty math has failed, because all RHS terms are less than unity, so must be the LHS. That is, apparently perversely, increasing CO2 concentration reduces surface temperature.
John,
You got the first factor inverted. PRad is in the denominator in the first formula and should switch to the numerator.
I had realised the error. But thanks all the same
John Millett,
The example is simply to illustrate the effect that a high concentration of “greenhouse” gases can have using a simple set of equations that (almost) anyone can understand. As we increase the number of “demonstration layers” we reach a point for that atmosphere where the layer becomes optically thin and so does not emit like a blackbody. This means the number of layers cannot be arbitrarily increased.
In any case the real calculation for such an atmosphere uses the radiative transfer equations. This becomes a pair of differential equations with boundary conditions and the result has become known as the semi-gray model.
You can see it explained in plenty of detail in The Mystery of Tau – Miskolczi – Part Five – Equation Soufflé, with the full derivation in this comment.
SoD,
Is there a way to email you or the site?
Email is scienceofdoom – you know what goes here – gmail.com
Pekka,
“You got the first factor inverted. PRad is in the denominator in the first formula and should switch to the numerator.”
As indicated, in a contemplative corner I realised the error. Still in that corner, there is more to this, isn’t there?
Via the gas laws, the ratio Prad/P’rad would be the reciprocal of the ratio T’rad/Trad.
(Prad/P’rad)^(R/Cp) would be less than (Prad/P’rad) because the exponent is less than unity and the product with (T’rad/Trad) would be less than unity, leading to the overall result – a warmer surface induced by adding CO2 (if, as Leonard argues, adding CO2 pushes radiation to space higher in the atmosphere).
John,
Using the gas law to conclude that the ratio Prad/P’rad is the reciprocal of the ratio T’rad/Trad requires knowing that the volume is unchanged, i.e. the conclusion is right for gas in a bottle, but not for gas in atmosphere where the volume is changing. Without the change in the volume the temperature would also be constant. All derivations related to adiabatic processes for rising air are specifically about adiabatic expansion.
One place, where you can find the derivations is in the lecture notes of Rodrigo Caballero on atmospheric physics. Although the material is originally based on a graduate level course, the chapter 2 is relatively accessible with only little background in thermodynamics.
John Millet,
The balance of energy in and out is the source of an equilibrium temperature value (I am not talking of the intermediate process, but final long term average value at equilibrium). The average effective location of the outgoing temperature is the altitude where that calculated temperature value occurs (it is not this simple, since the actual outgoing altitudes vary from the surface to very high, but an effective average can be found to simplify the problem, and does a fairly good job). The mechanism of moving the effective average altitude upward with increase in absorbing gases is simply that it is the partial pressure of absorbing gases, not total atmospheric pressure, that mainly determines the amount of absorption at any location, and thus the average location where the radiation finely leaves the atmosphere moves to a higher altitude with increased partial pressure. The mechanism that drives the lapse rate is not directly dependent on the optical absorption or value of absolute temperature (for fixed Cp and sufficient mixing of the atmosphere), so if the average altitude of outgoing radiation is raised, the surface will heat up due to the integrated value of the lapse rate over the greater distance. The average actual lapse rate is actually fairly constant over the distance to the average altitude of outgoing radiation (-6.5 C/km), so the estimation is simple. Ratios of temperature and level of back and forward radiation adjust to these facts, and not the other way around.
“…..the surface will heat up due to the integrated value of the lapse rate over the greater distance”.
The only way the surface will heat up is by storing energy; it won’t respond to a computation. The question is how does increasing CO2 cause the surface to store energy? That wouldn’t increase the solar supply, You reject increase in supply from “back-radiation”, favouring reduction in upward radiative flux as the cause. This flux would reduce if the surface surroundings warmed; but this would involve the rejected”back-radiation”. The question posed has no obvious answer. Resolution of the conundrum could be to recognise that increasing CO2 raises not only the effective radiating plane but also emissive power (overlooked as a result of the over-simplifying blackbody assumption), thus maintaining flux intensity despite the lower radiating temperature and eliminating the need for the elusive warmer surface.
John,
You are certainly right in saying that the surface warms only when energy is stored at (and below) the surface. From the point of view of the surface the only immediate effect of a sudden addition in CO2 is to increase the downwelling radiation. Nothing else affects surface before warming has had time to proceed.
Gradually the surface warms and that leads towards a new equilibrium with more convection and latent heat transfer. Also the emission from the surface increases but not as much as the downwelling radiation which is increased both as a direct consequence of additional CO2 and because of warmer troposphere.
The changes at the surface are complex and difficult to calculate quantitatively, only the qualitative description given above is easy to produce. Therefore most people prefer to look at the energy balance at some altitude above the troposphere. The heat capacity of the troposphere is small in comparison with the top mixed layer of the oceans and also in comparison with the annual energy fluxes. Therefore the net energy flux at the surface must be very close to the net energy flux at any level above the troposphere when considered on annual or multiannual time scales.
In a warmer troposphere there’s more IR both up and down and there’s also more convection and transport of latent heat. Above the troposphere we are bound by the requirement that OLR must balance solar SW that is absorbed below that altitude. When we are high enough to be sure that downwelling LWIR is very small we know that upwards LWIR cannot increase with warmer surface any more. The higher up those levels are the warmer the surface is. To calculate quantitatively the change in surface temperature we need more detailed knowledge about the changes in altitudes, temperatures at those altitudes and lapse rates to relate the temperature of the top of troposphere to the surface temperature.
Pekka,
“From the point of view of the surface the only immediate effect of a sudden addition in CO2 is to increase the downwelling radiation. Nothing else affects surface before warming has had time to proceed.
Gradually the surface warms…..”
A surface warming due to storage of atmospheric down-welling radiation requires spontaneous flow of energy from a cold region to a hot one, a violation of 2LoT. It also exposes the flaw in SOD’s explaining away the violation provided outflow exceeds inflow – in that case the surface would be cooling, not warming. Leonard Weinstein recognises the problem but, in my opinion, hasn’t been able to demonstrate how the warming surface is due to storage of solar, not atmospheric, radiation. A third explanation – there is no surface warming – would obviate the impasse. Might this result if adding CO2 raised not only the radiating plane (as Leonard argues and SOD I think would agree – although DeWitt Payne, using MODTRAN, shows a warmer radiating plane) but also emissive power which all three assume to be the theoretically maximum at the outset? Emissive power would be enhanced by both increased emitter mass and longer path, an offset to reduced outward flux density due to colder emitting temperature. Under DeWitt’s finding, the offset would be less as the effect of path length would be reversed.
Taking a different approach: the atmosphere’s radiative balance is in deficit – more energy is lost to space than is gained from the sun and from the surface. The radiative deficit is balanced by non-radiative fluxes from the surface. Adding CO2 would increase the solar gain, that from the surface being unaffected – an overall reduction in the deficit. The atmosphere’s extra solar gain is the surface’s loss. The surface stores less solar energy and its temperature rises less than before. A cooler surface supplies less non-radiative flux, matching the reduced demand due to the lesser radiative deficit. A cooler surface implies less evaporation and a drier climate. This condition in turn implies less cloud, lower albedo, more solar energy storage at the surface and rising surface temperature – automatic negative feedback stabilising surface temperature.
John Millett,
Not much point having this discussion on each and every article. Clearly you have zero chance of ever understanding radiative heat transfer. Please can you instead go ahead and raise your unique concepts – that are contrary to all heat transfer textbooks – in The Amazing Case of Back Radiation.
Or in the article where the extracts from the six heat transfer textbooks are shown. Perhaps in that article you can explain why they are all wrong.
John Millett says
“A surface warming due to storage of atmospheric down-welling radiation requires spontaneous flow of energy from a cold region to a hot one, a violation of 2LoT..”
What the second law states is that HEAT cannot flow spontaneously from a lower to a higher temperature.
In the case of a purely radiative exchange, the HEAT would be the net radiative flux.
Heat has the ability to do thermodynamic work.
I have come up with a neat logical proof that a warmer surface can absorb energy from a colder surface.
Three objects separated by a vacuum can ‘see’ each other.
Object A is at 320K
Object B is at 300K
Object C is at 280K
All three objects will emit 10um photons as part of their BB spectrum.
All would agree that object B will absorb a 10um photon from A.
However a 10um photon from C is identical in all respects.
Photons are also Bosons so it is impossible to differentiate them.
So by logic if B absorbs a 10um photon from A it must absorb one from C.
Some Climate Science experts including SoD think its rather tiresome to differentiate between the terms heat, infra red radiation, energy and work.
They quote from textbooks that are rather careless in the use of thermodynamic terminology.
So on and on the confusion spreads.
The angels in heaven will rejoice when SoD recommends his readers to study the Carnot Cycle and banish forever the pointless confusion.
Bryan,
The word “heat” is used in perfectly good thermodynamic texts in many different ways. When the only thermodynamics that we had was classical thermodynamics without any statistical theory or micro level physical explanations to back it up it was essential that the definitions were taken literately. Thermodynamics of that era was an axiomatic mathematically formulated theory that could not be explained by deeper understanding but that had been found to be true wherever it had been properly tested.
For more than 150 years we have had a deeper understanding based on some simple properties of micro level physics and statistical analysis. There were originally some serious problems in the statistical theory but they have been resolved by quantum mechanics. Thus we can now discuss the physical processes as you did with the example of photons. Having the understanding of what kind of energy can be classified as heat energy we are not any more limited by the axiomatic approach. Some of the ways that are presently natural contradict the classical view that heat can be identified only in the flow of heat as it’s now possible to determine the absolute value of heat energy in some body or some volume of gas.
Similarly we can discuss the two components of energy transfer whose difference was the heat flow of axiomatic thermodynamics. Sticking to the definitions of past centuries is now rather a burden than the only acceptable choice. Discussing the two components separately is very useful in case of radiative heat transfer but does not make much sense in case of heat conduction.
It’s good to know the different ways the word “heat” is used but it’s pointless to claim that only one of the ways is correct.
Pekka Pirilä says
“It’s good to know the different ways the word “heat” is used but it’s pointless to claim that only one of the ways is correct.”
Perhaps I’m old fashioned!
Maybe you can give me an example from the thermodynamics section of a modern University Physics Textbook where heat is said to flow spontaneously from a colder to a warmer surface.
Until then I cannot help thinking that a little ‘wriggle room’ is required to help the IPCC current greenhouse theory evade the second law of thermodynamics
For readers’ benefit I will collect mine and Bryan’s contribution to the debate on this blog over the last two years or so.
Readers will see what a shining light Bryan has been in explaining the simple thermodynamic truth that the colder atmosphere causes a warmer surface than would have occurred without the colder atmosphere.
We will see what a contribution he has made and how consistently and how clearly he has articulated these thermodynamic basics. And, of course, how quickly he clarified his position on this confused topic when any reader requested it.
With a few plain sentences Bryan has forever banished confusion and everyone has been clear on whether or not energy from the colder atmosphere is or isn’t absorbed by the earth’s surface and does or doesn’t change its temperature.
His clarity on the use of the word heat is of course at the center of his clear exposition of cause and effect.
Alternatively readers might realize that Bryan has taken two years to come to terms with the basic fact that a colder atmosphere can increase the temperature of a warmer surface, and attempts to conceal his embarrassment on this topic by repeating a mantra. We will see. The blog tells a tale.
Unfortunately the moderator has decided that such an investigation would be a breach of Blog Etiquette so interested readers will need to review the past discussions for themselves.
SoD
DeWitt Payne and Pekka Pirilä have both recommend the lecture notes by
Rodrigo Caballero.
Rodrigo’s use of the term ‘heat’ is exactly the same as my own.
You were correct to pose the question of what happens to radiation from a colder source on arrival at a warmer surface.
In my early replies I said something like…. ‘I don’t know’.
I think that this is the correct answer if you are uncertain, unless you are on some kind of ego trip.
In my defence I would point out that not a lot of attention is paid to the question in thermodynamics text books.
The major point of their writing was to find the efficiency of converting thermal energy into work.
The back radiation plays no part in this so it is almost totally ignored.
On further investigation I have concluded that this ‘colder’ radiation is absorbed subject to the constraints of absorbency of the warmer material.
However the ‘colder’ radiation cannot of itself ‘up-convert’ its nature to increase the temperature of the warmer surface.
Nor can radiative energy be continually recycled without entropy gain.
Rather the effect is to reduce the net radiative flux from the warmer surface making its heat loss less.
If the warmer surface’s internal production of thermal energy continues unaltered its temperature will increase.
None of this is controversial.
I can give you a long list of Climate Science professionals who use the Carnot Cycle as a structure for the vertical temperature behavior of the tropopause.
As Rodrigo shows , there is nothing inconsistent about using technically correct thermodynamic terminology and expressing views about atmospheric science.
Bryan,
The axiomatic definition of heat is certainly consistent, but that’s not the only meaning of the word “heat”.
People, who have never learned any thermodynamics know the word “heat” and have a rather good understanding of what that is. This common language meaning of the word is used by physicists as well. A more precise definition of stored heat energy can be given although textbooks may tell that such a concept does not exist in classical thermodynamics.
Basically we can divide the energy of any body or other system that has some limits to two parts: “organized energy” and “disorganized energy”. The organized energy includes things like the kinetic energy of the motion of a body or a macroscopic parcel of gas as a whole, the potential energy of those bodies or parcels and also energy related to the pressure of a parcel of gas. The disorganized energy is energy related to the motion of and interactions of individual molecules relative to their surrounding. This disorganized energy can typically be characterized by statistical distributions of the energies of each molecule and each degree of freedom of those molecules. These statistical distributions include the Maxwell-Boltzmann distribution of molecular velocities in gas and many other distributions related to rotations, vibrations etc. This disorganized energy is heat energy. There’s typically a local thermal equilibrium characterized by local temperature that determines the form of each of these statistical distributions.
Radiation can get its energy from heat energy of the neighborhood of the point of emission and it can deliver its energy to the heat energy at another location. That can happen both from warmer to colder and from colder to warmer. According to Kirchoff’s law the former is always stronger when radiation between two bodies or parcels of gas is considered excluding the role of all radiation that does not involve both bodies. The classical thermodynamics doesn’t discuss these details, because it’s an extremely limited way of looking at the physics. It’s a very valuable way but it’s looking at the system from outside the “black box” where everything really happens in all its detail. The more modern approaches to physics can look also inside the box and tell in detail, what’s going on there.
The concept of heat in classical thermodynamics remains correct for classical thermodynamics, but that does not allow for condemning different uses of the word when we are looking at things classical thermodynamics cannot discuss. Radiative heat transfer is one of those things because classical thermodynamics does not know what radiation or radiative heat transfer is. Classical thermodynamics knows only the net sum of all components of heat transfer, not anything of its division nor absolute values for heat that’s stored in a volume at any moment.
The second law does not tell that net radiative heat transfer is always from warmer to colder, it tells only that the total net heat transfer including all mechanisms goes that way. We need something more, the Kirchoff’s law, to make the statement for the radiative energy transfer separately.
Pekka Pirilä,
If both the hot and cold areas have absorption and emission coefficients that are not significantly temperature dependent, the radiation energy transfer equation does tell us that net radiative heat transfer is always from warmer to colder independent of the conduction and convection. You do not need anything else.
Leonard,
That’s exactly what I meant in saying that Kirchoff’s law guarantees that the net transfer is from warmer to colder. Or actually Kirchoff’s law in its modern form tells more. It tells that for every wavelength separately there’s more radiative energy transfer from the warmed body to the colder one than in the opposite direction. I don’t know any other (independent) law that could tell either that detailed information or in a generally valid way tell that the total net radiative heat transfer is always from the hot to the cold. (Again including only the radiation that is emitted from one of the bodies and absorbed by the other excluding all radiation that’s emitted or absorbed by other matter or escapes to free space.)
I didn’t mean to contradict any standard physical knowledge, but I wanted to tell that the classical thermodynamics cannot say anything about the subprocesses. The Second law is a statement on the sum of all subprocesses and tells nothing on the further details. I made this statement to emphasize, how much more we know when we have also the micro level physical knowledge and the statistical derivation of thermodynamics.
Pekka Pirilä,
Pardon, but my comment also need to say that the coefficients are the same for the two regions. There are possibilities that unequal one would require additional information.
Hi SoD, sorry to be late to the party but I have a question about something you said:
“We increase the amount of CO2 in the atmosphere but at the surface the change in downwards longwave radiation (DLR) from the atmosphere is pretty small, perhaps insignificant.
By comparison, at the top of atmosphere (TOA) the radiative effect is significant. The atmosphere becomes more opaque, so the flux from each level to space is reduced by the intervening atmosphere. Therefore, the emission of radiation moves upwards, and “moving upwards” means from a colder part of the atmosphere. Colder atmospheres radiate less brightly and so the TOA flux is reduced.
This reduces the cooling to space”
Well we and nature have added quite a lot more co2, but rather than the cooling to space being reduced, OLR seems to have increased by around 1.4W/m^2 since 1950 (radiosondes), and by around 0.5W/m^2 since 1980 (satellites).
Why is that?
Tallbloke,
On your own blog you said:
It’s great to see such high standards of ethics from you and certainly your laudable approach ensured that I stopped posting any questions on your blog.
But it does have me wondering, not for the first time, why you are posting a question here.
If you seek answers you should seek them elsewhere.
SoD, You have some really important, well written and informative science on your blog. I find it a source of reference and is much appreciated.
However i think you may be doing your self a disservice by over-reacting to perceived criticism.
Clivebest,
Tallbloke accused me of altering other peoples’ comments on my blog to overcome my difficulty with their “excellent arguments”.
By any standard that I know it is an accusation of dishonesty.
My “over-reaction” to actual libel was to no longer post comments on tallblokes’ blog and to question why on earth he has posted comments on this blog given his claim.
I could do over-reaction. It would look a lot different, believe me.
Clive: SoD and I are well on the way to resolving this ancient dispute and hopefully normal friendly scientific discourse will be resumed shortly.
SoD,
You say:
“And of course, one of the biggest questions in an atmosphere with more CO2 is how water vapor concentration changes in response to surface temperature change. Changes in water vapor have multiple effects, but the one for consideration here is the change to the lapse rate. The dry adiabatic lapse rate is 9.8 °C/km, while the moist adiabatic lapse rate varies from 4 °C/km in the tropics near the surface (where the water vapor concentration is highest).
Consider an atmosphere where the temperature reduces by 15 °C in 2km. Dry air moving upwards reduces in temperature by 20 °C – which is colder than the surrounding air – and so it sinks back. Very moist air moving upwards reduces in temperature by about 10 °C – which is warmer than the surrounding air – and so it keeps rising.
So more moisture reduces the lapse rate, effectively making the atmosphere more prone to convection – moving heat into the upper troposphere more effectively.”
Very interesting, but is it fair to ask how this behavior is consistent with positive water vapor feedback? It would seem to be consistent with the opposite given the process of convection primarily accelerates radiative cooling by moving energy non-radiatively higher up in the atmosphere where when radiated it has a greater chance of passing through the remaining atmosphere into space.
RW,
You are correct. This is a negative feedback.
If you take a look at this graphic, which was shown in Visualizing the Climate Response summarizing the results of various climate models:
you can see that the lapse rate feedback is a negative feedback, the water vapor (radiative) feedback is a positive feedback and combined they still result in a positive feedback.
Do you know if these calculations include increased cooling as a result of increased removal of energy as latent heat from the surface as more water evaporates?
Increased evaporation is included. It’s closely related to the reduced lapse rate in the atmosphere as both are parts of enhanced transport of energy from surface to atmosphere as latent heat. Evaporation takes energy from the surface and condensation releases that heat higher up in the atmosphere.
When evaporation takes energy from the surface the temperature difference of the surface and the lowest atmosphere is decreased and that leads to a reduction in both net radiative heat transfer and convection near surface. Thus the total energy transfer which includes all three forms of heat transfer does not change nearly as much as the latent heat transfer alone. Their sum is controlled by the energy balance of the surface and the share of each in the sum depends on the strength of evaporation.
Looking at the graphic, I guess not. It seems to me this would be equally as significant (if not more so) as the lapse rate feedback.
RW,
There’s no way you can see anything of that in the graphic, but it’s there.
Pekka,
OK, I think I understand. Thanks for the explanation.
Pekka Pirilä
In your post above you say:
This would only be true if the planetary surface were isothermal, but it’s not. The combination of poles colder than the equator and planetary rotation will create circulation and that circulation will create a lapse rate close to the adiabatic rate pretty much everywhere even if the atmosphere were perfectly transparent at all wavelengths. We hashed this out a long time ago at Nick Stokes site and here. See also SoD’s next post: Atmospheric Circulation-Part One
I’m a little surprised no one called you on this, although I only skimmed the thread comments so I may have missed something.
DeWitt Payne,
The point you make is familiar to me but I believe it’s not correct. The reason is in the fact that without radiative heat transfer the atmosphere can be heated rather efficiently by the hottest areas of the surface but there are no efficient mechanisms that can cool the atmosphere anywhere on the Earth. Thus practically the whole atmosphere would warm up to a temperature close to the warmest surface areas.
That’s a little oversimplified, but close to what would result as far as I can see. In areas where the surface is colder than the atmosphere a very thin layer of strong temperature inversion would develop. Some circulation would be maintained in the stationary state but only at very low altitudes and mainly around the highest temperature spot on the surface. The rest of the atmosphere would be warmer than the surface below, stratified and thus prevents convection effectively.
It’s true that conduction is extremely weak. As conduction is the process that would ultimately lead to the isothermal state, it’s possible that my argument fails. It’s possible that I overlook some other very weak mechanism that would still be stronger than conduction. It’s possible that my view that the low altitude circulation that involves convective heating from the hottest spot and conductive heat transfer through the thin inversion layer in other areas would not leave the rest of the atmosphere fully stratified.
Even so I have not seen any real arguments against my reasoning, all the counterarguments have been presented by people who have not yet gone through all steps of my argumentation or by people who don’t state specific enough reasons for not agreeing with my view on the ultimate outcome in that imaginary situation.
I have had some discussion on these issues on my own site under “random topics” but not with anyone with strong physics background. Thus I have not felt strongly contested.
Both N2 and O2 have a tiny but still finite emissivity. So the atmosphere would never reach an isothermal temperature of say T=255K, since as the atmosphere warms the N2,O2 radiation loss to space would increase as T^4. Convection would be able to maintain some lapse rate to balance the N2 O2 radiation loss.
My comment was for an imaginary situation with exactly zero emissivity. When we start to discuss counterfactual situations it’s common that people make differing assumptions.
It’s been modeled and apparently conduction is enough because the surface boundary layer would be thinned by winds from the convection cells. I don’t have the link for the article on modeling a planet with a transparent atmosphere and can’t find it in a quick search.
When I asked Gavin Schmidt, who knows a lot more than I do about the subject, he specifically rejected the idea that the atmosphere would be isothermal vertically. The details would depend on other properties of the atmosphere, whether the conditions for baroclinic instability are achieved in the mid-latitudes for example.
Let’s look at it another way. Suppose we postulate that the atmosphere is so viscous that convection is impossible. Would the atmosphere be isothermal? I don’t think so. The surface at the poles would be much colder than the equator and vertical conduction would be faster than horizontal conduction because the distance is shorter. If a non-convecting atmosphere isn’t isothermal, then it is even less likely that an atmosphere with low viscosity would be isothermal because any vertical movement the atmosphere will create a temperature gradient. And there will be vertical movement driven by the horizontal flow created by the pressure gradient force.
Your proposed isothermal atmosphere might, in fact, be stable. But I don’t see how you could get there. Formation of circulation cells would act to reduce heat transfer from the equator to the poles.
DeWitt Payne,
As should be clear from my above comments my proposal is based on intuition of one physicist. We seem to agree that it’s validity is determined by quantitative factors. The situation is so extremely different from the real atmosphere that I have doubts on everybody’s intuition including experienced climate modelers – as I have doubts also on my own intuition.
I thought that no-one would have been interested enough in this kind of unrealistic case to construct a model that’s really applicable to it. (I don’t think that any standard atmospheric model would have been built having the applicability to this case in mind.) Perhaps someone has. If so it would be intellectually interesting to learn about that.
Whatever the right answer is, I don’t see how it would have anything more than a curiosity interest. Trying to figure out what could happen may be educative – and essentially as educative when the outcome is false than when the outcome is right as long as the physics is taken qualitatively correctly into account.
Pekka,
I suspect this is a thought experiment perhaps taken too far. How high above the planet would the temperature remain isothermal ? If such a thermal boundary were to exist then above it there would be a temperature discontinuity with outer space @ 3K. This would surely violate the 2nd law of thermodynamics at that boundary.
Clivebest,
That’s not a relevant consideration. The temperature at the outer edge of the atmosphere may have any value without problems of that nature. That’s true for the real atmosphere as well. The temperature of the Earth atmosphere is actually very high as far out as defining a temperature for it is meaningful.
Pekka,
OK – so the bottom line is:
There can be no greenhouse effect without a lapse rate, and there can be no lapse rate without a greenhouse effect.
Do you agree ?
Clivebest,
I agree on that, but i add that there may be a lapse rate without any significant GHE.
My proposal is that the atmosphere would be significantly warmer than the average surface temperature. It would be coupled effectively only to the warmest spot of the surface and have very little effect on the surface temperature which would be essentially the same as without atmosphere. That would apply to all atmosphere except for a very thin layer near surface. That atmosphere would have zero lapse rate almost everywhere.
The other alternative that DeWitt Payne considers likely has a dry adiabatic lapse rate over a significant range that could be almost as high as the present troposphere because the theory of optically thin atmosphere tells about such a troposphere. That atmosphere would, however, not have any greenhouse effect either. The surface temperature would be essentially the same as in my alternative, but the upper troposphere would be much colder.
I must add that it’s not clear what the height of the troposphere would be in absence of all radiative heat transfer. The theory of optically thin atmosphere is based on the assumption that there’s some radiative heat transfer but the absorptivity is so small that almost all radiation of all wavelengths passes through the atmosphere without being absorbed. At the same time it’s, however, assumed that radiative heat transfer is much stronger than conduction which is not true when the absorptivity/emissivity is exactly zero. This is one reason for my conclusion that the height of the troposphere would be very small. We would have only a isothermal stratosphere above a very thin layer of temperature inversion.
[...] temperature increase. Then it checks between each layer to see if the lapse rate is exceeded (see Temperature Profile in the Atmosphere – The Lapse Rate). This means the atmosphere would be unstable, resulting in [...]