Guest Post by Willis Eschenbach
I’ve been reflecting over the last few days about how the climate system of the earth functions as a giant natural heat engine. A “heat engine”, whether natural or man-made, is a mechanism that converts heat into mechanical energy of some kind. In the case of the climate system, the heat of the sun is converted into the mechanical energy of the ocean and the atmosphere. The seawater and atmosphere are what are called the “working fluids” of the heat engine. The movement of the air and the seawater transports an almost unimaginably large amount of heat from the tropics to the poles. Now, none of the above are new ideas, or are original with me. I simply got to wondering about what the CERES data could show regarding the poleward transport of that energy by the climate heat engine. Figure 1 gives that result:
Figure 1. Exports of energy from the tropics, in W/m2, averaged over the exporting area. The figures show the net of the energy entering and leaving the TOA above each 1°x1° gridcell. It is calculated from the CERES data as solar minus upwelling radiation (longwave + shortwave). Of course, if more energy is constantly entering a TOA gridcell than is leaving it, that energy must be being exported horizontally. The average amount exported from between the two light blue bands is 44 W/m2 (amount exported / exporting area).
We can see some interesting aspects of the climate heat engine in this graph.
First, like all heat engines, the climate heat engine doesn’t work off of a temperature. It works off of a temperature difference. A heat engine needs both a hot end and a cold end. After the working fluid is heated at the hot end, and the engine has extracted work from incoming energy, the remaining heat must be rejected from the working fluid. To do this, the working fluid must be moved to some location where the temperature is lower than at the hot end of the engine.
As a result, there is a constant flow of energy across the blue line. In part this is because at the poles, so little energy is coming from the sun. Over Antarctica and the Arctic ocean, the sun is only providing about a quarter of the radiated longwave energy, only about 40 W/m2, with the remainder being energy exported from the tropics. The energy is transported by the two working fluids, seawater and air. In total, the CERES data shows that there is a constant energy flux across those blue lines of about six petawatts (6e+15 watts) flowing northwards, and six petawatts flowing southwards for a total of twelve petawatts. And how much energy is twelve petawatts when it’s at home?
Well … at present all of humanity consumes about fifteen terawatts (15e+12) on a global average basis. This means that the amount of energy constantly flowing from the equator to the poles is about eight-hundred times the total energy utilized by humans … as I said, it’s an almost unimaginable amount of energy. Not only that, but that 12 petawatts is only 10% of the 120 petawatts of solar energy that is constantly being absorbed by the climate system.
Next, over the land, the area which is importing energy is much closer to the equator than over the sea. I assume this is because of the huge heat capacity of the ocean, and its consequent ability to transport the heat further polewards.
Next, overall the ocean is receiving more energy than it radiates, so it is exporting energy … and the land is radiating more than it receives, so it is getting energy from the ocean. In part, this is because of the difference in solar heating. Figure 2, which looks much like Figure 1, shows the net amount of solar radiation absorbed by the climate system. I do love investigating this stuff, there’s so much to learn. For example, I was unaware that the land, on average, receives about 40 W/m2 less energy from the sun than does the ocean, as is shown in Figure 2.
(Daedalus, of course, would not let this opportunity pass without pointing out that this means we could easily control the planet’s temperature by the simple expedient of increasing the amount of land. For each square metre of land added, we get 40 W/m2 less absorbed energy over that square metre, which is about ten doublings of CO2. And the amount would be perhaps double that in tropical waters. So Daedalus calculates that if we make land by filling in shallow tropical oceans equal to say a mere 5% of the planet, it would avoid an amount of downwelling radiation equal to a doubling of CO2. The best part of Daedalus’s plan is his slogan, “We have to pave the planet to save the planet” … but I digress).
Figure 2. Net solar energy entering the climate system, in watts per square metre (W/m2). Annual averages.
You can see the wide range in the amount of sunlight hitting the earth, from a low of 48 W/m2 at the poles to a high of 365 W/m2 in parts of the tropics.
Now, I bring up these two Figures to highlight the concept of the climate system as a huge natural heat engine. As with all heat engines, energy enters at the hot end, in this case the tropics. It is converted into mechanical motion of seawater and air, which transports the excess heat to the poles where it is radiated to space.
Now, the way that we control the output of a heat engine is by using something called a “throttle”. A throttle controls the amount of energy entering a heat engine. A throttle is what is controlled by the gas pedal in a car. As the name suggests, a throttle restricts the energy entering the system. As a result, the throttle controls the operating parameters (temperature, work produced, etc.) of the heat engine.
So the question naturally arises … in the climate heat engine, what functions as the throttle? The answer, of course, is the clouds. They restrict the amount of energy entering the system. And where is the most advantageous place to throttle the heat engine shown in Figure 2? Well, you have to do it at the hot end where the energy enters the system. And you’d want to do it near the equator, where you can choke off the most energy.
In practice, a large amount of this throttling occurs at the Inter-Tropical Convergence Zone (ITCZ). As the name suggests, this is where the two separately circulating hemispheric air masses interact. On average this is north of the equator in the Pacific and Atlantic, and south of the equator in the Indian Ocean. The ITCZ is revealed most clearly by Figure 3, which shows how much sunlight the planet is reflecting.
Figure 3. Total reflected solar radiation. Areas of low reflection are shown in red, because the low reflection leads to increased solar heating. The average ITCZ can be seen as the yellow/green areas just above the Equator in the Atlantic and Pacific, and just below the Equator in the Indian Ocean.
In Figure 3, we can see how the ITCZ clouds are throttling the incoming solar energy. Were it not for the clouds, the tropical oceans in that area would reflect less than 80 W/m2 (as we see in the red areas outlined above and below the ITCZ) and the oceans would be much warmer. By throttling the incoming sunshine, areas near the Equator end up much cooler than they would be otherwise.
Now … all of the above has been done with averages. But the clouds don’t form based on average conditions. They form based only and solely on current conditions. And the nature of the tropical clouds is that generally, the clouds don’t form in the mornings, when the sea surface is cool from its nocturnal overturning.
Instead, the clouds form after the ocean has warmed up to some critical temperature. Once it passes that point, and generally over a period of less than an hour, a fully-developed cumulus cloud layer emerges. The emergence is threshold based. The important thing to note about this process is that the critical threshold at which the clouds form is based on temperature and the physics of air, wind and water. The threshold is not based on CO2. It is not a function of instantaneous forcing. The threshold is based on temperature and pressure and the physics of the immediate situation.
This means that the tropical clouds emerge earlier when the morning is warmer than usual. And when the morning is cooler, the cumulus emerge later or not at all. So if on average there is a bit more forcing, from solar cycles or changes in CO2 or excess water vapor in the air, the clouds form earlier, and the excess forcing is neatly counteracted.
Now, if my hypothesis is correct, then we should be able to find evidence for this dependence of the tropical clouds on the temperature. If the situation is in fact as I’ve stated above, where the tropical clouds act as a throttle because they increase when the temperatures go up, then evidence would be found in the correlation of surface temperature with albedo. Figure 4 shows that relationship.
Figure 4. Correlation of surface temperature and albedo, calculated on a 1°x1° gridcell basis. Blue and green areas are where albedo and temperature are negatively correlated. Red and orange show positive correlation, where increasing albedo is associated with increasing temperature.
Over the extratropical land, because of the association of ice and snow (high albedo) and low temperatures, the correlation between temperature and albedo is negative. However, remember that little of the suns energy is going there.
In the tropics where the majority of energy enters the system, on the other hand, warmer surface temperatures lead to more clouds, so the correlation is positive, and strongly positive in some areas.
Now, consider what happens when increasing clouds cause a reduction in temperature, and increasing temperatures cause an increase in clouds. At some point, the two lines will cross, and the temperature will oscillate around that set point. When the surface is cooler than that temperature, clouds will form later, and there will be less clouds, sun will pour in uninterrupted, and the surface will warm up.
And when the surface is warmer than that temperature, clouds will form earlier, there will be more clouds, and higher albedo, and more reflection, and the surface will cool down.
Net result? A very effective thermostat. This thermostat works in conjunction with other longer-term thermostatic phenomena to maintain the amazing thermal stability of the planet. People agonize about a change of six-tenths of a degree last century … but consider the following:
• The climate system is only running at about 70% throttle.
• The average temperature of the system is ~ 286K.
• The throttle of the climate system is controlled by nothing more solid than clouds, which are changing constantly.
• The global average surface temperature is maintained at a level significantly warmer than what would be predicted for a planet without an atmosphere containing water vapor, CO2, and other greenhouse gases.
Despite all of that, over the previous century the total variation in temperature was ≈ ± 0.3K. This is a variation of less than a tenth of one percent.
For a system as large, complex, ephemeral, and possibly unstable as the climate, I see this as clear evidence for the existence of a thermostatic system of some sort controlling the temperature. Perhaps the system doesn’t work as I have posited above … but it is clear to me that there must be some kind of system keeping the temperature variations within a tenth of a percent over a century.
Regards to all,
w.
PS—The instability of a modeled climate system without some thermostatic mechanism is well illustrated by the thousands of runs of the ClimatePredictionNet climate model:
Note how many of the runs end up in unrealistically high or low temperatures, due to the lack of any thermostatic control mechanisms.
I wrote “the heat capacity is greater with increasing pressure and that’s a major factor on the other side of the planet away from the sun for a rotating planet.”
I should add that “major factor” pales in comparison to the heat capacity of the earth’s oceans which continue to warm the atmosphere at night.
” TimTheToolMan says:
December 26, 2013 at 3:47 am
gbaikie writes “Well I think there would a adiabatic lapse rate on Saturn’s moon, Titan.” etc
I expect all real planets with real atmospheres have adiabatic lapse rates because they all have GHGs which absorb energy radiated by the planet and radiate it away from higher up. But this is a thought experiment designed to show that its not the pressure alone that sets the surface temperature. ”
Well, it’s well known that water vapor affect lapse rate by reducing it.
And requires no thought experiment to know that it’s not only about pressure.
Though it more to do with density difference than pressure- though they are
related.
I believe it’s mostly to do with water not being a ideal gas which mostly
related to adiabatic lapse rates. Of course water vapor is less dense
than air.
But in any case, Wet vs dry adiabatic lapse rates is:
Saturated adiabatic lapse rate: “A typical value is around 5 °C/km”
Dry adiabatic lapse rate: “The rate of temperature decrease is 9.8 °C/km”
http://en.wikipedia.org/wiki/Lapse_rate
Varies due to moist and temperature. But it’s also rather
consistent, if you know temperature at lower elevation is cooler
and it’s raining one could know at higher elevation it’s probably snowing.
So this “greenhouse gas” apparently reduces lapse rater, or “make it” warmer
at higher elevation.
But it not about it’s radiant properties, but rather because it condenses
and evaporates at temperatures found in earth’s atmosphere.
“Of course once you add GHGs everything changes and IMO the pressure does impact on the surface temperature because the heat capacity is greater with increasing pressure and that’s a major factor on the other side of the planet away from the sun for a rotating planet.”
Well, in trace amounts water gas can change it. And if CO2 could condense- or it was cold enough it too would condense and have some affect on lapse rate. But other than H20, tiny amounts GHG don’t affect earth’s lapse rates.
Nor does warming or cooling from night and day affect lapse rate in significant degree- though night and day warming do affect amount moisture content of air, and as said moisture content has a significant affect.
Since when has it been mandatory for a planet’s atmosphere to have ‘greenhouse gases’ before it can have an adiabatic lapse rate? All that is needed is gravity and enough heat on the surface to prevent the atmosphere freezing out.
gbaikie writes “But it not about it’s radiant properties, but rather because it condenses
and evaporates at temperatures found in earth’s atmosphere.”
There are many processes that effect energy transport in the atmosphere and I agree that the energy transported by latent heat is a very important one.
Richard111 says “Since when has it been mandatory for a planet’s atmosphere to have ‘greenhouse gases’ before it can have an adiabatic lapse rate?”
In this thought experiment, the atmosphere cant lose energy because it cant radiate. It can only gain it via conduction until the whole atmosphere is isothermal and the same temperature as the planet’s surface (which is also the same temperature all over in this thought experiment). At that point it will neither gain nor lose energy.
At that point, how can it have an adiabatic lapse rate?
How can energy at a solid surface be used for two purposes simultaneously ?
Energy radiated is not available for conduction and energy used for conduction is not available for radiation.
To assert otherwise as Willis and AGW proponents do is to breach the law of conservation of energy, surely?
I think the only solution is to separate the effective radiating height from the height at which the temperature is such that S-B is satisfied.
As far as I can tell everyone has been treating them as one and the same.
Thus for a completely radiatively inert atmosphere the effective radiating height must always be the surface but nonetheless, if mass in gaseous form is present then heat will be conducted upward and there will still be a decline in temperature with height, up to and beyond the height at which S-B is satisfied, That S-B height is then off the ground even though the effective radiating height remains on the ground.
What the addition of radiative gases then achieves must be to also lift the effective radiating level off he ground to bring the effective radiating level closer in height to the height at which S-B is satisfied.
If all energy transfers were radiative with no conduction at all then both the effective radiating height and the S-B height would be together at the surface.There could be no atmosphere present with any mass capable of absorbing via conduction.
The more conduction there is the wider the two heights separate as the S-B level rises independently of the effective radiating level.
The more radiative gases there are the more the two heights move back together as the effective radiation level also lifts off the surface towards the higher S-B level.
The outcome of the shifting balance between the two heights is shifting air circulation patterns (via density variations induced by uneven conduction) and thus climate changes but any climate changes arising from radiation variations are infinitesimal because the main driver of the so called greenhouse effect is atmospheric mass absorbing energy by conduction and the radiative component is trivial in comparison.
Those shifting air circulation patterns transport energy to and fro as necessary between the
S-B height and the effective radiating height to ensure that the latter always has the right amount of energy to match energy in with energy out.
The logical summation must be that at any height below the effective radiating level the radiation emanating from the surface ‘leaks’ away into conduction to the mass of the atmosphere (from the surface)
Between the effective radiating height and the S-B level energy is still filtering upward via conduction but in that region no additional energy is leaking away from the radiative exchange. so that by the time one reaches the S-B level the maximum conducting capability of atmospheric mass has been achieved leaving the remaining outward radiative flux from the lower effective radiating level equal to the incoming radiative flux.
Willis Eschenbach says:
December 26, 2013 at 3:07 am
“And that will increase the heat difference from the equator to the poles. Remember that we get about seven times the insolation at the equator as at the poles.”
Seven times?
I am interested how this is arrived it.
Is this pointing at the sun? Or level to the ground?
It seems if pointing at sun and in cloudy coastal region at equator, you could possibly do
better than 1/7th in polar region particular in the half of year one has sunlight, but the
average surface area would seem to me to get less than 1/7th.
Willis Eschenbach says:
December 25, 2013 at 9:58 am
“But since the IR is usually absorbed and re-radiated more than once as it makes its way out of the atmosphere, adding more CO2 definitely changes the picture. This is because increasing the CO2 concentration increases the average number of times that the IR will be absorbed on its path through the atmosphere, which increases the poorly named “greenhouse effect”.”
—————-
But, , adding more CO2, even doubling it to 800 ppm, definitely doesn’t change the picture that much …… simply because at 800 ppm there is still plenty of space between each CO2 molecule to permit a majority of the IR to pass thru without being absorbed, …… right?
And the IR that is absorbed by a CO2 molecule is absorbed from a “point” source and re-emitted in all directions thus very little of it is transmitted directly back toward the earth’s surface, ….. right?
And increasing the IR absorbing H2O vapor from say 12,000 ppm to say 24,000 ppm will definitely change the picture more so than will 800 ppm of CO2 because there is almost 30 times more H2O vapor molecules than there are CO2 molecules, …… right?
And based on the Specific Heat Capacity of the two different molecules, increasing the H2O vapor content by 400 ppm will cause a greater “greenhouse effect” than will the increasing of the CO2 content by 400 ppm, ……. right?
Willis 11:34pm: Thanks, I read thru your linked post. Your “Mistress” graph correctly shows: S-B Avg. Lunar Temperature -2.5C in agreement with the NASA page.
In this thread you write 5:41pm: “But the moon gets the same solar radiation as the earth, about 340 W/m2 with an equivalent blackbody temperature of about 5°C.”
My post in effect was pointing out you were correct in the chart of earlier “Mistress” post. Can you explain the difference (-2.5C vs. 5C) shown in this thread? Your conclusion clipped here in “Mistress” post seems ok with Diviner papers and within the limited in situ temperature experiments to date:
“So there is no contradiction at all between the lunar temperature and the S-B calculation.”
Kristian 1:35am: “Trick, there is no ‘surface temperature formula’.”
Kindly refer to Bohren 2006 p. 33 for a basic, simple “surface temperature formula” determining the global surface Tmean=288K from measurements each of solar irradiance, albedo, surface and atm. emissivity globally temporally and spatially avg.d.
You should get a hint from this that there are more factors than just weight of atm. and solar irradiance determining near surface Tmean. Similar texts show the same.
******
1:37am: “Right”
Ok, so the links you posted do not show “vacuum” or “much, much” as a restriction to S-B. In fact, no text book does either.
******
1:52am: “…upward and downward components of this actual upward energy flow..”
Kristian gets it right according to modern text books. UWIR and DWIR. Find both from Planck Law based radiation theory and both from in field calibrated radiometers on satellites, surface instrumentation and exoplanet/solar observing instruments.
Willis Eschenbach says:
December 25, 2013 at 9:58 am
“Sorry … I don’t believe that about the weather changing at some point in the lunar cycle. It’s not true, as far as I know, in anything but the most general sense, that of “persistence”. ”
—————-
Willis, I had never heard of the “moon wind” before now and thus enjoyed reading your commentary on it.
And I don’t blame you a bit for not believing the “moon change” prediction …………. because I didn’t either the first time I was told about it. As a matter of fact, I “badmouthed” my best friend when he made the “prediction” in my presence.
It was many years ago when I was living in upstate New York and my best friend and I was outside loading up “cut” firewood to haul in for our wood burning stoves. And “boy o’ boy” was it cold that day, like 10 degrees F below 0 (zero) …. and had been like that for the past week. Anyway, I was getting cold, tired, frustrated and PO’ed …. and looked at my friend and said, ”I wish to hell it would warm up”. He looked back at me and said, … “Not until the moon changes”.
Well now, in a few short words I told him what I thought about his prediction. But then “Mercy me”, those below ZERO temps persisted for another 6 days or so, …. the Moon changed, …. and “BINGO”, ….. the temperature the next day rose up into the upper 20’s. Just like Carl had predicted.
But that really didn’t make me a “believer” cause I figured it was a lucky guess. But after many years and me making the same prediction, and being correct far more often than not, I have to believe there is a science based explanation for it. But I don’t have a clue what it might be.
Maybe I’ve been extremely lucky …. or maybe that “moon wind” triggers it, …. who knows?
***
Willis Eschenbach says:
December 25, 2013 at 10:51 am
Thanks, beng. I presented it as a “thought experiment”, not as an analogue of a real world. I want to make it clear why, if the atmosphere is transparent to IR (e.g. argon, which neither emits nor absorbs thermal IR), the pressure of the atmosphere alone cannot warm the planet. See my post called “A Matter of Some Gravity“.
***
Thanks for responding. I’ve read & agreed with about everything you’ve ever posted, so I knew you were simply setting up a thought experiment. Others refuse to “get” it, tho.
Your images at the top are worth thousands of words, and saved in my “library”.
Pressure on its own does nothing.
What warms the surface above S-B is the amount of atmospheric mass available to absorb energy from the surface by conduction and the amount of work required to hold that mass off the surface against the force of gravity.
The effective radiant temperature of the sky as seen from the surface is directly related to the local dew point.
The following study uses real world measurements (gasp!) to calculate actual effective radiant temperatures of the sky to calculate the heat loss by radiant energy flux of solar heating ponds (ocean analog anyone?)
The formulas are on pages 3 and 4 of the paper.
http://www.ceen.unomaha.edu/solar/documents/sol_29.pdf
——–
Inverting that view, looking down on the earth from outer space, it is also reasonable to presume the that the same relationship holds for the effective radiant energy loss to space from the atmosphere. It most likely being directly related to the dew point and moisture in the atmosphere and its maximum altitude of significant mixing of surface moisture would dominate our heat loss in the IR window that water vapor absorbs and emits in.
The effective emitting surface of the atmosphere based on that assumption would be the cloud tops and the effective upper surface of the moist tropospheric atmosphere. I have seen references that place the average radiant surface height at about 14,000 ft elevation which is a reasonable approximation of the top of the warm moist surface air excluding the cloud tops.
I think some investigation would be appropriate looking measurement of the effective radiant surface to space correlated with balloon soundings and the atmospheres moisture/dew point profile with height. I suspect such an experiment would find that the surface is not some specific altitude but a “moisture surface” at the top of the warm moist surface air mass.
Willis 11:34pm “As a result, different arrangements of the same amount of energy flux will have different resultant average temperatures.”
Magnificent climate heat engine nature has to arrive at a single temperature though. How does nature pick that “one.” There is a very elegant concept of how science can proceed to find the single temperature. I would be very interested & excited to discuss the details but maybe different thread needed. That discussion will hijack this one if not already. Teaser follows to see if raise interest.
******
Willis will find the answer in the Hamiltonian concept. The control volume (CV) system path from a to b will be chosen by nature based on minimizing the total energy finding that one path; only one path can have “the” min. energy among many possible paths. Mathematically the task is to set up to formalize the total energy and minimize it to find nature’s chosen path, way beyond this simple atm. site.
For Willis’ imagined “Moon Mistress” + argon atm. control volume wherein the total energy (TE) is constant. Consider the total energy:
TE = H (the hamiltonian construct) = measure of the total energy in a thermo. system.
Restrict to conservative, isotropic, homogenous system (and others like scleronomic, holonomic) like the real moon but with imagined argon atm.
H = enthalpy = Internal energy (U) +/- external work done to/from system CV (W) (= U + pV for a parcel).
TE of a single molecule = PE + KE translational + KE rotational + KE vibrational + PE vibrational + E electronic plus ….even more like Van der Waals, electrostatic… go for the complete list to a text book (this will drop out Stephen – like when a recipe calls for taking a clean dish, it drops me out).
The KE translational is the one related to temperature as Willis points out: KE & temperature are not conserved only enthalpy (system TE) is conserved. As T increases, KE increases. But Willis holds TE constant. Some other energy must be used up, in this case PE say.
KE up, PE down, TE constant. This CAN happen Willis, it is called Kelvin-Helmholtz contraction to increase average temperature. But I don’t think this is what Willis is talking about.
I don’t actually see what Willis means so will defer until any other discussion interest is shown from this teaser.
TimTheToolMan says, December 26, 2013 at 1:50 am:
“Why do you think there needs to be an adiabatic lapse rate (at equilibrium in the Willis’ thought experiment atmosphere)? It is possible to have a gas at say 300K, at all ranges of pressure. At equilibrium the gas wont be moving so there are no parcels rising, dropping pressure and cooling.
The key is that once energy gets into the thought experiment atmosphere, it stays there. In real life, of course, the atmosphere is cooling and this makes all the difference.”
Do you get the concept of cooling by expansion, Tim? The atmosphere has no lid.
Is it really possible to have an isothermal gas which is heated from below and expands upward and which goes from 1000mb at the constant heat source to 150mb 12-13 km away from it.
How would that work?
It’s easy to get tangled up in these hypothetical scenarios …
Actually the atmosphere is already ‘isoenergetic’ (is there a better word ?).
Molecules at the surface have the same energy content as those at the top of the atmosphere but as one goes up kinetic energy (heat) is replaced by gravitational potential energy (not heat).
That gives a neat reason as to why an isothermal atmosphere (same temperature all the way up) is not physically possible.
If it were possible then there would be the bizarre scenario of the energy content of individual molecules increasing with height.
The topmost molecules would be the same temperature as surface molecules but would additionally carry a full allowance of gravitational potential energy too.
Such energy rich molecules high up would be rapidly lost to space because the gravitational field could not constrain them.
TimTheToolMan says, December 26, 2013 at 1:53 am:
“I did actually. Your points are all valid until equilibrium is reached OR the atmosphere is cooling. But this thought experiment is where equilibrium has been reached (and the atmosphere is isothermal) and does not cool.”
There will be no isothermal equilibrium in an air column with a gravity induced pressure/density gradient, which is heated from one end and which is free to expand. The temperature profile will simply lift from an ever hottter ground until the atmosphere gradually starts getting whisked off into space.
Stephen 8:21am: “Pressure on its own does nothing.”
Pressure does set up atm. hydrostatic equilibrium for large CVs, a condition for further study of stuff like lapse rate, energy balance and theory of column entropy maximization thru energy minimization.
“What warms the surface above S-B…”
The surface isn’t any warmer than S-B; surface on avg. radiates at exactly S-B except for transients as S-B requires a thermo. system in equilibrium.
But I think I know what Stephen means, he is writing about Teff=255K and Tmean=288K. These two temperatures can be calculated from measured inputs by same “surface temperature formula” I cited for Kristian at 6:24am.
Konrad says, December 25, 2013 at 5:27 pm:
““For a gas column in a gravity field, the relative height of energy entry and exit from the column is critical to determining the average temperature of the gas column.” – K.
(note – it has taken “Trick” over a year to concede that the above statement was true, which should give some indication of it’s importance.)”
I can see why. Because it isn’t true. This is just the ever perpetuated nonsense about the ‘effective radiating level’.
Why would there be a direct connection between the total radiative flux that a planet emits to space and the physical temperature of some specific layer within that planet’s atmosphere? The final amount of energy being shed to space by a planet over a certain period of time simply needs to match the amount of energy that same planet absorbs from its star within an equal period of time. The actual temperature of the planet or any layer within it is inconsequential to this amount.
Try to work out the ‘average temperatures’ of the gas columns (in effect, the tropospheres) of Venus and Mars and compare these to the planets’ estimated BB emission fluxes to space. There is no connection.
Stephen Wilde says, December 26, 2013 at 8:21 am:
“Pressure on its own does nothing.
What warms the surface above S-B is the amount of atmospheric mass available to absorb energy from the surface by conduction and the amount of work required to hold that mass off the surface against the force of gravity.”
I think we’re moving towards a general understanding, Stephen.
Steven writes “The topmost molecules would be the same temperature as surface molecules but would additionally carry a full allowance of gravitational potential energy too.”
An interesting thought. Energy density is probably the same throughout the column though when you add the potential energy and I suspect entropy to be at a maximum. What other configuration is at a higher entropy?
Still your suggestion is worthy of further research to get a better understanding…
No that hypothetical was discussed in my post above regarding Willis’s scenario of a super insulating silo full of gas. If it was infact isothermal you would have a pressure gradient (maximum at bottom and minimum at top), and a gravitational potential energy gradient (maximum at top and minimum at bottom).
Once you remove the isothermal constraint then you also get an temperature gradient driven by the ideal gas law. Maximum temperature at the bottom and minimum temperature at the top, where you give up pressure potential energy for thermal potential energy.
The real question is what are the bounds or conditions which specify where that partition of energy between pressure and temperature divide up the potential energy.
I suspect the “set point” for the temperature gradient is the temperature span that at the effective radiating surface to the 2.7K temperature of space, (top of radiating atmosphere) equals the SB temperature based on the power in power out from the sun and geological heat inputs at the bottom.
So you have (if my suspension is correct) three key values:
Atmospheric mass and gravitational field strength of the planet atmosphere system.
This defines the pressure at the bottom of the column in the isothermal case, and the gradient of gravitational and pressure potential energy through out its length.
Then you define some point in the middle of the column (probably the effective upper surface of the dominant GHG which is water vapor in our case) where the temperature would have to be equal to the SB value based on energy flows. Once that pressure/altitude/temperature triplet is defined the entire partition of pressure and temperature through out the column in the non-isothemal case becomes defined.
In a mixed gas atmosphere with multiple active GHG’s you would have an effective altitude for radiation to space from each constituent gas. There should be only one temperature gradient which would satisfy all those effective radiating surfaces. Thermal radiation would force the thermal profile to that one solution and pressure would follow according to the ideal gas law.
Once that equilibrium was established you have defined how much warmer the surface will be than an ideal black body in order to achieve the proper energy density of radiation to space at the altitude of the atmospheres effective radiation surface defined by all the GHG components in the atmosphere.
Your variable should be:
mass and radius of planet (defines gravitational constant)
mass of atmosphere (defines limiting surface level pressure for an iso thermal column)
partition of GHG’s in the atmosphere and their effective radiating altitude which will satisfy the SB energy balance of outgoing radiation to space for power in vs power out from all sources.
This defines some unique point in the column and its required temperature to satisfy SB.
Once that value is defined the ideal gas law will define how the potential energy of pressure is converted to temperature through out the length of the column (exclusive of local heating effects like ozone heating of the stratosphere).
You should be able to find all of those values either discretely or using an iterative process to find the temperature profile mandated by the GHG mixtures and their effective radiating surface in the atmosphere to satisfy SB and the power in power out equality.
This would be the lapse rate and temperature profile of the atmosphere in question less any energy present as kinetic energy of mass motion (updrafts, lateral winds, jetstream winds etc.)
Trick says, December 26, 2013 at 6:24 am:
“Kindly refer to Bohren 2006 p. 33 for a basic, simple “surface temperature formula” determining the global surface Tmean=288K from measurements each of solar irradiance, albedo, surface and atm. emissivity globally temporally and spatially avg.d.”
Starting with the known answer and then go backwards, pretending to be showing how to arrive at it, isn’t very impressive. But I guess you find Trenberth & Kiehl’s energy budget diagram for Earth most convincing …
So go to a planet where we do not already know the surface temperature, only its solar input and the content of radiatively active gases in its atmosphere. Then work out its surface temperature from this. This should work for all planets with such an atmosphere, shouldn’t it? You wanted me to find the temperature from just the TSI and atmospheric weight, implying that if I can’t provide an equation, my argument would be invalidated.
“You should get a hint from this that there are more factors than just weight of atm. and solar irradiance determining near surface Tmean. Similar texts show the same.”
Stop putting words in my mouth, Trick. I’ve never said that ‘solar irradiance’ is what should be used. You did. I said ‘solar input’. That’s after albedo and atmospheric absorption is taken into account. The solar energy actually being absorbed by the global surface.
Larry writes “Maximum temperature at the bottom and minimum temperature at the top, where you give up pressure potential energy for thermal potential energy.”
This still describes an intermediate point and not equilibrium. Warm gas from below can (and will) still rise and conduction upwards can also happen. Expansion cannot continue forever and is bound by the energy defined by the temperature.