I haven’t had time to delve into this, but there seems to be a general interest in emissivity through several lines of investigation on the talkshop recently. Physics makes definitions of things in ideal conditions. Emissivity is defined as the radiation a body will emit at a specific temperature. This quantity is crucial to our understanding of the way Earth balances its energy budget of incoming solar energy with emission from various parts of the system. However, emissivity at different wavelengths forms a curve, it isn’t the same at all wavelengths for a specific material. Moreover, in a non-vacuum, radiation isn’t the only means by which energy can leave a body. Conduction, latent heat of vaporisation (evaporation) and convection also play a role, and dominate over radiation in the Earth’s troposphere.
The most important material to consider so far as Earthj’s energy balance is concerned is seawater, since it covers 70% of the planet.
Contributor ‘Max’ turned up some interesting plots for the emissivity of seawater (and land) the other day, which seem to contradict each other. Here are two of them:
MODIS satellite image showing emissivity of around 0.7 at 0.83um for the ocean
ICESS seawater emissivity curve showing 0.983 emissivity at 8.3um
Why the difference?
Wayne Jackson recently posted an alternative energy budget which finds that the ‘effective’ or ‘operational’ emissivity of the surface is around 0.67.
This seems to show that we need to subtract the energy involved in the latent heat and conduction from the figure given by the (in)famous Trenberth and Keihl energy budget diagram for the long wave radiation going up from the surface. But it is claimed that their figure of 356W/m^2 is measured by radiometers. Many people dispute the accuracy and calibration of these devices, but assuming it is a true average of measurements, how can we reconcile the difference?
Could it be that the long wave radiation being exchanged in the air is simply a transient expression of the energy being moved by convection and latent heat? This would make the long wave energy flux within the troposphere more a ‘symptom’ of its energy content than a cause of its temperature or the lapse rate, since it is constantly cancelling out at each altitude level, apart from the relatively small component of the upward radiation which escapes to space through the ‘atmospheric window’.
Several people commenting on their own and each others investigations in this area have been spread across several threads recently. I’m posting this one to get them all together in one place to discuss these issues. I suggest we make a conscious effort not to get sidetracked by anyone, mentioning no names Tim Folkerts, who tries to obfuscate the issue with energy budget calculations which assume a perfect emissivity of 1 or an arbitrary figure such as 0.9 for any part of the system.
Have at it! 
Stephen says: “The problem with the account of Tim and Bryan is that they propose that the effect of GHGs, by reducing the rate of heat loss, both warms the surface AND expands the atmosphere.”
Take 1 m^3 of gas near the surface. Seal it in a flexible adiabatic container. Add energy to the gas.
As a result the The container will both expand a bit AND the gas inside will warm a bit.
The problem with Stephen’s account is that he seems to be proposing that the gas will expand with no change in temperature.
[Reply] Ah, PET bottle kitchen science done without the PET bottle….
Steven Wilde says
“the Ideal Gas Law ( IGL )….. cannot relate to the whole atmosphere”
Let us assume average pressure (p ) of the atmosphere is constant. Actually pressure changes steadily going up. ( Lapse rate )
PV = nRT let P = a constant, then
V = a constant x T
V is directly proportional to T ( Boyle’s Law 1662 )
The atmosphere is not a sphere it is thicker at the hot equator and thinner at the cold poles. A greater volume of air where it is hot and and less volume where it is colder.
That is a greater T leads to greater V, in line with the IGL.
How does the radiative theory explain the changing height of the atmosphere ?
Steve also says
“out in space Temperature is inversely proportional to Volume for any gas accumulation ”
Please explain what you mean by this .
If you look at Jupiter, the temperature and pressure increase together all the way down.
http://math.ucr.edu/home/baez/entropy.html
Steven Wilde says
“the Ideal Gas Law ( IGL )….. cannot relate to the whole atmosphere”
Let us assume average pressure (p ) of the atmosphere is constant. Actually pressure changes steadily going up. ( Lapse rate )
PV = nRT let P = a constant, then
V = a constant x T
V is directly proportional to T ( Boyle’s Law 1662 )
The atmosphere is not a sphere it is thicker at the hot equator and thinner at the cold poles. A greater volume of air when hot and and less volume when colder.
That is a greater T leads to greater V, IGL gets it right, as usual.
Steven also says
“out in space Temperature is inversely proportional to Volume for any gas accumulation ”
Please explain and give evidence for this statement .
“
So far, we’ve seen the entropy of a gas cloud actually decreases as it collapses under its own gravity. At this point, you should be dying to see how I’m going to rescue the 2nd law of thermodynamics! But before I do that, I want to point out another odd fact: our gravitationally bound ball of gas has a negative specific heat! In other words, the less energy it has, the hotter it gets.
To see why, let’s figure out the relation between the temperature and energy of this ball of gas. Remember, the virial theorem says that K = -P/2, so P = -2K, so the total energy of the gas ball is
E = K + P = -K
On the other hand, we’ve already said that
K ~ NT
so we must have
T ~ -E/N
In other words: THE LESS ENERGY THE GAS HAS, THE HIGHER ITS TEMPERATURE BECOMES.
Sounds paradoxical, eh?
It’s not really so weird if you think about it. As the gas ball collapses, it loses energy: the kinetic energy goes up, but the potential energy goes down even faster! Since the kinetic energy goes up, the gas gets hot. Energy goes down, temperature goes up!
In fact, it’s typical for a gravitationally bound system to have a negative specific heat. Imagine a satellite so low that it starts running into the earth’s atmosphere and spiralling down. As it loses energy, it gets hotter, and finally burns up!
This feature of gravitationally bound systems makes them quite tricky. Only systems with positive specific heat can be in thermal equilibrium with their environment. So gravitationally bound systems can never be in thermal equilibrium with their environment! They always want to keep shrinking, thus losing energy and gaining entropy.” ~Baez
___________________________
Still wondering if no one other than tallbloke sees the significance in the correction of: P = εσA(T⁴) to: P = εσA(Th⁴ – Tc⁴) for a surface radiating into an atmosphere of similar but lower temperature?
Stephen 1:03pm: “..assuming no one can say that (VT=nRE) is flawed and I’m waiting on that before going deeper.”
Check the SI units. Here’s what I get first try, anyone else?
VT=nRE
T = nRE/V = (length^0.5)/sec which seems odd. T should come out in Kelvin, an SI base unit.
Roger Clague asked:
“out in space Temperature is inversely proportional to Volume for any gas accumulation ”
“Please explain and give evidence for this statement .”
A ball of gas gets hotter when volume decreases and colder when volume decreases.
In space the only means of shrinking volume is by increasing mass and the gravitational field arising from that mass so more massive molecules will give a higher temperature for a smaller volume and less massive molecules will give a lower temperature for a larger volume.
But at the moment my main concern is as to the validity of the new equation that I proposed.
It looks to me that it works.
Roger also said:
“Let us assume average pressure (p ) of the atmosphere is constant. Actually pressure changes steadily going up. ( Lapse rate )”
Contradictory. You cannot assume P as a constant when it declines steadily going up.
For an individual parcel of air within an atmosphere P can vary because the height of the parcel can be changed.
For a planet with an atmosphere viewed from outside P cannot change because surface P is the same whether the atmosphere expands or contracts.
So one needs a different equation than the Ideal Gas Law to deal with an entire atmosphere correctly.
That equation needs to bridge the gap between decompression causing a fall in temperature and compression causing a rise in temperature (my adiabatic loop).
Both processes are competing and are in balance within an atmosphere at equilibrium.
If one increases the energy that the system is capable of holding by increasing mass, gravity or insolation then both processes ramp up equally so both T and V can change.
If one does not increase the energy that the system is capable of holding but instead just change the speed at which energy flows through then only V can change.
Think of a jar of water filled to the brim.
Adding more water without increasing the size of the jar increases the volume of water but the excess just flows straight out and you have no more in the jar than before.
Mass, gravity and insolation in combination set the size of the jar.
More KE supplied to the atmosphere without increasing the amount that the atmosphere can hold just leads to that KE flowing straight out.
The increased atmospheric height and the consequent conversion of more KE to PE represents the extra KE flowing straight out to PE.
On the other hand a decreased atmospheric height and the conversion of more PE to KE represents more KE flowing back in.
You can also consider the variable store of PE as an overdraft facility that the atmosphere can draw on to maintain stability.
The biggest conceptual problem for radiative theory enthusiasts is grasping the idea that V and E (in the form KE + PE) can change in tandem without involving T.
My equation shows how it can be done by placing T and E on opposite sides of the equation and then allowing KE and PE to vary freely in response to a change in V.
I’m reconciled to this idea taking some time to register even if it is right.
Hi Trick. I think we need to expand this one out.
……..(number of moles) *
(molar mass constant)* (KE+PE)T= _______________________________________________________
………V * (average atomic weight of proportionate constituents) *
(molar mass constant)Which looks like it ends up as Joules per volume, which sounds half reasonable. I might be wrong though.
tallbloke 4:40pm: T should come out simply in degrees Kelvin, right? Base SI unit. Anything else is an issue, maybe not a problem. See if anyone else tries, I can go thru each step later, hard to type quickly, readably as your post is difficult to interpret. KE+PE units are mass * (length/sec)^2.
Stephen 4:27pm: “In space the only means of shrinking volume is by increasing mass…”
A “cloud” of gas in space can still contract its volume with fixed amount of mass. Saturn has been doing that contraction slowly long time, pushing out more heat than it receives from sun. See Kelvin-Helmholtz mechanism.
As the link to Baez’s page and quote I provided mentioned, gravitationally bound system has a negative specific heat, so we have to toss out any illusions that it will be in thermal equilibrium with it’s environment.
Similarly while volume decreases, temperature and pressure increase, yet energy and entropy both decrease.
What’s that I said? Entropy decreases?
Yes, Baez left it as work for the reader, but here’s the answer: radiation carries away a lot of entropy.
As a hypothetical non-radiating gas can not undergo this loss of entropy to the background of space, there is absolutely no reason to assume it will be in ANYTHING RESEMBLING AN EQUILIBRIUM STATE THAT IS ANYTHING LIKE OUR OWN ATMOSPHERE… the inability to lose energy gained by collisions with lower molecules means the column of gas would be much taller, if it even remained associated with the surface rather than winding up scattered to infinity.
Trick: Although K is a base si unit, it doesn’t tell us much about how it arises. Wiki says this about the stat mech approach to temperature:
Statistical mechanics approach to temperature
Statistical mechanics provides a microscopic explanation of temperature, based on macroscopic systems’ being composed of many particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena in terms of the mechanics of the molecules and ions, and statistical assessments of their joint adventures. In the statistical thermodynamic approach, degrees of freedom are used instead of particles.
On the molecular level, temperature is the result of the motion of the particles that constitute the material. Moving particles carry kinetic energy. Temperature increases as this motion and the kinetic energy increase. The motion may be the translational motion of particles, or the energy of the particle due to molecular vibration or the excitation of an electron energy level.
So in one sense, it seems Stephen is ending up with KE on both sides of his equation, which might be a problem, because if they cancel, there won’t be anything left on one side of the equation. DANGER! WILL ROBINSON
Please do go through your working, it will be instructional, and emotional, probably.
Stephen, TimF is right, you seem to imagine that if you heat a parcel all goes into the expansion and that is blatantly incorrect. The expansion is one R(universal) worth, the other cp minus one R(universal) goes into all of the degrees of freedom of that gas mixture and part of that is a linear velocity increase (temperature also goes up) That IS the difference in ‘cp’ and ‘cv’.
Next, in E = PE + KE, that is probably incomplete, should be something like E = KE + k.PE or E = k.KE * PE, take you choice, for I bet ‘k’ will not equal one, that is, one unit or KE probably does not equate to one unit of gravitational PE from additional height.
Next, you are missing a ‘divide by m3 or divide by V (volume)’ in you energy term.
V.T = n.R.(E/m3) or V.T = n.R.(E/V) or just cancel both volumes to T = n.R.E or T = n.R.(KE+k.PE).
At least now the units are correct if that now makes any physical sense to you.
You seem to be looking for some equation that says the Earth can not warm or cool because of a volume change or something else will cancel the temperature change. Well, good luck.
However if you are looking for something that cancels *part* of the warming from an additional amount of energy, I gave that explanation to you long ago in my comment on how the atmosphere ‘puffs up’ or the volume increases in the day and contracts at night returning *part* of the energy to temperature. I pointed at UniSys’s site to show this occurring. But Stephen, that is only one R(universal) fraction of the energy in question of the ‘cp’, not the entire ‘cp’ heat capacity.
Steven W says
“So I suggest this: VT = nRE
(where E is KE + PE)”
That is
VT = a constant
This predicts increase in T reduces V
But we find in our atmosphere increase in T increases V. The troposphere height is greater at the equator than the poles.
So your equation makes incorrect predictions.
Steven W says
“You cannot assume P as a constant when it declines steadily going up.”
It is you who decided to make pressure ( p ) a constant. I am agreeing with that and saying why.
The IGL was discovered from experiments on small volumes at the surface. It was assumed that gravity was constant at top and bottom.
In the atmosphere there is a pressure profile because gravity does decline and has a noticable effect over the larger distance.
The “average pressure” is that which would exist if gravity did not also decline steadily going up. As is assumed for the IGL.
Wayne: T=nRE was what Stephen was proposing. Thanks for the elucidation which helps expand it out and illuminate the consequences. SO, are you happy with T=nRE as well? Is this a novel formula? I appreciate you were already there with your own descriptive analysis. Is this the convergence we have been awaiting?
So in stat thermo terms can we consider T to be the expression of KE as wikipedia says? If so, what are the consequences? Would we be left with KE=1/n.R.k.PE ?
Well I think it is clear that expansion results in more PE relative to KE when the amount of KE is limited by energy coming in from outside the atmosphere plus the ability of mass and gravity to be able to hold on to it.
The issue then is whether the increase in PE utilises all the KE generated when (or if) a GHG causes net warming.
Contributors here are suggesting that somehow the amount of mass , gravity and insolation does NOT limit the amount of KE that an atmosphere can contain. I think that requires some explanation.
How exactly could an atmosphere retain more KE if mass, gravity and insolation are all unchanged ?
Furthermore we are not all agreed as to whether CO2 has a net warming or a net cooling or a zero effect.
Suricat and others have pointed out that water vapour does not change the lapse rate (thereby expanding the atmosphere) by virtue of its radiative characteristics but rather via the phase changes of water.
Ozone in the stratosphere changes the lapse rate (thereby expanding the atmosphere) by virtue of its interaction with incoming solar energy which is quite different to the proposed AGW interaction of CO2 with upward longwave from the surface.
In the cases of the phase changes of water and the ozone reaction with incoming solar energy why would the expansion not absorb all the extra KE as PE ?
So does CO2 have a net warming or cooling effect or is its effect zero ?
More absorption is matched by more radiation isn’t it so why would there be any net warming or cooling given that the extra absorption results in a new radiative window to space?
If the net effect of CO2 is zero we no longer have to consider whether it expands or contracts the atmosphere in the first place.
Two questions arise from the above:
i) Can an atmosphere hold on to more KE (without it converting to PE) if mass, gravity and incoming energy remain the same ?
ii) Is the net effect of more CO2 warming, cooling or zero ?
The answers will determine whether or not I am barking up the wrong tree.
I would apologise for wasting everyone’s time if I turn out to be wrong but in this case I think my questions are reasonable given the apparent paucity of knowledge on both those issues.
Tallbloke, I don’t know yet. I prefer a slow pace to let it roll around upstairs a bit, rearrange the equation and terms, try some actual cases to see it makes physical sense.
One thing, volume is completely gone. What do we have? A ‘T’, ‘R’ and ‘n’ number of moles …
Wait a second !!! Something seems wrong in that first equation and I accepted and used it without a question:
V.T = n.R.E, that doesn’t seem right at all.
PV = nRT –> T / V = P / n.R ….. ???? Sorry, I didn’t start far enough back in all of these comments.
Oops, I need to go back and see how Stephen even came up with that V.T = n.R.E equation, it seems something’s amiss.
Have a b-day party I can’t miss so may not be back till this eve on this.
[Reply] My bad, I forgot about the V on the left.
wayne said:
“T = n.R.E ”
I was hoping someone would refine my equation to the minimal form but is that right ?
A rise in E being the total of RE + PE would give a rise in T BUT within E PE is replacing KE to prevent a rise in T.
Do we need and adjustment in there to account for the conversion of KE to PE ?
We need V on the left to deal with the effect of the KE to PE conversion on the right don’t we ?
I’m curious what the virial theorem effect is here…
For a gravitationally bound ball of gas which is on average unchanged and the positions and velocities are bounded, you then have KE = -PE/2.
*Which on average has temperature unchanged* is what that should have said.
wayne 6:04pm: “V.T = n.R.(E/V) or just cancel both volumes to T = n.R.E”
Need VT=nREV to cancel V from both sides. Your actual result would have V^2 on the left (multiply both sides by V).
tallbloke 5:39pm: “Please do go through your working, it will be instructional, and emotional, probably”
Emotional? Around here? Nahhh….
I can think of one mistake I might have made, will double check & post later; won’t end up Kelvin on RHS even then. Maybe someone beats me to it. It is ok to end up with KE on both sides, in fact need to end up with KE or “some unit” the same on both sides, ha. Kelvin=Kelvin is what is needed for T=nRE/V. Don’t see a Kelvin in RHS of your 1st try 4:40pm.
See, not even something as basic as a unit is easy. I commend a Prof. or TA for pointing that out to me (gruffly & in red) on some exam right after a -5 points or something.
The tricky bit is how best to incorporate the effect of the KE to PE conversion as a response to V so that T (and KE) remains dependent on mass gravity and energy supply from outside the atmosphere.
I’ve had a go at coming up with a suitable equation but I think it is beyond my mathematical skills.
The conversion of KE to PE as a result of changes in V caused by changes other than mass gravity and insolation would seem to be best represented as a separate process independent of the main show but I’ve no idea how to express that mathematically.
To my mind TV = nRE seems to work well enough as long as the constituents of E namely PE and KE are free to vary freely in response to changes in V because that also affects T but perhaps there is a more convincing way to express the relationships since I see that some here are not convinced.
I may just have to leave it at that and see what transpires.
Let’s keep it simple.
Add say I kg of CO2 to an atmosphere.
Assume that CO2 has a net warming effect (it might actually have a net cooling effect).
That 1 kg of CO2 provides say 10 Joules of extra energy which raises the atmosphere 1 metre.
I know the proportions are unrealistic but we are keeping it simple.
That extra 10 Joules has to be supplied constantly if the atmosphere is to stay 1 metre higher.
Meanwhile the extra 1 metre height has converted 10 Joules from KE to PE.
How is the temperature expected to increase ?
If the atmosphere had NOT expanded and converted the extra Joules to PE then there would have been an imbalance at top of atmosphere with too much KE in the system and more going out than coming in.
The fact of the expansion prevents any such imbalance.
PE is our global thermostat.
I say the equations have to follow reality rather than vice versa. We should be able to construct equations that cover that scenario.
Is there anything here of use? Various ideal gas equations…
http://en.wikipedia.org/wiki/Isentropic_process
Thanks Oldbrew.
A bit technical for me but someone might be able to use it.
tallbloke 5:39pm “Please do go through your working..”
Units used in IGL from here which may itself have flaws so find your own 1st principle I’m lazy, and given SI has 7 base units that aren’t derived:
http://www.webqc.org/ideal_gas_law.html
and kinetic energy = ½ mass*velocity^2 = ½ *kg* (metre/sec)^2, drop the unitless ½ my choice or carry the 1/2 might be your choice, if so, DIY:
KV=nRE
K*metre^3 = mol * (Joules/mol-K) * kg*meter^2/sec^2
Multiply both sides by K, divide both sides by metre^2, cancel the mol/mol:
K^2 * metre =joules*kg/sec^2
A joule is energy expended by force of 1 nt moved thru distance 1 metre.
K^2 * metre = Nt*metre*kg/sec^2
Cancel metre both sides, take square root both sides:
K = (Nt*kg)^0.5/ sec.
K= (force*mass)^0.5/sec.
This above is odd in and of itself.
Sec. and mass are base units, force is derived unit so can take this further with F=ma=kg*metre/sec^2; this is where I screwed up earlier. Happens. Press on regardless, sub. in Force = kg*metre/sec^2.
K= (kg*metre/sec^2*kg)^0.5/sec
K=(kg^2/sec^2 *metre)^0.5/sec
K=Kg/sec * metre^0.5/sec
K= (length^0.5) * mass/sec^2
These are all SI base units. So the last eqn. units (if replicable) says this is how a Kelvin is derived but a Kelvin is a base unit also, so there is a flaw somewhere. Unless someone spots another “issue which may not be a problem” in my SI “working”. Which is maybe possible and if so, definitely emotional.
Stephen 9:13pm: “Add say I kg of CO2 to an atmosphere. Assume that CO2 has a net warming effect (it might actually have a net cooling effect).”
Neither happens net if the CO2 is added at the same temp. from existing carbon & O2 at that temp.
The C & O2 simply convert their existing energy into CO2 say by Stephen’s breathing (well, unless if E=mc^2 is important & it is not). Cannot warm (increase) nor cool (decrease) net energy unless energy is added or subtracted to/from earth/atm. system. This is why control volumes are so important and why they invented 1st law.
The infrared active gas CO2 affects the flow of energy, slowing the cooling of the surface and up to somewhere thus slowing the warming of the upper atm. by the exact same amount since the energy doesn’t flow there conserving energy in the earth/atm. system. 1st law is important as is control volume to see 1st law accounting for energy is conserved.
“That 1 kg of CO2 provides say 10 Joules of extra energy.”
No it doesn’t unless you want to use e=mc^2, convert some mass to energy, which isn’t the case.
“How is the temperature expected to increase?”
Net, it doesn’t. Energy in the control volume is the same, simply breathe in change C and O2 into CO2 which affects the energy flow only within the system, no net energy added.
“The fact of the expansion prevents any such imbalance.”
There is no atm. net expansion, no energy changed in the control volume of the earth/atm.
“We should be able to construct equations that cover that scenario.”
We can but not considering mass, insolation, gravity only – have to use them, control volume & albedo, atm. emissivity in 1st law equil. condition as up there in the top post (roughly give or take some rounded numbers):
1370 * 0.7 – 4*sigma*(1-0.8/2) * Tsurface avg. ^4 solve for Teq. atm. near surface =289K
Spending so much bandwidth on PV=nRT why not just spend it understanding the provenance of something like this that works fine, in concert with all the thermo grand masters findings and experiments.
Quoth tallbloke again: “…go through your working, it will be instructional, and emotional, probably.”
Trick: I think where we are heading to, Albedo will turn out to be emergent from the fundamentals. We won’t need to have it as a given. Better to go the other way round from gas laws and latent heat which actually control near surface to tropopause. Not radiation only model.
Yeah tallbloke. Both IGL and radiation are cool to learn about, don’t exclude either I say. Though some more bandwidth spent on hacking thru radiation would be helpful. Certainly albedo will change, it does now – it is hard to measure and we don’t have records like global spatial and temporal sampled Tavg. over the century. Figure albedo out from internal flows if you can, then apply result to radiative flows – the one & only game in town for external earth/atm. system energy flow.
Science will get better at albedo measures I bet. Maybe even atm. global avg. emissivity measures eventually.
Want/need (Aristotle terms) to get a handle on both Stephen’s adiabatic and diabatic process. That means internal control volume energy flow (thermals, evap. transp.)and external control volume energy flow (SW in, LW out radiation).
That LW is so pesky, can’t “see” it, ghost like. Faith based? No, my bare feet, cloudy night temperature difference vs. clear night & logical science learned from reliable thermo grand master 1st principles et. al. sources doing relevant experiments say LW must exist in significant quantity even if can’t see it.
Would you say the atmosphere is bound by gravity?
In rough hydrostatic equilibrium.
TB.
I thought this thread was dead. The new ‘page’ style configuration threw me a bit as well, but ‘my how this thread has progressed’ (I’ve spent most of Sunday reading it)!
I think Stephen’s new attempt at a formulation originated from here:
http://tallbloke.wordpress.com/2013/01/13/stephen-wilde-greenhouse-gases-and-the-ideal-gas-law/#comments
Where I hinted that the DALR didn’t/couldn’t include include latency for an ‘ELR’ (environmental lapse rate), or a ‘WLR’ (wet lapse rate) when implementing the PV=nRT equation. Thus, can’t represent Earth’s atmosphere as a ‘true’ analogy.
IMHO. A change in the constant R isn’t the correct approach when considering a WLR, so I suggested a ‘binary’ formula that measured the ‘latency’ properties of the system.
I repeat this post here:
“Stephen Wilde says: January 17, 2013 at 9:02 pm
“Does that make more sense?”
It’s beginning to. Let’s go back to the original equation of “PV=nRT”. This works fine where the ‘Molar’ constituents remain unchanged, but this isn’t the case for Earth’s atmosphere. WV is added to the atmosphere at the Earth’s surface and precipitated out at some altitude or other. This ‘equation’ needs to be modified/edited for a better representation that can model Earth’s atmosphere.
We need to add a P2, V2, n2 and T2 to accommodate the ‘phase transition’ elements.
Best regards, Ray.”
Feel free to read the entire thread, but the important point here is to arrive at a ‘formula’ that describes the WLR better than Stephen or I can (my math ‘sucks’ too).
Any suggestions?
Best regards, Ray.
I mean is it likely that the atmosphere will spontaneously cease to be found within a given volume surrounding the gravity well?
There is an upper bound on the position and volume for a gas cloud in a gravity well assuming work is not done to it.
So one can say it is bound by gravity, right?
What does that mean for the specific heat of that atmosphere?
Max asks – “..is it likely that the atmosphere will spontaneously cease to be found within a given volume surrounding the gravity well?”
If earth like g well, a molecule of N2 won’t spontaneously achieve escape velocity. It is non-zero possible to get a spontaneous kick to high N2 velocity but the probability is near nil that velocity would be greater than 22,500 m/sec. N2 velocity most probable by M-B distr. is around 400 m/sec at the surface, going down at altitude as N2 (T)^0.5.
I interpret Max has an answer for the Cp, fill me in.
A column of gas suspended in a gravity well does not behave in what might be considered “typical” manners for a system which is in thermal equilibrium.
If you poured a cloud of gas into a container sitting in a gravity well, as the gas molecules began to fill the container the distribution would not be even throughout the container, and as the density near the bottom increased, so would the temperature there.
…
What is less obvious is that this would reduce the energy and entropy of the gas column as a whole.
…
Why would that be the case?
The position phase space of column of gas collapsing under gravity is necessarily reduced for the molecules near the densest regions, one would expect the momentum phase space to expand, but if this were the case the cloud would not collapse under gravity.
If both portions of the phase space shrink, the entropy goes down for the gas molecules, which should be setting off “HERESY” alarms in your head by now.
Don’t fret though, emission of radiation by the gas molecules allows the entropy to increase and escape the gas cloud, as radiation is a great way to jack up the entropy of a system.
In the case of a non-radiating system, there must be something carrying entropy away or else the system will not collapse under gravity.
For a globular cluster the evaporation of stars from the cluster serves this purpose, and similarly for one of the oft-discussed hypothetically non-greenhouse atmospheres, the only way to carry away entropy would be to lose molecules directly.
…
These situations I am describing are cases where a system would have a negative specific heat, losing energy raises the temperature in system collapsing under gravity.
Thermal equilibrium assumptions require positive specific heat, and thus any such arguments which hinge upon flatly declaring “1st law” or “2nd law” or whatnot should probably be checked for this source of error.
While yes, the laws of thermodynamics do hold, they do not always hold in the manner you expect.
First, thanks Trick for catching my slip on the V². That was a dumb one. I learned don’t write a complex comment while also trying to get ready for a birthday party!
Stephen, let’s start over. I do seem to sense what you are trying to get across by saying all of these words but it seems a bit confusing to me.
You may not realize that the KE > PE and PE > KE you keep speaking of are already embedded within the Ideal Gas Law itself. I’ve mentioned this before but for one last try look carefully at the form of the IGL:
R is the universal gas constant
Rair = n × R / m
ρ = V / m
so,
P / ρ = Rair × T.
Rair is the specific gas constant for air as we now know it today. For a moment, let it remain constant with no additions or removals of water vapor or co2 that do cause a slight change in that value.
‘n’ is the number moles in a one square meter gas column, for the same reason, let that remain constant for a moment.
Same for ‘P’, keep the mass of the column fixed. That will flex with changes in the composition also.
By that equation of the IGL, if ‘T’ rises, the density has to decrease so that the ‘P/ρ’ ratio proportionally rises.
You can now see this example two different ways depending on your preferred viewpoint.
If you are thinking of a fixed one cubic meter or unit control volume, since the density dropped, some of the particles within were forced out of that unit cube and since we are also speaking of that unit cube being within a unit area column the particles forced out go strictly upward, lifting the column above and some KE > PE.
If you are viewing it as a variable height cube or even as an entire unit column as a whole, then after the density drop caused by the ‘T’ increase, the volume or column will be taller so once again some KE changes to PE.
In both cases KE > PE, the effects are identical, but that is being accounted for in what the IGL implies itself. You cannot then say that KE > PE recursively causes further changes through the IGL to alter the original causal ‘T’.
Do you agree with just that much? If so, that clarifies one whole slew of words and we might then tackle what happens when the actual composition of the column’s air is altered which it seems to underlie your entire concept.
The IGL is an instantaneous state of the gases that must hold and has nothing to do with why the lapse is the way it is.
I also assume we are still speaking of a multi-decadal world-average column aren’t we?
–
Another matter since it’s fresh and I just read many of your comment, back to lapse rates for a moment. It seems you and I differ in some respects on this subject.
You seem to start at the DALR and I start at a vertical or zero lapse rate. So here’s how I see it and see if you agree or where you disagree.
A non-radiating dry atmosphere would be basically zero or a vertical line on a T by altitude graph. To me this question was answered on one of the Graeff posts. Ferd, br1, and I all did simulations and they showed no natural DALR lapse, in fact, none at all.
Now add some radiation, emissions and absorptions, occurring within the gases, h20 and co2 but no state change yet, I see two completely opposite effects occurring at this isolated pointi n the example.
At the top few kilometers just under the ToA, radiation is escaping to space increasing as you get closer to the ToA, and that cools the top of the atmosphere pushing that vertical lapse line (0.0 K/km) on the graph to the left or cooler, leaning it over counter-clockwise. In the bottom few kilometers just above the surface there is great absorption due to the high density of the gases and this warms the lower portion pushing the bottom of that lapse line to the right, or warmer, again counter-clockwise. Since there are no state changes occurring at this point in this example, you end up at the DALR, -9.8 K/km slope.
From here on we may agree.
Now add water vapor’s state change to the picture. Near the surface you have evaporation which cools the lower atmosphere pushing the bottom of that line back to the left or cooler, clockwise this time, just a bit though. At or below the ToA, you have condensation and warming that pushes the top portion of that line back to the right, warmer and clockwise again. You end up at the averaged ELR, -6.5 K/km.
Add even more state changing water vapor and it even magnifies both of those effects, top and bottom, above and below, rotating the line even further clockwise to the wet lapse rate of even further, sometime much more, to or past the -5.0 K/km and you have an unstable atmosphere and storms.
Do you see it that way or where might we differ?
Thanks for the considered comments wayne. There is a lot there for me to consider but a few points stand out:
i) “Same for ‘P’, keep the mass of the column fixed”
I’m puzzled by that. Isn’t pressure a consequence of the strength of the gravitational field too ?
Furthermore the mass of the column isn’t fixed unless you also widen the column with height to reflect the spherical nature of the planet. The mass of the entire atmosphere is fixed but each unit of volume within the atmosphere has less mass if the atmosphere expands.
ii) “cannot then say that KE > PE recursively causes further changes through the IGL to alter the original causal ‘T’.”
I’m not saying that. I’m saying that the temperature will depend on the amount of KE but the height of the atmosphere depends on KE+PE.
The amount of energy flowing through MUST be regulated so as to match energy in at top of atmosphere so if one keeps the incoming energy the same but there is more KE than needed to balance it then one can only regain balance if one expands the atmosphere thereby converting ALL the excess KE to PE. So you don’t get a rise in T in the first place (except maybe as a lagging feature while the system adjusts) You just get an immediate expansion which keeps the amount of KE steady so as to retain top of atmosphere balance. Assuming GHGs do increase KE in the first place which we don’t all agree on.
If not all the excess KE were converted to PE then there would still be too much KE and thus too high a temperature so that energy out would be more than energy in permanently.
The Earth’s temperature must be exactly right to match energy flowing in. Therefore the amount of KE must be limited to that figure and T must be controlled in some manner. We just need to find the right variant on the IGL.
iii) “A non-radiating dry atmosphere would be basically zero or a vertical line on a T by altitude graph”
My problem with that is that in reality there is a pressure gradient set by gravity and the reduction of pressure with height leads to a lapse rate even with no radiative capability.
Otherwise one would have the impossible scenario of a sudden and complete drop of temperature from that of the atmosphere to that of space at top of atmosphere in the width of a molecule.
It is the pressure gradient that determines the lapse rate which determines atmospheric height and which gradually replaces KE with PE all the way up until the top of the atmosphere is the same temperature as that of space.
So there is a lapse rate set by gravity via the pressure gradient which can never be vertical.
I like the idea of the lapse rate moving clockwise and counterclockwise as one goes up but that is already apparent in the ‘W’ shape of Earth’s vertical temperature profile. But the starting point cannot be vertical due to the pressure gradient.
I’m pretty sure that it is the pressure gradient which biases the starting lapse towards cooling with height that allows total energy (KE+PE) to control the height of the atmosphere rather than just KE.
It is like that jar of water I mentioned. The system can only retain as much KE as gives it the right temperature to radiate out to match incoming energy. Any more and the excess just slops over the ‘rim’ and becomes PE instead.
I think my equation VT=nRE, where E=KE+PE and the proportions can vary, comes close.
wayne.
I can tell you why the lapse rate is not vertical.
That would represent no atmosphere and no gravity like the moon.
The surface gets hot and radiates straight out but from just above the surface upward there is no further loss of energy because there isn’t any.
A horizontal lapse rate represents infinitely powerful gravity and an infinitely dense atmosphere, a black hole where nothing gets out.
The slope of the lapse rate therefore depends on gravity forming a pressure gradient and the stronger the gravitational field the shallower the slope becomes.
So the natural lapse rate for a given gravitational field is actually somewhere between 12noon and 3pm using the clock analogy.
You are right to say that composition can vary the lapse rate but in the end the average of all lapse rates within the vertical column must equal the lapse rate set by gravity.
However it is not necessarily radiative characteristics that change the lapse rate.More likely it is other qualities such as phase changes in the case of water vapour or the absorption ability of ozone when hit by solar shortwave.
I think it likely that radiative characteristics go straight to a volume increase with possibly no change in lapse rate and because the pressure gradient biases the system towards cooling with height it goes straight to PE and not KE simply because it does cause expansion rather than a change in the lapse rate.
Having gone to PE in a higher atmosphere the vertical height of the adiabatic loop increases and it takes longer for KE to be returned to the surface by the descending half of the loop.
So,
IF (not demonstrated to me as yet) CO2 holds more energy for longer then it raises the atmosphere to create a delay in the return of KE from the adiabatic loop to the surface and the net effect on T is zero.
Stephen and Tallbloke:
You guys are going to find this paper a ‘must read’ and very interesting though if you are not that familiar with statistical mechanics, you might just try to grasp the essence of the words:
Atmospheric absorption by IR-sensitive molecules
http://www.tech-know-group.com/papers/IR-absorption_updated.pdf
I came across this after writing my last comment to Stephen, just a few minutes ago, but I can already tell it’s important to know. Here is someone capable of doing the heavy-lifting statistical td analysis. Even has a bit on lapses too Stephen, but I haven’t even read it in detail myself.
–
“You are right to say that composition can vary the lapse rate …”
When you say ‘composition’ you seem to mean water vapor exclusively, I meant any changes in O2, N2, Ar, CO2 concentrations not necessarily including H2O and state change. No, I didn’t say that per se, I said the composition would change all of ‘P’, ‘n’, and ‘Rair’. For me to say that about the lapse rates I would need to dig a bit… the answer to my answer to that is not on the top of my head.
It’ll take me a while, some times hours to read your comment back to me one sentence at a time, so I might comment back a bit later, but that was on comment that popped right out at me.
[Reply] As I said the other day on the emissivity thread, that paper has much to commend it, though it does confuse ‘heat’ and ‘energy’ more than I like.
“As I said the other day on the emissivity thread, that paper has much to commend it, though it does confuse ‘heat’ and ‘energy’ more than I like.”
Somehow I missed that in the comments but thanks much, I’ll watch out as I read it.
Stephen Wilde says:
January 21, 2013 at 7:43 pm
Question ( i )
THe IGL is a model. We let pressure start off constant. Gravity will create a lapse rate. We ignore the small change in volume caused by increasing height
Question ( iii )
Even N2 and O2 absorb and radiate a bit. So there is always a lapse rate
In ( ii ) you say
“The amount of energy flowing through MUST be regulated so as to match energy in at top of atmosphere”
We are applying the IGL and the Law of conservation of energy ( in particular KE and PE ) to a small vertical column of and within the atmosphere. We assume all columns are the same. So our result is also for the atmosphere as a whole.
We are not considering energy flow in the atmosphere or energy entering the atmosphere.
wayne:
You know things make a lot more sense for my hypothesis if the effect of CO2 is nominally cooling. It goes like this:
i) CO2 in an atmosphere allows more radiative energy out to space than does a less radiatively active atmosphere.
ii) Atmosphere cools and so contracts.
iii) Contraction results in faster conversion of PE to KE by speeding up my adiabatic loop. It speeds up because it doesn’t have to go so high.
iv) The additional KE is attributed incorrectly to the CO2 and is taken to be a net warming effect.
v) But it isn’t because all the extra KE is doing is offsetting the cooling effect of more upward radiation.
vi) Net effect of more CO2 being zero.
Doesn’t it make more sense that way around ?
Roger Clague:
i) You shouldn’t ignore the ‘small’ change in volume. CO2 produces a ‘small’ change in energy flow rates.
ii) My point is that due to the pressure gradient there is a lapse rate even if the entire atmosphere is radiatively inert.
iii) You should be considering energy flow in the atmosphere AND energy entering the atmosphere. That is what makes it all clear. There can be no equilibrium and therefore no atmosphere unless somehow the system always adjusts to ensure that the flow through the atmosphere always results in energy out equalling energy in. Subject to internally generated variations around the mean.
Stephen Wilde suggests “i) CO2 in an atmosphere allows more radiative energy out to space than does a less radiatively active atmosphere.”
No.
Cold CO2 in the upper atmosphere radiates LESS in the 15 um band than the warm ground radiates in the 15 um band. So less radiation will escape to space with cold CO2 blocking the copious IR from the warm ground and replacing it with sparse IR from the cold upper atmosphere (until the surface warms enough to make up the difference).
wayne says: January 21, 2013 at 9:02 pm
“You guys are going to find this paper a ‘must read’ and very interesting though if you are not that familiar with statistical mechanics, you might just try to grasp the essence of the words …
There is no statistical mechanics in this paper as far as I can see, just plain old thermodynamics.
And as Tallbloke says, it confuses heat and energy. And it assumes that a two-sided object emits thermal radiation from only one side. Unfortunately, he then spends ~ 30 pages solving the wrong equations, based on radiation from only one side of an object.
Tim Folkerts says: January 22, 2013 at 1:12 am
“Cold CO2 in the upper atmosphere radiates LESS in the 15 um band than the warm ground radiates in the 15 um band. So less radiation will escape to space with cold CO2 blocking the copious IR from the warm ground and replacing it with sparse IR from the cold upper atmosphere (until the surface warms enough to make up the difference).”
???
You’re comparing apples with pears! Do you mean that the “15 um band” isn’t so profuse/radiant where CO2 is cold at that altitude? Surely that can only indicate that most of the 15 um band has already been radiated above TOA?
How does CO2 cause “blocking” of the “copious IR from the warm ground and replacing it with sparse IR from the cold upper atmosphere”???
I avidly await your response, but I need to sleep just now.
Best regards, Ray.
Whoa, that Reynen paper getting posted just now is trippy, that’s what I was ranting about in the adiabatic thread.
“How does CO2 cause “blocking” of the “copious IR from the warm ground and replacing it with sparse IR from the cold upper atmosphere”???
With all due respect, if you don’t understand the basic IR properties of GHGs (they absorb and emit IR) & the Stephan-Boltzmann Law (warm matter emits more IR than cold matter), then I won’t be able to explain this in a brief post here. This was the guts of a different post, which should explain this better ( https://tallbloke.wordpress.com/2012/12/06/tim-folkerts-simple-argument-supporting-a-radiative-greenhouse-effect/ ).
Tim Folkerts says: January 22, 2013 at 5:05 pm
“With all due respect……”
Look deeper into a ‘wet lapse rate’ and you may find the GHE that you were looking for in your link.
CO2 has little ‘hidden’ energy.
Best regards, Ray.
Ray,
“The greenhouse effect” is a function of the lapse rate and of the IR properties. It is not one or the other. So no amount of looking at just ‘wet lapse rate’ or at just the IR properties will give people a full understanding.
Tim Folkerts says: January 23, 2013 at 8:24 pm
“Ray,
“The greenhouse effect” is a function of the lapse rate and of the IR properties. It is not one or the other. So no amount of looking at just ‘wet lapse rate’ or at just the IR properties will give people a full understanding.”
I concur!
So why discuss all the complexities of ‘spectral lines’, ‘depths to extinction’, ‘TOA’ and ‘thermal IR/spectral IR’ when these approaches need a ‘LBL’ (line by line) analysis that takes a super-computer to work through for a global analysis. It takes the ‘focus’ away from the ‘atmospheric hydro-cycle’, ‘ELR’ and ‘latent heat’. All LBL calculations are for a ‘DLR’ (dry lapse rate) anyhow, so what do they miss out on? GHE! They CAN’T model clouds, or the top of the ‘greenhouse’, (which is at ~the tropopause).
Why not treat Earth’s atmosphere as a ‘radiative interface’ that shows TOA from the ‘surface’ up to ‘~mid stratosphere’ (depending on the altitude that you understand doesn’t ‘re-heat/insulate’ the surface. Mark altitudes as ‘bands’ that represent the percentage of TOA for both ‘incoming’ and ‘out going’ radiation (including the surface). This’ll give people some idea of what goes where so they can continue to speculate a warming or cooling scenario and let the people that want to discuss the ‘validity’ of the ‘apportioned bands’ continue their discussions.
Oh, wait! Trenberth et al already did this. However, they were hampered by incomplete data (they have my sympathy) and produced a graphic that has come to be known as ‘The Cartoon’ in climate circles. It really does need to be depicted with ‘finer’ detail. Does this ‘dissuade’ others from this approach? Probably.
IMHO, we need to include the ‘entire’ atmospheric hydro-cycle (including clouds) to enable us to express the full function of the GHE.
BTW. My apology for evoking your response to a ‘rhetorical’ question by me! I need to remember to make my rhetoric more obvious and less ‘cryptic’.
I guess I’m just getting too cynical in my old age.
Best regards, Ray.
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