## Sunday, November 30, 2014

### Why Greenhouse Gases Don't Affect the Greenhouse Equation or Lapse Rate

Some commenters on the greenhouse equation believe that greenhouse gas radiative forcing controls the adiabatic lapse rate, and claim without any mathematics or evidence, that that's allegedly how greenhouse gases control the Earth surface temperature. We'll now show the reasons why this claim is incorrect:

1. The adiabatic lapse rate equation is

dT = (-g/Cp)*dh

where

dT = change in temperature
dh = change in height
g = gravitational constant
Cp = heat capacity at constant pressure

Thus change in temperature from the lapse rate is dependent upon 3 variables that have no dependence whatsoever upon radiative forcing from greenhouse gases. None.

Note temperature is inversely related to heat capacity (Cp), thus, water vapor increases heat capacity but this decreases temperature by up to 25C as we calculated in the first post of this series, due to the lapse rate changing from a dry to a wet adiabatic lapse rate. This proves water vapor acts as a negative-feedback cooling agent.

N2, O2, and CO2 heat capacities (Cp) are less than half that of water vapor, but are all very similar. At only 0.04% of the atmosphere, an increase in CO2 would cause a trivial increase in Cp, which since the lapse rate equation says Cp and temperature are inversely related, would cause a slight cooling.

2. Secondly, even if the atmosphere was 100% nitrogen N2, with no greenhouse gases, the pressure change with altitude and thus convection and the lapse rate would be almost the same as the current atmosphere.

We can prove this using the well-known barometric formulae, which are based on the ideal gas law and kinetics of gases (a "Boltzmann distribution"), are completely independent of greenhouse gas radiative forcing, and demonstrate a 100% greenhouse-free atmosphere of the same mass would have a nearly identical lapse rate, nearly identical height at the center of mass, and the surface would be just as warm or warmer than the current atmosphere.

As the lecture notes below show, to answer the question,
"What is the ratio of atmospheric pressure in Denver at 1 mile to that at sea level (assume the atmosphere is 100% Nitrogen N2)?
The solution uses the molecular weight of N2, the Boltzmann gas constant, Avogadro's number (constant) and well known standard barometric formula to determine the pressure ratio between sea level and one mile is 0.822, which is the same ratio (0.823) calculated by the US Standard Atmosphere calculator for our current atmosphere. Therefore the presence of greenhouse gases in our atmosphere insignificantly affect the barometric formulae, ideal gas law, and convection which are the basis of the greenhouse equation.

We show using the same barometric formula for our atmosphere that the center of mass and equilibrium temperature with the Sun occur at ~5100 meter height:

 Solving for the center of mass of our atmosphere, which is located at 0.50 atmospheres, and which sets the location of the ERL at 255K and near mid-point of the lapse rate

Compared to a pure Nitrogen N2 atmosphere in which the center of mass is only slightly higher altitude and at the equilibrium temperature with the Sun at ~5300 meter height:

 Solving for the center of mass of a pure Nitrogen atmosphere, which is also is located at 0.5 atmospheres, and which sets the location of the ERL at 255K and near mid-point of the lapse rate

Thus, a 100% Nitrogen atmosphere without any greenhouse gases would have an atmosphere with essentially the same dry adiabatic lapse rate (10C/km) as Earth's, and the average adiabatic lapse rate in a N2 atmosphere would be higher than Earth's average 6.5C/km lapse rate due to the lack of water vapor, which increases Cp to decrease the lapse rate and cause cooling.

Additional slides from the lecture notes above on why the composition of gases don't significantly affect the barometric formulae or ideal gas law:

1. MS, keep up the good work, very appreciated.

Sorry to be a "picker of nits" but you wrote;

"Note temperature is inversely related to temperature"

When I think you probaly meant to write;

Note temperature is inversely related to "thermal capacity".

A minor transcribing flaw in otherwise very high quality work.

Hard to imagine something that is inversely related to itself, but I have met a few "odd ducks" along the way where this might apply.....

Cheers, Kevin

1. Oh yes, thank you.

Oddly, maybe I was thinking about the radiative greenhouse theory being inversely related to itself ;-)

2. I'm sorry, but as with your "gravitational greenhouse effect" posts, I'm afraid your analysis goes off the rails before you even get going.

The adiabatic lapse rate is a "one way" stability limit. If the actual lapse rate is less than the adiabatic lapse rate, it will NOT evolve toward the adiabatic rate. This is how temperature inversions can be maintained for long periods of time (for months in polar winters).

However, if the actual lapse rate is greater than the adiabatic, upward convection will kick in, and the rate will evolve toward the adiabatic.

Why would the actual lapse rate pass the adiabatic? This happens when solar shortwave radiation heats the surface, but radiatively active gases absorb the longwave radiation from the surface. This often tends to set up a "radiative lapse rate" in the atmosphere that would be greater than the adiabatic rate, but this causes convection to kick in to drive the rate toward adiabatic.

With the present levels of radiatively active gases in the atmosphere, it is common that the radiative lapse rate (what would occur if you could inhibit convection) is greater than adiabatic. Without these gases, there would be no radiative lapse rate, and therefore no convergence toward the adiabatic lapse rate.

So even though the computation of the magnitude of the adiabatic lapse rate does not use the radiative properties of the gases, the only reason we commonly see the adiabatic lapse rate is due to the radiative properties of the gases.

1. I'm sorry but your comments are nothing but strawmen and handwaving. I'm well aware the average LR is ~6.5, wet ~5, dry 9.8, and that they can go beyond those limits and be brought back. So what. Doesn't change anything at all about the global AVERAGE I'm using. Strawman.

"radiative lapse rate" what the heck is that. Give me the equation. Good luck because it doesn't exist. Dt]dh=-g/Cp. Nothing whatsoever to do with radiative forcing. You have confused cause and effect. Solar radiative forcing heats the surface which drives negative feedback convection, which dominates the troposphere. Has nothing to do with greenhouse gas RF.

I've provided a mathematical equation that explains the temperature within 0.02C of the 1976 US Standard Atmosphere at every single meter (on global average) from the surface all the way to 12000 meters, entirely without any GHG radiative forcing whatsoever.

Either specifically falsify the math with math or don't comment further.

"the only reason we commonly see the adiabatic lapse rate is due to the radiative properties of the gases"

Did you even read the post? I just explained and calculated the lapse rate would be higher than Earth's in a 100% N2 atmosphere. Either do your own calculations proving me wrong or stop wasting my time.

2. HS,

Captain Curt is right about one thing. Radiation does not affect the ADIBATIC lapse rate. It does however affect the ENVIRONMENTAL lapse rate, the actual tropospheric temperature gradient.

But it doesn't do it at all the way he claims. The only time and place on Earth that a pure 'radiative atmospheric temperature gradient' is established is in the polar winter. What happens is this: Everything cools progressively, because there is no heat input from the Sun, neither during the night nor during the day. Everything cools by radiation to space. The surface cools fastest, thus a near-surface temperature inversion is created, where the 'bottom' of the atmospheric gradient starts climbing from the top of the inversion (everything from a 100 m to 2 km thick). Since the gradient is now set by radiation alone, there is no real tropopause. The gradient moves up through the troposphere AND lower stratosphere up to the point where the Sun is no longer below the horizon; at mid-winter over the pole, this would be somewhere between 20 and 25 km up.

The polar winter 'radiative' atmospheric temperature gradient is a negative one, above the surface inversion layer. The coldest level in the global atmosphere is in the lower winter stratosphere above Antarctica (85-90C below zero).

The point is, however, this 'radiative' gradient (no convection involved, rather the constant radiative subsidence of stratospheric air down to the surface inversion layer, from where it spreads out from the pole) is MUCH less steep than the adiabatic lapse rate, from about 4.5 K/km in the lower parts to about 1.5 K/km in the upper reaches, the mean hovering around 2.5-3 K/km. As you will notice, it is also not a constant gradient, but reduces as you move up.

Captain Curt says something else that is silly: "If the actual lapse rate is less than the adiabatic lapse rate, it will NOT evolve toward the adiabatic rate."

Er, without proper solar heating, then yes. But we're living on planet Earth, aren't we. Solar heating is precisely what drives the atmospheric circulation. Captain Curt appears to want to imply that you can just lower the lapse rate below the adiabatic lapse rate and then get rid of convection, take it out of the equation. His approach fails as soon as you allow the Sun to shine down on the surface, heating it.

3. "Thus change in temperature from the lapse rate is dependent upon 3 variables that have no dependence whatsoever upon radiative forcing from greenhouse gases. None."
Not so fast. Your differential equation does not depend explicitly on it, but the equation by itself only describes a family of curves. For a specific solution, you must impose boundary conditions, and those boundary conditions do depend on radiative properties. Simply putting in numbers for the boundary conditions based on observations is not explanatory, and yields a tautological result.
In order to have a lapse rate, you must have a heat sink in the atmosphere. Otherwise, the specific solution becomes the constant solution. That heat sink is provided by radiating gases.
You can think of it in lower dimensions as the 2d plot of a pyramid, with the base at the surface, and the tip at the effective radiating height (ERH). If you add more GHGs, you increase the ERH, which broadens the base at the surface, producing higher surface temperatures.
That's basically the GHE which produces warming of the surface, according to the regnant theory. However, there is a problem with it. You may increase the ERH, but you also increase the efficiency of radiation, so the pyramid reaches higher, but its sides become steeper, with the result that the base does not broaden as much as it might. Indeed, it may even shrink in breadth, depending upon the current state of the system. And then, in addition, there is the issue of convection of water vapor to atmospheric heights, which also has an impact on the shape of the pyramid.
I don't think anyone really has a good handle on all of the impacts and, in view of the "pause", the net effect of increasing CO2 in the atmosphere appears to be negligible for the current configuration of the Earth and its surface, oceans, and atmosphere. But, I think you are going too far in reducing the solution to something so simple, and neglecting the key role played by boundary conditions in the specific solution of the equation.

4. "For a specific solution, you must impose boundary conditions, and those boundary conditions do depend on radiative properties."

Here are the boundary conditions:

A shell containing the atmospheric mass with the inner surface at the opaque surface of the Earth where P=1 atmosphere, and the outer surface where the atmospheric mass ends at the boundary of space and P=0

I clearly specify that all E in to this atmospheric shell must always equal E out.

"Simply putting in numbers for the boundary conditions based on observations is not explanatory, and yields a tautological result."

The boundary conditions I specified are constant, including atmospheric mass, gravity, and P=1 at surface and P=0 at the boundary with space. Te with the Sun is also assumed to be a constant. None of these change on a global average basis.

The fact is the equation perfectly reproduces the 1976 US Standard Atmosphere temperature for every single meter from the surface to up to ~11,000 meters without ANY of the missing 150W/m2 total greenhouse gas forcing.

So you can do all the handwaving you like about strawman, which I've now disproven, but that is not in the least showing there's anything wrong with this theory/equation and in fact shows the radiative GHE is totally wrong and backwards. The pressure forcing GHE causes the increase in temperature, which GHGs help to COOL.

5. "...and the outer surface where the atmospheric mass ends at the boundary of space and P=0."

And, where is that? The lapse rate is only negative to the top of the troposphere, then becomes positive in the stratosphere before becoming negative again in the mesosphere. Does gravity do all that? How?

http://www.windows2universe.org/earth/images/profile_jpg_image.html

Again, choosing the effective boundary for space based on observations yields a tautological result. It does not tell you why the boundary forms or should be chosen at that particular height. The troposphere happens to be where most of the IR radiating gases in the Earth's atmosphere are located. That is why there is a negative lapse rate there, because that provides the heat sink needed to establish it.

"I clearly specify that all E in to this atmospheric shell must always equal E out"

For equilibrium. The energy flux in must equal the energy flux out for equilibrium. But, they do not have to be equal at all times. If there is a temporary disparity for a given control volume, then energy will either accumulate or dissipate from that volume. People often get confused on this issue, because of the conservation of energy. But, we are not talking about energy, but of energy flux, a measure of energy per unit of time, a.k.a., power. Power is measured in watts, energy in joules. A watt is a joule per second. Two very different things, as different as velocity and position.

6. We are calculating the effect of the mass of the entire atmosphere from the surface to the thermosphere within the troposphere ONLY. The center of the entire mass of the entire atmosphere including everything above the troposphere is where P=log(1atm/2), which happens to be on global average ~5100 meters asl. One-half of the weight of the entire atmosphere lies above 5100 meters asl and one-half the weight of the entire atmosphere lies below 5100 meters asl. Therefore, the boundary conditions for determining the gravitational forcing upon the troposphere ONLY have to include ALL of the weight pushing on the troposphere from above to calculate the center of mass of the entire mass of the entire atmosphere.

I'm very well aware the lapse rate/convection only applies to the troposphere, and as Robinson & Catling Nature 2014, that's because the atmosphere becomes too thin above ~2 bar to sustain convection, and that's where radiative cooling from GHGs takes over from the top of the troposphere all the way to the top of the thermosphere. Thus, the atmosphere above the troposphere is merely helping the underlying troposphere to cool radiatively to space and has no effect of increasing temps in the troposphere other than mass.

This is proven by the fact that this single equation, designed for the troposphere only, perfectly reproduces the entire 1976 US Standard Atmosphere within 0.02K at every single meter from the surface to ~12,000 meters. The rest of the atmosphere above is merely a passive heat sink to enhance radiation to space.

You can hem and haw all you want with strawmen, but the burden of proof is now to explain, if there is an error in the math and physics, how it is possible for this equation to explain the temperature precisely and without GHG RF. The only true RF is from the Sun, GHGs are passive cooling agents from the surface to top of the thermosphere.

7. I am sorry to say so, because I value your website very much, and believe it has brought many interesting subjects forward, and I applaud all your effort.

But, I do believe you are tilting at windmills here. The equation fits because you made it fit, by choosing the boundary condition which makes it fit. As I said, it is tautological.

To give an example - suppose I throw a ball up in the air. We know that it is going to have a vertical trajectory approximately satisfying

d^2y/dt^2 = -g

because of gravity. The solution space of this equation, with initial condition y = 0, is

y = a*t - 0.5*g*t^2

for some constant a. You look at the trajectory and determine a = 100 feet/sec. I say a is the initial vertical velocity and you say no, the equation is independent of initial velocity, so the trajectory has nothing to do with it. And, the proof, you say, is that the equation fits the trajectory.

The math you present is not new. It is standard textbook. What is new is only your assertion that the boundary condition is independent of radiation from the lowest energy emitters in the atmosphere. In the example above, if there is no initial velocity, there is no vertical trajectory - the ball just sits on my hand. Similarly, if there are no radiating gases in the atmosphere, there is no lapse rate. The atmosphere would become isothermal.

It must become isothermal in such a situation because gravity is a conservative force - there is no net work done in moving from higher to lower altitude and back again. If gravity alone were enough to produce a temperature differential, then you could hypothetically use that differential to construct a heat engine, from which work could be derived, creating a perpetuum mobile of the 2nd kind.

How? Well, you pipe the hotter air at the surface to the top of a tower, and release it to drive a generator. The generator provides you free electricity by turning the heat into kinetic energy, and thence into electrical energy. There is no limit for how much of the gas you can pipe there, or how long you can do it, because the gravity effect always gives you a healthy lapse rate. This is, quite simply, not possible.

There are many flaws in the chain of logic which leads from human release of CO2 into the atmosphere to substantial greenhouse heating of the surface. This is not one of them. The basic "greenhouse" effect is not fundamentally wrong. It is constructively wrong. Or, inductively wrong. Or, something. It is a real effect in isolation. It just doesn't work on this Earth in its present state for CO2 in particular, because there are many confounding factors which exert a greater influence, and actively oppose it, rendering it negligible overall.

8. More irrelevant handwaving and a lot of words that prove absolutely nothing, and contain astonishing errors, for example, you once again make the completely false assumption non-IR-active gases do not have convection or adiabatic expansion and compression. Please look up the convection coefficients for N2, O2, and Argon and then work out the formulae for convection and prove it to me using their convection coefficients that these non-GHGs cannot convect.

Don't provide me with any more of your supposed physics lessons before providing me with proof including working out the mathematics of the convection formulae using the convection coefficients of N2, O2, and Argon first before commenting further debunking strawmen.

After you have done all of that and proven and shown me your work, then read this simple lesson on adiabatic processes, gravitational forcing on ideal gases, and derivation of the adiabatic lapse rate = -g/Cp, which has absolutely nothing whatsoever, no how, no way, to do with anything at all regarding greenhouse gas radiative forcing ever. Period.

Then provide me with your equation you claim that shows me specifically how GHG radiative forcing affects -g/Cp.

As to your assertion "What is new is only your assertion that the boundary condition is independent of radiation from the lowest energy emitters in the atmosphere" it's very simple

CO2 at 15u peak emission has an equivalent BB peak emission temperature of -80C, which is colder than any other part of the atmosphere (with the only exception of the Mesopause, which just so happens to be right at -80C:

http://navier.engr.colostate.edu/whatische/images/ChEL03t02f01.jpg

Why do you suppose that is? Hint: Has to do with CO2 BB emission peak

Then, after providing all of the above, please let me know your groundbreaking physics theory proving a cold body (CO2) radiating at a peak radiating temp of -80C makes a much warmer body at -18C warmer by an additional 33C all the way to 15C.

I say instead CO2 is a passive radiator that increases radiative surface area and radiative loss to space from the surface to thermosphere it cools, just because I don't like to break any laws.

9. The cold body doesn't have to heat the warm body, it merely has to prevent it from cooling, long enough that additional energy from the Sun pools as heat at the surface. Net flow of heat is always from hotter to colder. But, the distribution of retained heat can be rearranged.

Yes, CO2 is a radiator. But, it is also an absorber. It is legitimate to question which effect dominates to produce heating or cooling at the surface. It is not legitimate to claim that gravity does the work to heat the surface. Gravity, being a conservative force, can do no net work to heat the surface.

GHG radiative forcing does not affect g/Cp. It affects the point at which (effective) P = 0.

That is all I can say. Beyond it, I can only echo Cromwell's plea.

10. The same radiative GHE nonsense that "slowing cooling means warming," i.e. cooling is the new warming. Cooling means cooling and warming means warming. If you choose to believe the fantasy that a cold "blackbody" CO2 both absorbing/emitting at 15 microns, which by Wien's Displacement Law, is a peak radiating temperature of -80C (please note the minus sign that comes before the 80C) is causing a much hotter body at Te -18C to warm up by an additional 33C, you go right ahead and stay in La-La-Land, because I can't help you any further.

"It is not legitimate to claim that gravity does the work to heat the surface. Gravity, being a conservative force, can do no net work to heat the surface."

Is that so, well please tell the people who derived the barometric formulae from Newton's second law of motion: gravitational FORCE on the atmosphere = F = ma = mg in the case of the atmospheric mass. And please let all the meteorologists, pilots, etc. know that the barometric formula thus has to be discarded according to you, even though it perfectly calculates the temperature at any height as a function of PRESSURE.

Please also let the author of these lecture slides know that his 3rd slide on the first law of thermodynamics showing how the solar RF (dQ) has to balance with the work(W) or (pda) for the atmosphere which is continuously being done by gravity on adiabatic gases on the right-side of the equation

"GHG radiative forcing does not affect g/Cp. It affects the point at which (effective) P = 0."

First sentence is correct, but what the heck is "It affects the point at which (effective) P = 0" supposed to mean. Show your work.

3. For me, what seems to be missing is an explanation as to how energy gets radiated off this planet in LWIR absorption bands. According to AGW theory the non greenhouse gases do not participate in actually radiating LWIR energy themselves. We must remember that a good absorber is also a good radiator. Convection and H2O phase change may be the primary movers of this energy through the atmosphere but radiation is the only way the energy gets off this planet. Clearly if there were no greenhouse gases then LWIR absorption band radiation would not be an issue because there would be no LWIR absorption bands.

1. GHGs are good absorbers and radiators, increase radiative surface area and loss of radiation to space. What I'm saying is that T is a function of Pressure, and greenhouse gas absorption/emission spectra is due to that increase in T from the gravitational forcing, not the other way around.

Only one of these theories can explain the 33C GHE, and this one is the only one that doesn't violate multiple physical laws and observations.

2. "Clearly if there were no greenhouse gases then LWIR absorption band radiation would not be an issue because there would be no LWIR absorption bands."

All radiation to space would then be from the surface.

If one adds GHGs then some radiates out to space from witin the atmosphere but correspondingly less radiates directly out to space from the surface.

3. All matter absorbs heat and this includes the Nitrogen and Oxygen in the atmosphere. All matter above absolute zero emits radiation, hence Nitrogen and Oxygen emit radiation into space.

4. MS,

It would be very sad if all this effort were to simply be ignored by the vested interests.

Have you any plans to avoid that ?

1. As you and I have known for years, it's extremely difficult to show why a paradigm shift in scientific thought is necessary when people have wasted entire careers espousing and explaining the wrong theory. It's humiliating and seriously damages their credibility in the eyes of others, so that's why I believe it will be fought tooth and nail despite the overwhelming evidence.

I appreciate your help in explaining this to others across the blogosphere and internet, etc. since it's way more than I can handle. That's why I'm currently spending time developing posts such as this one that debunk the false claims and strawmen about it that the warmers and lukewarmers are promulgating.

Keep strong, the science and truth will eventually win out but it will no doubt be a very long and hard fought battle as it always is with a scientific paradigm shift. Ironically if people had just listened to one of the greatest physicists of all time Maxwell who was the 1st to describe the gravito-thermal GHE, we would have avoided all the wrought from 2nd rate Arrhenius.

5. 'Falsification of the Atmospheric CO2 Greenhouse Effects Within the Frame of Physics' is a scientific paper that appeared in the March 2009 edition of 'International Journal of Modern Physics'. The German authors were Dr Gerhard Gerlich and Dr Ralf Tscheuschner.

I have examined the work of those who have subsequently disputed the above mentioned paper, and I have examined the responses by Gerlich and Tscheusner in debunking the critics of their paper.

I have yet to find a credible scientific paper that debunks the March 2009 scientific paper of Gerlich and Tscheuschner.

6. 2. Secondly, even if the atmosphere was 100% nitrogen N2, with no greenhouse gases, the pressure change with altitude and thus convection and the lapse rate would be almost the same as the current atmosphere.

Only problem would be, that the effective radiation level would be ground, because the atmosphere do not radiate.

1. Absolutely, in this case of a 100% N2 atmosphere, the surface temperature would be Ts = Te + (the gravitothermal GHE of 33K) = at least 288K (and I calculate around 306K due to the lack of WV decreasing the lapse rate to the average on Earth)

And that 288K+ at the surface would then radiate directly to space due to the absense of GHGs.

A perfect example of how the radiative GHE has things backwards, GHGs cool the planet by increasing radiative surface area and Cp.

2. I follow you partly. The received average radiation is 340W/m2 giving 7C if emissivity =1. It is not and it is certainly not the same for the received radiation from the Sun and the LWIR radiated from the ground. In fact the outgoing emissivity is close to 1 but the ingoing is less than 1.
If the ground was 288K it would radiate almost 390W/m2 far more than received.

P.S. It is confusing that I miss my posting when I lock in. Could'nt you make lock in before posting, or make it so that it was not lost.

3. No, the energy received by the surface is the sum of

240 W/m2 from the Sun + at least 150 W/m2 from gravitational forcing F=ma=mg

Total: 390 W/m2 out

Explain how GHGs on Earth create 150 W/m2 out of nothing, and explain how greenhouse gases on Uranus amplify outgoing energy by over 83,000 times over incoming energy:

http://hockeyschtick.blogspot.com/2014/11/how-can-uranus-have-storms-hot-enough.html

7. Could be i am a little slow, but i like to understand.
How is it the sun only gives 240W/m2 in a clear N2 atmosphere?
The gravitational forcing must work both ways so that raising air looses 150W/m2, making the sum 0, or just keeping up the thermal gradient.
I really like your posts, but have some problems with an atmosphere without GHG.
I thaught the ground temperature would be much lower than with GHG, and then giving some difficulty with your theory.

1. I was trying to make the comparison simple by making the theoretical 100% N2 planet have the same surface solar insolation as our atmosphere, leaving the surface solar insolation constant for both planets, but I'll work through both examples:

We calculate above that center of mass of atmosphere on the 100% N2 Earth is slightly higher at ~5300 m vs our Earth ~5100 m.

1. Earth with 100% N2 atmosphere assuming surface solar insolation 240W/m2 (same as solar insolation at the surface on our earth after the 30% albedo = 342 W/m2 - 30% = 240 W/m2)

Solar radiative forcing at surface: 240
Gravitational forcing (F=mg) causing temperature enhancement at surface = (5.2 km height at center of mass) * (10 K/km lapse rate) = 52K

255K + 52K = 307K at the surface, then use SB law to determine W/m2 from the surface directly to space.

2. Earth with 100% N2 atmosphere assuming surface solar insolation = 342 W/m2 = (1367 W/m2)/4 and zero albedo:

Solar radiative forcing at surface: 342 W/m2 by SB law 279K

Gravitational forcing (F=mg) causing temperature enhancement at surface = (5.2 km height at center of mass) * (10 K/km lapse rate) = 52K

279K + 52K = 331K at the surface, then use SB law to determine 681 W/m2 from the surface directly to space.

2. in the first example with 307K at the surface, this equates by SB law to 504 W/m2 directly from the surface to space

Thus without assuming a 30% albedo the pure N2 planet would be 24K hotter.

8. My fault to miss the albedo, so i agree on the 240W/m2 received radiation and it equals -18 SB wise with e=1.
Unfortunately i can not follow the rest of the argumentations, except that without the albedo it would be 24 K hotter, but it can not have a higher temperature than to emit the same amount of radiation that it receives. What goes in must equal what goes out you have stated yourself.
From where should these extra gravitational heat come if not from the sun.
I am still confused but on a slightly higher level.
In both your examples the out going radiation is larger than the in going which can only keep on for a short time. I can't see it otherwise than with N2 atmosphere the Earth will be colder and the top or middle atmosphere also colder.
It is just an example but you put it up yourself.
It is in my opinien essential with the GHG's, because they establish a radiation level as you explain, especially water vapor is important both as GHG and by producing clouds and precipitation.
In that way it is the GHG's that establish a radiation level and temperature at that level, whereafter the lapse rate determines the temperature at ground. So is my understanding now.

1. Gravity is a strong forcing on mass, and in the case of gases raises the temperature by increasing pressure at the surface.

The barometric formula itself is derived from Newton's second law of motion F=ma and thus in the case of the atmosphere F=mg. This gravitational forcing compressing gases at the surface (via ideal gas law) plus solar radiative forcing is what increases the surface temperature to greater than what the solar radiative forcing alone can provide.

This is the only possible explanation why Uranus emits 83,000X more radiation to space than it receives from the Sun. Note Uranus is a gas planet with no volcanoes:

http://hockeyschtick.blogspot.com/2014/11/how-can-uranus-have-storms-hot-enough.html

The only explanation why Uranus and other gas planets can emit more to space than they receive from the Sun is gravitational forcing causing increased T via the ideal gas law.

9. MS

This is interesting:

It seems that there are a number of possible reasons why a planet might emit more than it receives from the sun but in the case of Uranus they say:

"Interestingly, Uranus doesn't appear to have significant excess heat"

but given the very high gas temperatures they must simply mean that it does not emit much excess heat to space i.e. it is in approximate thermal balance with the sun.

Obviously the 'surface' (however defined) is hot enough to emit at 83,000 times more than it receives from the sun but the heat is not actually getting out in the form of thermal emissions.

That fits with the proposition that the excess heat within the compressed atmosphere is a result of adiabatic recycling of energy being conducted and convected up and down within the gases in just the same way that I propose the Earth radiates to space at 255K from a surface at 288K but recycles the other 33K adiabatically.

That is different from one off gravitational compression and I think that is where the AGW proponents go wrong.

The adiabatic process involves continuous pumping up by the sun in regions of ascent, continuous compression by gravity in regions of descent and so constant replenishment of the surface kinetic energy needed to sustain the process and thereby keep the weight of the atmosphere suspended off the surface.

Adiabatic decompression and compression is quite different from simple gravitational compression and given that Uranus has very hot gases but is in approximate thermal balance with solar radiation it is a good example to use.