We are constantly being told that the Greenhouse effect is due to a radiative process. I want to show simply that it is not. Instead as per Ned Nikolov & Karl Zeller I want to show that from first principles it can be shown to be pressure related.
To do this I simply take the pressure curve for an atmosphere:
p = p0 (1 – L.h/T0) ^ (g.M/R0.L)
Where
p = pressure at height h (pa)
p0 = pressure at surface (pa)
L = Lapse rate (=g/Cp) (J/(kg.K)
h = height (m)
T0 = Temperature at surface (k)
g = gravity (m/S2)
M = Molar mass of dry air (0.0289644 kg/mol)
R0. = Universal gas constant (8.31447 J/(mol.k)
Then all we do is to turn this around and express it in terms of the pressure and height of the tropopause (0.1bar or 10,000pa as per Robinson & Catling: “Common 0.1 bar tropopause in thick atmospheres set by pressure-dependent infrared transparency”)
T0 = L.htrop/{1- (Ptrop/p0)^(R0.L/g.M)}
| Venus | Titan | Earth | Triton | |
| Actual Temp (k) | 737 | 93.7 | 287.4 | 39 |
| Predicted Temp (k) | 657.43 | 80.5 | 294.5 | -.74 |
| Difference (k) | 79.57 11%) |
13.2 (14%) |
-7.2 (-2%) |
39.4 (100%) |
So with a very simple turn of the formula without any reference to radiation, radiation trapping greenhouse gases etc., for 3 out of the 4 examples here, I can predict the temperature to about 10% of its value.
Please note again. This temperature is calculated without reference to incoming radiation in any shape or form. The equation does not contain any hidden temperature offset. All it is doing is scaling up the temperature from surface to tropospheric temperature (L.htrop) by a factor. Yes if we included the absolute temperature of the troposphere – we’d easily get the surface if we also knew the surface-troposphere temperature drop. But that figure is not in the equation.
And the factor is the relative size of surface pressure compared to nominal tropospheric pressure (@0.1bar) to the power of (R0.L/g.M). So it is pressure not radiation related.
Now if we look at the power term (R0.L/g.M). R/m is the specific Gas constant Rspecific And
Rspecific = Cp – Cv
where cp is the specific heat for a constant pressure and cv is the specific heat for a constant volume. And because lapse rate L = g/Cp (gravity divided by specific heat capacity for a given mass)
L/g = 1/ Cp
So …
(R0.L/g.M) = (Cp – Cv)/Cp = 1 – Cv/Cp
Which given many atmospheres have a similar composition will be a constant and clearly has nothing to do with radiation or irradiance. If we ignore constants and simplify we get:
T0 = TSurface_trop / (1- (Ptrop/pSurface)^z)
z = (R0.L/g.M)
Yep, that is how to calculate non phase change laps rate for situations of moderate insolation induced convection (atmospheric expansion sunward). Unfortunately Earth has much airborne water, continually changing between all six phases. Perhaps in 200-300 years Earthlings will get a clue as to how that might work, if they survive! 🙂
“Which given many atmospheres have a similar composition will be a constant and clearly has nothing to do with radiation or irradiance. If we ignore constants and simplify we get:
T0 = TSurface_trop / (1- (Ptrop/pSurface)^z)”
Yup! That is the correct alphabet soup; but not the learning of something that may actually work. That requires spontaneous dispatch of EMR flux (power) to space from the atmosphere. Can you please define your exponent term (z)?
Perhaps that is called the isentropic exponent (k) or its reciprocal. For N2, O2, (7/5), (5/7). This is degrees of freedom between 2D/3D, pressure/density, for each gas molecule. Kindergarten stuff for well paid aeronautical engineers! Again this depends not on ‘radiance'(field strength), but instead proper (measurable) radiative flux,spontaneously emitted from all of that same atmosphere in the direction of space! Surface EMR is silly, and not needed on this water world!! The cooling efficacy of that outward flux determines the absolute value of any location including the surface, but never the slope of the lapse. Your CAGW Clowns have never demonstrated any ‘scientific method’ whatsoever; only, only a total lack of competence! Such may apply even more to the hoy-poloy LUKE WARMERS, who can only believe their educational brainwashing! 🙂
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It’s an interesting equation – I’d be interested to see whether you agree with the general view on the next article
http://scottishsceptic.co.uk/2017/03/28/proof-disproved-and-then-further-proof-re-global-temperature/a
“Can you please define your exponent term (z)”
No! It looks like voodoo gibberish to me …
And I was hoping someone would be able to tell me what it was.
“This is degrees of freedom between 2D/3D, pressure/density, for each gas molecule.”
“This is degrees of freedom between 2D/3D, pressure/density, for each gas molecule.”
This is degrees of freedom between 2D/3D, pressure/density, for each gas molecule.
(Doing lines loses something in the days of copy-n-paste)
Is that important or can I happily ignore it?
“Again this depends not on ‘radiance'(field strength), but instead proper (measurable) radiative flux,spontaneously emitted from all of that same atmosphere in the direction of space!”
That sounds important but I don’t understand it. Can you point me to any links that would explain it in simple terms.
Scottish-Sceptic says: 28th March 2017 at 10:55 am
(“Can you please define your exponent term (z)”)
“No! It looks like voodoo gibberish to me …
And I was hoping someone would be able to tell me what it was.”
I did but you seemed to miss it! Look up the ratio of Gas specific heats Cp/Cv, or Gamma in chemistry, isentropic exponent in engineering.
(“This is degrees of freedom between 2D/3D, pressure/density, for each gas molecule.”)
“Is that important or can I happily ignore it?”
I was trying to explain how this is derived in science and engineering! Happily ignore it, unless you are interested in how this atmosphere physically works.
“That sounds important but I don’t understand it. Can you point me to any links that would explain it in simple terms.”
No! All links are commandeered by the Climate Clowns and the Blasphemy of exit flux originating in the atmosphere rather than their imagined ‘surface’ would destroy their scam. Please understand any mass with sensible heat ‘can’ spontaneously emit EMR flux as a function of its own electromagnetic field strength at each frequency, however, how much is spontaneous, is limited by the surround field strength. When the opposing field strengths are the same (thermally same temperature) there is no physical EMR flux in either direction.