Saturday, September 19, 2015

Why 'greenhouse gases' don't 'trap heat' in the atmosphere

Optical and electronic engineer KevinK, a frequent contributor to the Hockey Schtick, posted an excellent comment a couple days ago on the WUWT post How Reliable are the Climate Models, and with which I fully agree, and have elevated to a post here. 

 KevinK elegantly explains why the Arrhenius radiative greenhouse effect essential to the theory of catastrophic anthropogenic global warming (CAGW) is fictional, and confuses the actual cause (the 33C gravito-thermal greenhouse effect of Maxwell, Clausius, Carnot, Boltzmann, Feynman, US Standard Atmosphere, the HS greenhouse equation, et al) with the effect (IR absorption and emission from IR-active 'greenhouse gases'). 





Mike Jonas writes:
“Carbon Dioxide (CO2) : At last we come to something which is quite well understood. The ability of CO2 to absorb and re-emit a specific part of the light spectrum is well understood and well quantified, supported by a multitude of laboratory experiments.”
Yes indeed this is not in doubt. However, the result of this phenomenon in the climate is still very much in doubt. Especially with regard to the “average” temperature. Aside from the fact that an “average temperature” has no useful meaning. I’m reminded of the old observation that if one of your feet is in ice water and the other is in boiling water you are “on average” quite comfortable overall.
Here is where the alleged “GHE” breaks down. There are numerous examples of human designed optical systems (aka applied radiation physics) that exhibit “back radiation”. Including the optical integrating sphere and the multi layer optical interference filter. In both cases “back radiation” certainly exists, but it can be difficult to measure. In neither case does the “back radiation” alone cause the source to “reach a higher temperature”.
In the specific case of an optical integrating sphere the interior surface of the sphere (highly reflective) becomes a “virtual light source”. This concept of a virtual source is somewhat specific to the optical engineering community. It helps with understanding (and predicting) the paths that photons will follow through a system. However (and this is a very big however) it DOES NOT predict the energy present at any point in the system.
In the case of an optical integrating sphere with an incandescent filament (aka a light bulb) inside this “back radiation” merely delays the elapsed travel time of the photons flowing through the system. This is a result of the photons “bouncing back and forth” inside the sphere until they find an “exit port”.
This is known as the “transient response” of an optical integrating sphere. 
This is a somewhat obscure but still well understood concept. If you inject an input “pulse” of light (off, then quickly on, then quickly off again) this transient response function will create a “stretched” pulse of output light. Specifically this square input pulse is no longer a square output pulse since some photons will quickly find an exit port and others will “bounce near and far” before exiting the sphere.
The gaseous atmosphere of the Earth is quite like an optical integrating sphere in this regard. The photons arriving from the Sun and being converted to emitted IR radiation (still a form of light or electromagnetic radiation and following all of the same rules/laws) simply bounce “back and forth” between the atmosphere and the surface. All this bouncing merely delays the flow of energy through the system as the energy alternates between light energy and thermal energy.
Given the dimensions of the atmosphere (about 5 miles high) and the velocity of light (still considered quite speedy) this alleged “GHE” merely delays the flow of energy (arriving as sunlight) through the system by a few tens of milliseconds. The specific delay for any given photon is of course described by a statistical distribution.
Since the period of the arriving light is about 24 hours this delay of a few tens of milliseconds has no effect on the “average temperature” at the surface of the Earth.
Another example of “back radiation” and its practical uses is the multi layer optical interference coating. This is the highly engineered coating on most modern optical lenses. It appears slightly purple when observed off-axis. The purpose of this coating is to reduce reflections from the surface of a lens.
These coatings have greatly improved the quality of photographs and videos by increasing contrast and reducing “ghost images” (images that are created by the individual surfaces inside a modern optical lens).
These coatings function by delaying “following photons” by a time equivalent to a fraction of the wavelength of the arriving light. By creating exactly the correct delay interval the reflected light is exactly “out of phase” from the arriving light and destructive optical interference occurs. This moves the optical energy to a location inside the optical lens where it is no longer subject to surface reflections.
Both of these “applied radiation physics” effects/techniques have been applied for decades and are quite well understood.
The alleged “radiative greenhouse effect” merely delays the flow of energy through the system and has no effect on the “average temperature”. It does change the response time of the gases in the climate. Since the gases have the smallest thermal capacity of all the components present (Oceans, land masses, atmosphere) the idea that they are controlling the “average temperature” is quite ludicrous.
Modeling these radiative effects in the climate is probably impossible. The required spatial distances are sub-micron the the time steps necessary are in the nanosecond range. There would need to be a increase of computing power of about ten orders of magnitude to even begin to attempt this.
There is of course a gravitational greenhouse effect whereby the effects of gravity acting on the gases in the atmosphere of the Earth predict quite well (see the US standard atmosphere model last updated in 1976) the temperature of the atmosphere of the Earth with no use of radiative effects at all.
It is quite sad that all this effort has been wasted on modeling the “unmodelable”.
Cheers, KevinK.
Reply

    • Bubba, thank you.
      I did submit a somewhat whimsical explanation of this delay line effect to Anthony several years ago.
      I have submitted a more detailed explanation to other climate science sites as well.
      The “radiative greenhouse effect” is merely a form of hybrid optical/thermal delay line. It has no effect on the “average” temperature at the surface of the Earth.
      Cheers, KevinK
    • KevinK – Your comment is at a greater level of detail than my article, so as suggested would be better as a separate article. I note your “Since the gases have the smallest thermal capacity of all the components present (Oceans, land masses, atmosphere) the idea that they are controlling the “average temperature” is quite ludicrous.“, but to my mind the GHG theory whereby some outgoing IR is in effect turned back and thus affects surface temperature is at least prima facie credible [HS Comment: No, that's not credible, radiation from cold blackbodies cannot ever warm/increase the temperature/frequency/energy of hotter blackbodies, ever, proven by Planck's Law of Blackbody Radiation and Quantum theory]. I’m prepared to work with this version (even though, just like everything else, science may one day overturn it) while there are such glaring errors elsewhere.
  • KevinK,
    I think that is the best comment I have read here in several weeks at least. (a high complement considering the quality of the comments here)
    I do hope that you will offer that comment as a post, that it is posted, and that then the moderation allow a full and complete debate on all parts of it. There are many of us who think the mass of the atmosphere along with gravity is the main reason for the misnamed “green house effect” along with H2O in all its phases.
    ~ Mark
    Reply
    • The thermal capacity of water is much greater than CO2.
      This is why the main purpose of indoor air conditioning is to remove the water vapor first and then secondarily reduce the temperature of the now dryer air.
    • Kevin, Liquid water yes, because of it’s much greater density. However the difference between water in the vapor stage and CO2 is much, much smaller.
      Regardless, the warming affect of water occurs even when it is the air aloft that is damp and the air at the surface is dry. IE, clouds.       [HS comment: No many papers prove the net effect of clouds is cooling, although they can reduce convective cooling somewhat, but which has nothing to do with radiative forcing. In addition, increased water vapor increases the heat capacity Cp of the atmosphere, which decreases the lapse rate, which COOLs the surface].
  • Has anyone calculated the average delay for a photon that is within one of CO2 absorbtion bands?
    I strongly suspect that it is more than a few milliseconds. Given that the direction of the photon when it is re-emitted is random, it could be down as easily as up, if it is sideways, it will have many miles of dense atmosphere to traverse compared to up.
    Reply
    • At about 22 minutes, Dr. Happer shows the “xylophone effect” on a CO2 molecule.https://youtu.be/gMdYmAo08O4
      Here is an email exchange between Dave Burton and Will Happer concerning the issue of “re-emitting” a photon v. collisions with other molecules in the air, mostly N2 of course:
      A portion of their discussion:
      After hearing Will’s lecture, Dave asks:
      1. At low altitudes, the mean time between molecular collisions, through which an excited CO2 molecule can transfer its energy to another gas molecule (usually N2) is on the order of 1 nanosecond.
      2. The mean decay time for an excited CO2 molecule to emit an IR photon is on the order of 1 second (a billion times as long).
      Did I understand that correctly?
      Will replies: [YES, PRECISELY. I ATTACH A PAPER ON RADIATIVE LIFETIMES OF CO2 FROM THE CO2 LASER COMMUNITY. YOU SHOULD LOOK AT THE BENDING-MODE TRANSITIONS, FOR EXAMPLE, 010 – 000. AS I THINK I MAY HAVE INDICATED ON SLIDE 24, THE RADIATIVE DECAY RATES FOR THE BENDING MODE ALSO DEPEND ON VIBRATION AND ROTATIONAL QUANTUM NUMBERS, AND THEY CAN BE A FEW ORDERS OF MAGNITUDE SLOWER THAN 1 S^{-1} FOR HIGHER EXCITED STATES. THIS IS BECAUSE OF SMALL MATRIX ELEMENTS FOR THE TRANSITION MOMENTS.]
      Dave: You didn’t mention it, but I assume H2O molecules have a similar decay time to emit an IR photon. Is that right, too?
      [YES. I CAN’T IMMEDIATELY FIND A SIMILAR PAPER TO THE ONE I ATTACHED ABOUT CO2, BUT THESE TRANSITIONS HAVE BEEN CAREFULLY STUDIED IN CONNECTION WITH INTERSTELLAR MASERS. I ATTACH SOME NICE VIEWGRAPHS THAT SUMMARIZE THE ISSUES, A FEW OF WHICH TOUCH ON H2O, ONE OF THE IMPORTANT INTERSTELLAR MOLECULES. ALAS, THE SLIDES DO NOT INCLUDE A TABLE OF LIFETIMES. BUT YOU SHOULD BE ABLE TO TRACK THEM DOWN FROM REFERENCES ON THE VIEWGRAPHS IF YOU LIKE. ROUGHLY SPEAKING, THE RADIATIVE LIFETIMES OF ELECTRIC DIPOLE MOMENTS SCALE AS THE CUBE OF THE WAVELENTH AND INVERSELY AS THE SQUARE OF THE ELECTRIC DIPOLE MATRIX ELEMENT (FROM BASIC QUANTUM MECHANICS) SO IF AN ATOM HAS A RADIATIVE LIFETIME OF 16 NSEC AT A WAVELENGTH OF 0.6 MIRONS (SODIUM), A CO2 BENDING MODE TRANSITION, WITH A WAVELENGTH OF 15 MICRONS AND ABOUT 1/30 THE MATRIX ELEMENT SHOULD HAVE A LIFETIME OF ORDER 16 (30)^2 (15/.6)^3 NS = 0.2 S.
      Dave: So, after a CO2 (or H2O) molecule absorbs a 15 micron IR photon, about 99.9999999% of the time it will give up its energy by collision with another gas molecule, not by re-emission of another photon. Is that true (assuming that I counted the right number of nines)?
      Will: [YES, ABSOLUTELY.]
      Dave: In other words, the very widely repeated description of GHG molecules absorbing infrared photons and then re-emitting them in random directions is only correct for about one absorbed photon in a billion. True?
      Will: [YES, IT IS THIS EXTREME SLOWNESS OF RADIATIVE DECAY RATES THAT ALLOWS THE CO2 MOLECULES IN THE ATMOSPHERE TO HAVE VERY NEARLY THE SAME VIBRATION-ROTATION TEMPERATURE OF THE LOCAL AIR MOLECULES.]
    • HS comment: Whether the true delay is microseconds to minutes makes little difference, since a 12 hour night can easily erase & reverse this "radiative heat trapping," with no net effect on a daily, annual, or multi-decadal basis whatsoever. 
  • There can only be one and only one 33C greenhouse effect: 1) the 33C Arrhenius radiative GHE, or 2) the 33C Maxwell et al gravito-thermal GHE, otherwise the greenhouse effect would be double (66C) that observed. Clearly, overwhelming evidence, such as the above, favors the gravito-thermal GHE by lightyears. 
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Saturday, September 12, 2015

Strong evidence of negative-feedback from clouds






The Cloud feedback

by Cederlöf. Google translation from the Stockholm Initiative site 
In the comments to my last post, led the signature "Slabadang" me on an interesting track. He claimed that the clouds varied in tune with the solar radiation. If this would be the clouds would have a negative feedback and thus balance the climate. I downloaded the satellite data from CERES to check his data.
Below is how the global cloud cover varies with the global solar radiation. The reason that solar radiation varies over the year is that the Earth is in an elliptical orbit around the sun. When we in the northern hemisphere has winter, we are therefore closest to the sun. However, it is the angle to the sun which means we have winter.

The global cloud cover and solar radiation variation over the year. The cloud cover is an average of the years 2000 to 2014.
So it is a poor correlation between cloud cover and solar radiation if you look at the Earth as a whole. However piling a completely different picture up if you instead look at the two hemispheres:

The cloud cover and solar radiation variation over the year in the northern hemisphere.

The cloud cover and solar radiation variation over the year in the northern hemisphere.
For the two hemispheres, there is thus a very good correlation between solar radiation and cloud cover. The reason that you can not see any correlation globally is likely that these variations are so much less that they drown out the noise of the large variations in the hemispheres.
It is thus clear that cloud cover increases when solar radiation increases. Then the sun's rays do not reach the earth's surface and then counteracts the clouds changes. The same must therefore apply to the carbon dioxide effect. When it increases, the clouds that counteract the temperature change. Here we have again an example that there is a negative feedback and not a positive feedback that the whole scare propaganda in climate science based.
Note also that the clouds are much larger in the southern hemisphere than it is in the northern hemisphere. The reason for this is that there are more clouds over the oceans, and there's a lot more sea in the southern hemisphere.
Climate sensitivity
It is thus more clouds in the southern hemisphere, and the temperature is also lower. Looking at 1000hPa level (near surface), the average temperature of the southern hemisphere 14.4C and for the northern hemisphere 16.5C. After millions of years of energy storage in the oceans of the southern hemisphere, then the temperature is still much lower. One can not interpret it otherwise than that the oceans hold temperature. A major reason for this must be that the clouds in the southern hemisphere allows the sun's rays do not reach the earth's surface.
In the southern hemisphere, the average cloud cover 65.5% and in the northern hemisphere 57.6%, according to CERES-date. If the average solar radiation is 237W / m2 can then southern hemisphere approximately 7.9% of 237W / m2 = 18.7W / m2 less sun than the Northern Hemisphere. Now this is probably a little high counted for even if the cloud cover is 100%, the clouds themselves to radiate towards the Earth's surface.
The difference in temperature between the southern and northern hemisphere is thus 2.1c and the difference in solar is about 18.7W / m2. It allows every Watt / m2, equivalent to about 0.11 degree. A doubling of carbon dioxide levels will provide approximately 3.7W / m2, it therefore corresponds to approximately 0.4 degrees (climate sensitivity). Now I have probably figured a little low, since the change in insolation probably figured a little high, and there may also be other reasons that the temperature between the hemispheres differ. But it is still very far from the many degrees of climate sensitivity horror forecasts suggest. I have previously calculated the climate sensitivity of about 0.3 degrees by looking at seasonal variations (here).
Related Posts:
  1. Further evidence of the seas negative feedback 
  2. Open examination 
  3. Year without a summer, and positive feedback 
  4. Issues concerning climate inertia 
  5. If the cycle of heat 

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Tuesday, September 1, 2015

Why the effective radiating level (ERL) is always located at the center of mass of the atmosphere & not controlled by greenhouse gas concentrations

The Arrhenius radiative greenhouse effect proponents, having abandoned "back-radiation" from greenhouse gases as the explanation of the greenhouse effect, now claim global warming is instead due to an increase of the "effective radiating height" or "effective radiating level" [ERL] of greenhouse gases in the atmosphere. So the theory goes, an increase of CO2 levels will cause longwave (~15 micron) infrared emissions from CO2 to occur from colder heights in the atmosphere, and since colder blackbodies emit less radiation, more radiation will allegedly be "trapped" by the colder CO2 "blackbody" in the fabled tropospheric "hot spot" & unable to escape to space. 

 In contrast, the competing 33C gravito-thermal greenhouse effect of Maxwell, Clausius, Carnot, Boltzmann, Feynman, Poisson, Helmholtz, et al, shows that the "effective radiating level" or ERL is fixed at the center of mass (COM) of the atmosphere.

 As we can see in Fig 1a, the observed ERL or "emission level for OLR (Outgoing Longwave Radiation)" global average is right around 500 millibars or 0.49 atmospheres ~ 0.5 atmospheres, exactly at the center of mass of the entire atmosphere as predicted in the HS greenhouse equation below. 

The HS greenhouse equation "triangulates" the geopotential height of the 255K ERL at the center of mass using:

 1. The center of mass (COM) of the atmosphere where P=0.5 atmospheres (after density correction), i.e. exactly one-half of the surface pressure
2. The adiabatic lapse rate = -(gravitational acceleration constant g)/(heat capacity at constant pressure Cp)
3. The equilibrium temperature of Earth with the Sun = 255K

 all of which are essentially constants in the atmosphere, and without any knowledge of the surface temperature, greenhouse gas concentrations, or Arrhenius "radiative forcing" from greenhouse gases.  

 Why use the center of mass of the atmosphere in calculation of the gravito-thermal greenhouse effect? Because the force of gravity by Newton's Second Law is F = ma = mg, and for a system of particles like our atmosphere, one must determine the center of mass in applying Newton's 2nd Law F = mg to the force of gravity. 

Thus, since the height of the ERL is fixed at the COM, and the COM is essentially a constant, the height of the ERL will not change, regardless of greenhouse gas concentrations.

In addition, in the longwave infrared band of Earth’s thermal radiation, the only band in which CO2 absorbs and emits is centered at ~15 microns. The kinetic temperature of the surrounding atmosphere and the CO2 molecules has nothing to do with the fact that CO2 emits at a fixed ~15 microns in the longwave IR due to its fixed molecular structure bending transitions. The entire atmosphere surface to space is warmer than the CO2 “equivalent partial blackbody” fixed band-emitting temperature of 193K at ~15 microns.

Also, absorption followed by emission of a photon by CO2 only takes microseconds, and all the bouncing around at the speed of light between greenhouse gases in the atmosphere only delays the average photon a few milliseconds on its way from the surface to space. Thus, the only "slowing of cooling" or "heat trapping" by CO2 absorption/emission is a few milliseconds and easily reversed and erased over a 12 hour night. 

Addition of more CO2 increases the few milliseconds delay by adding a few more milliseconds, but once again is easily reversed and erased over a 12 hour night.

More importantly, increased CO2 increases radiative surface area, which increases radiative loss to space. That’s why increased CO2 cools the stratosphere through thermosphere, and troposphere as well as I’ve shown.

And even more importantly, the probability of CO2 transferring heat by collisions with N2/O2 in the troposphere is about 2 orders of magnitude higher than emitting a photon, which increases convective cooling.

An earlier post also provides nine additional reasons why the effective radiating level (ERL) is always located at the center of mass of the atmosphere & not controlled by greenhouse gas concentrations.

Thus, the false notion that global warming is instead due to an increase of the "effective radiating height" or "effective radiating level" [ERL] of greenhouse gases in the atmosphere is effectively disproven.

The HS greenhouse equation and quick & dirty explanation below, followed by the derivation from first principles:
The "Greenhouse Equation" calculates temperature (T) at any location from the surface to the top of the troposphere as a function of atmospheric mass/gravity/pressure and radiative forcing from the Sun only, and without any radiative forcing from greenhouse gases. Note the pressure (P) divided by 2 in the greenhouse equation is the pressure at the center of mass of the atmosphere (after density correction), where the temperature and height are equal to the equilibrium temperature with the Sun and ERL respectively.

http://hockeyschtick.blogspot.com/2014/11/quick-and-dirty-explanation-of.html

We will use the ideal gas law, 1st law of thermodynamics, Newton's second law of motion (F = ma), and well-known barometric formulae in this derivation to very accurately determine Earth's surface temperature, the height in the atmosphere at which the effective equilibrium temperature of Earth with the Sun is located, and show that this height is located as expected at the center of mass of the atmosphere on Earth and Titan.

We will show that the mass/pressure greenhouse effect theory can also be used to accurately determine the temperatures at any height in the troposphere from the surface to the tropopause, and compute the mass/gravity/pressure greenhouse effect to be 33.15C, the same as determined from radiative climate models and the conventional radiative greenhouse effect theory. 

1. Conservation of energy and the ideal gas law

We will start once again with the ideal gas law 

PV = nRT (1)

an equation of state that relates the pressure P, volume V, temperature T, number of moles n of gas and the gas law constant R = 8.3144621 J/(mol K). 

The properties of gases fall into two categories: 

1. Extensive variables are proportional to the size of the system: volume, mass, energy
2. Intensive variables do not depend on the size of the system: pressure, temperature, density

To conserve energy (and to ensure that no radiative imbalances from greenhouse gases are affecting this derivation) of the mass/gravity/pressure greenhouse effect, we assume

Energy incoming from the Sun (Ein) = Energy out (Eout) from Earth to space

Observations indeed show Ein = Eout = 240 W/m2 (2)

which by the Stefan-Boltzmann law equates to a blackbody radiating at 255 K or -18C, which we will call the effective or equilibrium temperature (Te) between the Sun and Earth. As seen by satellites, the Earth radiates at the equilibrium temperature 255K from an average height referred to as the "effective radiating level" or ERL or "effective radiating height."

2. Determine the "gravity forcing" upon the atmosphere

Returning to the ideal gas law above, pressure is expressed using a variety of measurement units including atmospheres, bars, and Pascals, and for this derivation we will use units in atmospheres, which is defined as the pressure at mean sea level at the latitude of Paris, France in terms of Newtons per square meter [N/m2]

Newtons per square meter corresponds to the force per unit area [or "gravity forcing" upon the atmospheric mass per unit area of the Earth surface]. 

Now let's determine the mass of the atmosphere above one square meter at the Earth surface:

By Newton's 2nd law of motion equation, force (F) is 

F = ma  (3)   where m = mass and a = acceleration

As we noted above, the atmospheric pressure is a force or forcing per unit area. The force in this case is the weight (note weight is not the same as mass and is in physical definitions of mass, length, time-2) or mass of the atmosphere times the gravitational acceleration, therefore

F = mg  (4) where g is the gravitational constant 9.8 m/s2, i.e. the acceleration due to gravity in meters per second squared.

If we assume that g is a constant for the entire column of the atmosphere above the 1 meter2 area (A) we obtain

m = PA/g = (1.0325 x 10^5 N/m2 )(1 m2 )/(9.8 m/s2 ) = 1.05 x 10^4 kg

thus, the weight of the atmosphere over 1 square meter of the surface is 10,500 kilograms, quite a remarkable gravitational forcing upon the atmosphere.

If m is the mass of the atmosphere and g is the gravitational acceleration, the gravitational force is thus

F = mg (4)

The density (p) is the mass (m) per unit Volume (V), thus,

p = m/V

SI units of pressure refer to N/m2 as the Pascal (Pa). There are 1.0325 x 10^5 Pa per atmosphere (unit). 

Starting again with equation (3) above

F = ma  (3)

F = mg  (4)

F = (PA/g)g = PA  (5)

P = F/A = mg/A = phAg/A = phg (6) 

where 

h=height along either a gas or liquid column under pressure or gravity field
g = gravitational constant
p = density = mass/volume

3. Determine the atmospheric pressures from gravitational forcing, and the height of the effective equilibrium temperature (ERL)

Now we will determine the atmospheric pressures in a gravitational field using (6) above

First let's determine the pressure at the ERL since the temperature must equal the equilibrium temperature of 255K at the ERL.

The pressure is a function of height 

P(h) = ρgh (7)

and the change in pressure dP is related to the change in height dh by 

dP = -ρg dh (8)

The minus sign arises from the fact that pressure decreases with height, subject to an adjustment for density which changes with height. We will determine this adjustment from the ideal gas law. The density is 

ρ = nM/V  (9)

where n is the number of moles, M is the molar mass, and V is the volume. We can obtain n/V from the ideal gas law: 

n/V = P/RT (10)

thus 

ρ = MP/RT  (11)

We can now substitute the density into the pressure vs. height formula:

dP = -(MPg/RT)dh  (12)

 ∫dP/P = -(Mg/RT) ∫dh  (13) (the first integral is from 1 to P, second from 0 to h)  

ln(P) = -(Mgh/RT)  (14)

P = e^-((Mgh/(RT))  (15)

We will now determine the height (h) at the ERL where the temperature = the effective equilibrium temperature = 255K, and without use of radiative forcing from greenhouse gases.

Plugging in numbers of M = 29 grams/mole (0.029 kg/mole) as average molar mass for atmosphere, g = 9.8 m/s^2, Pressure = 0.50 atmospheres at the approximate center of mass of the atmosphere, R=8.31, and T=Te=255K effective equilibrium temperature we obtain:

0.50 atmosphere P at the ERL= e^-((.029*9.8*5100)/(8.31*255))

So the height of the ERL set by gravity forcing is located at 5100 meters and is where T=Te=255K and pressure = 0.5 atmospheres, right at the center of mass of the atmosphere as we predicted from our gravity forcing hypothesis. 

4. Determine the temperatures at any location in the troposphere, and the magnitude of the mass/pressure greenhouse effect

Now that we have solved for the location of the ERL at 5100 meters, we can use the adiabatic lapse rate equation to determine all troposphere temperatures from the surface up to the ERL at 255K and then up to the top of the troposphere. The derivation of the lapse rate equation from the ideal gas law and 1st law of thermodynamics is described in this post, thus will not be repeated here, except to mention that the derivation of the lapse rate 

dT/dh = -g/Cp where Cp = heat capacity of the atmosphere at constant pressure

is also completely independent of any radiative forcing from greenhouse gases, greenhouse gas concentrations, emission/absorption spectra from greenhouse gases, etc., and is solely a function of gravity and heat capacity of the atmosphere. 

Plugging the average 6.5C/km lapse rate and 5100 meter or 5.1 km height of the ERL we determine above into our derived lapse rate equation (#6 from prior post) gives

T = -18C - (6.5C/km × (h - 5.1km)) 

Using this equation we can perfectly reproduce the temperature at any height in the troposphere as shown in Fig 1. At the surface, h = 0, thus temperature at the surface Ts is calculated as

Ts = -18 - (6.5 × (0 - 5.1)) 

Ts = -18 + 33.15C (gravity forced greenhouse effect)

Ts = 15.15°C or 288.3°K at the surface

which is exactly the same as determined by satellite observations and is 33.15C above the equilibrium temperature -18C or 255K with the Sun as expected.

Thus, we have determined the entire 33.15C greenhouse effect, the surface temperature, and the temperature of the troposphere at any height, and the height at which the equilibrium temperature with the Sun occurs at the ERL entirely on the basis of the Newton's 2nd law of motion, the 1st law of thermodynamics, and the ideal gas law, without use of radiative forcing from greenhouse gases, nor the concentrations of greenhouse gases, nor the emission/absorption spectra of greenhouse gases at any point in this derivation, demonstrating that the entire 33C greenhouse effect is dependent upon atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases. Also note, it is absolutely impossible for the conventional radiative theory of the greenhouse effect to also be correct, since if that was the case, the Earth's greenhouse effect would be at least double (66C+ rather than 33C). 

In essence, the radiative theory of the greenhouse effect confuses cause and effect. As we have shown, temperature is a function of pressure, and absorption/emission of IR from greenhouse gases is a function of temperature. The radiative theory tries to turn that around to claim IR emission from greenhouse gases controls the temperature, the heights of the ERL and tropopause, and thus the lapse rate, pressure, gravity, and heat capacity of the atmosphere, which is absurd and clearly disproven by basic thermodynamics and observations. The radiative greenhouse theory also makes the absurd assumption a cold body can make a hot body hotter,disproven by Pictet's experiment 214 years ago, the 1st and 2nd laws of thermodynamics, the principle of maximum entropy production, Planck's law, the Pauli exclusion principle, and quantum mechanics. There is one and only one greenhouse effect theory compatible with all of these basic physical laws and millions of observations. Can you guess which one it is?


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