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Saturday, November 28, 2015

Why greenhouse gas radiative forcing doesn't explain Earth's energy budget

Wednesday, November 26, 2014
 Original link:
We have previously demonstrated that the atmospheric mass/gravity/pressure theory of the 33C greenhouse effect explains Earth's surface temperature and the temperatures throughout the troposphere, rather than radiative forcing from greenhouse gases.

We have also demonstrated why the atmospheric mass/gravity/pressure theory of the greenhouse effect also perfectly explains the observed greenhouse effect on Titan, the closest Earth analog in our solar system, and the only planet other than Earth with an atmosphere comprised of mostly non-greenhouse gases (Titan: 98.4% Nitrogen, 0.1% hydrogen, and only 1.5% greenhouse gas methane compared to Earth's 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide).

We now address three additional reasons why the conventional anthropogenic CO2 warming theory is flawed due to incorrect assumptions regarding the energy budget. In contrast, the mass/gravity/pressure alternative greenhouse theory is entirely 
compatible with Earth's energy budget, physical laws, and observations. 

The radiative greenhouse theory is commonly represented by the Earth energy budget devised by Kiehl and Trenberth as shown in this diagram from their 2008 publication:

Trenberth, Fasullo, Kiehl 2008 Earth energy budget shows "atmospheric window" transmitting only 40 W/m2 from the surface directly to space
which shows an "atmospheric window" where the greenhouse gases don't significantly absorb/emit infrared radiation, and thus most of this radiation travels directly from the surface to space unimpeded by greenhouse gases, or any radiative forcing as a result. 

The "atmospheric window" of radiation direct to space falls between 8-12 micron wavelengths, as shown in the figures above and below, which includes the peak emission wavelengths (~8-11 microns) from Earth, thus ~80% of these peak emissions from Earth pass directly to space without being absorbed or emitted by greenhouse gases, thus don't contribute to radiative forcing. 

Blue curve shows the Planck curve assuming Earth radiated as a true blackbody, with peak emissions located at ~10 microns, which is at the middle of the 8-12 micron "atmospheric window" that is not absorbed/emitted by greenhouse gases.
However, according to the Trenberth et al Earth energy budget above, only 40 W/m2 passes through the "atmospheric window," i.e. only 10% of the 396 W/m2 radiative surface emissions in his energy budget.

The Planck–Einstein relation is a formula integral to quantum mechanics, and states that the energy of a photon (E) is proportional to its frequency (ν). The constant of proportionality, h, is known as the Planck constant:

and since frequency v is inversely related to wavelength λ by

v = c/
λ where c = speed of light


E = hc/λ

thus, the shorter the wavelength/higher the frequency of a photon, the higher the energy it contains.

Therefore, the highest energy photons at the short 8-12 micron wavelengths emitted from Earth's surface fall within the direct atmospheric window to space without any interaction with greenhouse gases.

We can get a sense for the huge effect just a few microns change in wavelength has on the corresponding blackbody emission temperature by plotting the peak blackbody emission wavelength in microns vs. the peak emission temperature of a blackbody determined by Wien's Displacement Law, which shows the emission temperature at the beginning of the atmospheric window at 8 microns is 89C, dropping all the way down to -31.7C at the end of the atmospheric window at 12 microns, a temperature change of 120.7C.

The catastrophic greenhouse gas CO2, however, absorbs and emits line spectra centered around 15 microns, so what does Wien's displacement law calculate for a blackbody (which CO2 is not) emitting at 15 microns? Whoa, a toasty peak emission temperature of minus 80C:

Thus, the radiative greenhouse theory makes the absurd assumption that CO2 radiating at a blackbody temperature of -80C contributes 20% of the radiative greenhouse effect and heats the Earth by 6.6C from the equilibrium temperature with the Sun of -18C to -11.4C. How can a cold body radiating at -80C cause a hotter body at -18C to warm by 6.6C or at all? 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 all prove it cannot. CO2 radiating at an equivalent blackbody temperature of  -80C cannot possibly account for 20% of the ~33C greenhouse effect to cause 20% of the warming from -18C to 15C.

Further, even within the CO2 equivalent -80C blackbody emission peak at 15 microns [line spectra range ~13.5 - 17 microns], the CO2 and water vapor absorption/emission spectra significantly overlap such that almost 70% is independently due to water vapor and thus would be completely unaffected by increased CO2. Thus, despite overwhelming evidence that CO2 cannot significantly warm the planet, if you still believe the radiative greenhouse theory and reject the alternate mass/pressure greenhouse theory, the overlapping spectra of CO2 with water vapor prove CO2 is a bit player at most:

Shaded area shows difference between CO2 and water vapor absorption/emission spectra

Blowup of above figure. Area with asterisk is absorbed by CO2 only, remainder below overlaps with absorption spectra of water vapor.

Another huge flaw in Trenberth's energy budget is the false assumption that infrared radiation from greenhouse gases can heat the oceans, and just as effectively as the land surface. This is disproven by both theory and observations, since IR can only penetrate the ocean surface a few microns to cause evaporative cooling of the ocean skin surface, not warming. Since the oceans cover 70% of the Earth's surface, this problem alone suggests the radiative greenhouse theory is exaggerated by at least 70% (not even considering the cooling effect of evaporation and that evaporation results in clouds and further cooling).

These are only three of many fatal flaws of conventional radiative greenhouse theory. There is one and only one explanation for the entire ~33C greenhouse effect that satisfies all physical laws and is in accordance with millions of weather balloon and satellite observations, the atmospheric mass/gravity/pressure greenhouse theory. 

  1. Kiehl and Trenberth omit kinetic energy returning to the near surface within air that has descended and warmed adiabatically.

    That omission throws the energy budget out which is why they then have to propose extra downward radiation from GHGs to make the energy budget balance.

    DWIR from GHGs cannot raise the surface temperature above the S-B expectation of 255K because convection works to negate the thermal effect of downward radiation from within the atmosphere.

    The entire 33K surface temperature enhancement is induced by the mass of the atmosphere exchanging energy with the surface via adiabatic ascent and descent within the gravitational field.

    The energy engaged in that conductive exchange cannot also be involved in the radiative exchange with space because the same package of energy cannot be involved in two processes at once.

    The amount of energy tied up in the conductive exchange is related to atmospheric density simply because the more mass available within a given volume to acquire energy from the surface by conduction the greater the proportion of solar energy that will be diverted from outward radiation to space.

  2. "Therefore, the highest energy photons at the short 8-12 micron wavelengths emitted from Earth's surface fall within the direct atmospheric window to space without any interaction with greenhouse gases."

    The 8-12 micron wavelengths are not short. Did you intend to write:

    Therefore, the highest energy photons at the shorter end of the long-wave 8-12 micron wavelengths emitted from Earth's surface fall within the direct atmospheric window to space without any interaction with greenhouse gases.
  3. As this site and others have pointed out, recent temperature observations have diverged a bit from GCM predictions

    “If you can’t explain the pause, you can’t explain the cause”

    However, unless I missed something, if this new theory is correct then CO2 released since the industrial revolution should have cooled the atmosphere. There would also be a cooling feedback due to reduced humidity.

    This theory needs to match real world data at least as well, and preferably better than the widely believed AGW theory.

    Between the two theories, which provides the closest match for the warming over the last century and the paleoclimate record?
    Do we need to find a whole new explanation for Climate Change as well?

    I’m a skeptic. I’m skeptical about economic predictions, based on crop predictions, based on climate predictions.

    I’m also skeptical about claims that decades of theory and research is fundamentally flawed and should be scrapped altogether.

    This needs supporting evidence and lots of it.
  4. Anonymous.

    Although GHGs have a nominal cooling effect by radiating directly to space that is offset by convective changes for a zero net effect on surface temperature for reasons I have explained elsewhere.

    You can call that a third theory if you wish.

    The changes in global temperature have other, natural causes involving solar effects on the stratosphere and mesosphere.


    1. Hi Stephen,

      I've only just stumbled on all this, so I've not been following any discussion, I'm afraid.

      Just to clarify, are you saying that the "atmospheric mass/gravity/pressure theory of the 33C greenhouse effect" * predicts a cooling by CO2 and water, but you have proposed an alternative (or at least a variation) that has a net neutral effect?

      If so is there a summary online you could link to? Or is it somewhere in the comments of other articles?

      Sounds like I didn't misunderstand too much though and this theory (and I guess to a lesser extent, yours) will rely on another factor to explain any warming? Is solar variation still considered the prime candidate if AGW isn't the cause? It's not mentioned as much as it used to be, so I wasn't sure if it had been ruled out?

      * Seriously, couldn't someone have thought of a snappier name for this And the acronym is utterly ridiculous- The AMGPT33CGE? That will never catch on.
    2. Hi Anonymous.

      What seems to happen is that radiative gases allow energy to leak out to space from the adiabatic convective cycle within the atmosphere.

      The result is that less kinetic energy is returned to the surface in adiabatic descent than is taken up by adiabatic ascent which should cool the surface.

      However that means that the atmosphere does not expand as much as it would have done without GHGs so the air at the surface remains denser than would otherwise have been the case.

      Denser air at the surface absorbs more of the solar throughput by conduction and convection which should warm the surface.

      I suggest that the two processes cancel each other out.

      As far as I know it is only I who have pointed trhis out so far.
  5. I dont catch your 80% of radiation from Earth in the atmospheric window. With 15C mean temperature it is 25% that falls inside 8 to 12 um, meaning close to 100W/m2. That temperature has a peak at 10um anyway.


    1. The ~80% figure is from ~80% transmittance within the atmospheric window from 8-12 microns, such as shown in this graph:

      What I am saying is that within the 8-12u window, ~80% of the IR from the surface passes directly to space. I suppose the other 20% is scattered by water vapor/clouds I presume. Using your assumption of 100W/m2 emission from surface, thus ~80% of 100W/m2 or 80W/m2 goes directly to space, double what Trenberth claims.
  6. I think you're discerning for yourself some of the common thinking errors around "climate science" - the aggregation of what should be distinct, and the dissection of entities.
    From your recent post, you offer a "GHE" for the air, and another for the surface, both distinct from HockeyStick's cloud model.
    I sugggest you carry these through to your present deconstruction of the TFK2008 diagram; ie
    > a deep-cloud/moist-adiabat sector (OLR, DLR, etc);
    > a "greenhouse-gas" sector (OLR, DLR);
    > a surface sector (OLR);
    the whole being linked only at the surface.

    Several of the flows shown should be combined as double-headed arrows, as they represent exchanges or transactions, where only the nett is important.
    I feel we need to get the "shape" exactly right before running the numbers.
    Peter Shaw

Derivation of the entire 33°C greenhouse effect without radiative forcing from greenhouse gases

Sunday, November 23, 2014
Original post:

We will derive the entire 33°C greenhouse effect using the 1st law of thermodynamics and 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, thus demonstrating that the entire 33C greenhouse effect is dependent upon atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases. Secondly, we will show why multiple observations perfectly confirm the mass/gravity/pressure theory of the greenhouse effect, and disprove the radiative forcing theory of the greenhouse effect.

Note, this physical derivation is absolutely not suggesting the ~33C greenhouse effect doesn't exist. On the contrary, the physical derivation and observations demonstrate the 33C greenhouse effect does exist, but is explained by a different mechanism not dependent on radiative forcing from greenhouse gases. Also note, it is impossible for both explanations of the greenhouse effect to be true, since the global temperature would have to increase by an additional 33C (at least) above the present. You cannot have it both ways. We will show how the 
mass/gravity/pressure theory causes the temperature gradient and that the emission spectra of greenhouse gases seen from space are a consequence rather than the cause of that temperature gradient. 

This derivation uses very well-known physical principles and barometric formulae possibly first described by the great physicist Maxwell in 1872, who demonstrated that the atmospheric temperature gradient and greenhouse effect are due to pressure from Earth's gravitational field, not radiative forcing. Maxwell makes no mention of any influence of radiation as the cause of the temperature gradient of the atmosphere, but rather relates temperature at a given height to pressure. He discusses the convective (dominated) equilibrium of the atmosphere in his book Theory of Heat, pp. 330-331:

"...In the convective equilibrium of temperature, the absolute temperature is proportional to the pressure raised to the power (γ-1)/γ, or 0,29..."
Twenty four years later, Arrhenius devised his radiative forcing theory of the greenhouse effect, which unfortunately makes a huge false assumption that convection doesn't dominate over radiative-convective equilibrium in the lower atmosphere, and thus Arrhenius completely ignored the dominant negative-feedback of convection over radiative forcing in his temperature derivations. Johns Hopkins physicist RW Wood completely demolished Arrhennius' theory in 1909, as did other published papers in 1963, 1966, 1973, (and others below), but it still refuses to die given its convenience to climate alarm.

We now know from Robinson & Catling's paper in Nature 2014 (and others) that radiative-convective equilibrium on all planets with thick atmospheres in our solar system (including Earth of course) is dominated by convection/pressure/lapse rate in the troposphere up to where the tropopause begins at pressure = 0.1bar. When P < 0.1 bar, the atmosphere is too thin to sustain convection and radiation from greenhouse gases takes over to cause cooling of the stratosphere and above. 

Since Maxwell's book was published in 1872, many others have confirmed that the greenhouse effect is due to atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases, including Hans JelbringConnolly & ConnollyNikolov & ZellerMario Berberan-Santos et alClaes Johnson and hereVelasco et alGiovanni Vladilo et alHeinz ThiemeJacques HenryStephen WildeAlberto MiatelloGerhard Gerlich and Ralf D. TscheuschnerVerity JonesWilliam C. Gilbert & hereRichard C. TolmanLorenz & McKayPeter Morecombe, Robinson and Catling, and many others, so this concept is not new and preceded the Arrhenius theory. 

Step 1: Derivation of the dry adiabatic lapse rate from the 1st Law of Thermodynamics and ideal gas law:

First, the basic assumption can be adopted that the atmosphere, in hydrostatic terms, is a self-gravitating system in constant hydrostatic equilibrium due to the balance of the two opposing forces of gravity and the atmospheric pressure gradient, according to the equation:

 dP/dz = - ρ × g (1)

where ρ is the density (mass per volume) and g the acceleration due to gravity. This equation, from a mathematical point of view, can be derived by considering the hydrostatic equilibrium function as a system of partial derivatives depending on P and ρ and considering all three spatial dimensions:

 ∂P/∂x = ρ × X, ∂P/∂y = ρ × Y, ∂P/∂z = ρ × Z (2)

As, within a fluid mass in equilibrium, pressure and density does not vary along the horizontal axes (X and Y), the related partial derivatives equal zero. But, in the remaining vertical dimension, the partial derivative is non-zero, with density and pressure varying inversely as a function of fluid height (density and pressure decrease with increasing height relative to the bottom) and, considering gravitational force as a constant connected to the measure of density, thus equation (2) can be derived.

For a precise calculation involving the valid parameters, the 1st Law of Thermodynamics can be used:

 Δ U = Q – W (3)

where U is the total internal energy of the system, Q its heat energy, and W the mechanical work the system is undergoing. Applying this relationship to Earth's atmosphere, yields:

 U = C(p)T + gh (4)

where U is the total energy of atmospheric system in hydrostatic equilibrium and equal to the sum of the thermal energy (kinetic plus dissipative and vibro-rotational), the specific heat C(p) multiplied by the temperature T plus the gravitational potential energy, with gravitational force g at height h of the gas. In this case, because the force of gravity has a negative sign as the system is undergoing work, the potential energy ( -g × h) can be equated to the mechanical work (-W) that the system undergoes in the 1st Law of Thermodynamics.

Based on this equation, the atmosphere's "average" temperature change can be found for any point with the system in equilibrium; for now and for simplicity, weather phenomena and disturbances at specific locations are not considered because, with the system in overall hydrostatic and macroscopic equilibrium, any local internal, microclimatic perturbation by definition triggers a rebalancing reaction. In fact, to calculate the energy change of the system in equilibrium (here U is constant) as a function of temperature and height change, differentiation yields: 

dU = 0 = C(p)dT + gdh,

which becomes: 

dT/dh = -g/C(p), or dT = (-g/C(p))dh.  [Dry adiabatic lapse rate equation]

This is a splendid equation, describing precisely the temperatures’ distribution of a gas (as the air of Earth’s atmosphere) in hydrostatic equilibrium between the 2 forces of the lapse-rate (preventing the collapse of the atmosphere at the Earth’s surface) and gravity (preventing the escape of the atmosphere in the void of space). 

In other words, temperature variation (dT) is a function of altitude variation (dh), whose solution at any point of height (h°) and for any temperature (T°), can be found by integrating as follows:

∫dT = -g/C(p) × ∫dh (5)

and whose solution is:

 T - T° = -g/C(p) × (h - h°)   (6)


T – T° = ∆ T (or dT) = Interval of temperatures
g = Gravitational acceleration constant = 9.8 m/s^2
h – h° = ∆ h (or dh) = Space interval (vertical) in the atmosphere
Cp = heat capacity at constant pressure

Step 2: Determine the height at the center of mass of the atmosphere

We are determining the temperature gradient within the mass of the atmosphere using a linear function of atmospheric mass (the lapse rate), therefore the equilibrium temperature is located at the center of mass. The "effective radiating level" or ERL of planetary atmospheres is located at the approximate center of mass of the atmosphere where the temperature is equal to the equilibrium temperature with the Sun. The equilibrium temperature of Earth with the Sun is commonly assumed to be 255K or -18C as calculated here. As a rough approximation, this height is where the pressure is ~50% of the surface pressure. It is also located at the approximate half-point of the troposphere temperature profile set by the linear adiabatic lapse rate, since to conserve energy in the troposphere, the increase in temperature from the ERL to the surface is offset by the temperature decrease from the ERL to the tropopause.

Fig 1. From Robinson & Catling, Nature, 2014 with added notations in red showing at the center of mass of Earth's atmosphere at ~0.5 bar the temperature is ~255K, which is equal to the equilibrium temperature with the Sun. Robinson & Catling also demonstrated that the height of the tropopause is at 0.1 bar for all the planets in our solar system with thick atmospheres, as also shown by this figure, and that convection dominates over radiative-convective equilibrium in the troposphere to produce the troposphere lapse rates of each of these planets as shown above. R&C also show the lapse rates of each of these planets are remarkably similar despite very large differences in greenhouse gas composition and equilibrium temperatures with the Sun, once again proving pressure, not radiative forcing from greenhouse gases, determines tropospheric temperatures. 

Step 3: Determine the surface temperature

For Earth, surface pressure is 1 bar, so the ERL is located where the pressure ~0.5 bar, which is near the middle of the ~10 km high troposphere at ~5km. The average lapse rate on Earth is 6.5C/km, intermediate between the 10C/km dry adiabatic lapse rate and the 5C/km wet adiabatic lapse rate, since the atmosphere on average is intermediate between dry and saturated with water vapor. 

Plugging the average 6.5C/km lapse rate and 5km height of the ERL into our equation (6) above gives

T = -18 - (6.5 × (h - 5)) 

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)) 

Ts = -18 + 32.5  

Ts = 14.5°C or 288°K

which is the same as determined by satellite observations and is ~33C above the equilibrium temperature with the Sun.

Thus, we have determined the entire 33C greenhouse effect, the surface temperature, and the temperature of the troposphere at any height, entirely on the basis of the 1st law of thermodynamics and 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.

The greenhouse gas water vapor does have a very large negative-feedback cooling effect on the surface and atmospheric temperature by reducing the lapse rate by half from the 10C/km dry rate to the 5C/km wet rate. Increased water vapor increases the heat capacity of the atmosphere Cp, which is inversely related to temperature by the lapse rate equation above:

dT/dh = -g/Cp

Plugging these lapse rates into our formula for Ts above:

Ts = -18 - (10 × (0 - 5)) = 32C using dry adiabatic lapse rate

Ts = -18 - (5 × (0 - 5)) = 7C using wet adiabatic lapse rate [fully saturated]

showing a cooling effect of up to 25C just from changes in the lapse rate from water vapor. Water vapor also cools the planet via evaporation and clouds, and which is confirmed by observations. Water vapor is thus proven by observations and theory to be a strong negative-feedback cooling agent, not a positive-feedback warming agent as assumed by the overheated climate models to amplify warming projections by a factor of 3-5 times. 

What about CO2? At only 0.04% of the atmosphere, CO2 contributes negligibly to atmospheric mass and only slightly increases the heat capacity Cp of the atmosphere, which as we have shown above, is inversely related to temperature. CO2 would thus act as a cooling agent by slightly increasing troposphere heat capacity. Increased CO2 also increases the radiative surface area of the atmosphere to enhance outgoing radiation to space, analogous to putting a larger heat sink on your microprocessor which increases radiative surface area and convection to cause cooling. 

It is well-known that CO2 and ozone are the primary cooling agents of the stratosphere up to the thermosphere, but even the warmist proponents are unable to agree on a coherent explanation why CO2 would assume the opposite role of a warming agent in the troposphere. As the mass/gravity/pressure greenhouse theory shows, and just like water vapor, CO2 also acts to cool the troposphere, and the rest of the atmosphere by increasing radiative surface loss and outgoing radiation to space. 

Millions of weather balloon observations confirm that there is no greenhouse gas-induced "hot spot" in the mid-upper troposphere, which is the alleged "fingerprint of AGW." The 2nd law of thermodynamics principle of maximum entropy production also explains why such a "hot spot" will not form. However, observations do show a cooling of the stratosphere over the satellite era, which would be consistent with increased CO2 increasing outgoing radiation to space. Observations also show an increase of outgoing longwave radiation to space over the past 62 years, which is entirely consistent with increased outgoing radiation from greenhouse gases and a decrease of "heat trapping", the opposite of AGW theory. 

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 and thus pressure 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?

Update: The atmospheric center of mass assumption in step 2 above also appears to be applicable to Titan, the closest Earth analog with a thick atmosphere in our solar system. For Titan, the surface temperature is 94K, equilibrium temperature with the Sun is 82K, and surface pressure is 1.47 bar. 

Thus, the center of mass of the atmosphere is located at ~1.47/2 = ~0.74 bar, which observations show is where Titan's atmospheric temperature is ~82K, the same as the equilibrium temperature with the Sun. I have added the notations in red to Robinson and Catling's graph below:

Update 2: Some still claim the ERL is set by radiative forcing, but this is false because:

1) A purely radiative model of the atmosphere without convection sets the ERL too high, at ~7km instead of ~5 km where observations show it is located. At 7km altitude, observations show the temperature to be 242K instead of the equilibrium temperature of 255K.

Solely radiative "greybody" model of the atmosphere without convection shown in blue. I have added in red the actual temperatures from the US Standard Atmosphere calculator. Note how the purely radiative model is up to 20K hotter, e.g. at the top of the troposphere, than the observations show. This is because convection dominates and "short-circuits" radiative forcing in the troposphere to cause cooling.

Open symbols show no relationship between tropopause height and troposphere temperatures
That's because, as Robinson and Catling have shown, the height of the troposphere and the adiabatic lapse rate that extends from the 0.1 bar tropopause all the way to the surface is controlled by pressure, not temperature nor radiative forcing from greenhouse gases:
"At higher pressures [P > 0.1 bar], atmospheres become opaque to thermal radiation, causing temperatures to increase with depth and convection to ensue. A common dependence of infrared opacity on pressure, arising from the shared physics of molecular absorption, sets the 0.1 bar tropopause"

3. We have already shown that temperature is a function of pressure, and radiance and emission spectra from greenhouse gases are in turn a function of temperature, not the other way around.