Simplistic Climate Models: Warming or Cooling?

The above graph (in particular the top one) can be seen as the fundamental graph of CO2 alarmism. The dip in the top graph around the wavelength 15 mu, is the essence: We will come back to this below after a digression.

Roger Taguchi on Climate Etc points to the following important fact:

• As I have stated, individual gas molecules cannot emit black body radiation,which is a continuous spectrum (N2 and O2 cannot emit any IR, black body or otherwise, and CO2 and other greenhouse gases can emit only over narrow bands, so their emission is by definition not continuous and therefore not black body).
• Black body radiation can only be emitted by condensed states like solids and liquids (or by free electrons in the conduction bands of metallic solids, or in plasmas such as in the interior and photosphere of the Sun).
• The reason is that in condensed states there are many, many weaker vibrations due to van der Waals' (intermolecular) forces, as well as stronger vibrations within molecules. Combinations of the weaker and stronger vibrations and their overtones allows for a continuous spectrum extending from low frequencies to high frequencies.
• So the IR that escapes from the Earth to outer space, both in the daytime and at night, comes from the solid and liquid surface of the Earth, not some "emitting layer(s)" in the atmosphere.

Following up on the post Simple Model for Radiative Transfer, we collect the following facts:

1. The blackbody temperature of the Earth at its viewing angle of 0.005^2 of the Sun at 5778 K, comes out by Stefan-Boltzmann's Law as 255 K. To be compared with the 288 K observed.
2. Without an atmosphere the Earth surface temperature could thus be 255 K, and thus the total effect of the atmosphere is + 33 C.
3. The observed lapse rate is 6.5 K/km with atmosphere, which means that the blackbody temperature of 255 K can be allocated to a height of about 5 km as if the Earth with a 5 km thick opaque atmospheric layer L was one blackbody with a transparent atmosphere above 5 km. The thicker L is the warmer the Earth surface will be through the lapse rate.

We now ask what the effect on the Earth surface temperature would be of changing the radiative properties of the atmospheric layer L assuming a radiation model of the form

• (1) dT/dX + E T = - 6.5 for X in the interval (0,5),

where dT/dX models convective/radiative transport and A T(X) models radiation to outer space at height X with E a positive emission coefficient, with solution

• T(X) = T(0)exp(-EX) - 6.5 (1 - exp(-EX))/E,

where T(0) is the surface temperature. With E tending to 0 corresponding to a fully opaque atmospheric layer L, we have T(X) = T(0) - 6.5 X, and thus T(0) = 288 K if T(5) = 255 K.

We now ask what the effect will be of increasing E from 0, corresponding to letting L become

increasingly transparent from fully opaque. Integration of (1) over (0,5) gives

• (2) T(0) - T(5) - 33 = integral E T(X) dX = Q1 = total emission from L to outer space

Energy balance gives

• (3) Q1 + sigma T(5)^4 = Q,

where sigma T(5)^4 is radiation from the top of L by Stefan-Boltzmann and Q is given total insolation. Differentiation of (2) with respect to E using (2) gives

• dT(0)/dE - dT(5)/dE + 4 sigma T(5)^4/T(5) dT(5)/dE = 0

where with sigma T(5)^4 ~ 240 W/m2,

• sigma T(5)^4/T(5) ~ 240/273 ~ 1

and thus

• dT(0)/dE ~ - 3 dT(5)/dE

Now, if E increases from 0, T(5) will decrease since less radiation will have to be emitted at X = 5, and thus T(0) will increase. Or put differently, as E decreases T(0) will decrease, that is increasing opacity may cause cooling of the Earth surface.

The above argument should be compared with the standard "greenhouse effect" argument where increasing opacity would correspond to an increasing thickness of the opaque layer and thereby would correspond to surface warming. The determining factors are the lapse rate, and the thickness of the absorbing atmosphere, and the lapse rate is mainly determined by thermodynamics (forced by radiation).

We thus have two simplistic models giving different effects of increasing opacity: cooling or warming, as you like. The conclusion is that a simplistic model of a "greenhouse effect" should be viewed with skepticism: it may give a correct indication about reality or not. When you have several simplistic arguments with contradictory results, one of them may be correct, but you don't know which.

But it is possible that a more complete model combining thermodynamics and radiation can give meaningful results, most likely showing that increased CO2 has neglible warming/cooling effect.

Back to the top graph of

Outgoing Longwave Radiation as seen by a satellite at a height of 20 km:

We see a dip in the emission curve in a band around 15 mu m emitted at a temperature 220 K from a height of a bit less than 20 km, while outside the band the radiation is emitted from the Earth surface at about 270 K. The dip comes from the "greenhouse gases" (mainly water vapour and some CO2) which absorb radiation from the Earth surface emitted at 270 say and and re-emitting less radiation at 220 K and thus acting as a "warming blanket" causing the "radiative forcing" of the "greenhouse effect". The idea is that the "greenhouse effect" corresponds to the area of the dip shows the "greenhouse effect" as a combined effect of water vapor and CO2

capable of warming the Earth surface temperature by 33 C as compared to a fully transparent atmosphere.

But what does the satellite measure? The IR-meter of the satellite (presumably) measures the temperature of the closest emitting surface and the total radiance is probably computed by Stefan Boltzmann's Law as if all emission came from the top layer. This means that it is not straight away to connect the dip to "radiative forcing" in particular not from the trace gas CO2. In any case the top graph is of interest and it is important to make a correct interpretation of the instrument reading....this is also important as concerns the interpretation of the graph below supposedly depicting "downwelling longwave radiation" from the atmosphere...to be continued...

Pierrehumbert pumps out the CO2 radiation message in Physics Today without even mentioning the crucial role of the thermodynamic lapse rate:

• Infrared radiative transfer theory, one of the most productive physical theories of the past century, has unlocked myriad secrets of the universe including that of planetary temperature and the connection between global warming and greenhouse gases.

As far I can see, this is stunning disinformation: planetary climate is complex thermodynamics with radiative forcing, not more or less trivial radiative transfer.