lördag 2 april 2011

Simplistic Climate Models: Warming or Cooling?

From Grant Petty (2006)

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.

7 kommentarer:

  1. "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."

    So.. not so.

    Claes, why do you keep embarrassing yourself citing rookie mistakes.

    The person you cite has missed the important point that the absorptivity of many gases is a strong function of wavelength.

    So no gas emits as a blackbody.

    But several gases emit very close to a blackbody in certain wavelength bands.

    The important point to understand is that CO2 and water vapor have bands where they are very strong absorbers (and, therefore, very strong emitters).

    CO2 is well-mixed so this happens independently of latitude for 14-16um. Water vapor has a much higher concentration in warmer climates so there is a latitude/seasonal dependence, but where water vapor is present in significant concentrations it has very strong absorption/emission in a number of bands.

    This is easy to see in every spectral measurement of upward radiation by satellite and every downward surface measurement.

    Watch out for the forthcoming Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Ten on Science of Doom where these spectral measurements will be shown.

  2. Sure I know. What is embarrasing is that everybody is talking about a "greenhouse effect" but nobody knows what it is, if it is warming, cooling or nothing. That is embarrassing.

  3. "No one knows what it is"


    Why not do your readers a favor and analyse a real paper on the subject.

    I recommend Ramanathan & Coakley (1978): Climate modeling through radiative-convective models.

    Everyone who understands atmospheric physics knows what it is.

    Solution of the radiative transfer equations with a convective adjustment provides a repeatable no-feedback result of 3.7W/m^2 radiative forcing for doubling of CO2.

  4. Ramanathan&Coakley is also severely simplistic, since real thermodynamics is not included. It may be correct or not correct, impossible to say which without a better model.

  5. Nice.

    Love your work. If it's all so simplistic why are the theory and experiment so close?

    Shown in Theory and Experiment – Atmospheric Radiation - and, of course, in your personal copy of Goody & Yung, Atmospheric Radiation: Theoretical Basis.

    The paper which contains the first spectral comparison is The Infrared Interferometer Experiment on Nimbus 3, by Conrath et al, JGR (1970).

    It's a fluke!

    And the 100,000+ measurements of TOA OLR vs theory in Dessler's paper.

    It's a fluke!

    And the DLR spectra?

    They made it up!

  6. No, radiation spectra are interesting and they say something, but what is not clear at all, since the Earth surface temperature comes out from complex thermodynamics with gravitation upon radiative forcing. Radiation spectra alone cannot tell the effect of somewhat increased CO2, or is this what you are saying, that they can?