The chapter "Climate Thermodynamics - 4 Lapse Rate and Global Warming/Cooling" starts off badly:

The effective blackbody temperature of the Earth with atmosphere is -18C, which can be allocated to a TOA at an altitude of 5 km at a lapse rate of 6.5C/km connecting TOA to an Earth surface at 15C with a total warming of 5 × 6.5 = 33C. The lapse rate determines the surface temperature since the TOA temperature is determined to balance a basically constant insolation. What is then the main factor determining the lapse rate? Is it radiation or thermodynamics, or both?Mr Johnson may be a mathematician, but he's not a climatologist nor a physicist. I'm none of those, but I can spot the equivalent of a "schoolboy howler" when I see one. Let's analyse the first sentence; TOA (Top of Atmosphere) is considered to be around 23 km altitude. The "-18C" has to have been calculated using the Stefan-Boltzmann equation, using the average radiation-to-space value of 240 W/m² (watts per sq. metre). This does indeed give a result of -18°C, and the average temperature at a height of 5 km is indeed -18°C, but there's a snag. The radiation to space comes from more than one source, and its profile is not a complete Planck curve, as required if the Stefan-Boltzmann equation is to be used.

What's a Planck curve?

These are Planck curves for various blackbody temperatures. The total radiation intensity is related to the area under the curve; the higher the temperature, the "fatter" the curve, and the further the peak moves towards the higher frequencies. Radiation to space is far from a perfect curve:

The section from 800 to 1300 cm−1 is termed the "atmospheric window", that portion of the infrared spectrum for which the atmosphere is largely transparent. In that section, radiation to space is mostly from the surface. The two large dips are due to absorption by CO2, with a much smaller downward spike from methane (CH4) at 1300. The ragged area on the left is due to the relatively small amount of water vapour in the upper atmosphere.

The 240 W/m² cannot be assigned to a single source, neither can it represent radiation from a single thin atmospheric layer.

**Half**the mass of the atmosphere is above the calculated height of 5 km, which is far below the maximum height of clouds, and less than 2/3 the height of Everest.

The next sentence is convoluted logic: "The lapse rate determines the surface temperature". It's the surface temperature and the temperature at various altitudes which determines the lapse rate, not the other way around.

In the chapter "Computational Blackbody Radiation" Johnson redefines the accepted nature and properties of a blackbody, and contradicts himself in the process. He says (my emphasis)

A blackbody acts like a transformer of radiation whichIn one paragraph we move from a black body which absorbs high-frequency radiation to one which absorbs all radiation. The implication is that a blackbody which absorbs low-frequency radiation (infrared) cannot emit in the same frequency range and vice-versa. "The net result is that a warm blackbody can heat a cold blackbody, but not the other way around", having just said that blackbodies absorb all frequencies. "A blackbody isabsorbs high-frequency radiationand emits low-frequency radiation. The temperature of the black-body determines a cut-off frequency for the emission, which increases linearly with the temperature: The warmer the blackbody is, the higher frequencies it can and will emit. Thus only frequencies below cut-off are emitted,while all frequencies are being absorbed.

heated only by frequencies which it cannot emit, but has to store as heat

energy" - then it can't be a blackbody, which as he said

**absorbs all frequencies**. This is the preamble to "proving" that atmospheric back-radiation "doesn't exist". Manufacturers of radiation pyrometers have been deceiving their customers for decades seemingly, and yet no-one noticed?

There's more - a

**lot**more, but enough said I think.

Update: 9th August 2011

I take back what I said in that last sentence, having re-read (and it's not easy) Johnson's two chapters. Mr.J doesn't appear to understand that radiation is a thermodynamic process, or that thermodynamics is simply a branch of science. Heat can be transformed into radiation and vice-versa. He calls non-radiative heat-transfer

*thermodynamics*yet radiation is just radiation. They're both thermodynamic processes. In his chapter "Climate Thermodynamics" (should it have been called "Climate Thermodynamics and Radiation"?), by using this distinction he even confuses himself. Consider this for technobabble:

The heat is transported by the atmosphere in a combination of thermo-dynamics (turbulent convection and phase change in evaporation/condensation) and radiation, roughly 2/3 by thermodynamics and 1/3 by radiation. The thermodynamics involves positive radiative forcing balanced by evaporation at low latitudes/altitudes from a warm ocean causing warm air to rise-expand-cool including poleward motion followed by negative radiative forcing balanced by condensation at high latitudes/altitudes causing cool air to descend-contract-warm closing a thermodynamic cycle, as indicated in Fig. 1, during polar winter.In the first sentence, radiation is distinct from "thermodynamics". In the second, radiation is included in "thermodynamics". Confusing for the reader, and presumably confusing for Mr. J too.

Here's a more recent example, this time using one of two exactly opposite statements to support the "argument of the moment". In his chapter "Computational Blackbody Radiation" 7.13, Mr. J says (my bold):

The classical Stefan-Boltzmann’s Law R = σT^{4}gives the energy radiated from a blackbody of temperature T into an exterior at absolute zero temperature (0K). For the case of an exterior temperature T_{ext}above zero,standard literaturepresents the following modification:

R = σT^{4}- σT_{ext}^{4}

where the term σTIn a recent post on his blog, he says (my bold):_{ext}^{4 }conventionally represents ”backradiation” from the exterior to the blackbody.

The algorithm to compute DLR reflects a Stefan-Bolzmann's radiation law (SB) of the form(1) Q = sigma Te^4 - sigma Ta^4, where Te is the Earth surface/instrument temperature, expressing the net heat transfer Q as the difference between two-way gross heat transfer back and forth. DLR is then identified with the second term, see also the The Atmospheric Radiation Measurement Program.

But this form of SB is not found in the physics literature, where instead SB is written as

(2) Q = sigma (Te^4 - Ta^4),

which expresses net heat transfer from warm to cold. In this version it is impossible to single out the term sigma Ta^4 and claim it to represent DLR. In this version of SB there is no DLR, no back radiation, only net heat transfer.

We now see thetrick: Rewrite (2) as (1) by analgebraic manipulationand then interpret the miraculously appearing term sigma Ta^4 as DLR:

By a purely algebraic manipulation a massive physical flux of energy DLR has been created. With massive DLR it is possible to stir up CO2 alarm. This trick has fooled a whole world of climate scientists. Does it fool you?No-one can create something that doesn't exist by algebraically rearranging an expression. The two expressions Q = sigma (Te^4 - Ta^4), and Q = sigma Te^4 - sigma Ta^4 are of course effectively identical. The latter represents

**two**radiative fluxes, with Q being the net flux representing the energy transfer from hot to cold. The first expression (which he's happy to accept) gives

**exactly the same result**. and it

**doesn't actually matter**whether "back radiation" physically exists or not. Therefore in this instance, the "slayers" are endlessly wittering on about something which is irrelevant.

Mr.J is a mathematician, so must be exploiting similar "algebraic manipulation" frequently in his work. It's there large as life in his two chapters and on his blog. Can I infer therefore that he frequently sees

**miraculously appearing terms**in his equations? Of course I can - it's the way mathematical proofs are developed. Mr.J never mentions the word

**flux**(which is ubiquitous in radiative physics) in his two chapters. To do so might imply something physical, and that just wouldn't do. My answer to his question "did it fool you" is "no it didn't, and neither do you".

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