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Monckton on blackbody radiation

Posted By __Joanne Nova__ On December 20, 2011 @ 2:11 am In __Global Warming__ | __Comments Disabled__

I wrote to Christopher Monckton a while back to ask him about a post ** Blackbody – the key error in climate science, **and bless his soul, he whipped off a letter with his detailed answer and wrote it all back to me, saying that other people were asking him about that too. It’s a shame to keep it hidden and high time I brought it out. Usually this topic generates quite a discussion. Though, warning (!) it contains

Huffman asserts there is no measureable greenhouse effect on Venus and Earth and that the temperatures of both planets is determined by their distance to the sun. (Michael Hammer responded to that with an explanation of why we know **There is a Greenhouse Effect on Venus**). My unsophisticated thought was that if distance explained it all, then ergo, albedo would have no effect at all — as in zero — and it seems hard to believe that a black planet and a white planet the same distance from the sun would be at identical temperatures. (It doesn’t gel with my experience of a white car vs black car parked in the baking sun.) – Jo

…Huffman makes a point about albedo himself:

You cannot “correct for albedo” to use the Stefan-Boltzmann equation at the Earth’s surface, because a blackbody by definition has no albedo to “correct” for. This of course was confirmed in my previous Venus/Earth analysis, which showed there is simply no room for an albedo effect upon the long-term mean temperatures in the atmospheres of Venus and Earth

Dear Jo,

* *The blog posting to which you referred me,* Blackbody – the key error in climate science – *has elementary errors.

The posting begins by making the common error of assuming that a blackbody cannot have an albedo. Of course it can. The Stefan-Boltzmann equation accounts for albedo in the simplest possible way: by simply taking it that the fraction of incident radiation that is reflected away by the albedo of the Earth plays no part in the radiative transfer at the characteristic-emission surface. Here is how it’s done.

The characteristic-emission surface of the Earth is not the surface we stand on. It is about 5 km up in the troposphere, varying quite a bit with latitude. At that surface, by definition, incoming and outgoing radiative fluxes balance, and there are no non-radiative fluxes as there are at the Earth’s surface.

Without allowing for albedo, the incoming solar radiative flux *F *at the characteristic-emission altitude is 1368 Watts per square metre, measured by cavitometers on satellites. We must divide this value by 4 to allow for the fact that the Earth is a rotating sphere that presents itself to the incoming radiation as a disc: thus –

(1)

The fraction in (1) simply adjusts for the ratio of the surface area of a disk to that of a sphere.

Now, we allow for the Earth’s albedo *α*, which various authorities tell us is 0.3 –

(2)

In (2), *F *is now the net incoming (and, by definition, outgoing) radiative flux at the characteristic-emission surface. We treat the emissivity *ε* of that surface as approximately unity (this is the usual assumption), and we recall that the Stefan-Boltzmann constant *σ* = 5.67 x 10^{–8} W m^{–2} K^{–4}, we are now in a position to plug the value *F *= 239.4 W m^{–2} into the Stefan-Boltzmann equation (3), so as to discover the mean effective temperature *T *of the Earth at its characteristic-emission altitude –

(3)

Now, to obtain a first approximation to the value of the Planck or zero-feedback climate-sensitivity parameter *λ*_{0}, we treat the two Greek-lettered values as constant, so that we can omit them, and take the first differential (4) of the Stefan-Boltzmann equation, thus –

(4)

Or, retaining the two constants this time, one can do it this way –

(4a)

^{
}

However, although (exasperatingly, and as usual) the IPCC doesn’t explain this, one also has to make allowance for latitudinal variations in the temperature *T *at the characteristic-emission surface. To settle this long-vexed question once and for all, I recently obtained 30 years’ temperature data for 73 distinct zones of latitude in the mid-troposphere from the ever-splendid John Christy and Roy Spencer at UAH, and performed a Herculean calculation allowing for the different areas of the various latitude zones and also for the different mean zenith angles of the Sun at each zone.

The result, after these and other appropriate adjustments: *λ*_{0} = 0.313 K W^{–1} m^{2}. And the IPCc’s value, which one may derive from a characteristically obscurantist footnote on p. 631 of the *Fourth Assessment Report *(2007), is the reciprocal of 3.2, or – er – 0.313. So the IPCC has this one right. It is also quite clear from the above calculations that it has correctly allowed for the Earth’s albedo, contrary to what the posting asserts.

The error that was made here was to assume that a blackbody necessarily has no albedo. One can of course have an astronomical body one part of whose surface is reflective (i.e. possessing an albedo) and part of whose surface is a blackbody. That is the Earth.

** **The posting next asserts that climate scientists are defining what it calls their “effective blackbody” as “inside the solid Earth”. As explained above, all serious climate scientists calculate the effective temperature of the Earth at the characteristic-emission altitude, some 5 km above the Earth’s surface. Since we know by repeated measurements that the temperature lapse rate in the troposphere is very close to linear at 6.5 K km^{–1}, and recalling that today’s mean surface temperature is 288 K and that the characteristic-emission altitude is 5 km up, we can verify that we got our characteristic-emission temperature calculation correct by (5) below –

(5)

And that is close enough to the value we first determined in (3) above.

The posting says that the blackbody system “must” be defined as being outside the atmosphere altogether, away from all non-radiative transports. There is no scientific basis for any such assertion. At the characteristic-emission altitude, well within the troposphere, there is so little non-radiative transport that it can safely be left out of account. And it is from that altitude, and only from that altitude, one optical depth into the atmosphere, that satellites “see” radiation emerging from the Earth’s surface.

The posting asserts, again without scientific foundation, that scientists ought to leave the albedo out of account when calculating the Earth’s effective temperature. Since three-tenths of the incoming radiation is simply reflected back out into Space at visible and ultra-violet (i.e. short to very short wave) wavelengths, it will not interact with greenhouse-gas molecules on its way out, and is therefore correctly omitted from the calculation of the Earth’s effective temperature.

**Error 1, **that a blackbody cannot have an albedo, is then repeated.

I conclude that if one attempts to use the Stefan-Boltzmann equation at the Earth’s surface rather than at the characteristic-emission altitude then one must also take into account non-radiative transports. This is done by Kimoto (2009, Eq. 18) by the simple (some have said “too simple”) expedient of including the non-radiative transports in the radiative-transport equation. What is interesting, though, is that Kiehl & Trenberth (1997), in their celebrated paper on the Earth’s energy budget, assume that the Stefan-Boltzmann equation holds at the surface, at least with respect to the radiative transport. Their diagram of incoming and outgoing fluxes shows three outbound fluxes at the surface: the radiative flux *F*_{rad} = 390 W m^{–2}, the non-radiative evapo-transpiration flux *F*_{evt} = 78 W m^{–2}, and the non-radiative thermal-convective flux *F*_{thc} = 24 W m^{–2}. They admit that they derived the value *F*_{rad} = 390 W m^{–2} by taking it as a “blackbody” value. What they did is shown in (6):

**=390.1 W m ^{–2} **

(6)

But that, of course, assumes that there is a strict Stefan-Boltzmann relation between surface temperature and surface radiative flux. If so, then the value of the Planck parameter is given in (7) –

(7)

Since evapo-transpiration and thermal convection increase with temperature, and evapo-transpiration does so three times faster than the models predict, one could adopt Kimoto’s approach and come to an approximation of the right answer by including the non-radiative transports in *F, *as (8) shows –

(8)

And that would give you a climate sensitivity less than a quarter of the IPCC’s central estimate. Hardly what Kiehl & Trenberth intended, one feels, but that’s what you get if you make an incorrect assumption, as they did, that the SB equation applies strictly at the Earth’s surface.

Monckton calculates just how much the IPCC exaggerate climate sensitivity.

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* Disclaimer: Views expressed in a guest post are those of the author.*

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