Measuring Temperature or Radiation

The comments to a previous post concern the central question of CO2 alarmism if the measured radiation spectra underlying the Kiehl-Trenberth's energy budget describe reality or fiction.

The is a question of measurement technique since the spectra are constructed by reading a certain instrument. Let us consider the principle of such an instrument in the form of an ideal blackbody B in radiative contact with an object O. The rate of radiative energy transfer E between the bodies is given by Stefan-Boltzmann's law

• E = alpha x gamma x T_B^4 - epsilon x gamma T_O^4 

where gamma is Stefan-Boltzmann's constant, alpha is the absorptivity of O, epsilon is the emissivity of O, T_B is the temperature of B and T_O that of O. By Kirchhoff's law alpha = epsilon and normalizing gamma to 1, we thus have

• E = epsilon x (T_B^4 - T_O^4).

Suppose now that we can measure E through the rate of change of the temperature of B since we can measure T_B with B acting as reference thermometer. We thus know T_B and E and want to determine the temperature T_O of O and epsilon x T_O^4 as radiation from O into a background of zero temperature (or the emissivity epsilon) 

We thus have one equation, but two unknowns to determine, so we seem to lack information. But there is one situation allowing the determination of T_O without knowing the emissivity epsilon, namely the case with E = 0, which gives T_O = T_B independent of the value of epsilon. 

In other words, by reading the thermometer B after radiative equilibration with O has been reached, the temperature of O can be read as the temperature of the thermometer. This is the normal use of a thermometer, like a fever thermometer, which gives the temperature after the reading of the thermometer has stabilized. 

To instantly read the rate of change of T_B, that is reading E, and then seek to reconstruct T_O and epsilon seems like shaky business, since the same reading can come from different combinations of epsilon and T_O: epsilon = 1, T_O = 10 and T_B = 1, would give (nearly) the same input as epsilon = 0.0001, T_O = 100 and T_B = 1.

We understand that measuring temperature is easy, because emissivity can be made irrelevant and the temperature T_B is read, while measuring radiation can be difficult because emissivity has to be taken into account and the rate of change of T_B is read.

We understand the the atmospheric radiation spectra are constructed assuming emissivity = 1 from temperature readings, and as such represent fiction rather than reality, because the emissivity can be much smaller than 1, as seems to be the case with atmospheric CO2.