What Does a Pyrgeometer Measure?

A pyrgeometer is presented as follows on Wikipedia:

• a device that measures the atmospheric infra-red radiation spectrum that extends approximately from 4.5 µm to 100 µm.

A pyrgeometer consists of the following major components:

• A thermopile sensor which is sensitive to radiation in a broad range from 200 nm to 100 µm

• A silicon dome or window with a solar blind filter coating. It has a transmittance between 4.5 µm and 50 µm that eliminates solar shortwave radiation.

• A temperature sensor to measure the body temperature of the instrument.

• A sun shield to minimize heating of the instrument due to solar radiation.

The thermopile measures a voltage U_emf and then computes incoming radiance E_in according to the formula

where sigma is a known constant and T the measured temperature of the pyrometer with sigma x T^4 = E_out outgoing radiance and S is a sensitivity factor determined by calibration.

A thermopile is described as follows on Wikipedia as:

• an electronic device that converts thermal energy into electrical energy. It is composed of several thermocouples connected usually in series or, less commonly, in parallel,

with a thermocouple 

• consisting of two conductors of different materials (usually metal alloys) that produce a voltage in the vicinity of the point where the two conductors are in contact. The voltage produced is dependent on, but not necessarily proportional to, the difference of temperature of the junction to other parts of those conductors.

The input U_emf to the computation of the radiation E_in  is thus a voltage, and not energy, a voltage depending on the difference of the temperature of the radiating object and the instrument.

The pyrometer thus effectively measures the temperature of a radiating object, and then through a very simple formula, with a constant obtained by calibration, reports radiance. 

I show in How to Fool Yourself with a Pyrgeometer that the reported radiance is fiction, obtained from temperature by a simple formula. But reality is not that simple.

The key step to the fiction, is the translation of the measured voltage to fictional energy through the fudge factor S.

The problem with the relation E_in - E_out = U_emf/S with U_emf the measured voltage, is that what is de facto measured is a difference, while the quantity of interest E_in = E_out + U_emf/S is critically depending on E_out, which is not measured and thus unknown and as such subject to speculation, and on the constant S supposedly being determined by some form of calibration. Altogether, E_in may be more fiction than reality.