Infrared Imaging: Temperature vs Radiance

Here is some input to the ongoing discussion of IR measurement of temperature vs radiance.

Omega.com on Infrared Temperature Measurement Theory:

• An infrared thermometer measures temperature by detecting the infrared energy emitted by all materials which are at temperatures above absolute zero, (0°Kelvin). The most basic design consists of a lens to focus the infrared (IR) energy on to a detector, which converts the energy to an electrical signal that can be displayed in units of temperature after being compensated for ambient temperature variation.

Infrared Thermal Imaging by Vollmer and Mullman:

• The infrared detector or the detector system acts as transducer, which converts radiation into electrical signals. It forms the core of an IR imaging system. The quality of this transduction determines the performance of the imaging system to a great extent. 
• Infrared detectors can be separated into two groups: photon detectors and thermal detectors. 
• In photon (or quantum) detectors, a single-step transduction leads to changes of concentration or mobility of the free charge carriers in the detector element upon absorption of photons from the infrared radiation. 
• Thermal detectors can be treated as two-step transducers. First, the incident radiation is absorbed to change the temperature of a material. Second, the electrical output of the thermal sensor is produced by a respective change in some physical property of a material (e.g., temperature-dependent electrical resistance in a bolometer).

We understand that a two-step thermal detector (used for LWIR), 

• first detects the temperature of the object by absorbing incident radiation from the object into a detector until radiative equilibrium, with the detector at start at a lower temperature than the object, and reports a temperature difference vs the background temperature of the instrument, 
• then converts the temperature difference to an electrical signal which is calibrated to report the detected temperature of the object.

In short, a thermal detector reads temperature and not radiance. It is important to understand that the electrical signal is not generated by a flow of incoming photons, but by a temperature difference.
This may be a common misconception.

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. 

Measuring Temperature vs Emissivity

In a previous posts I showed that an ideal blackbody 1 of temperature T_1 can be used as a reference thermometer capable of measuring the temperature T_2 of a given body 2 through radiative equilibrium:

• alpha_2 sigma T_ 1^4 = beta_2 sigma T_2^4

where alpha_2 is the absorptivity of 2, epsilon_2 is the emissivity of 2, and 

• alpha_2 sigma T_ 1^4 is the energy absorbed by 2,
• beta_2 sigma T_2^4 is the energy emitted by 2.

Knowing that alpha_2 = epsilon_2 makes it possible to assign the temperature T_2 = T_1 to the given body from radiative equilibrium with the reference blackbody thermometer showing T_1.

Is it possible to also measure also the emissivity epsilon_2 (=alpha_2)? In the setting of the communicating vessels above, this means to measure the rate of the flow between the vessels as compared with measuring only the equal levels representing equal temperatures.

This would seem to equire non-equilibrium measurement  (since equilibrium only gives the temperature) recording the change of temperature of 1 while in radiative contact with 2 with T_2 different from T_1. Assuming T_2 > T_ 1, the rate of energy transfer from 2 to 1 would be

• epsilon_2 sigma T_2^4 - alpha_2 sigma T_1^4

which could be measured as a rate of change of T_1. Would this allow to determine epsilon_2 (= alpha_2)? Not easily, because we have two quantities to determine, epsilon_2 and T_2, but only one condition, the rate of change of T_1. To sum up:

• to measure temperature is easy (by equilibrium)
• to measure emissivity is hard (by non-equilbrium).

This directly connects to the previous post. Lacking measurement of emissivity, it may be tempting to assume that it is equal to 1, which may mean fooling yourself.

GHE: Elephant Discovered by Microscope

Let me sum up the two previous posts to make the argument clear. The crucial observations come from an infrared satellite thermometer in radiative contact with the Earth + atmosphere, which selectively can measure the temperature of different frequencies. Reading of the infrared thermometer shows the following temperatures:

1. 220 K for wave numbers 600 - 800 (attributed to the trace gas CO2 at the tropopause)
2. 288 K for wave numbers 800 - 1200 (attributed to the Earth surface)
3. 255 K for wave numbers below 600 (attributed to water vapor at 5km altitude). 

From these temperature reading the above radiance spectrum is constructed using Planck's law

• R(n) ~ T n^2

where R(n) is the radiance in W/m2 per unit of frequency, n is the frequency (~ wave number) and T the temperature (common for all frequencies).

The GHE is supposed to be the ditch in the radiance curve for wave numbers 600 - 800, which results from the drop in temperature from the reading of 288 K attributed to the Earth surface with a transparent atmosphere in the range 800 - 1200 of the atmospheric window, to the 220 K attributed to CO2 at the tropopause in the range 600 - 800 of absorption/emission of CO2.

Visibly, the drop in temperature from 288 to 220 K and the ditch in the spectrum in the range 600 - 800, is most substantial and hence the GHE must be most substantial, even if it is the effect of a trace gas. Right?

The key to the GHE is thus the reading by the infrared thermometer of a temperature of 220 K of the trace gas CO2. The thermometer could be the Nimbus 4 michelson interferometer first flown in 1970.

The thermometer reads the temperature of a radiating body from radiative equilibrium in the frequency range of the radiation of the body, and the thermometer can be designed to have a very narrow range allowing the selective reading of a specific frequency. The absorption/emission spectrum of CO2 has a very narrow spike at a wave number of 666 (wave length 15 micrometer) as seen in the following absorption spectrum:

    

Now, tuning the thermometer to the frequency of the CO2 spike makes it possible to read a temperature of atmospheric CO2 even if the concentration is very small, and increasing the sensitivity of the thermometer may compensate for any decrease of CO2.

In other words, even with a vanishingly small presence of CO2 in the atmosphere, a sufficiently sensitive thermometer would be able to report a temperature of 220 K in the range 600 - 800, as the evidence of a powerful GHE.

Evidently the Nimbus 4 thermometer was sensitive enough to report in 1970 the temperature of the atmospheric trace gas CO2 (390 ppm = 0.039%) to be 220 K in the troposphere.

This opened to the CO2 global warming alarm based on the argument that even if CO2 is a trace gas, it has the power of changing the climate of the Earth, with the evidence being the visible ditch in the radiance spectrum documented by the reading of the Nimbus 4 thermometer.

But the ditch in the radiance spectrum is constructed from a selective reading of the temperature of CO2 and may not represent reality, only the reading of a vanishingly small effect by a very sensitive thermometer.

The discovery of the GHE is thus directly connected to the use of the sensitive Nimbus 4 thermometer:

• The major effect of atmospheric CO2 is evidenced by a very sensitive instrument, as if an elephant is discovered by a microscope!    

PS Notice the connection with How to Fool Yourself with a Pyrgeometer. In both cases, it is the temperature which is measured and the radiance is computed. Recall that using an ideal blackbody as thermometer, allows the determination of the temperature of a body at distance without knowing the emissivity (=absorptivity) of the body: If the thermometer heats up then the body has a higher temperature, and if the thermometer cools then the body has a lower temperature. In other words, temperature can be measured at distance, but determining radiance requires emissivity which in general is unknown.