By Thorstein Seim and Borgar T. Olsen

A review in WattsUpWithThat was performed on our paper by Kevin Kilty. It is found here. The reviewer´s criticism of the paper was summed in 3 points:

  1. The construction, calibration and use of the IR sensors.
  2. The energy balance calculation which searches for, but cannot locate leaks of energy to explain the null result.
  3. The many explicit and implicit uses of the Stefan-Boltzmann formula which are erroneous, and which cast doubt, not on the Greenhouse effect, but on the null result here.

We will try to answer his criticism and add more of the experimental details that he requests. But let us first make a summary of the experiment.

The experiment

The purpose of the simulated earth/atmosphere experiment was to a) be able to measure IR radiation, b) to reduce thermal energy losses to the surroundings and c) to measure temperature more accurately.

The experimental setup is shown in Figure 1: The front camber was added in order to separate the CO2 gas from the air in the rear chamber. This reduces heat loss from the rear chamber through the two windows due to heat conduction.

Figure 1.  Experimental setup.

The one meter long, 50 cm wide and 30 cm high box, with a volume of 150 liters, is made of insulating 5 cm thick Styrofoam plates. The two chambers are separated by a 0.03 mm thin transparent plastic film. The window in the front of the box was also made from this film. The inner walls of the chambers (except the rear wall) are covered by thin, polished Al-foil. The Al-foil reflects most of the IR radiation and thereby reduces the heat loss through the walls. The length of the rear and front chamber is 30 and 70 cm, respectively. IR radiation was produced by heating a black-painted metal plate (or a thin, black painted Al-foil) to 100 oC by a 500W halogen lamp. A thermometer, measuring the gas temperature, was placed close to the roof in each chamber and screened from direct radiation from the heating plate.

An IR radiation detector is located in front of the window on the box (IR1). Another detector is placed behind the box (IR2) and measures IR backscatter radiation via a 6×6 cm window in the rear wall. To measure the heating of the inside of the rear Styrofoam wall with high accuracy, eight serial-connected and black-painted thermocouples was placed on the rear wall.

To avoid local convection and temperature gradients in the two chambers, a small fan with reduced speed is placed in each chamber. Energy input to the fans was small, only 0.6 watts. Since the gas expands during heating, each chamber has a small 5 mm aperture (covered with a piece of plastic) in the “roof” to avoid increasing the pressure. To check if infiltration from the surrounding air changes the amount of CO2 in the front, the CO2 level was inspected after the experiment. The chamber was still filled with CO2.

Construction, calibration and use of the IR sensors

To measure IR radiation and the backscatter generated by CO2, we constructed two IR detectors, using wide-band (3 to 24 μm) thermopile circuits with a nearly flat frequency response.

Calibration: To obtain a radiation spectrum close to that of a black radiator, we used a black iron pan, filled with water of temperature of 100 oC and allowed the temperature to fall to 15 oC. The measured relationship between the temperature of the radiating source and the output of the detector (in mV), is shown in Figure 2:

Figure 2. Temperature calibration.

We see that the relationship is non-linear, not linear as expected from the Seebeck effect. Instead, we find that the voltage response depends linearly on the energy density of the radiation from the IR source. We computed the IR energy density output E (W/m2) from the pan, using the equation E = σT4 (the Stefan-Boltzmann’s law) where σ = 5.67 *10-8 W/(m2K4) and T is the temperature in Kelvin. The result is shown in Figure 3.

Figure 3. IR radiation calibration.

Getting a linear relationship supports the assumption that we can use the S-B equation to quantify IR radiation with the detector. But the reviewer pointed out that the IR source is not a perfect black body, and the emitted IR radiation might then be slightly lower than indicated by the S-B law (probably reduced by ca. 5%).

The reviewer also pointed out that there was a voltage offset of ca 20 – 30 mV in the detector circuit output. This offset is very small, compared to the operating range of the IR detector of more than ± 5 volts. The circuit used is a well-known one, f. inst. suggested by Hamamatsu.

The reviewer writes: “The sensor contains in addition to a thermopile, a highly accurate negative temperature coefficient (NTC) thermistor to aid in building a temperature compensation circuit”.

We were warned against combining the NTC and the thermopile circuit to compensate for variation in device temperature. It is much better to make separate circuits for the thermopile and then do the temperature correction in the computing procedure.

FOV (field of view)  

The FOV of the detector is shown in Figure 4. A common way of defining the FOV is to use the half-angle, i.e. the value where the sensitivity is reduced to 50% of the maximum value. Figure 4 shows that the half-angle is close to ±5 degrees. At ±10 degrees ca 98% of the FOV is included.

With the length of one meter of the box the detector IR1 “sees” a circular area with a diameter of 35 cm, covering the heating plate and most of the rear wall. When the detector is placed in front of the window it then “sees” a 35 cm circular area of the 30 x 50 cm rear wall. The complete metal plate is “seen” within the half-angle FOV.

When the detector IR2 is measuring IR radiation from the interior of the box, it mainly “sees” the front chamber where the heated gas and windows radiates. The radiation is homogenously distributed across the two chambers, so the measurement situation is similar to that used during calibration.

Figure 4.

As the reviewer points out the IR1 detector “sees” more than the heating plate, but the plate covers the main part of what the FOV measures.

Temperature measurements

The temperature increase in the two chambers during heating was equal (within the measuring accuracy) with air or CO2 in the front chamber. See figure 5. This is the most important result in our study.

Figure 5. The heating of the air (with ca 400 ppm CO2) in the rear chamber is shown (upper curve). The curve is nearly identical when air (black dots) is replaced with close to 100% CO2 (red dots) in the front chamber. The heating of air (grey dots) and CO2 (purple dots) in the front chamber also follows a common heating curve for both gases. Average values from five measurements are shown.

The reviewer seems to misinterpret Figure 5:

“This experiment is now repeated with the front compartment filled with 100% CO2. Now emitted IR radiation from the aluminum plate is partially absorbed by CO2 raising the temperature of the front compartment to around 33C. This causes radiation passing through the front window to drop temporarily”.

This is definitely not what we say. The back chamber heats up from 20 oC to 46 oC (upper two curves) and in the front chamber from 20 oC to 32 oC (lower two curves). The point is that the curves are identical for plain air and for 100% CO2 in the front chamber. This was surprising to us, since NASA (and Al Gore) claimed that we should have extra warming from 100% CO2. Also, the radiation passing through the front window does not drop temporarily but approaches a constant value. See figure 6.

The missing IR is presumed to be redirected or reflected toward the rear compartment”.

We measure, not presume, that CO2 IR radiation is redirected or reflected toward the rear compartment.

IR measurements

The IR1 detector measured reduced IR output through the front window with CO2 in the front chamber.

Figure 6. Absorption of IR radiation. Range: 2.5 – 20 µm. Heating is done with the Al-plate.

The detector is pointing at the center of the 100 oC heating plate. With CO2 in the front chamber the IR radiation decreased 29.8 W/m2 or ca 10%. This is close to what we find from the HITRAN data-base, i.e. 11.6% for a 70 cm long tube. The slightly lower measured IR walue might be due to the fact that the detector FOV is slightly larger than the heating plate. Anyway, an error of a few % will not influence our results and conclusions in any significant way.

To find how much IR radiation is leaving trough the front window, we need to know how much it varies at different positions. For this we used a thermopile detector without a lens, giving it a wide FOV. The detector was used to measure IR output along the 50 cm wide front window. The spectral sensitivity is a narrow band in the 4 μm region where CO2 absorbs/emits IR radiation. The result is found in figure 7, showing that the output is close to constant, with roughly ±4 % variation.

Figure 7. IR output distribution along the front window.

The IR2 detector measured increased IR radiation hitting the rear wall with CO2 in the front chamber. See figure 8.

Figure 8. Backscatter (increased IR radiation measured by IR2), received by the rear wall of the box, increased 17 W/m2 with CO2 in the front box. Heating is done with the Al-foil.

The IR2 detector “sees” mainly the IR reflected from the two windows and the gas within the two chambers. The distribution of reflected IR is relatively homogenously distributed in the chambers, verified by figure 7. The measurement situation is therefore not very different from that used to calibrate the detector.

The reviewer have some objections:

“When the apparatus is in operation the aluminum plate at 100C radiates IR and causes the rear compartment to reach a steady temperature of about 46C. The authors “compute” the irradiance of the back surface using the Stefan-Boltzmann law.  When the front compartment is filled with air all of this “computed” IR power is supposed to exit the front window”. 

What we do: We use the calibrated IR detector IR1 to measure the amount of IR leaving through the front window, with air and then with CO2 in the front chamber. We find that more IR energy is absorbed in the box with CO2 in the front chamber. We use the calibrated IR detector IR2 to measure the amount of IR hitting the rear wall. We find that more IR energy is received by the rear wall with CO2 in the front chamber.

Misuse of the Stefan-Boltzmanns law?

Review comment:

“The apparatus here is not a cavity. It is transparent on one end and partially so on the other. Having a substantial fraction of its surface transparent means that placement of materials and their detailed radiation characteristics matter.[2] The first order of approximation to IR radiation from something that is not a cavity, and not isothermal, is to use the Stefan-Boltzmann law, but to assign appropriate emissivities less than 1.0 to different materials. The blackened aluminum radiator has an emissivity close to 1.0. It is perhaps 0.96, but the bare Styrofoam is far from black at IR wavelengths. An accepted estimate of emissivity of this material is 0.60; i.e. at any temperature it will radiate only 60% as strongly as the Stefan-Boltzmann law predicts”.

The reviewer states that we must include the emissivity ε in the S-B equation to get the correct relationship between temperature T and IR energy flow E:

E = εσT4

We are in an advantageous situation since we can measure the IR radiation and the temperature of Styrofoam when it is heated! This was done and we found that, in our experimental setup, the value of ε was measured to be 1.0 ± 0.025, not 0.6! So maybe the chambers behave a bit like a cavity after all… This result also negates the criticism of using the S-B equation in the calibration procedure.

Energy balance

Under Energy balance the reviewer claims that we have energy loss. Yes, of course. The radiation and thermal energy is flowing from the back wall through the front window (like IR from the earth surface to the space). After 30 minutes a close to steady state was established. IR energy from CO2 in the front chamber is partly lost through the front window, partly returned to the rear chamber. The point is that we do not observe any extra warming in the rear chamber despite of the increased level of IR radiation measured there. This is why we say that the back scatter heating theory might be wrong.

Energy content in gases

The reviewer presents an alternative theory:

 “An atmosphere containing 70 cm of 100% CO2 at a pressure of 100kPa has effective emissivity of about 14%. Once this gas absorbs its limit of 14% of IR from the back compartment (i.e. 14% of 80 watts) and reaches an equilibrium temperature it does not reradiate this backward, but rather in all directions. It is reflected many times from the aluminum foil, with 4% being absorbed with each reflection, some passes out the front EDTA window, some passes the intermediate EDTA window and reaches the rear compartment. This could easily be only 10% of what had been absorbed in the front compartment”.

It seems that the reviewer believes that the energy just disappears through the walls and windows. He suggests that only 10 % of the energy flow that has been absorbed by CO2 in the front chamber reaches the rear compartment, which is ca 2W/m2 of 20W/m2. However, we measure an increased energy flow of 17 W/m2, not 2W/m2, returned to the rear chamber,

“The gas in the rear compartment contains so little CO2 that its emissivity (which equals its absorptivity) is probably in the neighborhood of only 1%. Thus, the null result of this experiment, rather than being a surprise, should be entirely expected”.

It is correct that the air (as well as the windows) absorbs (and emit) IR radiation, but the absorption in air is much larger than 1%. This was tested by us in a 30 cm long box Styrofoam box with a single window. The IR emission from the air in the box increased linearly with temperature in the 15 – 35 oC range. The increase of IR emitted by the air was significant, about 30% of the increased radiation from the Styrofoam walls. (The relative humidity of the air was ca 30 – 35%).

By measuring IR emission with/without the window we found that roughly 30% of the increase in the measured IR was emitted by the window. Since the temperature of the  windows are the same with air and CO2, the IR contribution from them are also equal.

In Figure 8 the amount of IR radiation emitted back to the rear wall is shown, with air in both chambers (black circles). This is IR radiation received from the heated air and the heated windows. The measured IR increment is ca 65 W/m2, while the increase with CO2 in the front chamber is 17 W/m2, or an increase of about 25%. The radiation absorbed by the air is re-emitted in all directions and reflected by the Al-foil walls, with some absorption. By adding CO2 in the front chamber, less of the IR from the heating plate leaves the box through the front window. The IR2 detector shows that the IR level inside the rear chamber increases significantly, and remains high!

A final critical review comment:

“One additional error in applying the Stefan-Boltzmann law occurs in the translation of the calibration transfer function to an irradiance value. The calculation mentioned in the quotation about the calibration procedure implies a one-way transfer from the blackened pan to the sensor, when in fact the transfer is two way between the sensor and pan”.

Theoretically this could lead to an error, but it is too small to be measurable. The pan, filled with water, weighs 7 kilo, while the small detector weights ca 200 grams. It is placed only a few seconds in front of the pan and removed after the IR measurement is performed. The temperature of the detector is close to that of the surrounding room. The detector box is made of aluminum. When the measurements are done the box mainly reflects IR from the room, which is what the black pan “sees” between measurements!

Lessons learned

All of the reviewer´s statements about misuse of the S-B law has been rejected.

We were able to measure IR radiation with an accuracy of ±2.5 %.

IR backscatter from CO2 in the front chamber to the rear chamber does not increase the temperature of the rear wall and the air in the chamber, as assumed by the climate models.

via Watts Up With That?

May 15, 2021