The Greenhouse Effect was simulated in a laboratory setup, consisting of a heated ground area and two chambers, one filled with air and one filled with air or CO 2. While heating the gas the temperature and IR radiation in both chambers were measured. IR radiation was produced by heating a metal plate mounted on the rear wall. Reduced IR radiation through the front window was observed when the air in the foremost chamber was exchanged with CO 2. In the rear chamber, we observed increased IR radiation due to backscatter from the front chamber. Based on the Stefan Boltzmann’s law, this should increase the temperature of the air in the rear chamber by 2.4 to 4 degrees, but no such increase was found. A thermopile, made to increase the sensitivity and accuracy of the temperature measurements, showed that the temperature with CO 2 increased slightly, about 0.5%.
In 1859 John Tyndall [
1) The atmosphere is transparent to short-wave solar radiation that warms the surface of the Earth.
2) The heated soil and water emit long-wave radiation (IR radiation).
3) The IR radiation is captured by greenhouse gases and then sent out (emitted) in all directions.
4) Part of the emitted radiation (back radiation or backscatter) from greenhouse gases returns to the Earth’s surface and contributes to increased surface temperature; the rest is leaving the atmosphere. Humans’ increased emissions of greenhouse gases lead to an enhanced Greenhouse Effect.
This explanation is used by IPCC (the Intergovernmental Panel on Climate Change) and others [
The illustration in
In this simulated atmosphere/ground situation the ground, heated by the sun, is replaced by a warm black painted metal plate. The atmosphere above the “ground” is divided into two chambers, one above the “ground”, filled with air, and one on the top that can contain air or CO2. The heated metal plate emits IR-radiation that either leaves the container through the window on top, or is partly absorbed when CO2 is filled in the top compartment. The absorbed IR
radiation is then emitted in all directions, including backscatter that is returned to the air-filled bottom chamber. A thin window that does not, or very slightly, absorb IR radiation should be placed between the two chambers and on top of the container, indicated by broken lines in the figure. In the experiment, we shall measure the IR radiation and the temperatures in the two chambers. In addition, we will calculate the expected temperature changes in the air-filled bottom chamber, caused by changes in IR absorptions and backscatter.
The motivation for our setup is to create an experiment which could demonstrate the effect of not only doubling the CO2 concentration but to increase it by more than 2000 times.
The theory, used by IPCC to predict the warming of the Earth, is called radiative forcing. Radiative forcing F (in W/m2) is defined by IPCC as: “Change in energy flux caused by natural or anthropogenic drivers of climate change” [
Δ F = 5.35 × ln ( C C 0 ) (1a)
and
Δ T = λ × Δ F (1b)
where ΔF is the increase in CO2 backscatter radiation in W/m2, C is the concentration of CO2, C0 is the reference concentration in preindustrial times and ΔT is the resulting increase in temperature. The constant λ is ca. 0.8. In the IPCC climate report [
In our experiment, the CO2 concentration will increase from ca 0.04% (in air) to close to 100%. Based on Ln(100/0.04) = 7.82, this will increase the forcing to ΔF = 41.9 W/m2 and ΔT to ca 33˚C. However, we do not expect such a large temperature response, since many atmospheric factors influence the constants in Equation (1a) and Equation (1b).
Since we are measuring the small ΔT and ΔF a competing formula is the differential Stefan-Boltzmann law:
Δ T = Δ F 4 σ T 3 (2)
where σ = 5.67 × 10−8 W/(m2K4) and T is the temperature in Kelvin. For temperatures around 300 K gives the factor λ about 0.16. In addition, the length of the CO2 filled chamber should be large enough to provide a substantial absorption of IR radiation. From the Equation (1a) and Equation (1b), we therefore should expect a measurable temperature increase in the rear chamber. This is the core of the climate models, and we wanted to get experimental evidence for the dominating contribution from the CO2. The rear chamber with air should not change during the different experiments (with different gases in the front chamber).
For practical reasons the setup, shown in
The one meter long box, with a volume of 150 liters, is made of insulating 5 cm thick Styrofoam plates. The two chambers are separated by a thin EDTA (Ethylenediaminetetraacetic acid) plastic film that transmits more than 90% of visual light and IR radiation. The window in the front of the foremost chamber was also made of EDTA. The Styrofoam walls of the chambers (except the rear wall) are covered by thin 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 warming a metal plate, painted with heat-resistant, mat black paint, and mounted on the rear wall of the rear chamber. The rear wall, with an area of 0.15 m2, is made from Styrofoam.
The area of the metal plate is 0.036 m2. An increase in backscatter IR intensity with CO2 in the front chamber should then give us measurable changes in temperature of the rear wall and in the air in the rear chamber.
A thermometer, measuring the gas temperature, was placed close to the roof in each chamber and screened from radiation from the metal plate. (The temperature sensor is encapsulated in polished metal that reflects IR radiation).
The temperature of the rear Styrofoam wall was measured with a thermocouple, painted black (in order to absorb IR radiation). To avoid local convection and temperature gradients in the two chambers a small fan with reduced speed is placed in each chamber.
To measure absorption of IR radiation and the backscatter generated by CO2, two IR detectors were constructed and calibrated (IR1 and IR2). The CO2 concentration in the two chambers was measured with a self-calibrating CO2 gauge (ELMA DT-802D. Maximum: 10,000 ppm. Resolution: 1 ppm).
Our measurements of IR radiation should be compared with previous measurements. Data for IR absorption in CO2 can be found in the HITRAN [
The absorption A of IR radiation in the tube closely follows the function
A = 0.0188 × ln ( x ) + 0.1228 (3)
where x is the length in meter of the tube (the Beer-Lambert law). From this function, we estimate that in the 0.7 m long front chamber the IR absorption should be 11.6%.
The two IR detectors IR1 and IR2 use thermopile detectors [
radiation E in W/m2 from a black body source. The detectors and the calibration procedure are described in Appendix.
Assume first that we have air in both chambers. When the back wall starts to heat, the IR radiation from it increases. The Al foil on the walls inside the two chambers will reflect most of the IR radiation out through the front window. The strength of the escaping IR radiation can then be measured by the IR1 detector.
With CO2 in the front chamber, we expect that the IR radiation that is absorbed by the CO2 gas will reduce the amount of IR radiation out the front window. This reduction can be measured with the IR1 detector. Most of the absorbed IR radiation energy will then be returned to the rear wall and absorbed. The strength of this IR backscatter can be measured by the IR2 detector. This added energy will heat the rear wall and this will increase the temperature of the air in the rear chamber, according to the Greenhouse Effect. Without thermal losses we expect the IR output to increase again and stabilize at the same value found when the front chamber was filled with air.
To summarize:
1) We expect a warming effect of the back chamber and rear wall.
2) We do not expect any long term reduction of IR out of the front window.
3) We do expect increased IR density in the rear chamber.
However, we must expect some loss of the absorbed IR energy due to thermal losses through the walls of the two chambers.
In the first experiment we measured the gas temperatures when the black-painted Al-plate on the rear wall of chamber was heated to ca. 100˚C with the 500 W halogen lamp.
The rear wall of the box, surrounding the heated metal, consists of white Styrofoam. In order to check if the rear Styrofoam wall was heated by IR backscatter, a small, black-painted thermocouple was mounted on the wall (screened from radiation from the metal plate).
The results are shown in
IR radiation out of the front chamber window was measured by the IR1 detector, placed in front of the window and pointing at the Al-plate in the rear wall. When CO2 is filled in the front chamber, the IR-output from the plate and out through the front window is reduced, as shown in
From Equation (3) we found that the absorption is 11.6% for a 70 cm long tube. Heating with the black Al-plate (
the window from 413 to 714.5 W/m2, i.e. with 301.5 W/m2 with air in the front chamber. 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 Equation (3).
For comparison the IR radiation from the rear wall was computed, using the Stefan-Boltzmann’s law. For an ideal black body, the Stefan-Boltzmann’s law is expressed as
E = σ T 4 (4)
The area of the Al-plate is 0.036 m2 and 0.114 m2 for the Styrofoam area of the rear wall. The average temperature of the Al-plate is close to 100˚C or 373 K, the Styrofoam rear wall is assumed to have the same temperature as the air (about 46.5˚C or 319.5 K). The total IR radiation from the two sources is 107 W. The area of the front window is 0.15 m2 and the computed IR energy output is then 713 W/m2, i.e. close to the measured value.
Comparing Expected with Measured Temperature Increments from Increased IR RadiationWe have computed how much the change in temperature and IR radiation will be due to air or 100% CO2 in the front chamber.
For temperature computation the Equation (4) yields
T = E / σ 4 (5)
In
Argon is an inert gas that does not absorb IR radiation. When air was replaced by Argon in the front chamber the concentration of CO2 in the chamber was reduced from 660 to about 200 ppm, but the heating curves for air and Argon were still close to identical (see
The missing heating with CO2 might be expected if there are significant thermal losses through the walls of the box, in particular the rear wall. Such losses might attenuate the temperature changes when air is replaced by CO2 in the front chamber. Several modifications were therefore made to reduce thermal losses.
In
that might reduce the heating rate of the gases, it was substituted by a thin, black-painted Al-foil, weighing ca 6 grams, and the heating experiment was repeated. Again, the adding of CO2 in the front chamber gave close to identical heating curves for the two chambers.
When we warm the thin Al-foil the temperature of the foil increases quickly to 85˚C after ca 20 seconds and reaching a maximum value after ca 20 minutes. The average temperature of the plate is close to 100˚C.
The Argon experiment was also repeated when the Al-plate was replaced with the Al-foil. The heating curves (mean of two experiments) again showed near- identical results.
To reduce the thermal losses through the walls the thickness was increased from 5 to 10 cm. In addition, the rear wall with the heating plate was removed and replaced with a 10 cm thick Styrofoam plate. A black-painted tissue paper sheet, weighing 14 grams, was mounted on the inside of the new rear wall. To heat the tissue paper two halogen projectors (without heat filters) was placed in front of the window of the box and focused on the rear wall. The heating was then repeated with air and CO2, but the heating curves were again found to be close to identical for both gases.
In order to be able to measure and control the input heating energy a new heating plate, consisting of an black painted Al plate and power resistors, was mounted on the inside of the rear Styrofoam wall. The AC voltage of the heating plate could be adjusted by a variac and measured with a digital voltage meter. The heating experiment was then repeated with air and CO2, but the heating curves were again found to be close to identical for both gases.
The amount of absorbed IR through the front window, with CO2 in the front chamber, was ca 10% (
From the Stefan-Boltzmann law (Equation (4)), we can compute the expected temperature rise.
We get E(17.9˚C) = 406.0 W/m2 andE(50˚C) = 617 W/m2. E then increases by 211 W/m2. When E(50˚C) increases by 10% or 21.1 W/m2, then Equation (5) gives T = 52.7˚C i.e. an increase by 2.7˚C. This is very close to the measured temperature increment of 2.8˚C, indicating that thermic losses must be small.
We calculated the absorbed energy in each part of our experimental setup during the heating curves by the density, specific heat capacity, etc. given in the Science Data Book [
The IR backscatter was measured with the IR-detector placed behind the box (IR2) during heating with the Al-foil. The result is presented in
Is the temperature increment with CO2 too low to be detected by a single thermocouple? To check this, a thermopile was constructed, consisting of eight serial connected thermocouples and placed on the rear inner wall of the box. The measurement tip of the thermocouples was painted black with paint containing carbon in order to ensure heating by IR radiation. Finally, the voltage signal from the serially connected thermocouples was amplified 50 times. The advantage of this construction, compared to the IR detector used by us, was that the reference connection, with temperature T2, was placed outside the box at room temperature. (The room temperature only increased 0.2˚C during the experiment). The voltage was measured with a digital voltage-meter and found to be 36.5 mV per thermocouple. The CO2 experiment was then repeated and the result is shown in
Each axis in
Many references in the IPCC reports refer to the forcing of increased IR radiation on the temperature. This factor is much discussed [
It could be argued that since we have constant pressure in the chambers, the extra heating due to CO2 backscatter is lost due to extra work done by the gas on the atmosphere. But this work W is the same for all three gases. With constant pressure p it is given by:
W = p Δ V = n R Δ T (6)
where ΔV and ΔT is the change in volume and temperature, n the number of moles and R is the ideal gas constant. Since the expansion of the gases, and the work done by volume expansion, only take place during heating and not at the final steady-state, the computation of expected temperature increase, with CO2 in the front chamber (Section 3.2.1), is assumed valid. In the final steady state the extra energy flow from backscatter IR continues with ca 180 J per minute (20 W/m2 × 0.15 m2 × 60 sec) and should lead to increased temperature.
To measure IR radiation we used a detector containing a thermopile. Both the thermocouple and the thermopile utilize the Seebeck effect [
Δ V = S × ( T 1 − T 2 ) (7)
where S is the relative Seebeck coefficient. In a thermopile, a number of thermocouples are serially connected, thus increasing the sensitivity of the detector considerably.
When the thermopile in the IR detector is heated by absorbed IR radiation its voltage response increases. The detector heats up and increases its voltage when irradiated by IR from CO2. So why did the 8-element thermopile we constructed give only a very small response to increased IR backscatter? The answer lies in the construction of the IR detector. Its thermopile is encapsulated and the air surrounding the detector capsule cannot remove heat from it, as it happens for the one we constructed. For the IR detector used by us, the temperature sensitivity was 11 μV/˚C, but for the 8-element thermopile the sensitivity was only ca. 1.2 μV/˚C. The reason is that the IR detectors are equipped with a large number of thermocouples. A Google search on the Internet revealed detectors that contained between 80 and 200 thermocouples! So the engineers, constructing these devices, seem to know that the heating response is very small and that the number of thermocouples needs to be large.
The results of our study show the near-identical heating curves when we change from air to 100% CO2 or to Argon gas with low CO2 concentration. Nevertheless, we observed absorption of IR radiation in the front chamber. We also observed the increased radiation density in the rear chamber due to the backscatter from CO2. The change in observed backscatter radiation should give us a measurable temperature increase of 2.4 to 4 K by using the Stefan Boltzmann law. But we only observe a very slight temperature increase due to CO2 backscatter. This indicates that heating, due to IR backscatter from CO2, is much less than what is assumed from the Stefan Boltzmann law or from the forcing Equation (1a) and Equation (1b). The near-identical heating curves for all the three gases indicate that the thermal energy transfer is only driven by the temperature of the back wall of the rear chamber. Without extra heating of the walls in the rear chamber, the air temperature cannot increase. These findings might question the fundament of the forcing laws used by the IPCC. Another possibility is that our setup has unexplained heat losses that cancel the effect of the increased backscatter IR and prevent higher temperatures in the rear chamber, but after testing this and finding only slight losses, we do not see that this could be the case.
We would like to thank Prof. Øyvind Grøn (Institute of Physics, University of Oslo) for careful reading of the manuscript and fruitful comments.
The authors declare no conflicts of interest regarding the publication of this paper.
Seim, T.O. and Olsen, B.T. (2020) The Influence of IR Absorption and Backscatter Radiation from CO2 on Air Temperature during Heating in a Simulated Earth/Atmosphere Experiment. Atmospheric and Climate Sciences, 10, 168-185. https://doi.org/10.4236/acs.2020.102009
To measure IR radiation we used thermopile detectors. We used a wide-band detector with a close to constant response from 3 to 24 µm [
The calibration procedure, performed in room temperature, was as follows:
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˚C and allowed fall to 15˚C. (The blackness of the iron pan was created by burning in a layer of oil, forming a layer of black carbon). The temperature of the pan was measured with a Fluke 62 Max IR thermometer and the voltage output of the detectors was measured with a digital voltmeter. See FigureA1. In addition, we computed the IR energy output E (W/m2) from the pan, using Equation (4) (the Stefan-Boltzmann’s law). The result is shown in FigureA2.
A2. Increasing the Accuracy of the MeasurementsTo obtain high precision in the temperature measurements we must control external factors that might lead to deviating results. One is the AC voltage that may vary during heating. This will change the energy output from the halogen lamp. The AC voltage was monitored/adjusted by using a digital voltmeter with high resolution. We also measured the variation in the output of the lamp when the AC voltage varied about 5% and found that if the variation was less than 1% a very slight variation was found in the light output from the lamp. If the voltage fluctuated more than 1% the experiment was repeated.
The other main factor that will influence the measurement is a variation in room temperature between the two measurement series (first with air in the front chamber, then with CO2 or Argon). If the room temperature varied the temperature curves altered. As control two measurements were made where we changed the room temperature 0.9 degrees. See FigureA3.
By adding the difference of the two-room temperatures to the lower curve in FigureA3 gave a common start value for both curves and two near-identical curves with a common end temperature. See FigureA4. In the experiments, this adjustment was made if the room temperature varied, but only if the variation was less than one degree. Normal variation was about 0.4˚C.
A3. The Kinetic Energy AccountFrom the specific heat capacity, the mass of the gases and material used and the temperature increase of the gases in the two chambers, we calculate the heat absorbed [
| Density (kg/m3) | Mass in front chamber (kg) | Mass in rear Chamber (kg) | Specific heat capacity Cp (J/kg × K) | Heat (J) absorbed in Front chamber ΔT = 10K | Heat (J) absorbed in Rear chamber ΔT = 25K | |
|---|---|---|---|---|---|---|
| Air | 1.293 | 0.136 | 0.058 | 993 | 1348 | 1444 |
| CO2 | 1.977 | 0.208 | 0.089 | 834 | 1731 | 1855** |
| Argon | 1.784 | 0.187 | 0.080 | 524 | 982 | 1052** |
| Styrofoam 1 cm* | 15.6 | 0.175 | 0.093 | 1300 | 1137, ΔT = 5 K | 1209, ΔT = 10 K |
| Al-plate heating | 0.274*** | 880 | 6028, ΔT = 25K 24,112, ΔT = 100K | |||
| Al-foil heating | 0.006*** | 880 | 132, ΔT = 25K 528, ΔT = 100K | |||
| Al-foil all walls | 0.050*** | 880 | 616 (weighted average from both chambers) | |||
*The temperature of the outside walls increases ca 1˚C, partly due to increased room temperature. Based on the temperature gradient in the walls we assume that this is equivalent to heating about 1 cm of the wall material in the 30 minutes to ΔT = 5 K in the front chamber and 10 K in the rear chamber. **If those gases were also placed in the rear chamber, included for comparison only. ***Measured weight of material.