“The influence of IR Absorption and Backscatter Radiation from CO2…”

Kevin Kilty

A recent paper, describing an experiment purporting to be a laboratory model of the Greenhouse effect was mentioned several times recently on WUWT (February 6 and February 20) as one worth reviewing. The paper is open source, and may be found here.

Lately a brief discussion of this paper showed up on several threads on JoNova’s site. This prompted me to look at it in detail. While not saying much about the Greenhouse effect the paper does provide a couple of good lessons about experimental design, the Stefan-Boltzmann law, and peer review. Here is a brief overview.

Apparatus and operation overview

Figure 1, adapted from the paper shows the experimental apparatus. It consists of a box made of bright aluminum foil-covered styrofoam, sealed on its front by a thin EDTA film, and at the back end by nonfoil-covered styrofoam. The EDTA window allows an IR sensor a view toward the rear of the apparatus. This back end has a thin aluminum plate centered on it. This plate is heated by a lamp to a temperature near 100C. It also has a small 6×6  cm window of EDTA to allow a second IR sensor a view forward. The apparatus is divided into two compartments separated  by another EDTA film. Both compartments have a small opening in the top so as to maintain constant pressure irrespective of temperature and each compartment contains a small fan to circulate air vigorously enough to maintain a constant temperature throughout.

Figure 1 Adapted from Seim and Olsen, Atmospheric and Climate Sciences, 2020, 10, 168-185.

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.  

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. The missing IR is presumed to be redirected or reflected toward the rear compartment. This should raise temperature of the rear compartment, and this increasing temperature should return the front exiting radiation to its original value. However, when the experiment is run no increase of temperature of gases in the rear compartment is observed, nor does the back surface of the rear compartment show a temperature increase. The claim is made that this null result casts doubt on the currently accepted explanation of the Greenhouse effect. This null result is bolstered by an energy balance computation being unable to locate any wayward energy transfers.

Analysis of this as an experiment

There are three separate issues to clarify in this experiment. First, there is the construction and calibration of the IR sensors. Second, there is the energy balance calculation which searches for, but cannot locate leaks of energy to explain the null result. Third, there are 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.

Sensor construction and calibration

The sensor is a thermopile built by TE Connectivity (TS105-10L5.5MM thermopile sensor). Its data sheet can be found at the manufacturer’s site. The sensor contains in addition to a thermopile, a highly accurate negative temperature coefficient (NTC) thermistor to aid in building a temperature compensation circuit. It is widely accepted that a small object composed of any material what so ever, and a larger containing enclosure will not transfer net radiant energy between them when they have the same temperature. In fact, it would violate the second law of thermodynamics otherwise. A temperature compensating circuit is needed to force this constraint on the sensor as otherwise ambient temperature of the thermopile will confound its measure of radiant energy. Figure 2, from the manufacturer’s cut sheet, shows the transfer function of this sensor at a 25C ambient temperature. Note that the output of the sensor passes through zero at ambient temperature as it must.[1]

Figure 2 From TE Connectivity cut sheet for the TS105-10L5.5MM thermopile sensor

The authors built an amplifier with a voltage gain of 120 to raise the sensor signal to a level reasonably read with a voltmeter; and they calibrated their instrument by using it to measure blackbody radiation emitted by a blackened iron pan. They describe the process thusly.

“We used a black iron pan, filled with water of temperature 100C and allowed to fall to 15C. We measured temperature of the iron pan with a Fluke 62 Max IR thermometer, and the voltage output of the detectors was measured with a digital voltmeter….We computed the IR energy output using the Stefan-Boltzmann Law.” [emphasis is mine]

We presume that ambient temperature must have been no higher than 15C as this is the lowest temperature obtained in the calibration run. Their resulting transfer function, shown in Figure 3, unfortunately shows a sensor output of 25mV at 15C rather than zero. Thus their sensor is biased, and the bias is nearly 20% of the full range (120mV) they expect to measure — a very large bias at low signal levels, indeed. How this bias came to be is a mystery because they do not fully explain their circuitry construction. It may be an offset voltage amplified by their high-gain amplifier; or it may result from a failure to use temperature compensation available.

Figure 3 from Seim and Olsen, Atmospheric and Climate Sciences, 2020, 10, 168-185

One other problematic issue with this sensor involves its field of view (FOV).  The authors’ expectation is that the FOV is plus or minus 5 degrees, but the manufacturer’s data clearly shows that the full field of view is plus or minus 15 degrees. At least a quarter of the energy falling on the thermopile comes from beyond 5 degrees. Obviously there is a discrepancy between what the authors believe the sensor “sees” and what it actually does. This will lead to problems when the sensor is used with the apparatus when its view is unlike that of the blackened pan used for calibration.

Energy balance

Despite an effort by the authors to perform a thorough energy balance looking for unexpected leaks of energy, no completely credible energy balance is possible for the following deficiencies:

  1. We do know neither the thickness of the EDTA film nor the thermal conduction coefficient of the EDTA film plus air film at its surface. Yet, because the film separates warm gas from ambient air in several places, there must be heat transfer between the compartments or out of the apparatus entirely by conduction through the windows.
  2. If fans are installed in the compartments, then these act to dissipate electrical energy, but this dissipation is not specified.
  3. The openings meant to maintain constant pressure are also potentially sources of infiltration, but no estimate of this is made.
  4. We are told the EDTA film is about 90% transparent to light and IR, but we do not know if the remaining 10% is reflected or absorbed or a combination of both.

One can only conclude that there are many sources of uncertainty in the construction of the apparatus and in the construction and calibration of the sensors. These uncertainties are often additive and may reach a magnitude of 10% each.

Misuse of Stefan-Boltzmann

The Stefan-Boltzmann relationship applies to cavity radiation. A cavity has only a small connection to the outside world just large enough to make measurements of the radiation field inside. It is isothermal and behaves the same independently of what material it is made from.

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 aluminum foil has a low emissivity probably around 0.04. Its whole purpose is to not radiate IR. We don’t know about the EDTA film. 

The authors calculate that at steady state running, with the aluminum plate at 100C and the back surface styrofoam at 46.5C, the total irradiance (emitted power) of this surface is 107W. They use the Stefan-Boltzmann relationship to calculate this. However, taking emissivity of the materials involved into account the emitted power is only 80W.

The front sensor view of this back surface is not limited to a FOV of 5 degrees but is wider and so it captures unknown fractions of blackened aluminum and styrofoam. In fact it may be so wide as to view some of the aluminum covered styrofoam on the sides of the apparatus. This is nothing like the circumstances under which the authors built their calibration curve. The view of sensor 2 deviates even more from the calibration circumstances.

Thus, not only does the calculated irradiance seem in error by about 20% over erroneous use of the Stefan-Boltzmann law, but the known bias of the sensor combined with the issue of the calibration curve not pertaining to a view like that of the back plane of the apparatus, means that all the calculations and measurements are more interesting than they are believable.

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.

One more issue is important. The gas in the front compartment, even when composed of 100% CO2 is not a blackbody. Engineers involved in furnace calculations have developed correlations from experiments by which to estimate the effective emissivity of combustion atmospheres. From these a person can calculate that 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. 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.

Lessons learned

The null result of this experiment seems reasonable, but it says nothing about the Greenhouse effect.

The journal involved, one in the SCIRP family of publications, is peer-reviewed. Yet consider the effort one has to employ to review this article in a technical sense. The reviewer ought to have some expertise in transport calculations, especially radiation transport in enclosures, but also metrology and electronics. It is not reasonable to expect that all reviewers have the time or resources to do a job much beyond making sure a submitted paper meets minimal standards of scholarship. There are now too many papers submitted for the number of people willing to review. The lesson is that even in peer reviewed journals caveat emptor applies.

The authors build confidence in their work along the way with approximate calculations, and one might wonder why this consistency does not trump my alternative findings. I can only answer that there is something like a corollary to Murphy’s law which applies very broadly: There are many wrong ways to approximate and measure something, and they can all be made to agree with one another and with expectations.

Nothing substitutes for a critical, and sometimes brutal, independent review.

Notes:

1-Another way to look at this is to recognize that at equilibrium the sensor gathers radiation through its field of view and at the same time radiates back to its surroundings.

2-As an example a thermograph in Figure 4 below is of a brushed stainless beverage cup with a matte black cowboy icon printed on it. The cup is isothermal but the thermogram shows the printed area to appear much hotter than the brushed stainless. It is all a matter of the effective emissivity of the surface materials. Most of the apparently warm streaks on the cup are the reflections of warm objects in the surroundings.

Figure 4. Photo by K. Kilty.

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April 18, 2021 at 04:41AM