Source: email communication
Psychrometric chart use to understand warming from CO2 - Reply to Ferdinand Engelbeen
Douglas Lightfoot and Gerald Ratzer
July 28, 2024
Here is a direct quote from Ferdinand Engelbeen’s message of April 21, 2024.
“As said now several times, there is no error in your calculations or methods, that is absolutely not the problem with your work. The problem is that you make a conclusion that can't be taken from what you have done.”
Ferdinand considers the warming effect of CO2 to be controlled by infrared radiation (IR). He thinks that the radiation absorbed by CO2 controls the Earth’s temperature. Although he says nothing is wrong with our work, he dismisses it as irrelevant. We do not think the work of the scientists who built the basis for the psychrometric chart invented in 1904 and our work that supports it is irrelevant. The psychrometric chart has been proven for 120 years.
The basis for the psychrometric chart does not depend on CO2's radiation characteristics. The warming effect of CO2 is too small to be detected, so it is not in the chart.
The basis for Ferdinand’s insistence that radiation absorbed by CO2 is the most important factor is based on the cross-section of CO2. The crosssection of CO2 that absorbs radiation from the Sun increases by one million times between wavelength 11.19 and 19.03 micrometers, a millionth of a meter, with the maximum at 15 micrometers (670 wavenumber, cm-1). There is controversy over whether or not this is real and can affect the undetectable warming caused by CO2. The figure below is the basis for Ferdinand’s assertions. The wave number at 670 (the peak) equals 15 micrometers. (Try to think of what would happen if the warming effect of
CO2 were significant in the range of 500 to 850 wave numbers, and this warming increased by one million times and absorbed one million times as much IR as possible. We would probably be able to see something significant.)
A.
Because of this figure, Ferdinand assumes that the dip in the radiation from Earth, as shown in Figure B, is caused by CO2.
The wavelengths of CO2 and water vapor overlap at 15 micrometers and around it, as shown in Figure B below. There is no method of determining the amount of radiation from either water vapor or CO2.
Figure B.
Figure
The instrument on the satellite cannot determine how much of the
wavelength at 15 micrometers came from water vapor or CO2.
Thus, the dip labeled CO2 in the upper part of the figure is suspect. There is no reason to believe that it is caused by CO2.
The psychrometric chart would be wrong if the dip were caused by CO2. However, practical experience has proved the chart to be correct. The scientific basis for the psychrometric chart could not detect warming by CO2.
The evidence so far should be adequate to dismiss the undetected warming of the atmosphere by CO2. The radiation absorbed by CO2 is irrelevant.
We can further show that CO2's warming is undetectable by examining the cross-sections of CO2 and HITRAN.
The cross-sections of CO2 and water vapor have been measured separately. When the two gases are mixed, another cross-section measurement is made. The effect of each gas in the mixture is then determined using HITRAN.
The HITRAN results and the actual measurements are in Figure C below. The HITRAN results are on the left, and the measurements are on the right. I have been unable to determine how HITRAN treats CO2. It is most likely the IPCC concept that the warming effect of CO2 is logarithmic. If so, there is a problem in HITRAN because the warming effect of CO2 is a straight line.
Figure C.
It is essential to note the ratio of water molecules to CO2 molecules in the three sub-figures. Ferdinand implies that he accepts these ratios.
In the upper sub-figure, there are 83.8 to 107.4 molecules of water for each molecule of CO2. Thus, it is highly likely that the dip is caused by water vapor and not CO2. The CO2 stays the same in the middle sub-figure at one molecule, whereas water vapor is 83.8 to 40.4 molecules. In the bottom sub-figure, one molecule of CO2 and 0.8 to 40.4 molecules of water vapor. These sub-figures change as water vapor changes and the CO2 stays the same. There is no doubt that CO2 has little, if any influence.
Now, for the proof that warming caused by CO2 is a straight line.
The information available since November 2023 shows that the warming effect of CO2 is a straight line, not a logarithmic one.
Figure 1 from Reference [1] was made from the best information available in 2014 when it was constructed. The known information at the time was:
1. The IPCC logarithmic section of the curve in Figure 1 is from 275 to 375 ppm, i.e.,
ΔRF = 5.35LN(C/Co) . . . . . . . . . . .(1).
2. The curve must start at zero. The RF at zero CO2 is zero. This part of the curve runs from zero to 278 ppm.
3. The curve from 378 upwards reaches an asymptote at 654.6 ppm. As the number of molecules per cubic meter of CO2 increases, each molecule's warming effect will fall and ultimately become zero.
A quadratic curve that fell exactly over the logarithmic section started at zero and reached an asymptote at 654.6 ppm, which was determined by trial and error. The equation is:
RF = -0.00002480C2 + 0.0323109C .
.(2)
The Figure 1 curve showed that the maximum radiative forcing of CO2 was about 10.5 W m-2. A sine curve also satisfies the requirements and gives the same result. Similar figures made popular the erroneous concept that CO2's
Figure 1 This is Figure 4 from Reference [[i]]
warming was close to its upper limit.
While we relied on Figure 1 as our primary reference until November 2023, our understanding evolved with a new study titled The Sun and the Troposphere Control the Earth’s Temperature [2]. This study revealed that the warming effect of CO2 is seen in dry air as a straight line, while that of moist air is curved. See Figure 3 below.
In Figure 2, dry air constitutes all of the components of the Earth's atmosphere except water vapor, which includes all of the greenhouse gases, including CO2. Each of the greenhouse gases in Figure 2 is above its boiling point and, therefore, acts as an ideal gas, including CO2.
The ideal gas law is:
Where n is the number of moles of the gas, and R is the universal (or perfect) gas constant [3]. There are 8.314 Joules per degree Kelvin per mole.
At constant pressure, the volume of CO2 is proportional to the temperature (T). As the volume is proportional to the weight of CO2, i.e., a straight line, it is evident that its warming effect is also a straight line. Thus, these two methods show the warming effect of CO2 is a straight line.
Figure 2. Enthalpy of dry air vs. temperature for 240 measurements of temperature and relative humidity
Figure 3. The results of 400 Humidair calculations based on temperature and relative humidity measured in groups of 20, six hours apart over five days.
The equation starts at almost zero and reaches an asymptote at 128.7 kJ at 29.26oC.
The curve in Figure 3 is startlingly similar to that in Figure 1, including the quadratic equation.
Y = -0.004x2 + 1.0298x - 37.042 . . . . . . . . . . . .(4)
The blue line is the trendline inserted by Excel. Note that the R2 = 0.984 in Figure 3 is a high correlation. There is no doubt in Figure 3 that the curve is about water vapor, whereas the curve in Figure 1 is supposed to show that it is about CO2, although it is virtually exactly like the water vapor curve.
The enthalpy of CO2 in dry air is selected as zero at -37.04°C because this temperature is used as a reference point for calculating enthalpy. In thermodynamics, setting a substance's enthalpy to zero at a specific reference temperature is expected.
Sometime before TAR was published, there was confusion about what warming was caused by CO2 and what warming was caused by water vapor.
This could be explained by the fact that we now know that the warming effect of CO2 is too small to measure, i.e., undetectable.
Conclusions:
Here is the Intergovernmental Panel on Climate Change (IPCC) equation:
ΔRF = 5.35LN(C/Co) . . . . . . . . . . .(1)
This equation from Section 6.3.5 of the Third Assessment Report (TAR) has been used widely, but new evidence shows it is faulty. It leads to the erroneous conclusion that the warming effect of CO2 is close to its upper limit for warming the Earth’s atmosphere. The warming by CO2 is too small to detect, and that small amount is a straight line with temperature.
H. Douglas Lightfoot and Gerald Ratzer
July 28, 2024 References
[1] Lightfoot H D and Mamer O A, CALCULATION OF ATMOSPHERIC RADIATIVE FORCING (WARMING EFFECT) OF CARBON DIOXIDE AT ANY CONCENTRATION, ENERGY & ENVIRONMENT, VOLUME 25 No. 8 2014.
It is available at this Dropbox link: https://www.dropbox.com/scl/fi/xxzbcvfieceu1bcqm6jw8/Calculation-ofRF-of-CO2-at-any-concentration-2014.pdf? rlkey=cnqh6tpu3nf6kheyz4mp7x5il&dl=0
{2] Lightfoot H D and Ratzer G, The Sun and the Troposphere Control the Earth’s Temperature, Journal of Basic & Applied Sciences, 2023, 19, 163173
It is available at this Dropbox link: https://www.dropbox.com/scl/fi/apz61d4t9vhqux8282g81/The-Sun-andthe-Troposphere-Control-the-Earths-Temperature.pdf?
rlkey=tkewk5jg52e391ukjdrr9hn8v&dl=0
[3} The Ideal Gas Law is from: https://www.britannica.com/science/idealgas-law