Atmospheric IR Absorption

Representations of atmospheric infrared (ir)  light absorption and transmission in atmospheric, climate, and environmental science are incorrect, because they completely ignore the composition dependence of measured component ir absorption spectra, which results in claimed atmospheric trace gas  absorption that is orders of magnitude greater than it actually is.  Proper adjustment indicates that CO2 and CH4  absorbance values in literature ir spectra are too high by a factor of about 800 and 147,000, respectively, based on the NIST component ir spectra in our national database.

The Beer-Lambert or Beer's law describes the change in light intensity I of of unidirectional (x-direction) monochromatic (single wavelength) radiation passed through a path length p in a homogeneous single-phase sample of a single light-absorbing species, as measured in a spectrometer, as

  A = ε p C,

where absorbance A is defined as log (I₀/I) = log(1/T), Io is the light intensity of wavelength λ into the sample and I is the reduced intensity after passing through path length p, ε(λ) is the  molar absorption (or extinction) coefficient which is a function of wavelength (or wavenumber), pressure and temperature for each component, and C is the single absorbing component concentration, or molar density, in moles/volume.  Transmittance T is defined as the fraction of light transmitted, or I/I₀ = 10^-A.  The equation is simply an exponential decay function of light intensity with distance at fixed temperature and pressure, with an exponent equal to the negative of the extinction coefficient times the path length times concentration.  Absorbance is also proportional to component mole fraction, since mole fraction and concentration differ by a fixed factor for an ideal gas.  For multicomponent mixtures, component Transmittance values are additive (Absorbance is not).

Compositions of atmospheric trace gases are made at a high sample concentration Cs in absorbance measurement in order to see the full amplitude of the spectrum, and since at the very low atmospheric concentration Ca, absorbance is virtually immeasurable.  So according to Beer's law, measured absorbance of each component must be scaled by the ratio Ca/Cs to obtain the true atmospheric absorption at Ca.  But this has always been completely ignored by atmospheric and climate scientists, who use the the unadjusted measured component spectra at Cs to compute mixture transmittance at some set of atmospheric conditions.

The National Institute for Standards of Standards and Technology (NIST) is our national storehouse of chemical and physical measurements including infrared light absorption.  The measured NIST methane (CH4) ir absorbance spectrum¹ is shown below, and is measured at a stated composition of 25% methane (75% nitrogen), or 0.25 mole fraction, and it has an atmospheric mole fraction of 0.0000017.  So according to Beer's law, it must be scaled by the factor Ca/Cs = 0.0000068, making it disappear on that scale, and negligible.  Components with 0 composition obviously have 0 effect on anything!  But climate science says that methane is a significant contributor to global warming.  So claimed CH4 ir absorbance in the literature must be scaled down by a factor of about 147,000!

For example, from the below NIST methane spectrum measured at a mole fraction of 0.25, peak absorbance is about 1.6 at a wavenumber of about 1300 cm-1.  So absorbance at 0.0000017 atmospheric mole fraction is equal to 1.6(0.0000068) = 0.00001088 = log(1/T), so transmittance is equal to 10^-0.00001088  = 0.99997495, which means that only 0.002505% is absorbed over the 5 cm path length at atmospheric concentration. Transmittance of that wavelength claimed based on the unadjusted spectrum is 10^-1.6 = 0.025, meaning 97.5% is absorbed over the path length, under-represented in the literature by a factor of about 39,000.  So the presence of methane in our atmosphere cannot even be detected by infrared spectrography and it can't possibly appear in any atmospheric ir absorption or emission spectrum.

The measured NIST CO2 absorbance spectrum, also shown below, is measured at a stated mole fraction of 33.33% or 0.3333, while the atmospheric mole fraction is 0.04%, or 0.0004.  So the measured CO2 absorbance must be scaled by the factor 0.0004/0.3333 = 0.0012, or about 1/800. 

The measured NIST water vapor absorbance spectrum, also shown below, is measured at an undisclosed water composition, counter to NIST standards, but can be assumed to be saturated water vapor at lab conditions, since any other mixture would be relatively very difficult to accurately measure and create. Water vapor composition in air or nitrogen at lab conditions (75 deg. F, 1 atm) is about 2%, or 0.02 mole fraction, which is close to an average atmospheric value in the troposphere.  Where water is significantly present, all other trace gas effects are completely negligible with respect to infrared absorption, transmission, and emission. because of its much greater concentration and its wider absorption.

One can find hundreds of incorrect atmospheric infrared spectra by doing an image search for "atmospheric ir absorption".  All showing any effects of water plus CO2, CH4, or O3 on the same scale, or even just CO2 and CH4,  are completely wrong.  All represent CO2 and CH4 and all trace gas absorbance spectra at their measured compositions, although those are never stated or discussed and are completely ignored. Some such examples of calculated and even claimed measured atmospheric spectra are shown below the NIST component spectra.

In order to calculate infrared transmittance through the atmosphere, in addition to composition, temperature and pressure versus altitude we would also need to know extinction coefficients for all components ε_i(λ,P,T).  Measurements at other than lab conditions are difficult and not available. And composition and temperature profiles are highly variable.  But we can ask the question, what would the transmittance be over much larger path lengths for the peak component wave numbers using assumed fixed compositions and the known lab condition extinction coefficients ε_i(λ,1 atm, 75 deg. F).  Transmittance close to the surface can be well-approximated.