*Note: this page offers miscellaneous, possibly evolving, information intended to support the emergence of insight regarding a particular topic.It’s a resource to support my own thinking, and may or may not be useful to others.*

Many climate skeptics offer all manner of arguments claiming to prove that “CO_{2} absorbing 15-micron radiation can’t possibly warm air.” They apparently think that, if their assertion was true, it would falsify the Greenhouse effect (GHE) or falsify CO_{2} having a significant role in the GHE. It wouldn’t, because, in actuality, directly warming air is *not* how the GHE operates. So, whether or not CO_{2} absorbing radiation can warm air is of no relevance to the GHE.

But, the issue piqued my interest. The arguments claiming CO_{2} absorbing radiation can’t warm air are completely wrong, as I might explain elsewhere. Yet, while CO_{2} absorbing radiation *could* warm air, does it actually do so in the atmosphere? Or does CO_{2} in the atmosphere always emit more than it radiates, so that it always has a net cooling effect on the air?

The answer so far looks to be… “It’s complicated.” Greenhouse gasses seem to mostly have cooling effects on air, but may have warming effects if (a) their absorption band is at a shorter wavelength, or (b) the absorption is weak and the altitude is high. (However, the high-altitude results might change when I implement a model that reflects more of the physics—in particular, collisional-line-broadening.)

## Initial asssumptions

My plotted results in what follows relies on Analysis: Propagation of Thermal Radiation. The formulas rely on an assumption of “Local Thermal Equilibrium”, an assumption which is valid throughout the troposphere. I also assume that temperatures in the troposphere follow the profile in the International Standard Atmosphere. In addition, I initially assume that the absorption coefficient depends only on atmospheric density. Thus, I’m ignoring changes that occur as a result of changing spectral line collisional broadening. (I hope to remedy this limitation in later work.)

## Fluxes when absorption length is short

The theory says that the propagating thermal radiation intensity is simply a weighted average of the black-body emissions associated with the temperature of the atmosphere where the emissions are happening. At frequencies where the absorption length (i.e., the reciprocal of the absorption coefficient) is relatively short, the weighted average is localized to the atmosphere near the altitude where fluxes are measured. So, we would expect the fluxes to be closely related to the flux we would observe from a black-body at the same temperature as the atmosphere at that altitude.

To verify this, in the figure below, I’ve plotted upwelling flux, downwelling flux, and blackbody emissions, for radiation with a frequency (wavenumber) of 650 cm^{-1}, assuming a hypothetical gas with a sea-level absorption length of 100 m at that frequency.

The upwelling flux reflects the emissions associated with temperatures some distance below the measurement altitude. This pattern is disrupted slightly near the surface, since there is no even-lower-even-higher temperature to effect the emissions. Note: these particular plots assume the brightness temperature of the surface equals the air temperature at the surface. In practice, surface emissions might be higher or lower.

The upwelling flux has a higher value that the blackbody, at a given altitude, because it reflects emissions at a slightly lower altitudes, where temperatures were warmer. The upwelling flux has a lower value that the blackbody, at a given altitude, because it reflects emissions at a slightly lower altitudes, where temperatures were warmer.

If this interpretation is correct, we should be able to make the curves match if we shift them horizontally, so that we’re looking at the upwelling flux emitted in the vicinity of a particular altitude (and measured at a somewhat higher altitude) and the downwelling flux emitting in the vicinity of the same altitude (and measured at a somewhat lower altitude). These horizontally shifted curves are shown in the figure below.

A pretty good match is obtained by shifting the curves by 0.7 absorption lengths (with those absorption lengths adjusted for the density shift that occurs as altitude increases). The value 0.7 is purely empirical, and I haven’t investigated to what extent it might change as the sea-level absorption length changes.

## Heat Flux and Heat Transfer when absorption length is short

Upward heat flux is simply the upwelling flux minus the downwelling flux. This is plotted below.

Given the curve for heat flux, we can also deduce the rate of radiation heat transfer to or from the air. The rate of heat transfer to air is the negative derivative of heat flux with respect to altitude. The results are plotted below.

The plot is extended to higher altitudes below. The model is likely to become inaccurate as one approaches the tropopause.

Note that in the scenario considered here (with air following the International Standard Atmosphere temperature profile), radiative heat transfer always has a net cooling effect on air at all altitudes.

## Considering various wavelengths and absorption coefficients

Let’s look at the results for a variety of wavelengths and assumed absorption coefficients.

Heat gain is the negative derivative of heat flux. Heat gain/loss is plotted below. Positive values correspond to air gaining thermal energy, and negative values correspond to air losing thermal energy. Note that the Y-axis is linear in the range -10^{-4} to +10^{-4}, and logarithmic outside this range.

This information can be used to compute how much air would warm or cool due to radiation heat transfer if there weren’t other heat transfers happening which also affect air temperature. I’ve used the heat-capacity figure for dry air. Positive values represent air warming, and negative values represent air cooling. “Glitches” in the curves are a numerical artifact; they disappear if one choses the sampling points differently.

## Heat deposition/cooling according to other sources

A 20210 Earth’s Energy Budget diagram from NASA indicates total radiative heat flow into the atmosphere from the surface to be about 5 percent of 340 W/m^{2} = 17 W/m^{2}. I’m still trying to understand what that assertion is intended to mean. I’m hoping that when I implement more physics into my model the meaning might become clearer.

Mlynczak (2014) p. 21 indicates that, according to both measurements and models, the net effect of thermal radiation is *radiative cooling of the air at all frequencies and altitudes*. The cooling is relatively modest at wavenumbers around the CO_{2} 15-micron / 667-cm^{-1} absorption band, and is larger at lower and higher wavenumbers (which I believe are primarily associated with absorption by water vapor).