A characteristic of the effective transmittance profiles for some instrument channels is that they can be non-monotonic. The non-monotonicity is a result of the combination of the rates of change of the effective transmittance components.
As an example, consider AIRS channel 1463 in the M3 module (central frequency of about 1338cm-1). The figure below is a comparison of the convolved LBLRTM calculated transmittance using only the "dry" gas spectroscopic data (labeled as Tau(DRY)) and the effective dry gas transmittance (labeled as Tau(DRY*)). As can be seen, the two profiles are quite different and the effective gas transmittance decreases to a minimum at around 650hPa and then begins to increase.
The effective dry transmittance is derived from the total calculated transmittance and that due to water and ozone only, as shown in eqn.(1) above. The calculation of water vapor and ozone only transmittance is performed by only including the water vapor and ozone spectroscopic data in the LBLRTM calculation. A plot of the total transmittance, Tau(ALL), the water vapor and ozone only transmittance, Tau(WVO), and the effective dry transmittance, Tau(DRY*), is shown below.
A blowup of the region where the effective dry transmittance begins to increase is shown below. The two component transmittances, ALL and WVO, are small but nowhere near zero.
The three horizontal dashed lines simply indicate the layers where the effective dry transmittance slope changes sign, as shown explicitly in the plot below of the derivative of the transmittances with respect to the log of the pressure.
The derivative of the effective dry transmittance can also be expressed as the derivative of its components via the quotient rule,
.................................(4)
Plotting the two components defined via the numerator of eqn.(4), shown below, identifies why the effective dry transmittance begins to increase at the 650hPa level. When the rate of change of Tau(WVO) weighted by the total transmittance, Tau(ALL), becomes larger than the rate of change of the total transmittance weighted by Tau(WVO), the derivative of the effective dry transmittance changes sign.
