We left of the last post having found that brightness temperature was hopelessly asymmetric to radiance in the main CO2 deviation from the Planck temperature. This discovery dashed all hope of using brightness temperature to determine the temperatures of the individual lines. We were able to replicate the form of the radiance deviation using the S-B equation, but the resulting temperatures fall well below atmospheric temperature in the deeper parts of the deviation.
Above the asymmetry of brightness temperature to tropical 70 km radiance.
Above excellent symmetry using S-B with emissivity of 2.25, but temperatures of ~80 K at the bottom of the deviation. According to the Planck curves the bottom of the deviation is about 220K.
Nothing about this effort has been easy, and the only check we can use on the accuracy of the Planck curves for determining the radiative temperatures of individual lines is to use the temperature of the MODTRAN tropical lapse rate. We report here the results of stepping up in altitude and comparing the strong lines as determined by eyechrometer against our densified Planck curves, with the lapse temperatures of the chosen altitudes.
Above we see the eyechrometer results from our 5 degree densified Planck curves. The two fairly flat lines at the top are the top corners of the CO2 deviation, 544 and 792. It can be easily seen from the second graphic below that these change little with altitude. They bound the CO2 deviation, are among the weaker strong lines, and abut “windows” on either side that radiate to space at surface temperature. The next two lines are 598 and 742. They both drop off rapidly with opposite curves through the troposphere, and flatline through the rest of the section. The next two are the stronger lines 618 and 720. They behave more like the by far strongest line (magenta 668). The last two are 648 and 688. They are the boundaries of the rotational bands that follow the fundamental bend at 668. They define the zone of zero transmission to the tropopause, and follow 668 (and the lapse) through the troposphere. At 20 km, where the prominent “spike” at 668 begins, they diverge.
An effort was made in the above and prior graphics to crudely use line thickness proportional to absorption intensity. This is the difference between the apparent Planck temperature and the lapse temperature.The strongest line (668) shows the least discrepancy and three strongest lines generally have the least discrepancy. The discrepancy is least at one kilometer elevation.
The discrepancy is least at one kilometer elevation. This is not surprising because at one kilometer the deviation from Planck is very small.
Above the CO2 deviations are compared at 1 kilometer, 5 Kilometers, 10 kilometers, and 70 kilometers. The strong absorption lines are easily traced up in altitude. As we progress upward in altitude, the apparent Planck temperature becomes increasingly different from the lapse temperature for most lines up to the tropopause. From the tropopause to the stratopause the differences all lines decrease and reverse sign. The sign of difference reverses again from the stratopause to maximum MODTRAN elevation at 70 km.
Shown again above for convenience, positive numbers mean apparent Planck temperatures above the lapse temperature, and negative numbers mean apparent radiance temperatures below the lapse temperature.
The radiances and lapse temperatures are both averaged over the tropics, so the systematic discrepancies should mean something. The striking feature is that the sign of the discrepancies follows the lapse rate.
When you see a trend of apparent Planck temperatures decreasing relative to the lapse temperature in the stratosphere as the lapse temperature increases with altitude, it must mean that a significant part of the radiance is coming from below. Reversing this logic explains the discrepancies in the cooling with altitude regimes above and below the stratosphere.
MODTRAN has output of total transmission and surface emission we used to try and sort this out. The MODTRAN explanation of total transmission is fairly straightforward:
Slit function direct transmittance for the line-of-sight (LOS) path including all sources of molecular and particulate extinction.
We take this to mean what you see is what you got from below at the virtual sensor at your chosen altitude. We believe this should exclude the radiance produced at your chosen altitude. This would seem to be everything needed, but we noticed peculiar structure in the output surface emission:
Surface emission directly transmitted to the sensor in units of W cm-2 sr-1 / cm-1. If the LOS terminates at the ground, this term is computed as the product of the Planck surface emission, the directional emissivity, and the path transmittance. If the LOS does not terminate at the ground but a positive temperature is specified for input TPTEMP, SURF_EMIS will contain the transmitted surface emission of a target object. If the LOS does not terminate at the ground and input TPTEMP is zero, then SURF_EMIS is zero.
This sounds a lot like total transmission, but it seems unclear whether the surface in direct line of sight must always be the ground, or whether a different altitude and temperature can be specified.
We tried the “Ground Temperature Offset” feature to set one kilometer of lapse as the “surface” TPTEMP, but this merely moved identical radiance 6 degrees (the lapse) down the apparent Planck curves.
Above we find that Surface Emission and Transmission are very similar except in the lower wave numbers of the CO2 deviation, with emission being somewhat stronger than transmission where they diverge. We have no explanation and find neither useful in determining the radiance from below that seems to drive the difference between apparent Planck and lapse temperatures. In the zero transmission and emission zones, which are the same, there is still radiance from below. This radiance must come from surfaces above the ground.
In the next post we will take a stab at gauging above ground radiance (and possibly emissivity) using downward radiance.