## More on Transmittance Weighting functions

The transmittance weighting function represents the rate of change of transmittance with respect to height in the atmosphere (pressure level).

This figure is an example of transmittance weighting functions plotted for three sounding frequencies as a function of height (z) and pressure level (p). Transmittance weighting functions have a vertically localized distribution about some specific level in the atmosphere which can be determined by designing a sensing instrument which will measure upwelling radiance in the close proximity of a particular frequency. The correspondence between frequency at which a satellite sensor measures radiance and the atmospheric level at which the Planck function profile is maximally weighted is at the core of techniques for vertically sounding the atmosphere using upwelling radiation data. By choosing a set of frequencies at which radiance would be measured, a set of atmospheric levels at which the Planck function will have maximum impact on the radiance values is established. Differentiating the transmittance weighting function with respect to height (pressure) will yield the height in the atmosphere or the pressure level for which the weighting function achieves a maximum value. Since atmospheric transmittance does not increase uniformly with altitude, but increases in a non-linear fashion, its vertical derivitave (increase with decreasing atmospheric pressure or increasing altitude) achieves a maximum value at some pressure level. At this level the slope of the transmittance profile achieves a maximum value.

This figure is a display of transmittance and absorptance curves plotted at a function of height (z) and pressure level (p). Frequencies for which the weighting function peaks at a high altitude in the atmosphere will have transmittance values that are small or zero at the earth’s surface. As a result, a satellite sensor would receive most of its radiation from high atmospheric altitudes. In highly transparent atmospheric windows, the weighting function peak will be located at or near the Earth’s surface and a satellite sensor would receive most of its radiation from the surface contribution term (R(0)T(0)) since the surface transmittance value is high. For frequencies between these extremes, there would be a combination of surface and atmospheric contribution to the upwelling radiance received by a satellite sensor. This demonstrates that sampling atmospheric properties at particular altitudes involves making electromagnetic radiation measurements at particular frequencies. It is important to note that a set of sounding frequencies should be selected along the edge of an absorption band where an absorbing gas becomes increasingly more opaque. An absorption band is a range of frequencies in the electromagnetic spectrum within which radiation is absorbed by a substance.

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