The upwelling radiation sensed by a satellite sensor is governed by a) emission from the earth's surface transmitted through the atmosphere and b) emission from the atmospheric layers transmitted through the outer layers of the atmosphere.

The surface contribution to the upwelling radiation sensed at the top of the atmosphere for wavelength lambda is a product of the surface emissivity, the Planck function at the surface temperature, and the vertical transmittance through the depth of the atmosphere. This is written as:

The transmittance of upwelling radiation through the atmosphere is diminished exponentially with increasing path length,

where k is the absorption coefficient of the atmosphere and u is the density weighted path length.

The formulation for a discrete atmospheric layer is similar to that for the surface contribution except that the appropriate layer emissivity, Planck function at layer temperature , and vertical transmittance would be used. The contribution for all atmospheric layers is then,

The radiative transfer equation combines the surface and atmospheric contributions and for an infinitely layered atmosphere can be written:

Weighting functions and spectral bands

The term

in the radiative transfer equation is known as a weighting function. The weighting function, the derivative of transmittance with respect to height (pressure), specifies the relative contribution each atmospheric layer makes to the radiation emitted to space and thereby determines those regions of the atmosphere which are sensed from space at this wavelength. Sounding is accomplished with a group of spectral bands selected to detect radiation emitted from successively lower layers of the atmosphere.

The GOES-8 sounder weighting functions are presented in the following imagery grouped by wavelength:

This figure shows the GOES-8 sounder spectral bands together with depiction of the earth-emitted spectra; the carbon dioxide (CO2), moisture (H20), and ozone (O3) absorption bands are indicated. Around the broader CO2 and H20 absorption bands, vertical profiles of atmospheric parameters can be derived. Sampling the center of the absorption band yields radiation from the upper levels of the atmosphere (e.g., radiation from below has already been absorbed by the atmospheric gas). Sampling away from the center of the absorption band yields radiation from successively lower levels of the atmosphere. In the wings of the absorption band are the windows that view to the bottom of the atmosphere. Thus, as a spectral band is moved toward the center of the absorption band, the radiation brightness temperature decreases due to the decrease of temperature with altitude in the lower atmosphere. GOES-8 selection of spectral bands in and around the CO2 and H20 absorbing bands is designed to yield information about the vertical structure of atmospheric temperature and moisture.

Because the concentration of CO2 is nearly uniform in the atmosphere, the weighting functions specific to the CO2 absorbing bands show little variation with location. However, water vapor concentrations vary greatly from one location to another. The non-uniform concentration of water vapor in the atmosphere will cause the weighting functions specific to the H2O absorbing bands to vary by location. This effect can be demonstrated by selecting two locations in different airmasses. Station 72210 (Tampa, Florida) is relatively warm and moist compared to station 72230 (Central Alabama). The impact on the water vapor specific weighting functions caused by the variation of moisture is evident. The radiances yielded by the H2O absorbing bands in the drier atmosphere will correspond to levels closer to the surface than those for the more moist atmosphere.

Profile Retrievals

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