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Although the ozone concentration peaks in the stratosphere, the radiance contribution from the troposphere is not negligible due to the increased temperature near the earth's surface. Tropospheric radiance can be minimized by choosing a spectral region whose weighting function peaks at a maximum altitude (van Delst, 1996).
The atmospheric window baseline radiance, , must be separated from the measured radiance, , in the spectral region of interest to yield the contribution due to ozone, ,
Microwindow radiance, centered at 1080 cm, is converted to a brightness temperature, which represents the baseline window value. is then calculated from the derived brightness temperature at the ozone wavenumber; which is chosen in the 9.6 m wings, 1063 cm, to represent upper atmospheric emission.
Given at each time interval in the data set and a clear sky reference value, , one can use Beer's Law (neglecting cloud reflectance of surface emission) to determine the cloud optical depth, ,
The error associated with this approach is obvious when the reference radiance is specified in layers,
where and represent ozone radiance above and below the cloud, respectively, and the spectral dependence is implied. A further assumption requires that the ozone emitted radiance within the cloud and atmospheric transmissivity below the cloud are negligible. Substitution of Equation 18 into Equation 19 produces
Therefore, knowledge of the ozone radiance below the cloud is necessary to properly determine the optical depth using this technique. This results in an underestimated optical depth measurement. Application of FASCOD3P data below the cloud base is utilized to determine . Unfortunately, a local ozone profile is not available and a mid-latitude standard model is assumed. Nonetheless, this provides a first order correction to the measured cloud radiance.