ABSTRACT
Now, if we allow the temperature in the atmosphere to change with height above the surface, we can solve the equation of radiative transfer in a manner similar to the one outlined above. However, when the temperature and pressure change with altitude, we can approximate the temperature behavior of the atmosphere by dividing it into many homogeneous, horizontal layers; we then perform the computation layer by layer. Figure 4-3 shows an atmosphere with several layers: the temperature of layer n is Tn, and its optical thickness t n. (Where the context makes it unnecessary, I will
drop the subscript ? that indicates the wavelength dependence.) In order to calculate the reflected radiation, start at the topmost layer, and calculate the downwelling radiation at each level:
where In - (µ) is the intensity emitted downward from the bottom of the nth layer in
the direction µ. Average these intensities over angle to find the mean downwelling intensity; multiply by [1-e(?)] to get the reflected component. In practice, for a diffuse surface, we can calculate the downwelling radiation at an angle of 45°, which is where sin? cos ? is maximum, and use that value. Let Idn be the average downwelling radiance at 45°: the radiance upward incident at the bottom layer is
Figure 4-3. Temperatures and optical depths in the model atmosphere.
