Geometry

The directional aspects of radiative transfer are most naturally expressed in spherical coordinates, illustrated in Figure 1. Location is specified by radius r from the origin, zenith angle q, and azimuthal angle j, with differential increments dr, rdq, and . The amount of radiation depends on direction, which in three dimensions is specified with solid angle W, measured in steradians (str). The differential element dW is the product of the polar and azimuthal angle differentials. There are 4p steradians in a sphere:

Polar angle is often replaced with its cosine , so that . Polar angle is measured relative to a beam directed upwards, so q=? and µ=-1 for a beam pointing straight down and µ>0 for radiation traveling upwards.
 
 

1. Geometry in polar coordinates. Radius r is measured from the origin, zenith angle q from the vertical, and azimuthal angle j from the south.

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