METO 621 - ATMOSPHERIC RADIATION

HOMEWORK #4

DUE APRIL 8 , 2010

(1)      Develop the coupled integral-differential equations for a two stream model for slab geometry. Assume isotropic scattering, a homogeneous atmosphere, a black lower boundary and thermal emission. Explain what assumptions have been made, e.g. a mean zenith angle. How is this mean angle calculated? For what radiative quantities is the two stream model the most accurate?

(2)   Ignore the thermal emission term in the equations developed in question 1. Now develop the analytic solutions to the two equations. Assume that the intensity incident at the top of the slab is a constant (Prototype problem 1).

Develop approximate solutions for the flux reflectance, the flux absorptance, and the flux transmission..