1. METO 621 Lesson 15

2. Prototype Problem #1 Semi-infinite slab

4. Prototype Problem #1 Angular distribution of the Intensity

5. Adding-Doubling Techniques Consider two layers in the atmosphere with the same reflectance and transmittance. Then the combined reflectance and transmittance of the two layers can be written as

6. Adding-Doubling Techniques

7. The advantage of the technique is that one can start with thin layers – small optical depths – which are easier to handle mathematically. There is no limit as to how many of the layers one eventually adds. If the two layers are dissimilar, then we must take into account that the transmittance and reflectance will be different for illumination from above and below. The equations for the combined reflectance and transmittance can also be determined.

8. Adding-Doubling Techniques From above From below

9. Adding-Doubling Techniques

10. Discrete Ordinate Method – Isotropic Scattering The solution of the isotropic scattering problem involves the following integral over angle In the two stream method we replaced the integration over  with the simple formula

11. Discrete Ordinate Method – Isotropic Scattering This is obviously a crude approximation. We can improve the accuracy by including more points in a numerical quadrature formula Where w’ j is a quadrature weight, and u j is the discrete ordinate Most commonly used radiative transfer computer codes is DISORT – DIScreteOrdinateRadiativeTransfer