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METO 621

METO 621. Lesson 15. Prototype Problem #1 Semi-infinite slab. Prototype Problem #1 Semi-infinite slab. Prototype Problem #1 Angular distribution of the Intensity. Adding-Doubling Techniques.

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METO 621

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  1. METO 621 Lesson 15

  2. Prototype Problem #1Semi-infinite slab

  3. Prototype Problem #1Semi-infinite slab

  4. Prototype Problem #1Angular 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. Adding-Doubling Techniques • 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 m 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 uj is the discrete ordinate • Most commonly used radiative transfer computer codes is DISORT – DIScreteOrdinateRadiativeTransfer

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