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This lesson explores the Adding-Doubling Techniques used in radiative transfer, particularly for semi-infinite slabs and angular distribution of intensity. It discusses the combined reflectance and transmittance of two atmospheric layers with the same attributes, alongside their mathematical handling using thin layers. Furthermore, it examines how different layers affect transmittance and reflectance depending on illumination direction. The integration of isotropic scattering through the Discrete Ordinate Method is also covered, enhancing accuracy in radiative transfer computations, exemplified by the use of DISORT codes.
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METO 621 Lesson 15
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
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.
Adding-Doubling Techniques • From above • From below
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
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
