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METO 621

This lesson explores the concepts of thermal emission and absorption from surfaces, analyzing how energy is emitted relative to a blackbody model, and defining essential terms such as spectral directional emittance and absorptance. We also discuss Kirchhoff's Law, which states that good absorbers are also good emitters, and delve into surface reflection properties using Bidirectional Reflectance Distribution Function (BRDF). Furthermore, the lesson addresses scattering's role in radiative transfer, particularly in planetary media, and examines the equations governing these phenomena.

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METO 621

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  1. METO 621 LESSON 8

  2. Thermal emission from a surface be the emitted energy from a flat surface of temperature Ts , within the solid angle dw in the direction W. A blackbody would emit Bn(Ts)cosqdw. The spectral directional emittance is defined as • Let

  3. Thermal emission from a surface • In general e depends on the direction of emission, the surface temperature, and the frequency of the radiation. A surface for which eis unity for all directions and frequencies is a blackbody. A hypothetical surface for which e = constant<1 for all frequencies is a graybody.

  4. Flux emittance • The energy emitted into 2p steradians relative to a blackbody is defined as the flux or bulk emittance

  5. Absorption by a surface • Let a surface be illuminated by a downward intensity I. Then a certain amount of this energy will be absorbed by the surface. We define the spectral directional absorptance as: • The minus sign in -Wemphasizes the downward direction of the incident radiation

  6. Absorption by a surface • Similar to emission, we can define a flux absorptance • Kirchoff showed that for an opaque surface • That is, a good absorber is also a good emitter, and vice-versa

  7. Surface reflection : the BRDF

  8. BRDF

  9. Surface reflectance - BRDF

  10. Collimated incidence

  11. Collimated Incidence - Lambert Surface • If the incident light is direct sunlight then

  12. Collimated Incidence - Specular reflectance • Here the reflected intensity is directed along the angle of reflection only. • Hence q’=q and f=f’+p • Spectral reflection function rS(n,q) • and the reflected flux:

  13. Absorption and Scattering in Planetary Media • Kirchoff’s Law for volume absorption and Emission

  14. Differential equation of Radiative Transfer • Consider conservative scattering - no change in frequency. • Assume the incident radiation is collimated • We now need to look more closely at the secondary ‘emission’ that results from scattering. Remember that from the definition of the intensity that

  15. Differential Equation of Radiative Transfer • The radiative energy scattered in all directions is • We are interested in that fraction of the scattered energy that is directed into the solid angle dwcentered about the direction W. • This fraction is proportional to

  16. Differential Equation of Radiative Transfer • If we multiply the scattered energy by this fraction and then integrate over all incoming angles, we get the total scattered energy emerging from the volume element in the direction W, • The emission coefficient for scattering is

  17. Differential Equation of Radiative Transfer • The source function for scattering is thus • The quantity s(n)/k(n) is called the single-scattering albedo and given the symbol a(n). • If thermal emission is involved, (1-a) is the volume emittance e.

  18. Differential Equation of Radiative Transfer • The complete time-independent radiative transfer equation which includes both multiple scattering and absorption is

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