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METO 621

METO 621. LESSON 8. Thermal emission from a surface. be the emitted. energy from a flat surface of temperature T s , within the solid angle d w in the direction W. A blackbody would emit B n (T s )cos q d w. The spectral directional emittance is defined as. Let.

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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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