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Presentation for chapters 5 and 6

Presentation for chapters 5 and 6. LIST OF CONTENTS. Surfaces - Emission and Absorption Surfaces - Reflection Radiative Transfer in the Atmosphere-Ocean System Examples of Phase Functions Rayleigh Phase Function Mie-Debye Phase Function Henyey-Greenstein Phase Function

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Presentation for chapters 5 and 6

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  1. Presentation for chapters 5 and 6

  2. LIST OF CONTENTS • Surfaces - Emission and Absorption • Surfaces - Reflection • Radiative Transfer in the Atmosphere-Ocean System • Examples of Phase Functions • Rayleigh Phase Function • Mie-Debye Phase Function • Henyey-Greenstein Phase Function • Scaling Transformations • Remarks on Scaling Approximations

  3. SURFACES - EMISSION AND ABSORPTION • Energy emitted by a surface into whole hemisphere - spectral flux emittance: • Energy absorped when radiation incident over whole hemisphere – spectral flux absorptance: • Kirchoff’s Law for Opaque Surface: Energy emitted relative to that of a blackbody

  4. 2. SURFACES - REFLECTION • Ratio between reflected intensity and incident energy – Bidirectional Reflectance Distribution Function (BRDF): • Lambert surface – reflected intensity is completely uniform . • Specular surface – reflected intensity in one direction • In general: BRDF has one specular and one diffuse component:

  5. SURFACE REFLECTION Analytic reflectance expressions

  6. Transmission through a slab • Transmitance • Transimitted intensity leaving the medium in downward direction

  7. TRANSMISSION THROUGH A SLAB For collimated beam: • Transmitted intensity is • Flux transmitted

  8. TRANSMISSION THROUGH A SLAB • Flux transmitance is

  9. RADIATIVE TRANSFER EQUATION

  10. RADIATIVE TRANSFER EQUATION • For Zero scattering

  11. RADIATIVE TRANSFER IN THE ATMOSPHERE-OCEAN SYSTEM • The refractive index is in the atmosphere and in the ocean. • In aquatic media, radiative transfer similar to gaseous media • In pure aquatic media Density fluctuations lead to Rayleigh-like scattering. • In principle: Snell’s law and Fresnel’s equations describe radiative coupling between the two media if ocean surface is calm. • Complications are due to multiple scattering and total internal reflection as below

  12. RADIATIVE TRANSFER IN THE ATMOSPHERE-OCEAN SYSTEM • Demarcation between the refractive and the total reflective region in the ocean is given by the critical angle, whose cosine is: • where • Beams in region I cannot reach the atmosphere directly • Must be scattered into region II first

  13. EXAMPLES OF PHASE FUNCTIONS • We can ignore polarization effects in many applications eg: • Heating/cooling of medium,Photodissociation of molecules’Biological dose rates • Because: Error is very small compared to uncertainties determining optical properties of medium. • Since we are interested in energy transfer -> concentrate on the phase function

  14. RAYLEIGH PHASE FUNCTION • Incident wave induces a motion (of bound electrons) which is in phase with the wave ,nucleus provides a ’restoring force’ for electronic motion • All parts of molecule subjected to same value of E-field and the oscillating charge radiates secondary waves • Molecule extracts energy from wave and re-radiates in all directions • For isotropic molecule, unpolarized incidenradiation:

  15. RAYLEIGH PHASE FUNCTION • Expanding in terms of incident and scattered angles: • Azimuthal-averaged phase function is:

  16. RAYLEIGH PHASE FUNCTION • By expressing in terms of Legendre Polynomials: • Asymmetry factor for Rayleigh phase function is zero (because of orthogonality of Legendre Polynomials): • Only non-zero moment is

  17. MIE-DEBYE PHASE FUNCTION • Scattering by spherical particles • Scattering by larger particles: -> Strong forward scattering – diffraction peak in forward direction! • Why? • For a scattering object small compared to wavelength: -> Emission add together coherently because all oscillating dipoles are subject to the same field

  18. MIE-DEBYE PHASE FUNCTION • For a scattering object large compared to wavelength: • All parts of dipole no longer in phase • We find that: • Scattered wavelets in forward direction: always in phase • Scattered wavelets in other directions: mutual cancellations, partial interference

  19. HENYEY-GREENSTEIN PHASE FUNCTION • A one-parameter phase function first proposed in 1941: • No physical basis, but very popular because of the remarkable feature: • Legendre polynomial coeffients are simply: • Only first moment of phase function must be specified, thus HG expansion is simply:

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