Meto 621
Sponsored Links
This presentation is the property of its rightful owner.
1 / 18

METO 621 PowerPoint PPT Presentation


  • 72 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

METO 621

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


METO 621

LESSON 8


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


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.


Flux emittance

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


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


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


Surface reflection : the BRDF


BRDF


Surface reflectance - BRDF


Collimated incidence


Collimated Incidence - Lambert Surface

  • If the incident light is direct sunlight then


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:


Absorption and Scattering in Planetary Media

  • Kirchoff’s Law for volume absorption and Emission


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


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


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


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.


Differential Equation of Radiative Transfer

  • The complete time-independent radiative transfer equation which includes both multiple scattering and absorption is


  • Login