# METO 621 - PowerPoint PPT Presentation

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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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## 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:

### 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

### 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