Lecture 5: Thermal Emission

Chapter 6, Petty

We thank Prof. Cheng-ta Cheng for sharing his online notes on this subject.

Thermal Emission• Principal source of longwave radiation. Emission is the process by

which some of the internal energy of a material is converted into radiant energy.

• We absorb longwave radiation that is emitted by our environment and our own body also lose heat energy via

emission of radiation. (but why don’t we feel it)

• Possible to derive the relationship between temperature and thermal emission from first principle (quantum mechanics and statistical thermodynamics).

• Here we will just directly explain the general characteristics of thermal emission.

• In thermodynamics, the internal energy is the total energy contained by a thermodynamic system

• Internal energy has two major components, kinetic energy and potential energy. The kinetic energy is due to the motion of the system's particles (translations, rotations, vibrations), and the potential energy is associated with the static constituents of matter, static electric energy of atoms within molecules or crystals, and the static energy of chemical bonds

• First Law of Thermodynamics/ Internal Energy

http://www.youtube.com/watch?v=Xb05CaG7TsQ

Key facts about thermal emission• Planck’s function

Planck curve

Planck’s Function

• Blackbody doesn't emit equal amounts of radiation at all wavelengths

• Most of the energy is radiated within a relatively narrow band of wavelengths.

• The exact amount of energy emitted at a particular wavelength lambda is given by the Planck function:

Planck’s function

• Planck’s function is seen to have its peak at a wavelength that is inversely proportional to absolute temperature.

- At any given wavelength, emission increases monotonically with increasing temperature.

- Emission is not symmetrically distributed about its peak.

Planck’s Function (cont.)

Solar Spectrum

Intensity and Wavelength of Emitted Radiation : Earth and Sun

Wein’s Displacement Law

mT = 2897.9 m K

Gives the wavelength of the maximum emission of a blackbody, which is inversely proportional to its temperature

Earth @ 300K: ~10 mSun @ 6000K: ~0.5 m

What is a “blackbody”

- An object that absorbs radiation perfectly

- absorptivity, a=1

Answer:

Stefan-Boltzmann Law

Stefan-Boltzmann Law

Emissivity and Kirchoff’s Law

Actual irradiance bya non-blackbodyat wavelength

Emittance: Often referred to as emissivity

Emissivity is a function of the wavelength of radiation and the viewing angle and) is the ratio of energy radiated by the material to energy radiated by a black body at the same temperature

absorbed/ incident

Absorptivity (r , reflectivity; t , transmissivity)

Stefan-Boltzmann Law

Answer:

Rayleigh-Jeans Approximation

Rayleigh-Jeans Approximation

Emissivity

• What is a “emissivity”?

-the ratio of what is emitted by a given surface to what would be emitted if it were a blackbody.

-emissivity at a single wavelength (remote sensing, intensities)

- emissivity over a broad range of wavelengths (energy transfer, fluxes).

Monochromatic Emissivity

Graybody Emissivity

(Jin and Liang, 2006 J. of Climate)MODIS broadband emissivity

Jan 2003

July 2001

Kirchhoff’s Law

Kirchhoff’s Law• Local Thermodynamic Equilibrium

Brightness temperature

Brightness temperature

Brightness temperature

Answer:

Brightness temperature

Answer:

Brightness temperature

Answer:

When Des Thermal Emission Matter?

• When one can and can’t ignore thermal emission from the earth and the atmosphere?– At what wavelength? Solar radiation only,

Both solar radiation and thermal emission, Thermal Emission only?

4μm

When Does Thermal Emission Matter?

Applications to Meteorology, Climatology and Remote Sensing

• graybody approximation to SW and LW radiation.

• SW absorptivity, asw=(1-A).• LW absorptivity, alw=ε LW emissivity.• Emitted LW flux = εσT4, and ε≈1.• Emission in SW band is negelected.• Radiative equilibrium is all fluxes balance at

each point in the system.• If not equilibrium, the radiative imbalance may

be interpreted as a heating or cooling rate

Applications to Meteorology, Climatology and Remote Sensing

Answer:

• Radiative Equilibrium in a Vacuum

• - Radiative Equilibrium in a Vacuum

Top-of-the-Atmosphere Global Radiation Balance

Top-of-the-Atmosphere Global Radiation Balance

The skin temperature used in calculating heat fluxes and radiation:G = f( Tskin

- Tsoil) Eq. (1)H = CDHU(Taero-Ta) Eq. (2)LE =CDEU(qTskin*-qa) Eq. (3)

(1-α)Sd +LWd-εσTskin4 -H-LE - G= 0

Rn

IR Imaging from Space

IR Imaging from Space

IR Imaging from Space