Radiative Transfer

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Radiative Transfer

• Intro

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Quiz
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Last Time

• Talked about the global energy surplus and
  deficit from the equator to the pole
• We will go a bit further into radiative transfer
  today so we get a generalized picture of how
  solar radiation is distributed over the Earth
• All the earths energy comes from the Sun (except
  very small portion from the Core)

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Back to Energy

• Potential energy- energy of position relative to
  some baseline in a field (gravitational PE)
• Internal Energy- energy that exists by virtue of
  an object that has a temperature
• 1 and 2 make up TPE
• Kinetic Energy- energy of motion (for our
  purposes ignore molecular level)
• Latent Heating- energy from phase change
• 5) Oceanic Heat Transport- cannot ignore even
  though it is a small part.

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Electromagnetic Spectrum

• X-Ray 0.01 microns
• Ultraviolet .1
• Visible .4 microns
• Near Infrared gt1-8 microns
• Microwave
• Radio
• Etc.

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EM Spectrum
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Wavelenght (?) Frequency (?)

• Inversely related
• Do a dimension analysis if you want
• C3108 m/s

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Solar Energy

• Output of energy by the sun is about 3.91026
  Watts (J/s)
• Flux densityEnergy/Surface area
• Flux density of Sun3.91026/(4pi(7108)2)6.
  34107 W/m2
• Earth intercepts only one 2-billionth of
  thissolar constant 1370 W/m2
• For a square meter at the top of atmos. 342.5
  W/m2

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Solar Activity

• Defn Solar luminosity Flux density of
  radiant energy from the sun that falls on a unit
  area held normal to the direction of the sun just
  outside the earths atmosphere
• Hotplate (1000 W over .2 m2 50000W/m2)
• Sun spots can cause a slight energy surplus for
  the Earth, little ice age (constant CO2 of 280
  ppm, thus solar variations?)

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Blackbody Radiation

• BB is a coherent mass of material (such as a
  surface or collection of molecules) which have
  the attribute that all radiation incident is
  absorbed
• Cor it can be shown that radiation emitted by a
  BB is the max possible by a real body at that
  temp (stars).
• Most of the light directed at a star is absorbed.
  It is therefore capable of absorbing all
  wavelengths of electromagnetic radiation, so is
  also capable of emitting all wavelengths of
  electromagnetic radiation.
• EmissivityAbsortivity100 for a blackbody

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Wiens Law

• Wavelength (max) 2897/T (T in K)
• Wavelength (microns) for peak emission for a
  blackbody at temp T
• Important consequencesolar radiation is
  concentrated more toward the visible and near
  infrared spectrum, where radiation emitted by
  planets tends to be long IR
• IR lost to space (IR heats atmos.)

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Stefan-Boltzmanns Law

• Energy emitted by a blackbody is proportional to
  T4
• EsigmaT4 (sigma is S-B const) 5.6710-8
• If the surface of the sun emitted as a BB then
  T5783 K
• We can set up an exercise to show that the
  effective BB temp of earth is 255 K
• This is not the temp if there was no atmosphere
  more to take into account besides an albedo
  assumption

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What is the point?

• Sun can be assumed a blackbody
• Earth is not
• Have to take into account absorptance of
  radiation absorbed by a sfc
• Emittance- of energy emitted at a sfc at a
  particular temp
• Transmittance- of energy passing through a
  substance (AT1)
• Reflectance (Albedo (a))- reflected
• For ATMS Refl.Abs.Trans.1
• Remote Sensing (OLR) and Gray Bodies next time