Satellites Observations

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Satellites Observations

• Temperature and albedo

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What we need to do

• How do we get values of temperature and albedo
  (reflectance) using the instruments on the
  satellites?

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Today Emission and Temperature

• And homework

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Emission

• Broadband emission
• Or blackbody emission
• All objects with temperatures above 0 K will emit
  radiation and the radiation that they emit is
  dependent upon the temperature.

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Plancks Law

• The energy emitted by an object is a function of
  its temperature
• The emitted spectrum is also a function of its
  temperature

From Wallace and Hobbs
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Blackbodies

• Perfect emitters give off the max energy for
  each wavelength at each temperature
• This is given by

B? Radiance at wavelength ?, and temperature T
(K) (in Wm-2sr-1µm-1) C speed of light h
Plancks constant (6.626 x 10-34Js) k
Boltzmanns constant (1.38 x 10-23 JK-1
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Solid angles

• The solid angle is the proportion of the surface
  area of a sphere subtended by the 2 dimensional
  angle. (See picture drawn on board)
• It is measured in steradians sr.

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Plancks function for different temps
From Kidder and Vonder Haar
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Not a blackbody
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Wiens displacement law

• Differentiate Plancks law to find maximum of
  function
• Where differential is 0
• Wiens law relates temperature to wavelength at
  which maximum energy is emitted
• Wavelength at which maximum energy is emitted is
  colour of emitting object

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dB/d? 0
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Total Energy Emitted

• Integrate Plancks function

An exercise for the student! EBB is total energy
of blackbody in Wm-2
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Stefan- Boltzmann Law

• E ?T4
• is Stefans constant
• 5.67 x 10-8 Wm-2K-4

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Emissivity

• Most objects are not blackbodies
• They emit less than the maximum amount of energy
  for their temperature
• Emissivity (? - sometimes called emittance)
  varies with wavelength
• ?? emitted radiation at ? / B? (T)
• For blackbodies ? 1

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Typical emissivities
From AMS Weather Satellites
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Quiz

• Where was the highest official temperature
  recorded?

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Measuring temperature

• Step 1 Calculate radiance (the amount of energy
  received by the sensor)
• Step 2 Invert Plancks equation to get
  temperature from energy emitted at a given
  wavelength

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Step 1
I is byte integer value c d are constants (we
calibrate the instrument to get this right) Do
not have to worry about incident solar radiation
and correct for it as the reflected radiation at
the wavelengths used is far smaller than that
emitted (especially at night!)
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Invert Plancks equation
Where c1 and c2 are constants found from Plancks
equation and n is the central wavenumber of the
IR channel (in µm-1) (Students are invited to
prove the validity of this conversion by messing
with Plancks equation.)
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Important point 1

• What we get is a radiation or brightness
  temperature
• This will not be the true temperature of the
  object and needs correcting for emissivity (if we
  know that)

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Important point 2

• What we get is a skin temperature
• This is the temperature of the surface rather
  than the bulk of the object
• The surroundings (energy transfers) are more
  closely related to total energy content rather
  than surface temperature

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Important Point 3

• Surface temperature is not surface air
  temperature (1.2m or 2m temperature)
• Think about how hot (cold) pavement is compared
  to the air above it

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Errors in T

• Due to scattering and absorption in the
  atmosphere
• In IR this is substantially due to water vapour
  which is variable
• Can be corrected for

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Absorption

• Chemistry!!!
• EM radiation comes in photons which are
  indivisible (wave-particle duality is a useful
  thing)
• A photon can be absorbed if the energy it has
  equals that needed by the absorbing medium for
  some energy transition

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Molecular absorption

• Most atmospheric gases are molecules (N2, O2, O3,
  CO2, H2O, etc)
• Molecules have energy levels related to the
  vibration of the bonds between atoms
• And they have rotational modes also
• These produce broader absorption bands

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Windows

• An atmospheric window is a part of the spectrum
  which is transparent to EM radiation
• Windows are crucial for life and remote sensing
  as they allow us to see through the atmosphere

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2 windows

• Visible 0.3 - 0.8µm
• IR 8 - 12µm

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Not windows

• Specific wavebands that are absorbed (and
  emitted) by particular molecular species are also
  useful
• Water vapour channel
• Ozone measurements

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Thin Ci

• This really screws things up avoid if possible
• Other problems are caused by Complex surfaces
  (eg. Urban areas) and Cu that are smaller than
  the pixel

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Albedo

• Albedo varies with wavelength
• Many substances have high albedo (reflectance) in
  the visible (e.g. snow), but low albedo in the
  microwave (e.g. snow)
• Can also have different albedo for different
  colours and therefore appear coloured (e.g.
  leaves)

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Measuring Reflectance (albedo)

• Measure the energy impacting the sensor in the
  visible waveband channel
• In Wm-2sr-1µm-1
• Energy reflected per unit time per unit area
  Normalised for width of waveband and solid angle
  view.

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Energy transitions

• Electrons in atoms are constrained to certain
  energy levels
• When a photon is absorbed it must move an
  electron from one level to another (quantisation)
• But quantum physics is a wonderful thing and
  Heisenberg said that everything is uncertain so
  energy bands have width

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Errors

• The measurement of albedo has errors due to the
  scattering and absorption of radiation in the
  atmosphere
• This is pretty constant and can be corrected for
  (unless a volcano has erupted)

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Review 1 EM

• What weve done to date
• Various parts of the EM spectrum (esp. those used
  in RS)
• What objects produce what types of EM (esp.
  things on and around the Earth)
• What happens to the light as it encounters matter
  (esp. the atmosphere)
• How wavelength is related to temperature