PHY2505 - Lecture 13

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PHY2505 - Lecture 13

• Remote sensing using emitted IR radiation

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Liou 7.4.1Revision
Solution Where Can assume emissivity 1,
m1 Why?
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Liou 7.4.1Monochromatic transmittance, T, and
weighting function
Change to pressure co-ordinates Recall Giving
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Liou 7.4.1 Instrument response function

• Need to convolve the emitted radiance with a
  function to represent the instrument response a
  slit function
• instrument has only a limited spectral bandwidth
• Assume spectral interval is small so replace
  with
• Then
• With

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Liou 7.4.1 Temperature and gas retrievals

Surface temperature Temperature
profiles Atmospheric window 800-1200cm-1
Gas phase profiles
CO2, 15um, 4.3um O3 9.6um H2O 6.3um
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Liou 7.4.2 Surface temperature determination

Define mean atmospheric temperature and
simplify for the case where you are measuring in
the window region Where iv, and transmission,
is mainly reduced by water
vapour and can be approximated by To subtract
the atmospheric component (eliminate ) we
take two measurements the split window
technique
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Liou 7.4.2 Split window technique

Applying the window equation to two
channels Want in terms of T2
Expand Planck function in terms of Taylor series
with respect to Ta Applying Taylor series
expansion and eliminating T-Ta Now replacing T
by Tb2 and Ts and using equation for I2 get
Radiance expressed as Brightness temperature
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Liou 7.4.2 Split window technique

Now replacing T by Tb2 and Ts and using equation
for I2 get With Gives where In practical use,
the Planck function is replaced by the Brightness
temperature and Ts estimated by
Equation for I2
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Liou 7.4.2 Application to sea surface
temperatures

From NOAA AVHRR data Retrieval from
regression In three channels (sum and
difference) 10.9, 12.0, 3.7um Satellite
measures SKIN temperature (first few mm) In situ
buoys are used to provide the coefficients a, b
and c, which relate these skin temperatures to
bulk temperature of water (McClain et al, 1985)
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Liou 7.4.3 Remote sensing of temperature profiles

• Kaplan (1959)
• Vertical resolution of the temperature field can
  be inferred from spectral distribution of
  atmospheric emission.
• Wings in a band see deep into the atmosphere
  while centre sees only the top layer absorption
  is strongly peaked in centre, so the mean free
  path of radiation is less for centre than wings..
• Can select different sounding wavelengths each to
  be sensitive to different layers..

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Liou 7.4.3 Illustration of concept

Assume (find Ts in practice
from preceding analysis) Write Solve for
this time taking into account variation
across spectral interval using reference
wavenumber, vr Express equation for Iv as
Fredholm Integral where
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Liou 7.4.3 Choosing spectral region

There are two gases that occur in uniform
abundance at altitude up to 100km, which also
show emission bands in regions convenient for
measurements CARBON DIOXIDE (365ppm) and OXYGEN
(volume mixing ratio 0.21)
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Liou 7.4.3 15um CO2 band as measured by IRIS
NIMBUS

Decrease of tropospheric temperature as altitude
increases Warming due to stratosphere
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Liou 7.4.3 Weighting functions

• An ideal weighting function would be a delta
  function all the contribution from that
  measurement at a single altitude..
• Weighting functions are constructed from
• where T can be calculated using a line-by-line
  code taking pressure and temperature proilfes
  into account
• CO2 transmittances in the 15um band are due to a
  number of different lines the v2 fundamental and
  hot bands..

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Liou 7.4.3 Example weighting functions
corresponding to 15um band intervals