Lecture 5: Radiative transfer theory where light comes from and how it gets to where it

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Tuesday, 19 January 2010
Lecture 5 Radiative transfer theory where
light comes from and how it gets to where its
going
Reading
Ch 1.2 review, 1.3, 1.4 http//hyperphysics.phy-as
tr.gsu.edu/hbase/atmos/blusky.html
(scattering) http//id.mind.net/zona/mstm/physics
/light/rayOptics/refraction/refraction1.html
(refraction) http//id.mind.net/zona/mstm/physics
/light/rayOptics/refraction/snellsLaw/snellsLaw1.h
tml (Snells Law) Review On Solid Angles, (class
website -- Ancillary folder Steradian.ppt)
Last lecture color theory data spaces color
mixtures absorption
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The Electromagnetic Spectrum (review)
Units Micrometer 10-6 m Nanometer 10-9 m
Light emitted by the sun
The Sun
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Light from Sun Light Reflected and Emitted by
Earth
W m-2 µm -1
W m-2 µm-1 sr-1
Wavelength, µm
The sun is not an ideal blackbody the 5800 K
figure and graph are simplifications
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Atmospheric Constituents
Constant Nitrogen (78.1) Oxygen (21)
Argon (0.94) Carbon Dioxide (0.033)
Neon Helium Krypton Xenon
Hydrogen Methane Nitrous Oxide
Variable Water Vapor (0 - 0.04) Ozone
(0 12x10-4) Sulfur Dioxide Nitrogen
Dioxide Ammonia Nitric Oxide
All contribute to scattering For absorption, O2,
O3, and N2 are important in the UV CO2 and H2O
are important in the IR (NIR, MIR, TIR)
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Solar spectra before and after passage through
the atmosphere
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Atmospheric transmission
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Modeling the atmosphere
To calculate t we need to know how k in the
Beer-Lambert-Bouguer Law (called b here) varies
with altitude. Modtran models the atmosphere as
thin homogeneous layers.
Modtran calculates k or b for each layer using
the vertical profile of temperature, pressure,
and composition (like water vapor). This
profile can be measured made using a balloon, or
a standard atmosphere can be assumed.
Fo is the incoming flux
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Radiosonde data
Mt Everest
Mt Rainier
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Radiant energy Q (J) - electromagnetic
energy Solar Irradiance Itoa(W m-2) -
Incoming radiation (quasi directional) from the
sun at the top of the atmosphere. Irradiance
Ig (W m-2) - Incoming hemispheric radiation at
ground. Comes from 1) direct sunlight and 2)
diffuse skylight (scattered by atmosphere). Downw
elling sky irradiance Is?(W m-2) hemispheric
radiation at ground Path Radiance - Ls? (W m-2
sr-1 ) (Lp in text) - directional radiation
scattered into the camera from the atmosphere
without touching the ground Transmissivity t -
the of incident energy that passes through the
atmosphere Radiance L (W m-2 sr-1)
directional energy density from an object.
Reflectance r -The of irradiance reflected
by a body in all directions (hemispheric rI) or
in a given direction (directional
rIp-1) Note reflectance is sometimes
considered to be the reflected radiance. In this
class, its use is restricted to the energy
reflected.
Terms and units used in radiative transfer
calculations
0.5º
Itoa
L
Ls?
Is?
Ig
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Radiative transfer equation
Parameters that relate to instrument and
atmospheric characteristics
DN aIgr b
This is what we want
Ig is the irradiance on the ground r is the
surface reflectance a b are parameters that
relate to instrument and atmospheric
characteristics
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Radiative transfer equation
DN aIgr b
DN g(ter tiItoacos(i)/p te rIs?/p
Ls?) o
g amplifier gain t atmospheric transmissivity e em
ergent angle i incident angle r reflectance Itoa s
olar irradiance at top of atmosphere Ig solar
irradiance at ground Is? down-welling sky
irradiance Ls? up-welling sky (path)
radiance o amplifier bias or offset
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The factor of p

• Consider a perfectly reflective (r100) diffuse
  Lambertian surface that reflects equally in all
  directions.

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The factor of p

• Consider a perfectly reflective (r100) diffuse
  Lambertian surface that reflects equally in all
  directions.

If irradiance on the surface is Ig, then the
irradiance from the surface is rIg Ig W m-2.
The radiance intercepted by a camera would be
rIg/p W m-2 sr-1. The factor p is the ratio
between the hemispheric radiance (irradiance) and
the directional radiance. The area of the sky
hemisphere is 2p sr (for a unit radius). So why
dont we divide by 2p instead of p?
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The factor of p

• Consider a perfectly reflective (r100) diffuse
  Lambertian surface that reflects equally in all
  directions.

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Itoa
Itoa cos(i)
i
Highlighted terms relate to the surface
Ls? (Lp)
ti
te
i
e
Igti Itoa cos(i)
r (ti Itoa cos(i)) /p reflected light
r reflectance
Lambertian surface
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Measured Ltoa DN(Itoa) a Itoa b
Itoa
Ltoate r (ti Itoa cos(i)) /p te r Is? /p
Ls?
Itoa cos(i)
i
Highlighted terms relate to the surface
Ls? (Lp)
ti
te
i
e
Igti Itoa cos(i)
r (ti Itoa cos(i)) /p reflected light
r reflectance
Lambertian surface
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Mauna Loa, Hawaii