Monday, Oct. 2:
Clear-sky radiation; solar attenuation,
Thermal
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nomenclature
Sun
Earth
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Y-axis:
Spectral radiance, aka monochromatic intensity
units: watts/(m^2*ster*wavelength)
Blackbody curves provide the envelope to Sun, earth emission
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Sun
Earth
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visible
Depth of penetraion into earth’s atmosphere of solar UV
1 Angstrom=
10-10 m.
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Photoionization @ wavelengths < 0.1 micron (1000 angstroms)
Photodissociation @ wavelengths < 0.24 microns: O2 -> 2O
Ozone dissociation @wavelengths < 0.31 micron
Visible spectrum 0.39 to 0.76 micron
Thermal Radiation:
• scattering negligible
• absorption,emission is what matters
Math gets complicated: thousands of absorption lines, each
varying individually with pressure, temperature
Natural
Lorentz (Pressure)
broadening:
Half-width goes as
P/T(0.5-1.0)
natural
absorption
Doppler broadening:
Half-width goes as T1/2
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< 20 km, pressure broadening
> 50 km Doppler broadening
(Freq shift)/half-width
Continuing efforts to improve database
on line absorption strengths and
Halfwidths: H20 continuum,
Microwave lines, are examples
16 micron
7 micron
Thermal
Radiation transmits through an atmospheric layer
According to:
+J ds
I = intensity
= air density
r = absorbing gas amount
k =mass extinction coeff.
rk = volume extinction coeff.
Inverse length unit
emission
Path length ds
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Extinction=scattering+absorption
~ 0
T=
Langley plot
e- sec 
Ln (Iinf/I) =sec
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Beer’s Law used to assess solar constant in pre-satellite
days, now used to calibrate instrumentation & determine
aerosol&cloud optical depth from ground
Transmission through a layer, ignoring scattering and emission:
dI = -I kabs sec dz
After integration:
T = e-
sec 
Beer’s Law or Lambert’s Law
T = transmissivity;  = optical depth, or thickness
Consequence: most
radiation is absorbed/emitted
at an optical depth of 1.
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brightening
Limb Effects
darkening
affects ALL terrestrial
remote sensing
Limb Sounding as a Remote Sensing Technique:
• first get the temperature from Planck function radiance
• then use radiance in an absorbing/emitting wavelength
to get atmospheric concentration at that height
HIRDLS
To calculate the broadband infrared emission,
One simplification is to group lines together,
Use spectral-band-average values for absorption “band” models.
A more elegant solution is to group lines by
their absorption lines strengths, and integrate
over that.
Only works in infrared
Full radiative transfer equation for infrared/microwave
(I.e. ignores scattering):
attenuation
emission
Plane-parallel approximation: the earth is flat.
-> the temperature, atmospheric density is a function of
height (or pressure) alone. Curvature of earth ignored,
atmosphere assumed to be horizontally homogeneous.
Flux density
with
“flux transmissivity”
Radiative heating rate profiles:
-or-
Cooling to space approximation:
Ignore all intervening layers
Manabe & Strickler, 1965
Rodgers & Walshaw, 1966, QJRMS
Remote temperature sensing
• CO2 particularly suited (well-mixed & emissive)
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(what part of the Earth is this from ?)
Weighting function
If scattering is also included:
3 radiatively-important
scatterer parameters:
• optical depth (how much stuff
Is there ?)
• single-scattering albedo ksca/(kscat + kabs) (how much got
Scattered rather than absorbed ?)
• asymmetry parameter g, or phase function P(cos :
(describe how it scatters)
Wednesday:
• results from top of atmosphere radiation
Balance
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• questions up to 4.40
• some other aerosol, greenhouse gas,
results
Whether/how solar radiation scatters when it impacts
gases,aerosols,clouds,the ocean surface depends on
1. ratio of scatterer size to wavelength:
Size parameter x = 2*pi*scatterer radius/wavelength
X large
Sunlight on a flat ocean
Sunlight on raindrops
X small
Scattering neglected
Microwave
(cm)
IR scattering off of air, aerosol
Microwave scattering off of clouds