Radiation: WHY CARE ???
• the ultimate energy source, driver for the general circulation
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• usefully applied in remote sensing (more and more)

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

• All objects radiate
• Blackbody: absorbs all, reflects none, emits isotropically
• Blackbody radiation observed first, only later described
• (Max) Planck function
• Integrated over all wavelengths: E=

T 4 ;
 x 10 -8 W m -2 K -4 ;
E is called irradiance, flux density. Units of W/m^2

• wavelength of the peak emission from dE/d(wavelength) = 0
• Wavelength max
(in microns) = 2897/T (in Kelvin)
• For Sun, = 6000 K, for Earth = 255 K
• => max. wavelength Sun = 0.475 micron (blue) , max wavelength Earth ~ 14 micron.
Explains spectral
Distribution of radiation

Energy absorbed from Sun establishes Earth’s mean T
Energy in=energy out
F sun
*pi*R 2 earth
= 4*pi*R 2 earth
*(1.-albedo)*(sigma*T global albedo ~ 0.3
4 earth
)
=> T earth
= 255 K
F sun
= 1368 W m -2
@ earth
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This + Wien’s law explains why earth’s radiation is in the infrared

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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: O
Ozone dissociation @wavelengths < 0.31 micron
2
-> 2O
Visible spectrum 0.39 to 0.76 micron

To understand Earth’s emission need…..
Kirchoff’s Law: emissivity = absorptivity, for a given wavelength
Also called Local Thermodynamic Equilibrium (LTE)
Holds up to 60 km

High solar transmissivity + low IR transmissivity =
Greenhouse effect
1.
2.
Consider multiple isothermal layers, each in radiative equilibrium. Each layer, opaque in the infrared, emits IR both up and down, while solar is only down
Top of atmosphere: F in
= F out incoming solar flux = outgoing IR flux
At surface, incoming solar flux + downwelling IR = outgoing IR
=> Outgoing IR at surface, with absorbing atmosphere > outgoing IR with no atmosphere

Manabe&Strickler, 1964:
Note ozone, surface T

Radiation transmits through an atmospheric layer
According to:
I = intensity
 = air density r = absorbing gas amount k =mass extinction coeff.
Path length ds
 rk = volume extinction coeff.
Inverse length unit
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Extinction=scattering+absorption

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
Microwave
(cm)
X small
Scattering neglected
IR scattering off of air, aerosol
Microwave scattering off of clouds

Rayleigh scattering: solar scattering off of gases proportional to (1/  
Solar scattering
R=10 -4  m
Gas (air)
R=0.1
 m aerosol
R=1  m
Cloud drops
Mie scattering:
1 < x < 50

Mie scattering: solar scattering off of cloud water and ice microwave scattering off of precipitation
Index of refraction is complex: real part = scattering imagery component=absorption m real
=1.33 for water, 1.3 for ice

water

Mie scattering: algorithms for spherical drops work very well.
Calculated radiance depends on drop size, wavelength, indx of refraction
Forward scattering
In direction of light
Backward scattering
Back towards viewer

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Secondary rainbox at 51 degrees

Glory: around the shadow of your head, or an airplane,
At the anti-solar point. - need small drops
“Heiligenschein”
Corona: often seen around the moon
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