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Radiation: WHY CARE ???
• the ultimate energy source, driver forthe general circulation
• usefully applied in remote sensing (moreand more)
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Sun Earth
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=T4 ; x 10-8 W m-2 K-4;E is called irradiance, flux density. Units of W/m^2
Wien’s Law• wavelength of the peak emission from
dE/d(wavelength) = 0• Wavelengthmax (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 spectralDistribution of radiation
Energy absorbed from Sun establishes Earth’s mean T
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Fsun= 1368 W m-2
@ earth
Energy in=energy outFsun*pi*R2
earth = 4*pi*R2earth*(1.-albedo)*(sigma*T4
earth) global albedo ~ 0.3=> Tearth = 255 K
This + Wien’s law explains why earth’s radiation is in the infrared
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Sun Earth
visible
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1 Angstrom=10-10 m.
Photoionization @ wavelengths < 0.1 micron (1000 angstroms)Photodissociation @ wavelengths < 0.24 microns: O2 -> 2OOzone dissociation @wavelengths < 0.31 micron
Depth of penetraion into earth’s atmosphere of solar UV
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
Consider multiple isothermal layers, each in radiative equilibrium. Each layer, opaque inthe infrared, emits IR both up and down, while solar is only downTop of atmosphere: Fin = Fout incoming solar flux = outgoing IR fluxAt surface, incoming solar flux + downwelling IR = outgoing IR
=> Outgoing IR at surface, with absorbing atmosphere > outgoing IR with no atmosphere
1.
2.
Manabe&Strickler, 1964:
Note ozone, surface T
Radiation transmits through an atmospheric layerAccording to:
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I = intensity= air densityr = absorbing gas amountk =mass extinction coeff.
rk = volume extinction coeff.Inverse length unit
Extinction=scattering+absorption
Path length ds
Whether/how solar radiation scatters when it impactsgases,aerosols,clouds,the ocean surface depends on
1. ratio of scatterer size to wavelength:
Size parameter x = 2*pi*scatterer radius/wavelength
X large
X small
Sunlight on a flat oceanSunlight on raindrops
IR scattering off of air, aerosolMicrowave scattering off of clouds
Microwave(cm)
Scattering neglected
Rayleigh scattering: solar scattering off of gasesproportional to (1/
aerosol
Cloud drops
R=10-4 m
R=1 m
R=0.1 m
Solar scattering
Gas (air)
Mie scattering:1 < x < 50
Mie scattering: solar scattering off of cloud water and icemicrowave scattering off of precipitation
Index of refraction is complex: real part = scatteringimagery component=absorption
mreal=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 scatteringIn direction of light
Backward scatteringBack 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
Corona: often seen around the moon
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“Heiligenschein”