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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”