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

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=  T 4 ;  x 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 Wavelength max (in microns) = 2897/T (in Kelvin) For Sun, = 6000 K, for Earth = 255 K => max. wavelength Sun = micron (blue), max wavelength Earth ~ 14 micron. Explains spectral Distribution of radiation

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

Sun Earth visible

1 Angstrom= m. wavelengths < 0.1 micron (1000 angstroms) wavelengths 2O Ozone < 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 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 1. 2.

Manabe&Strickler, 1964: Note ozone, surface T

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

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 X small Sunlight on a flat ocean Sunlight on raindrops IR scattering off of air, aerosol Microwave scattering off of clouds Microwave (cm) Scattering neglected

Rayleigh scattering: solar scattering off of gases proportional 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 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

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 “Heiligenschein”