BASIC RADIATIVE TRANSFER

RADIATION & BLACKBODIES Objects that absorb 100% of incoming radiation are called blackbodies For blackbodies, emission (  ) is given by the Planck function: max = hc/5kT Wien’s law Function of T only! max Radiation Flux (F)  [W/m 2 ] Intensity (I)  [W/m 2 /sr] Monochromatic Intensity (I )  [W/m 2 /sr/nm] B Kirchoff’s Law: absorptance = emittance Emittance: 1 <  < 0 for grey bodies (  =1 for blackbodies 

RADIATIVE TRANSFER EQUATION I ABCD A: Absorptance (Beer-Lambert Law) B: Emission (Kirchoff’s Law) C: Scattering Out D: Scattering In complex because of scattering from all directions, can be approximated as:

RADIATIVE TRANSFER EQUATION II Absorption and emission (depends on incident intensity and T of layer) Scattering (increase in outgoing if > I ) Extinction coefficient: Slant versus Vertical Radiation:  = optical depth  = total column optical depth

EXTINCTION = SCATTERING + ABSORPTION Scattering from milk, ink, and water on an overhead projector Transmission through milk, ink, and water projected onto a screen

RADIATIVE TRANSFER EQUATION III Single scattering albedo:   Simplification #1: No Scattering (valid for IR with no clouds) Schwarzchild’s Equation:  Can be solved explicitly (first order, linear ODE) Simplification #2: No Emission(valid for the UV/visible/near-IR)  Requires an understanding of scattering properties to solve

IN PRACTICE, THERE ARE MANY CONTRIBUTIONS TO ATMOSPHERIC RADIATION… Atmosphere Absorption Scattering Absorption on the ground Scattering / Reflection on the ground Scattering from a cloud Transmission through a cloud Scattering / reflection oh a cloud Scattering within a cloud Aerosol / Molecules Cloud Emission from a cloud Emission from the surface Emission from molecules Adapted from Andreas Richter

INTERACTION OF RADIATION WITH GASES Also in UV/vis: Ionization-dissociation Characterized by discrete spectral lines Characterized by absorption cross section

SPECTRA OF ATMOSPHERIC GASES HAVE FINITE WIDTHS Petty, 2004 Pressure (Lorentz) broadening can obscure individual lines

EXAMPLES OF ABSORPTION SPECTRA Transmittance 15  m3.6  m UV IR [Clerbaux et al., ACPD, 2009] Andreas Richter

SCATTERING If a photon is absorbed and then immediately re-emitted this is called scattering. It depends on particle shape, size, index of refraction, wavelength of incident radiation and the viewing geometry. Usually, scattered photons have the same wavelength (elastic scattering) but not the same direction as the original photon. Scattering regime can be assessed using the Mie parameter:  = 2  r / Mie-Scattering (0.1 <  < 50) Geometric (optics) scattering (  > 50) Rayleigh Scattering (  < 0.1) The phase function P(  ) gives the distribution of scattered intensity as a function of scattering angle; the integral over all wavelengths is 1. [Petty, 2004]

Reflectivity and Emissivity of Various Surface Types There can be little relationship between reflectivity at visible and infrared wavelengths! Surface TypeThermal Infrared Emissivity Water92-96 Fresh, dry snow Sand, dry84-90 Soil, moist95-98 Soil, dry90 Forest and shrubs90 Skin, human95 Concrete71-88 Polished aluminum1-5 Petty, 2004

SATELLITE ORBITS

POLAR ORBIT Most composition measurements thus far have been from low-elevation (LEO), sun- synchronous orbits. Sun-synchronous: satellite precesses at same rate as Earth revolves around Sun (~1°/day)  satellite crosses equator at same local time each day Pros: (1)Global coverage (2)High signal Cons: (1)Poor coverage (temporal, clouds) (2)Shorter instrument lifetime

EXAMPLE OF TERRA ORBIT GMT Local Time = GMT +longitude/15 Terra is daytime descending orbitWhen converted to local time, can see the same equator cross over ~10:30 & 22:30

SOLAR OCCULTATION ORBIT SCISAT-1 Orbit Pros: (1)Very good signal (new species!) (2)Good vertical resolution (3)No surface term to characterize Cons: (1)Poor coverage (~30 obs per day) (2)Lower troposphere not observed

Pros: (1)constant observation (diurnal profiles, cloud contamination less detrimental) (2)Longer instrument lifetime (less drag) Cons: (1)reduced signal (2)worse spatial resolution  limit of spatial resolution possible ~ 1km GEOSTATIONARY ORBIT Geostationary orbits (GEO) match the period of satellite rotation with the Earth’s rotation (altitude ~ 35,800 km), fixed over the equator (view up to 60°)

GEOSTATIONARY NETWORK OF THE FUTURE? GEO-CAPE NASA: 2016? Sentinel-4/5 ESA: 2017 GEO-Asia JAXA: 2017? All three likely to include composition measurements in both UV & IR