1165 Radiation19. Radiation and Optics in the Atmosphere and 19.3 Aerosols and Clouds ..............................1172 This chapter describes the fundamentals of ra- diation transport in general and in the Earth’s 19.4 Radiation and Climate ..........................1174 atmosphere. The role of atmospheric aerosol and 19.5 Applied Radiation Transport: Remote clouds are discussed and the connections between Sensing of Atmospheric Properties .........1176 radiation and climate are described. Finally, nat- 19.5.1 Trace Gases ................................1176 ural optical phenomena of the atmosphere are 19.5.2 The Fundamentals of DOAS ...........1176 discussed. 19.5.3 Variations of DOAS .......................1178 19.5.4 Atmospheric Aerosols...................1179 19.1 Radiation Transport 19.5.5 Determination of the Distribution in the Earth’s Atmosphere.....................1166 of Solar Photon Path Lengths........1181 19.1.1 Basic Quantities Related 19.6 Optical Phenomena in the Atmosphere...1182 to Radiation Transport .................1166 19.6.1 Characteristics 19.1.2 Absorption Processes ...................1166 of Light Scattering by Molecules 19.1.3 Rayleigh Scattering......................1166 and Particles ..............................1182 19.1.4 Raman Scattering........................1167 19.6.2 Mirages......................................1185 19.1.5 Mie Scattering.............................1168 19.6.3 Clear Sky: 19.2 The Radiation Transport Equation ..........1169 Blue Color and Polarization ..........1186 19.6.4 Rainbows 1187 19.2.1 Sink Terms (Extinction).................1169 ................................... 19.2.2 Source Terms 19.6.5 Coronas, Iridescence and Glories ...1189 19.6.6 Halos 1191 (Scattering and Thermal Emission). 1169 ......................................... 19.2.3 Simplification of the Radiation 19.6.7 The Color of the Sun and Sky ........1193 19.6.8 Clouds and Visibility 1195 Transport Equation......................1170 .................... 19.2.4 Light Attenuation 19.6.9 Miscellaneous .............................1196 in the Atmosphere ......................1171 References ..................................................1197 There are a multitude of processes in which electromag- where its energy is also changed. Inelastic scat- netic radiation interacts with the atmosphere: tering by molecules is called Raman scattering, where the energy of the scattered photon can • Absorption, i. e. radiation is removed from the ra- be reduced at the expense of energy transferred diation field and converted into some other form of to the scattering molecule (Stokes scattering). energy, e.g. heat. Absorption can be due to molecules Likewise, energy can be transferred from the (ther- Part D in the atmosphere (such as ozone, oxygen, or water mally excited) molecules to the photon (anti-Stokes vapor) or aerosols (such as soot), absorption of solar scattering). energy in the atmosphere is an important process in • Thermal emission from air molecules and aerosol 19 the climate system of the Earth. particles. The emission at any given wavelength can- • Elastic scattering, which – seen from an individual not exceed the Planck function (or emission from photon – changes its direction of propagation, but a black body) for the temperature of the atmo- not its energy (and hence wavelength or ‘color’). sphere, thus noticeable thermal emission only takes Scattering can be due to molecules (Rayleigh scat- place at infrared wavelengths longer than several tering) or aerosol particles (Mie scattering) present micrometers. Due to Kirchhoff’s law only absorb- in the air. ing gases (such as CO2,H2O, O3, but not the • Inelastic scattering where, as for elastic scatter- main components of air N2,O2, Ar), can emit ing, the direction of a photon is changed but radiation. 1166 Part D Selected Applications and Special Fields • Aerosol fluorescence. Excitation of molecules (broad band) fluorescence; this process will not be within aerosol particles by radiation can result in further discussed here. 19.1 Radiation Transport in the Earth’s Atmosphere In the following we introduce the basic quantities per- 19.1.3 Rayleigh Scattering tinent to the propagation of radiation in the atmosphere and discuss the fundamental laws governing radiation Elastic scattering (i. e. scattering without change of the transport in absorbing and scattering media, i. e. the photon energy) by air molecules is called Rayleigh scat- atmosphere. tering. While this is not an absorption process, light scattered out of the probing light beam will normally 19.1.1 Basic Quantities Related not reach the detector, thus for narrow beams it is justi- to Radiation Transport fied to treat Rayleigh scattering as an absorption process. 2 The Rayleigh scattering cross section σR(λ)(incm )is A light source will emit a certain amount W of energy given by [19.1]: in the form of radiation. π3 λ 2 − 2 Φ 24 n0( ) 1 1. The radiant flux is defined as the radiation en- σR(λ) = FK(λ) λ4 2 2 2 ergy W per unit time (regardless of the direction in Nair n0(λ) + 2 which it is emitted): 3 8π 2 ≈ n (λ)2 − 1 F (λ) , (19.5) radiated energy dW Ws λ4 2 0 K Φ = = = W 3 Nair time interval dt s (19.1) where: λ denotes the wavelength, n0(λ) is the real part of the wavelength-dependent index of refraction of air, N Φ air 2. The irradiance B is defined as the radiant flux is the number density of air (e.g. 2.4×1019 molec/cm3 received by an (‘illuminated’) area Ae: ◦ λ ≈ . at 20 C, 1 atm), FK( ) 1 061 is a correction for Φ W anisotropy (polarisability of air molecules). B = ; (19.2) 2 2 Note that n (λ) − 1 ≈ 2[n (λ) − 1]∝N ,since Ae m 0 0 air n0 ≈ 1 [in fact n0 (550 nm) = 1.000293], and 3. The radiation intensity is (Ω = solid angle): n0 − 1 ∝ Nair, thus σR(λ) is essentially independent Φ of Nair. On that basis a simplified expression for the I = [ / ]; (19.3) 2 Ω W sr Rayleigh scattering cross section (in cm )isgivenby Nicolet [19.2] 4. The radiance is (As = radiating area): . −28 Φ W σ λ ≈ 4 02 × 10 F = . (19.4) R( ) + (19.6) 2 λ4 x Ω As m sr Part D (All areas are assumed to be oriented perpendicular with to the direction of propagation of the radiation.) x = 0.04 19.1 for λ>0.55 μm , 19.1.2 Absorption Processes x = 0.389λ + 0.09426/λ − 0.3328 Radiation is absorbed by molecules in the atmosphere for 0.2 μm <λ<0.55 μm . (such as ozone, oxygen, or water vapor), aerosol (such For these simple estimates the Rayleigh scattering as soot) or liquid and solid water particles (cloud cross section can be written as droplets (ice crystals)). Absorption of solar ultravio- − let (UV) radiation at wavelengths below about 300 nm σ (λ) ≈ σ λ 4 R R0 by atmospheric O2 and O3 is important for life on − σ ≈ . 16 2 4 . (19.7) Earth. R0 4 4×10 cm nm for air Radiation and Optics in the Atmosphere 19.1 Radiation Transport in the Earth’s Atmosphere 1167 Rayleigh phase fuction molecule) changes its state of excitation during the scat- tering process. A part of the photons energy is then 90 2.0 passed from the photon to the molecule (Stokes lines, 120 60 ΔJ =+2, S-branch) or vice versa (anti-Stokes, ΔJ = 2, 1.5 O-branch). The term rotational Raman scattering (RRS) 150 30 is used if only the rotational excitation is affected 1.0 (Δv = 0). If the vibrational state also changes, the term 0.5 (rotational-) vibrational Raman scattering (VRS) is used (Δv =±1). Only discrete amounts of energy given by 0.0 180 0 the difference between the discrete excitation states can be absorbed/emitted. For air (O2 and N2) RRS frequency 0.5 shifts of up to ±200 cm−1 occur, for VRS a vibrational shift of ±2331 cm−1 for nitrogen and ±1555 cm−1 for 1.0 210 330 oxygen has to be added. The VRS is one order of mag- 1.5 nitude weaker than the RRS, and RRS is roughly one magnitude weaker than Rayleigh scattering. 240 300 2.0 In the following we give a quantitative description of 270 rotational- and vibrational-Raman scattering by O2 and Isotropic polarizability N2 [19.4–7]. The scattered power density Iv, →v, in Anisotropic polarizability J J [W/m2] scattered into the full solid angle 4π involving Fig. 19.1 Polar diagram of the Rayleigh scattering phase a transition (v, J → v, J) is given by [19.8]: function Φ(ϑ) for unpolarized incident light (dashed line, normalized to 2). The contribution of light polarized paral- Iv,J→v,J 2 ϑ lel to the scattering plane shows the sin dependence 1 −E(v,J )/kT = I σv, →v, LN g (2J + 1) e , of a Hertz dipole (dotted line, normalized to 1), with 0 J J air J Z ϑ = π/2 − ϑ being the angle between dipole axis and the (19.11) Poynting vector of the incident radiation, while the con- where I is the incident power density, N is the number tribution of light polarized perpendicular to the scattering 0 air of molecules in the scattering volume, L is the length plane (drawn line, normalized to 1) is independent of ϑ. of the volume and g is the statistical weight factor (plot by F. Filsinger) J of the initial rotational state due to the nuclear spin; J and v are the rotational and vibrational quantum num- The extinction coefficient due to Rayleigh scattering bers, respectively. The factor (2J + 1) accounts for the ε (λ) is then given by R degeneracy due to the magnetic quantum numbers while [− v, / ] εR(λ) = σR(λ)Nair . (19.8) exp E( J ) kT accounts for the population of the initial state of the molecule at temperature T.Thestate The Rayleigh scattering phase function (see sum Z is given by the product of the rotational state Fig.