ScatteringScattering fundamentalsScattering geometryWhen does scattering matter?Types of scatteringMore types of scatteringParameters governing scatteringAtmospheric particlesRefractive indices of substances (λ = 589 nm unless indicated)Light scattering regimesScattering phase functionsRayleigh scatteringRayleigh scattering phase functionRayleigh and Mie scatteringVariation in sky brightnessScattering from particles is much stronger than that from molecules.Scattering by a dipole arrayOptical phenomenaRainbowsSlide 21Slide 22Slide 23Slide 24Reddening/BlueingSlide 26Once in a blue moon…Scattering cross-sectionRadar observations of precipitationSlide 30Rayleigh regime for raindropsSlide 32Slide 33Slide 34Radar reflectivity exampleDirect and diffuse radiationVisibilitySlide 39Slide 40USA visibilitySlide 42ScatteringScattering fundamentals• Scattering can be broadly defined as the redirection of radiation out of the original direction of propagation, usually due to interactions with molecules and particles• Reflection, refraction, diffraction etc. are actually all just forms of scattering• Matter is composed of discrete electrical charges (atoms and molecules – dipoles)• Light is an oscillating EM field – excites charges, which radiate EM waves• These radiated EM waves are scattered waves, excited by a source external to the scatterer• The superposition of incident and scattered EM waves is what is observedScattering geometryForward scatteringBackward scattering(backscattering)When does scattering matter?• Scattering can be ignored whenever gains in intensity due to scattering along a line of sight are negligible compared to:• Losses due to extinction• Gains due to thermal emission• Usually satisfied in the thermal IR band and for microwave radiation when no precipitation (rain, snow etc.) is present• Also can be ignored when considering direct radiation from a point source, such as the sun• In the UV, visible and near-IR bands, scattering is the dominant source of radiation along any line of sight, other than that looking directly at the sunTypes of scattering• Elastic scattering – the wavelength (frequency) of the scattered light is the same as the incident light (Rayleigh and Mie scattering)• Inelastic scattering – the emitted radiation has a wavelength different from that of the incident radiation (Raman scattering, fluorescence)• Quasi-elastic scattering – the wavelength (frequency) of the scattered light shifts (e.g., in moving matter due to Doppler effects)More types of scattering• Single scattering: photons scattered only once• Prevails in optically thin media (τ << 1), since photons have a high probability of exiting the medium (e.g., a thin cloud) before being scattered again• Also favored in strongly absorbing media (ω << 1)• Multiple scattering: prevails in optically thick, strongly scattering and non-absorbing media• Photons may be scattered hundreds of times before emergingParameters governing scattering• (1) The wavelength (λ) of the incident radiation• (2) The size of the scattering particle, usually expressed as the non-dimensional size parameter, x:• r is the radius of a spherical particle, λ is wavelength• (3) The particle optical properties relative to the surrounding medium: the complex refractive index• Scattering regimes:• x << 1 : Rayleigh scattering• x ~ 1 : Mie scattering• x >>1 : Geometric scatteringx 2rAtmospheric particlesType Size Number concentrationGas molecule ~10-4 µm < 3×1019 cm-3Aerosol, Aitken < 0.1µm ~104 cm-3Aerosol, Large 0.1-1 µm ~102 cm-3Aerosol, Giant > 1 µm ~10-1 cm-3Cloud droplet 5-50 µm 102-103 cm-3Drizzle drop ~100 µm ~103 m-3Ice crystal 10-102 µm 103-105 m-3Rain drop 0.1-3 mm 10-103 m-3Graupel 0.1-3 mm 1-102 m-3Hailstone ~1 cm 10-2-1 m-3Insect ~1 cm <1 m-3Bird ~10 cm <10-4 m-3Airplane ~10-100 m <1 km-3Refractive indices of substances(λ = 589 nm unless indicated)Substance nrni(n = nr+ i ni)Water 1.333 0Water (ice) 1.309 0NaCl (salt) 1.544 0H2SO41.426 0(NH4)2SO41.521 0SiO21.55 0 (λ = 550 nm)Carbon 1.95 -0.79 (λ = 550 nm)Mineral dust 1.56 -0.006 (λ = 550 nm)The most significant absorbing component of atmospheric particles is elemental carbon (soot); reflected in the large value of the imaginary part of the refractive index.Other common atmospheric particles are purely scattering.Light scattering regimesThere are many regimes of particle scattering, depending on the particle size, the light wave-length, and the refractive index. This plot considers only single scattering by spheres. Multiple scattering and scattering by non-spherical objects can get really complex!Scattering phase functionsScattering phase functions derived from Mie theory (scattering by spherical particles)The scattering phase function, or phase function, gives the angular distribution of light intensity scattered by a particle at a given wavelengthForward scatteringRayleigh scattering• Scattering of light off air molecules is called Rayleigh Scattering• Involves particles much smaller than the wavelength of incident light• Responsible for the blue color of clear skyAtmospheric composition: N2 (78%), O2 (21%), Ar (1%)Size of N2 molecule: 0.31 nmSize of O2 molecule: 0.29 nmSize of Ar molecule: 0.3 nmVisible wavelengths ~400-700 nmRayleigh scattering phase function• E is the orientation of the electric field vector in the incident wave• Recall that scattered skylight is 100% polarized when viewing the sky at a 90º angle from the sun• Polarizability: ease with which electrons and nuclei can be displaced from their average positionsVertically polarizedHorizontally polarizedUnpolarizedRayleigh and Mie scattering• Scattering determines the brightness and color of the skyVariation in sky brightness• The horizon sky is usually brighter than the zenith sky• This is a result of single scattering (zenith) vs. multiple scattering (horizon)Scattering from particles is much stronger than that from molecules.They’re bigger, so they scatter more.For large particles, we must first consider the fine-scale scattering from the surface microstructure and then integrate over the larger scale structure. If the surface isn’t smooth, the scattering is incoherent.If the surfaces are smooth, then we use Snell’s Law and angle-of-incidence-equals-angle-of-reflection.Then we add up all the waves resulting from all the input waves, taking into account their coherence, too (Mie