12.2 Scattering of light

Light scattering in the atmosphere shapes our world in countless ways. From the blue sky above to the colors of sunset, it influences how sunlight travels through the air and reaches Earth's surface.

Understanding scattering helps explain atmospheric phenomena and improves climate models. We'll explore different types of scattering, their effects on visibility and radiation, and how scientists measure and model these processes.

Fundamentals of light scattering

• Scattering of light plays a crucial role in atmospheric physics by influencing the transmission of solar radiation through the atmosphere
• Understanding light scattering principles helps explain various atmospheric phenomena such as sky color, visibility, and cloud formation
• Light scattering impacts climate models and weather predictions by affecting the Earth's energy balance and atmospheric optical properties

Electromagnetic wave properties

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• Light consists of oscillating electric and magnetic fields propagating through space
• Characterized by wavelength, frequency, and amplitude
• Polarization describes the orientation of the electric field oscillations
• Electromagnetic spectrum ranges from radio waves to gamma rays (visible light occupies a small portion)

Particle-light interactions

• Occurs when light encounters particles suspended in the atmosphere
• Depends on particle size, shape, and composition relative to the incident light wavelength
• Results in changes to the direction, intensity, and polarization of the scattered light
• Scattering efficiency varies with the ratio of particle size to wavelength

Types of scattering processes

• Elastic scattering preserves the energy of the incident photon (Rayleigh, Mie)
• Inelastic scattering involves energy exchange between photon and particle (Raman)
• Coherent scattering maintains phase relationships between scattered waves
• Incoherent scattering involves random phase relationships among scattered waves

Rayleigh scattering

• Dominates in the upper atmosphere where particles are much smaller than the wavelength of light
• Responsible for the blue color of the sky and the reddening of sunlight during sunrise and sunset
• Crucial for understanding the transmission of solar radiation through the atmosphere

Molecular scattering theory

• Applies to particles much smaller than the wavelength of incident light ($d << \lambda$)
• Scattering intensity proportional to the sixth power of particle size
• Induced dipole moment in molecules causes re-radiation of incident light
• Symmetrical scattering pattern with equal forward and backward scattering

Wavelength dependence

• Scattering intensity inversely proportional to the fourth power of wavelength ($I \propto \lambda^{-4}$)
• Shorter wavelengths (blue light) scattered more strongly than longer wavelengths (red light)
• Explains why the sky appears blue during the day and red during sunrise/sunset
• Affects the spectral distribution of solar radiation reaching the Earth's surface

Atmospheric applications

• Used to study atmospheric composition and density profiles
• Explains the polarization of skylight
• Contributes to atmospheric extinction and visibility reduction
• Influences remote sensing techniques and satellite observations of the atmosphere

Mie scattering

• Describes light scattering by particles comparable in size to the wavelength of incident light
• Significant in the lower atmosphere where larger particles like aerosols and cloud droplets are present
• Affects visibility, cloud optical properties, and atmospheric radiative transfer

Aerosol particle interactions

• Applies to a wide range of particle sizes, from fine dust to cloud droplets
• Scattering efficiency depends on the complex refractive index of the particle
• Produces more complex scattering patterns than Rayleigh scattering
• Influences the direct and indirect effects of aerosols on climate

Size parameter significance

• Defined as the ratio of particle circumference to wavelength ($x = 2\pi r / \lambda$)
• Determines the scattering regime (Rayleigh when $x << 1$, Mie when $x \approx 1$)
• Affects the angular distribution and intensity of scattered light
• Critical for interpreting remote sensing data and modeling atmospheric radiative transfer

Angular distribution patterns

• Characterized by complex lobed structures in the scattering phase function
• Forward scattering becomes more pronounced as particle size increases
• Backscattering glory and rainbow effects occur for specific size parameters
• Polarization state of scattered light varies with scattering angle and particle properties

Multiple scattering

• Occurs when light undergoes repeated scattering events before reaching an observer
• Prevalent in optically thick media such as clouds and dense aerosol layers
• Complicates the interpretation of remote sensing measurements and radiative transfer calculations

Cloud optical properties

• Determined by liquid water content, droplet size distribution, and cloud thickness
• Affects cloud albedo, transmittance, and absorption of solar radiation
• Influences cloud radiative forcing and feedback mechanisms in the climate system
• Impacts precipitation formation and cloud lifetime

Radiative transfer equations

• Describe the propagation of radiation through scattering and absorbing media
• Account for emission, absorption, and scattering processes
• Include terms for single scattering albedo and phase function
• Solved numerically using methods such as discrete ordinates or Monte Carlo simulations

Scattering phase functions

• Describe the angular distribution of scattered light intensity
• Depend on particle size, shape, and composition
• Range from simple analytical forms (Rayleigh) to complex numerical solutions (Mie)
• Critical input for radiative transfer models and remote sensing retrievals

Raman scattering

• Inelastic scattering process involving energy exchange between photons and molecules
• Provides information about molecular vibrational and rotational states
• Used in atmospheric composition analysis and remote sensing applications

Inelastic scattering principles

• Incident photon excites molecule to a virtual energy state
• Molecule relaxes to a different vibrational or rotational state than the initial state
• Scattered photon has different energy (and wavelength) than the incident photon
• Stokes scattering (energy loss) and anti-Stokes scattering (energy gain) possible

Molecular vibrational states

• Correspond to specific energy levels of molecular bonds
• Determined by the molecular structure and composition
• Raman shift provides information about the vibrational modes of molecules
• Allows identification and quantification of atmospheric gases and aerosols

Atmospheric composition analysis

• Raman lidar systems used for profiling water vapor, temperature, and trace gases
• Enables detection of atmospheric pollutants and aerosol properties
• Complements other remote sensing techniques (infrared spectroscopy)
• Provides vertical distribution information with high spatial and temporal resolution

Scattering vs absorption

• Both processes contribute to the attenuation of light in the atmosphere
• Scattering redistributes energy spatially while absorption converts light to heat
• Relative importance depends on wavelength and atmospheric composition
• Critical for understanding the Earth's radiation budget and climate forcing

Extinction coefficient

• Measures the total attenuation of light due to scattering and absorption
• Defined as the sum of scattering and absorption coefficients
• Varies with wavelength, particle properties, and atmospheric composition
• Used in Beer-Lambert law to calculate transmission through the atmosphere

Single scattering albedo

• Ratio of scattering coefficient to extinction coefficient
• Ranges from 0 (pure absorption) to 1 (pure scattering)
• Depends on particle composition, size, and wavelength of incident light
• Critical parameter for determining the radiative effects of aerosols and clouds

Optical depth concept

• Dimensionless measure of the total extinction along a path through the atmosphere
• Integrated extinction coefficient over the path length
• Determines the transmittance of radiation through the atmosphere
• Used in satellite retrievals and radiative transfer calculations

Atmospheric effects of scattering

• Influences the distribution of solar radiation in the atmosphere and at the surface
• Affects atmospheric heating rates, photochemistry, and energy balance
• Contributes to various optical phenomena observed in the sky

Sky color explanation

• Blue sky results from Rayleigh scattering of sunlight by air molecules
• Reddening of the sky during sunrise and sunset due to longer path length through the atmosphere
• Green flash occasionally observed at sunset due to atmospheric refraction and scattering
• Variations in sky color influenced by aerosol content and atmospheric conditions

Visibility reduction

• Caused by scattering and absorption of light by particles and gases
• Depends on the concentration and properties of atmospheric aerosols
• Affects air quality, transportation safety, and aesthetic qualities of landscapes
• Quantified using visual range or meteorological optical range measurements

Twilight phenomena

• Belt of Venus (pink band above the horizon) caused by backscattered sunlight
• Earth's shadow visible as a dark band below the Belt of Venus
• Crepuscular rays (sunbeams) visible due to scattering by atmospheric particles
• Anticrepuscular rays appear in the opposite direction of the sun

Measurement techniques

• Various methods used to quantify atmospheric scattering properties
• Combine in-situ measurements with remote sensing techniques
• Provide data for validating atmospheric models and studying climate processes

Lidar remote sensing

• Uses laser pulses to measure atmospheric scattering and absorption
• Provides vertical profiles of aerosols, clouds, and trace gases
• Elastic lidar measures backscattered light at the same wavelength as the transmitted pulse
• Raman lidar detects inelastically scattered light for composition analysis

Nephelometer instrumentation

• Measures scattering coefficients of atmospheric particles
• Illuminates sample volume with light source (typically LED or laser)
• Detects scattered light at various angles (integrating nephelometer)
• Provides information on aerosol optical properties and size distribution

Satellite-based observations

• Global coverage of atmospheric scattering properties
• Passive sensors measure reflected solar radiation and thermal emission
• Active sensors (lidar, radar) provide vertical structure information
• Retrieval algorithms derive aerosol and cloud properties from multi-spectral observations

Scattering in climate models

• Representation of scattering processes crucial for accurate climate simulations
• Affects radiative transfer calculations and energy balance in the atmosphere
• Challenges include parameterization of sub-grid scale processes and computational efficiency

Aerosol-radiation interactions

• Direct effect alters the Earth's radiation budget through scattering and absorption
• Semi-direct effect influences cloud formation and atmospheric stability
• Indirect effects modify cloud microphysical properties and precipitation
• Representation in models requires accurate aerosol optical properties and distributions

Cloud-albedo feedback

• Changes in cloud properties affect the Earth's albedo and energy balance
• Influenced by aerosol-cloud interactions and thermodynamic processes
• Uncertainty in cloud feedback remains a major source of climate sensitivity spread in models
• Requires accurate representation of cloud microphysics and radiative properties

Radiative forcing calculations

• Quantify the impact of various factors on the Earth's energy balance
• Include contributions from greenhouse gases, aerosols, and land-use changes
• Scattering processes affect both shortwave and longwave radiative forcing
• Uncertainties in aerosol radiative forcing remain a significant challenge in climate projections