Optical radar measurements of the atmosphere
Optical radar investigations of atmosphere, and Mie scattering intensity functions for backscatter
MIE SCATTERING FUNCTION↗
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Radiative transfer theory for active remote sensing of a layer of nonspherical particles
The radiative transfer theory is applied to calculate the scattering by a layer of randomly positioned and oriented nonspherical particles. The scattering amplitude functions of each individual particle are calculated with Waterman's T matrix method, which utilizes vector spherical wave functions for expansion of incident, scattered, and surface fields. The orientation of the particles is described by a probability density function of the Eulerian angles of rotation. A rotation matrix is used to relate the T matrix of the principal frame to that of the natural frame of the particle. The extinction matrix and phase matrix of the radiative transfer equations are expressed in terms of the T matrix elements. The extinction matrix for nonspherical particles is generally nondiagonal. There are only two attenuation rates in a specified direction of propagation. The radiative transfer equations are solved by an iterative method to first order in albedo. Numerical results are illustrated as functions of incidence angle and frequency with applications to active remote sensing.
Tsang, L.↗
Asymmetry parameters of the phase function for densely packed scattering grains
Spatial correlation among densely packed particles can substantially change their single-scattering properties, thus making questionable the applicability of the independent scattering approximation in calculations of light scattering by planetary regoliths. The same problem arises in geophysics in light scattering computations for snow, frosts, and bare soil. In this paper, we use a dense-medium light-scattering theory based on the introduction of the static structure factor to calculate asymmetry parameters of the phase function for densely packed particles with real refractive indices 1.31 and 1.66, approximating water ice and soil particles, respectively, and imaginary refractive indices 0, 0.01, and 0.3. For sparsely distributed, independently scattering grains, the calculated asymmetry parameters are always positive and always larger than those for densely packed particles. For densely packed grains, the asymmetry parameters may be negative but only for radius-to-wavelength ratios from about 0.1 to about 0.4. With decreasing particle size, the calculated asymmetry parameters tend to zero independently of the compaction state. In the geometrical optics regime, the asymmetry parameters for densely packed scatterers are positive and very close to those for independently scattering grains. These results may have important implications for remote sensing of the Earth and solid planetary surfaces. In particular, it is demonstrated that negative asymmetry parameters derived with some approximate multiple-scattering theories may be physically irrelevant and can be the result of using an inaccurate bidirectional reflection function combined with the ill-conditionally of the inverse scattering problem.
Mishchenko, Michael I.↗
An Analysis of Neptune's Stratospheric Haze Using High-Phase-Angle Voyager Images
We have inverted high-phase-angle Voyager images of Neptune to determine the atmospheric extinction coefficient as a function of altitude and the scattering phase function at a reference altitude. Comparisons between theoretical model and observations help separate the contributions from molecular Rayleigh and aerosol scattering and help determine the variation of the aerosol size, concentration, and scattering properties with altitude. Further comparisons between models and data allow us to place constraints on the location and composition of the hazes, the concentration and downward flux of certain condensible hydrocarbon gases, the eddy diffusion coefficient in the lower stratosphere, and the thermal profile in parts of Neptune's stratosphere. We find that a distinct stratospheric haze layer exists near 12(sub -1, sup +1) mbar in Neptune's lower stratosphere, most probably due to condensed ethane. The derived stratospheric haze production rate of 1.0(sub -0.3, sup +0.2) x 10(exp -15) g cm(exp -2) sec(exp -1) is substantially lower than photochemical model predictions. Evidence for hazes at higher altitudes also exists. Unlike the situation on Uranus, large particles (0.08-0.11 microns) may be present at high altitudes on Neptune (e.g., near 0.5 mbar), well above the region in which we expect the major hydrocarbon species to condense. Near 28 mbar, the mean particle size is about 0.13(sub -0.02, sup +0.02) microns with a concentration of 5(sub -3, sup +3) particles cm(exp -3). The cumulative haze extinction optical depth above 15 mbar in the clear filter is approx. 3 x 10(exp -3), and much of this extinction is due to scattering rather than absorption; thus, if our limb-scan sites are typical, the hazes cannot account for the stratospheric temperature inversion on Neptune and may not contribute significantly to atmospheric heating. We compare the imaging results with the results from other observations, including those of the Voyager Photopolarimeter Subsystem, and discuss differences between Neptune and Uranus.
Moses, Julianne I.↗
Light scattering by randomly oriented cubes and parallelepipeds
In this paper, the geometric ray tracing theory for the scattering of light by hexagonal cylinders to cubes and parallelepipeds has been modified. Effects of the real and imaginary parts of the refractive index and aspect ratio of the particle on the scattering phase function and the degree of linear polarization are investigated. Causes of the physical features in the scattering polarization patterns are identified in terms of the scattering contribution due to geometric reflections and refractions. The single-scattering phase function and polarization data presented in this paper should be of some use for the interpretation of observed scattering and polarization data from planetary atmospheres and for the physical understanding of the transfer of radiation in an atmosphere containing nonspherical particles.
Liou, K. N.↗
Size estimates of Titan's aerosols based on Voyager high-phase-angle images
Limits on the physical properties of the scattering haze near the top of Titan's atmosphere are derived from data obtained from seven high-phase-angle images from Voyager 1 and 2. From the ratio of the intensities observed at two different high phase angles, an estimate can be made of the forward-scattering lobe of the single-scattering phase function. Comparing the forward-scattering estimate with diffraction lobes from particles of different radii, it is concluded that the average radius of the particles found in the upper few tenths of an optical depth exceeds 0.19 micron. Judging from data observed at four different phase angles, the haze particles probably have a refractive index near 1.6 and a mean size of about 0.5 micron, if the widths of their diffraction peaks are close to those for equal-volume spheres. However, the highly polarizing nature of the particles over a broad wavelength-bandpass (Tomasko and Smith, 1982; West et al, 1983) combined with their forward-scattering behavior makes it very unlikely that the particles are spherical. The nonsphericity contributes to the uncertainty about the radii of the particles, but it is thought that the average radius is several tenths of a micron.
Rages, K.↗
Random scattering approach to gravitational microlensing
Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.
Katz, N.↗
Highlights from 4STAR Sky-Scanning Retrievals of Aerosol Intensive Optical Properties from Multiple Field Campaigns with Detailed Comparisons of SSA Reported During SEAC4RS
The 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) instrument combines airborne sun tracking capabilities of the Ames Airborne Tracking Sun Photometer (AATS-14) with AERONET (Aerosol Robotic Network)-like sky-scanning capability and adds state-of-the-art fiber-coupled grating spectrometry to yield hyperspectral measurements of direct solar irradiance and angularly resolved sky radiance. The combination of sun-tracking and sky-scanning capability enables retrievals of wavelength-dependent aerosol optical depth (AOD), mode-resolved aerosol size distribution (SD), asphericity, and complex refractive index, and thus also the scattering phase function, asymmetry parameter, single-scattering albedo (SSA), and absorption aerosol optical thickness (AAOT). From 2012 to 2014 4STAR participated in four major field campaigns: the U.S. Dept. of Energy's TCAP (Two-Column Aerosol Project) I & II campaigns, and NASA's SEAC4RS (Studies of Emissions, Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys) and ARISE (Arctic Radiation - IceBridge Sea & Ice Experiment) campaigns. Establishing a strong performance record, 4STAR operated successfully on all flights conducted during each of these campaigns. Sky radiance spectra from scans in either constant azimuth (principal plane) or constant zenith angle (almucantar) were interspersed with direct beam measurements during level legs. During SEAC4RS and ARISE, 4STAR airborne measurements were augmented with flight-level albedo from the collocated Shortwave Spectral Flux Radiometer (SSFR) providing improved specification of below-aircraft radiative conditions for the retrieval. Calibrated radiances and retrieved products will be presented with particular emphasis on detailed comparisons of ambient SSA retrievals and measurements during SEAC4RS from 4STAR, AERONET, HSRL2 (High Spectral Resolution Lidar), and from in situ measurements.
Radiance↗
4STAR Sky-Scanning Retrievals of Aerosol Intensive Optical Properties from Multiple Field Campaigns with Detailed Comparisons of SSA Reported During SEAC4RS
The 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) instrument combines airborne sun tracking capabilities of the Ames Airborne Tracking Sun Photometer (AATS-14) with AERONET-like sky-scanning capability and adds state-of-the-art fiber-coupled grating spectrometry to yield hyper spectral measurements of direct solar irradiance and angularly resolved sky radiance. The combination of sun-tracking and sky-scanning capability enables retrievals of wavelength-dependent aerosol optical depth (AOD), mode-resolved aerosol size distribution (SD), asphericity, and complex refractive index, and thus also the scattering phase function, asymmetry parameter, single-scattering albedo (SSA), and absorption aerosol optical thickness (AAOT).From 2012 to 2014 4STAR participated in four major field campaigns: the U.S. Dept. of Energy TCAP I II campaigns, and NASAs SEAC4RS and ARISE campaigns. Establishing a strong performance record, 4STAR operated successfully on all flights conducted during each of these campaigns. Sky radiance spectra from scans in either constant azimuth (principal plane) or constant zenith angle (almucantar) were interspersed with direct beam measurements during level legs. During SEAC4RS and ARISE, 4STAR airborne measurements were augmented with flight-level albedo from the collocated Shortwave Spectral Flux Radiometer (SSFR) providing improved specification of below-aircraft radiative conditions for the retrieval. Calibrated radiances and retrieved products will be presented with particular emphasis on detailed comparisons of ambient SSA retrievals and measurements during SEAC4RS from 4STAR, AERONET, HSRL2, and from in situ measurements.
Flynn, Connor↗
Magnetic two-photon scattering and two-photon emission - Cross sections and redistribution functions
The magnetic two-photon scattering cross section is discussed within the framework of QED, and the corresponding scattering redistribution function for this process and its inverse, as well as the scattering source function are calculated explicitly. In a similar way, the magnetic two-photon emission process which follows the radiative excitation of Landau levels above ground is calculated. The two-photon scattering and two-photon emission are of the same order as the single-photon magnetic scattering. All three of these processes, and in optically thick cases also their inverses, are included in radiative transport calculations modeling accreting pulsars and gamma-ray bursters. These processes play a prominent role in determining the relative strength of the first two cyclotron harmonics, and their effects extend also to the higher harmonics.
Alexander, S. G.↗
2004: Finite-Difference Time Domain Solution of Light Scattering by an Infinite Dielectric Column Immersed in an Absorbing Medium
The two-dimensional (2-D) finite-difference time domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions, extinction and absorption efficiencies, are derived using an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approx .1%. The errors in the scattering phase functions are typically smaller than approx .4%. Using the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.
Sun, W.↗
Finite-Difference Time Domain Solution of Light Scattering and Absorption by Particles in an Absorbing Medium
The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than similar to 2%. The errors in the scattering phase functions are typically less than similar to 5%. The errors in the asymmetry factors are less than similar to 0.l%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model.
Sun, W.↗
The clouds of Venus - An anisotropic scattering model
The phase function for anisotropic scattering is applied to a homogeneous atmospheric model to ascertain the effects of anisotropy on the near-infrared spectrum of Venus. Young's (1971) equivalent widths for the 7820-A CO2 band are analyzed to derive allowed combinations of CO2 specific abundance, continuum albedo, pressure, and degree of anisotropy. From these combinations, values are derived for the photon mean free path and total optical thickness of the clouds. The Venera 10 measurement of the transmitted flux at 7200 A is then used in conjunction with spherical-albedo requirements to reduce the range of possible solutions to the equivalent-width analysis. Through the application of approximate similarity relations, the 'true' (i.e., anisotropic) atmospheric parameters are derived from the isotropic values. For an assumed Mie scatterer with an average anisotropy factor of 0.7, the results indicate a total optical thickness of about 55 with a single-scattering albedo of 0.9992 to 0.9995.
Lestrade, J. P.↗
What we Hope to Learn about Global Mineral Dust Aerosols from EOS Multi-Angle Imaging SpectroRadiometer (MISR)
On global scales, just a few broad atmospheric aerosol compositional groups are commonly observed. Of these, "mineral dust" is the only group which both contains non-spherical particles, and typically has size distributions with enough large particles for particle shape to affect its visible-light-scattering properties. The MISR instrument is scheduled for launch into a 10:30 AM sun-synchronous, polar orbit aboard the EOS Terra satellite in 1999. MISR will measure the upwelling visible radiance from Earth in 4 spectral bands centered at 446, 558, 672, and 866 nm, at each of 9 emission angles spread out in the forward and aft directions along the flight path at +/-70.5 deg, +/-60.0 deg, +/-45.6 deg, +/-26.1deg, and nadir. Over a period of 7 minutes, as the spacecraft flies along, a 360 km wide swath of Earth will successively be viewed by each of the cameras, allowing MISR to sample a very large range of scattering angles; in mid latitudes, the instrument will observe scattering angles between about 60 deg and 160 deg. Global coverage will be acquired about once in 9 days at the equator; the nominal mission lifetime is 6 years. The distinction in single scattering phase function between natural distributions of spherical and randomly oriented, non-spherical particles, with a broad range of aspect ratios, shows up strongly for scattering angles ranging from about 90 deg to near 180 deg. For non-spherical particle distributions, single scattering phase functions tend to be much flatter in this region than for spherical particles. Since MISR samples the relevant range of scattering angles very well, we expect to be able to make critical distinctions between natural distributions of spherical and randomly oriented, non-spherical particles with MISR data. We anticipate that the new multiangle, multispectral data from MISR will also contain other information about particle properties, a major step beyond current spacecraft remote sensing retrievals, which obtain aerosol optical depth based on entirely assumed particle microphysical properties. According to simulations over cloud-free, calm ocean, for pure particles with natural ranges of optical depth, particle size, and indices of refraction, MISR should retrieve column optical depth for all but the darkest particles, to an uncertainty of at most 0.05 or 20%, whichever is larger, even if the particle properties are poorly known. For one common particle type, soot, constraints on the optical depth over dark ocean are very poor. The simulated measurements also should allow us to separate two to four compositional groups based on indices of refraction, and to identify three to four distinct size groups between 0.1 and 2.0 microns characteristic radius at most latitudes. The technique is most sensitive to particle microphysical properties in the "accumulation mode" sizes. where particle scattering undergoes the transition from Rayleigh to large-particle regimes for the MISR wavelengths. Based on these results, we expect to distinguish air masses containing different aerosol types, routinely and globally, with multiangle remote sensing data. Such data complements in situ and field data, which can provide details about aerosol size and composition locally that are needed to assess the radiative effects of aerosols quantitatively. Both field data and correlations in space and time with likely source and sink regions will also be helpful in developing a global picture of mineral dust aerosol budgets. Further work on the expected sensitivity of MISR to natural mixtures of pure particles, including climatologically likely mineral dust components, is currently underway.
Kahn, Ralph↗
Spectrally-Invariant Approximation Within Atmospheric Radiative Transfer
Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These "spectrally invariant relationships" are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud~dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction. and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with ID radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.
Marshak, A.↗
Spectrally Invariant Approximation within Atmospheric Radiative Transfer
Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These spectrally invariant relationships are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.
Marshak, A.↗
Spectral Invariant Approximation within Atmospheric Radiative Transfer; Applications to EarthCare
Certain algebraic combinations of single-scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These "spectrally-invariant relationships" are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength-independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. We identify the conditions under which the spectrally-invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. Validity of the assumptions and accuracy of the approximation is tested with radiative transfer calculations. We discuss the physics behind this phenomenon and possible applications to remote sensing, climate, and the EarthCare, mission in particular.
Marshak, Alexander↗
Internal energy of reaction products by velocity analysis. i - scattered kbr' from the crossed molecular beam reaction k plus hbr.
Velocity distribution measurement of excited potassium bromide formed in reactive collision between crossed beams of K and HBr as function of scattering angle for selected K velocity
VELOCITY DISTRIBUTION↗