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NASA NTRS1985

Phase function, backscatter, extinction, and absorption for standard radiation atmosphere and El Chichon aerosol models at visible and near-infrared wavelengths

Tabular values of phase function, Legendre polynominal coefficients, 180 deg backscatter, and extinction cross section are given for eight wavelengths in the atmospheric windows between 0.4 and 2.2 microns. Also included are single scattering albedo, asymmetry factor, and refractive indices. These values are based on Mie theory calculations for the standard rediation atmospheres (continental, maritime, urban, unperturbed stratospheric, volcanic, upper atmospheric, soot, oceanic, dust, and water-soluble) assest measured volcanic aerosols at several time intervals following the El Chichon eruption. Comparisons of extinction to 180 deg backscatter for different aerosol models are presented and related to lidar data.

Whitlock, C. H.↗
NASA NTRS1987

An investigation of the forward scattering theorem

The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.

Karam, M. A.↗
NASA NTRS1991

Experimental study of cross-stream mixing in a cylindrical duct

An experimental investigation of cross stream injection and mixing was conducted with application to a low NO sub x combustor for the High Speed Civil Transport (HSCT). Mixing in a cylindrical chamber was studied for transverse injection from slanted slot and round orifice injectors. Momentum ratio, density ratio, and number were studied. Quantitative measurement of injectant concentration distributions were obtained by planar digital imaging of the Mie scattered light from an aerosol seed uniformly mixed with the injectant. The unmixedness, defined as the ratio of the r.m.s. concentration fluctuation to mean concentration in a plane perpendicular to the main flow direction, was found to be primarily a function of momentum ratio and injector spacing. An optimum spacing is indicated. Unmixedness is also a function of orifice size, or mass flow ratio, but the mass flow dependence can be accounted for by normalizing the unmixedness with its maximum theoretical value. The data indicate that a density ratio greater than unity retards mixing. It was found that above a certain momentum flux ratio, mixing with slanted slot injectors was better than with round hole injectors.

Vranos, A.↗
NASA NTRS1991

Experimental study of cross-stream mixing in a cylindrical duct

An experimental investigation of cross stream injection and mixing has been conducted with application to a low NO(x) combustor for the HSCT. Mixing in a cylindrical chamber has been studied for transverse injection from slanted slot and round orifice injectors. Momentum ratio, density ratio, and injector geometry were the primary variables. Slanted slots of various size, aspect ratio, and number were studied. Quantitative measurement of injectant concentration distributions were obtained by planar digital imaging of the Mie-scattered light from an aerosol seed uniformly mixed with the injectant. The unmixedness, defined as the ratio of the rms concentration fluctuation to mean concentration in a plane perpendicular to the main flow direction, was found to be primarily a function of momentum ratio and injector spacing. An optimum spacing is indicated. Unmixedness is also a function of orifice size, or mass flow ratio, but the mass flow dependence can be accounted for by normalizing the unmixedness with its maximum theoretical value. The data indicate that density ratio greater than unity retards mixing. It was found that above a certain momentum flux ratio, mixing with slanted slot injectors was better than with round hole injectors.

Vranos, A.↗
NASA NTRS1974

Optical image of a cometary nucleus: 1980 flyby of Comet Encke

The feasibility was investigated of obtaining optical images of a cometary nucleus via a flyby of Comet Encke. A physical model of the dust cloud surrounding the nucleus was developed by using available physical data and theoretical knowledge of cometary physics. Using this model and a Mie scattering code, calculations were made of the absolute surface brightness of the dust in the line of sight of the on-board camera and the relative surface brightness of the dust compared to the nucleus. The brightness was calculated as a function of heliocentric distance and for different phase angles (sun-comet-spacecraft angle).

Wells, W. C.↗
NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗
NASA NTRS2002

Retrievals of Profiles of Fine And Coarse Aerosols Using Lidar And Radiometric Space Measurements

In couple of years we expect the launch of the CALIPSO lidar spaceborne mission designed to observe aerosols and clouds. CALIPSO will collect profiles of the lidar attenuated backscattering coefficients in two spectral wavelengths (0.53 and 1.06 microns). Observations are provided along the track of the satellite around the globe from pole to pole. The attenuated backscattering coefficients are sensitive to the vertical distribution of aerosol particles, their shape and size. However the information is insufficient to be mapped into unique aerosol physical properties and vertical distribution. Infinite number of physical solutions can reconstruct the same two wavelength backscattered profile measured from space. CALIPSO will fly in formation with the Aqua satellite and the MODIS spectro-radiometer on board. Spectral radiances measured by MODIS in six channels between 0.55 and 2.13 microns simultaneously with the CALIPSO observations can constrain the solutions and resolve this ambiguity, albeit under some assumptions. In this paper we describe the inversion method and apply it to aircraft lidar and MODIS data collected over a dust storm off the coast of West Africa during the SHADE experiment. It is shown that the product of the single scattering albedo, omega, and the phase function, P, for backscattering can be retrieved from the synergism between measurements avoiding a priori hypotheses required for inverting lidar measurements alone. The resultant value of (omega)P(180 deg.) = 0.016/sr are significantly different from what is expected using Mie theory, but are in good agreement with recent results obtained from lidar observations of dust episodes. The inversion is robust in the presence of noise of 10% and 20% in the lidar signal in the 0.53 and 1.06 pm channels respectively. Calibration errors of the lidar of 5 to 10% can cause an error in optical thickness of 20 to 40% respectively in the tested cases. The lidar calibration errors cause degradation in the ability to fit the MODIS data. Therefore the MODIS measurements can be used to identify the calibration problem and correct for it. The CALIPSO-MODIS measurements of the profiles of fine and coarse aerosols, together with CALIPSO measurements of clouds vertical distribution, is expected to be critically important in understanding aerosol transport across continents and political boundaries, and to study aerosol-cloud interaction and its effect on precipitation and global forcing of climate.

Kaufman, Yoram↗
NASA NTRS2012

Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Mishchenko, Michael I.↗
NASA NTRS1971

Transfer of thermal microwaves in the atmosphere, volume 1

The Mie theory is used to determine the absorption and scattering properties of liquid hydrometeors at 27 microwave frequencies from 500 MHz to 60 GHz. Based on the Marshall-Palmer distribution of drop sizes, regression equations are developed for the volume absorption coefficient of rain as a function of its temperature and content of liquid water.

Paris, J. F.↗
NASA NTRS1979

Theory and experiment for passive microwave remote sensing of snowpacks

Both the theory and experiment for the passive remote sensing of snow with microwave radiometers have been studied. The volume scattering effects of snow are accounted for by incorporating Mie scattering theory into a radiative transfer model. The theory is applied to the interpretation of experimental data obtained from various snow measurements. The spectral and angular dependences of the brightness temperatures are illustrated and show good agreement between the theory and experiment. Brightness temperatures as a function of snow depths are also interpreted and discussed. It is observed that as the snow depth increases, the brightness temperature increases when the subsurface is an aluminum plate due to the fact that the plate is cold and snow absorption induces a brightening effect and the brightness temperature decreases when the subsurface is soil due to the fact that snow scattering induces darkening effects.

Kong, J. A.↗
NASA NTRS2018

Does Orbital Angular Momentum Have Effect on Laser’s Scattering by Molecular Atmosphere?

Lasers with orbital angular momentum (OAM) have potential applications in communication technology, manipulation of particles, and remote sensing. Because of its unusual light-scattering properties, the OAM laser’s interaction with a molecular atmosphere must be studied to ensure that it is not lossy for communication or remote-sensing applications that involve its transmission through an atmospheric environment. In this study, the finite-difference time-domain (FDTD) method [21] is applied to calculate the light scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre-Gaussian (LG) beams with OAM by very small dielectric particles. Not like Lorentz-Mie solutions, the FDTD method can calculate for particles off the central axis of the LG beam. It is found that when the particles are very small, and the topological charge number of the OAM of a laser is not extremely large, the laser’s OAM has little effect on the scattering phase function. This suggests that Rayleigh theory can be applied directly to calculate the light scattering by atmospheric molecules. The transmission of a laser beam with OAM in a molecular atmosphere is not different from that of a regular Gaussian beam.

Molecular atmosphere↗
NASA NTRS1971

An explicit form of the Mie phase matrix for multiple scattering calculations in the I, Q, U, and V representation

An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities.

Kattawar, G. W.↗
NASA NTRS2021

Polarimetric sensitivity of light-absorbing carbonaceous aerosols over ocean: A theoretical assessment

Visible-light-absorbing carbonaceous aerosols within the boundary layer affect the radiance and polarization states of the radiation at the top of the atmosphere. Remote sensing from suborbital and satellite-based platforms utilizes these radiance and polarization signals to retrieve the key properties of these aerosols. Recent retrieval algorithms have shown a progressive trend toward including multi-angular and multi-spectral polarimetric measurements to produce better retrieval accuracy in comparison to those using measurements based on a single viewing angle. Here, we perform a theoretical investigation of the top of atmosphere (TOA) radiance-related reflectance factor (bidirectional reflectance factor (BRF)) and the two types of polarimetry-related factors (polarized bidirectional reflectance factor (pBRF) and the degree of linear polarization (DoLP)) for different types of atmospheric light-absorbing carbonaceous aerosols as a function of particle size distribution. We selected three polarimetric bands corresponding to those utilized by NASA's Airborne Multiangle SpectroPolarimetric Imager (AirMSPI)—near-UV (470 nm), visible (660 nm), and near-infrared (865 nm)—for our simulations which were performed over ocean surface using the successive order of scattering (SOS) algorithm coupled to a Lorenz-Mie aerosol optics model. The analysis of particle phase matrix elements indicates a close relationship between the angular dependencies of DoLP and associated phase matrix components at the shortest polarimetric band (470 nm). Using Jacobian analysis, we find that the radiance- and polarimetry-related reflectance factors of weakly light-absorbing aerosols, such as brown carbon, are more sensitive to changes in particle size and imaginary refractive index in comparison with those of black carbon, which is strongly light-absorbing. Our results suggest that the DoLP data could be used by future retrieval algorithms for reliably estimating microphysical properties of absorbing carbonaceous aerosols with imaginary refractive index less than 0.4.

refractive index↗
NASA NTRS1972

Solar system applications of Mie theory and of radiative transfer of polarized light

A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.

Whitehill, L. P.↗
NASA NTRSDate not supplied

Velocity and Temperature Measurements in High-speed Flows with Naturally Present Dust Particles Using Rayleigh and Mie Scattering

Dust particles and occasional moisture condensations are unavoidable reality of all wind tunnels. On the path to pursue a goal of velocity and temperature measurements in large transonic and supersonic wind tunnels we have created a tabletop, spectrally resolved, Rayleigh-Mie scattering setup around a small jet fed by ambient and lightly seeded air to determine the viability and accuracy of the technique. The other reality of a wind tunnel setup is the background scattering or the glare at laser frequency, which contaminates the Rayleigh-Mie scattered light. This is simulated by backgrounds with different reflectivity towards the collection optics. Light from a CW laser is delivered via an optical fiber and the scattered light is spectrally resolved using a stabilized Fabry-Perot interferometer, followed by imaging on an EMCCD camera. A model of the of the combined background glare, Mie scattering, and the Rayleigh spectrum was fitted to the camera image using maximum likelihood estimation. Since the background glare occurs at the known frequency of the incident light and the Mie scattering peak corresponds to the Doppler shift from the bulk velocity, both were easily identified, and provided a measure of flow velocity. Preliminary results show that the Rayleigh spectrum can also be resolved, which provides a measure of temperature. It is observed that a slight drift of the laser frequency during data collection affected fitting of the model function leading to larger error. A feedback loop-based stabilization system is on development to take advantage of slight tunability of the laser via a piezo-control. Preliminary results are presented in the abstract. More extensive data from a systematic survey will be presented in the final paper.

Rayleigh scattering↗
NASA NTRS1994

Rigorous Justification of the Localized Approximation to the Beam-Shape Coefficients in Generalized Lorenz-Mie Theory: On-Axis Beams - Part 1

Generalized Lorenz-Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally most expensive feature of the theory is the evaluation of the beam-shape coefficients, which give the decomposition of the incident light beam into partial waves. The so-called localized approximation to these coefficients for a focused Gaussian beam is an analytical function whose use greatly simplifies Gaussian-beam scattering calculations. A mathematical justification and physical interpretation of the localized approximation is presented for on-axis beams.

Lock, James A.↗
NASA NTRS2015

Using Single-Scattering Albedo Spectral Curvature to Characterize East Asian Aerosol Mixtures

Spectral dependence of aerosol single-scattering albedo (SSA) has been used to infer aerosol composition. In particular, aerosol mixtures dominated by dust absorption will have monotonically increasing SSA with wavelength while that dominated by black carbon absorption has monotonically decreasing SSA spectra. However, by analyzing SSA measured at four wavelengths, 440, 675, 870, and 1020 nm from the Aerosol Robotic Network data set, we find that the SSA spectra over East Asia are frequently peaked at 675 nm. In these cases, we suggest that SSA spectral curvature, defined as the negative of the second derivative of SSA as a function of wavelength, can provide additional information on the composition of these aerosol mixtures. Aerosol SSA spectral curvatures for East Asia during fall and winter are considerably larger than those found in places primarily dominated by biomass burning or dust aerosols. SSA curvature is found to increase as the SSA magnitude decreases. The curvature increases with coarse mode fraction (CMF) to a CMF value of about 0.4, then slightly decreases or remains constant at larger CMF. Mie calculations further verify that the strongest SSA curvature occurs at approx. 40% dust fraction, with 10% scattering aerosol fraction. The nonmonotonic SSA spectral dependence is likely associated with enhanced absorption in the shortwave by dust, absorption by black carbon at longer wavelengths, and also the flattened absorption optical depth spectral dependence due to the increased particle size.

curvature↗
NASA NTRS2000

Measurements and Modeling of Aerosol Absorption and Single Scattering Albedo at Ambient Relative Hum

Uncertainties in the aerosol single scattering albedo have been identified to be an important source of errors in current large-scale model estimates of the direct aerosol radiative forcing of climate. A number of investigators have obtained estimates of the single scattering albedo from a variety of remote sensing and in situ measurements during aerosol field experiments. During the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX, 1996) for example, estimates of the aerosol single scattering albedo were obtained (1) as a best-fit parameter in comparing radiative flux changes measured by airborne pyranometer to those computed from independently measured aerosol properties; (2) from estimates of the aerosol complex index of refraction derived using a combination of airborne sunphotometer, lidar backscatter and in situ size distribution measurements; and (3) from airborne measurements of aerosol scattering and absorption using nephelometers and absorption photometers. In this paper, we briefly compare the results of the latter two methods for two TARFOX case studies, since those techniques provide height-resolved information about the aerosol single scattering albedo. Estimates of the aerosol single scattering albedo from nephelometer and absorption photometer measurements require knowledge of the scattering and absorption humidification (i.e., the increase in these properties in response to an increase in ambient relative humidity), since both measurements are usually carried out at a relative humidity different from the ambient atmosphere. In principle, the scattering humidification factor can be measured, but there is currently no technique widely available to measure the absorption of an aerosol sample as a function of relative humidity. Frequently, for lack of better knowledge, the absorption humidification is assumed to be unity (meaning that there is no change in aerosol absorption due to an increase in ambient relative humidity). This assumption then enters the estimate of the single scattering albedo at ambient relative humidity. To investigate the validity of this assumption we have carried out modeling studies of the absorption humidification factor, assuming that the aerosols contain an insoluble soot core and a coating which determines its hygroscopic growth behavior. The aerosol optical properties are then computed on the basis of the shell/core particle morphology using a Mie-code for concentric shells. From basic physical principles, it is conceivable that aerosol absorption increases when an atmospheric aerosol particle collects a non-absorbing shell, since the soot core is then exposed to an increased (focused) electric field strength. Indeed, our preliminary modeling studies show that the absorption of an atmospheric aerosol particle composed of a soot core and an aqueous sulfuric acid shell may increase by a factor of 50% due to a change in ambient relative humidity from 30 to 95%. We will show how this increased absorption is a function of the initial particle size and soot mass fraction.

Redemann, J.↗