Light from reflection nebulae. I.
Models of reflection nebulae light for single scattering, pure or modified by internal nebular extinction, on spherical grains imitating dielectric or metallic particles
ASTRONOMICAL MODEL↗
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Results for “MIE SCATTERING FUNCTION”
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Electromagnetic scattering from absorbing spheres.
Computational scheme for calculation of Mie cross sections of absorbing particles
MIE SCATTERING FUNCTION↗
Complex refractive index of Martian dust - Mariner 9 ultraviolet observations
Mariner 9 ultraviolet spectrometer observations of the 1971 dust clouds obscuring the surface of Mars have been analyzed by matching the observed dust phase function with Mie scattering calculations for size distributions of homogeneous and isotropic material. Preliminary results indicate an effective particle radius of not less than 0.2. The real component of the index of refraction is not less than 1.8 at both 268 and 305 nm; corresponding values for the imagery component are 0.02 and 0.01. These values are consistent with those found by Mead (1970) for the visible and near-visible wavelengths. The refractive index and the absorption coefficient increase rapidly with decreasing wavelength in going from the visible to the ultraviolet, indicating the presence of an ultraviolet absorption band which may shield organisms from ultraviolet irradiation.
Pang, K.↗
Microwave brightness of polar firn as measured by Nimbus 5 and 6 ESMR
The microwave emission from a half-space medium characterized by coordinate dependent scattering and absorbing centers was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. A Mie scattering phase function and surface polarization was included in the calculation. Also included are the physical temperature profile and the temperature variation of the index of refraction for ice. Using published values of grain size and temperature profile data of polar firn, the brightness temperature was calculated for the 1.55 cm and 0.8 cm wavelengths. For selected regions in Greenland and Antarctica, the results are in reasonable agreement with the observed Nimbus-5 and Nimbus-6 ESMR data.
Chang, A. T. C.↗
Effects of subsurface volume scattering on the lunar microwave brightness temperature spectrum
The effects of volumetric scattering on the lunar microwave brightness temperature are examined for a broad range of feasible lunar rock population distributions. Mie-scattering phase functions and the radiative transfer method are utilized. Surveyor and Apollo data relevant to lunar rock size distributions are discussed, and parameters are chosen for nine scattering models which liberally cover the range of studied rock population distributions. Scattering model brightness temperature predictions are analyzed in terms of the lunar disk center emission averaged over a lunation for wavelengths of 3-30 cm. The effects of scattering on the amplitude of disk center brightness temperature variations and resultant deductions of regolith electrical loss are examined. Constraints on the global scale variability of subsurface scatterers imposed by microwave brightness temperature maps are considered.
Keihm, S. J.↗
Passive and active remote sensing of atmospheric precipitation
Both passive and active remote sensing of atmospheric precipitation are studied with the vector radiative transfer equations by making use of the Mie scattering phase functions and incorporating the raindrop-size distributions. For passive remote sensing, the Gaussian quadrature method is employed to solve for the brightness temperatures. For active remote sensing, an iterative approach carrying out to the second order in albedo is used to calculate for the bistatic coefficients, the backscattering cross sections/unit volume, and the interchannel cross talks. The calculated results are plotted as a function of rainfall rates and compared to various available experimental data. The theoretical model is easily applied to the remote sensing of aerosol particles, smoke, fog, and haze at infrared and visible frequencies.
Jin, Y. Q.↗
Mie scattering and absorption cross sections for absorbing particles.
Mie scattering and absorption cross sections for spherical absorbing particles as function of complex refractive index
MIE SCATTERING FUNCTION↗
Calculations of reflected and transmitted radiance for earth's atmosphere.
Monte Carlo method to calculate reflected and transmitted radiance of earth atmosphere using exact scattering function for aerosols by Mie theory
Kattawar, G. W.↗
Determination of Atmospheric Aerosol Characteristics from the Polarization of Scattered Radiation
Aerosols affect the polarization of radiation in scattering, hence measured polarization can be used to infer the nature of the particles. Size distribution, particle shape, real and absorption parts of the complex refractive index affect the scattering. From Lorenz-Mie calculations of the 4-Stokes parameters as a function of scattering angle for various wavelengths the following polarization parameters were plotted: total intensity, intensity of polarization in plane of observation, intensity perpendicular to the plane of observation, polarization ratio, polarization (using all 4-Stokes parameters), plane of the polarization ellipse and its ellipticity. A six-component log-Gaussian size distribution model was used to study the effects of the nature of the polarization due to variations in the size distribution and complex refractive index. Though a rigorous inversion from measurements of scattering to detailed specification of aerosol characteristics is not possible, considerable information about the nature of the aerosols can be obtained. Only single scattering from aerosols was used in this paper. Also, the background due to Rayleigh gas scattering, the reduction of effects as a result of multiple scattering and polarization effects of possible ground background (airborne platforms) were not included.
Harris, F. S., Jr.↗
Airborne Laser Polar Nephelometer
A polar nephelometer has been developed at NCAR to measure the angular variation of the intensity of light scattered by air molecules and particles. The system has been designed for airborne measurements using outside air ducted through a 5-cm diameter airflow tube; the sample volume is that which is common to the intersection of a collimated source beam and the detector field of view within the airflow tube. The source is a linearly polarized helium-neon laser beam. The optical system defines a collimated field-of-view (0.5deg half-angle) through a series of diaphragms located behind a I72-mm focal length objective lens. A photomultiplier tube is located immediately behind an aperture in the focal plane of the objective lens. The laser beam is mechanically chopped (on-off) at a rate of 5 Hz; a two-channel pulse counter, synchronized to the laser output, measures the photomultiplier pulse rate with the light beam both on and off. The difference in these measured pulse rates is directly proportional to the intensity of the scattered light from the volume common to the intersection of the laser beam and the detector field-of-view. Measurements can be made at scattering angles from 15deg to 165deg with reference to the direction of propagation of the light beam. Intermediate angles are obtained by selecting the angular increments desired between these extreme angles (any multiple of 0.1deg can be selected for the angular increment; 5deg is used in normal operation). Pulses provided by digital circuits control a stepping motor which sequentially rotates the detector by pre-selected angular increments. The synchronous photon-counting system automatically begins measurement of the scattered-light intensity immediately after the rotation to a new angle has been completed. The instrument has been flown on the NASA Convair 990 airborne laboratory to obtain data on the complex index of refraction of atmospheric aerosols. A particle impaction device is operated simultaneously to collect particles from the same airflow tube used to make the scattered-light measurements. A size distribution function is obtained by analysis of the particles collected by the impaction device. Calculated values of the angular variation of the scattered-light intensity are obtained by applying Mie scattering theory to the observed size distribution function and assuming different values of the complex index of refraction of the particles. The calculated values are then compared with data on the actual variation of the scattered-light intensity obtained with the polar nephelometer. The most probable value of the complex refractive index is that which provides the best fit between the experimental light scattering data and the parameters calculated from the observed size distribution function.
Grams, Gerald W.↗
Double scattering corrections for the theory of the sun's aureole
Double scattering corrections for aureole radiances are calculated by adding the effects of two successive single scatterings. Atmospheric absorption, polarization, and variation of refractive index with altitude are ignored. Corrections due to spherical atmosphere were taken into account by the use of a generalized Chapman function. Realistic scattering phase functions based upon the Lorenz-Mie theory and model altitude-size distribution are used. The model distribution is assumed to be representable in terms of two separable particulate components. It was found that for a moderately clear day, tau (0) is approximately equal to 0.5, and for forward scattering angles, the radiance, B sub 2, due to double scattering is less than 6 percent of that due to single scattering.
Deepak, A.↗
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.↗
A new method to measure homogeneous nucleation rates in shock tubes
The centered expansion wave of a shock tube is utilized to expand and supersaturate a condensable vapor in small concentration in an inert carrier gas. The supersaturated state, located at the rear of the expansion wave, is preserved for a controlled period and then terminated by a recompressing shock wave. During the period of supersaturation, condensation nuclei are formed homogeneously. The nucleation rate is measured as a function of supersaturation by a Mie-light scattering technique. The method is tested using water and the results are compared with classical nucleation theory.
Peters, F.↗
A catalogue of normalized intensity functions and polarization from a cloud of particles with a size distribution of alpha to the minus 4th power
The Mie theory of light scattering by spheres was used to calculate the scattered intensity functions resulting from single scattering in a polydispersed collection of spheres. The distribution used behaves according to the inverse fourth power law; graphs and tables for the angular dependence of the intensity and polarization for this law are given. The effects of the particle size range and the integration increment are investigated.
Craven, P. D.↗
Physical retrieval of precipitation cell parameters using passive 118-GHz observations
Physical retrieval of precipitation parameters from 118-GHz spectra is investigated using an iterative planar-stratified numerical radiative-transfer model. Liquid and frozen hydrometeors are modeled as spherical Marshall-Palmer and Sekhon-Srivastava (SS) distributed Mie-scattering polydispersions, respectively, with Henyey-Greenstein phase functions. A comparison of 118-GHz rain-cell spectral perturbations observed during Cohmex with model calculations based on coincident radar data yields + or - 10 percent agreement over the convective core region, although a mean ice size 50 percent larger than that given by the SS distribution is required for agreement over the anvil region. A rain-cell model parameterized by top-altitude and total water density suggests that the dominant 118-GHz spectral modes can be used to retrieve top-layer altitude with rms errors of about 1-1.5 km, consistent with statistical retrieval results. Model calculations also suggest that cell density is not observable using 118-GHz spectra alone.
Gasiewski, A. J.↗
Intercomparison of Models Representing Direct Shortwave Radiative Forcing by Sulfate Aerosols
The importance of aerosols as agents of climate change has recently been highlighted. However, the magnitude of aerosol forcing by scattering of shortwave radiation (direct forcing) is still very uncertain even for the relatively well characterized sulfate aerosol. A potential source of uncertainty is in the model representation of aerosol optical properties and aerosol influences on radiative transfer in the atmosphere. Although radiative transfer methods and codes have been compared in the past, these comparisons have not focused on aerosol forcing (change in net radiative flux at the top of the atmosphere). Here we report results of a project involving 12 groups using 15 models to examine radiative forcing by sulfate aerosol for a wide range of values of particle radius, aerosol optical depth, surface albedo, and solar zenith angle. Among the models that were employed were high and low spectral resolution models incorporating a variety of radiative transfer approximations as well as a line-by-line model. The normalized forcings (forcing per sulfate column burden) obtained with the several radiative transfer models were examined, and the discrepancies were characterized. All models simulate forcings of comparable amplitude and exhibit a similar dependence on input parameters. As expected for a non-light-absorbing aerosol, forcings were negative (cooling influence) except at high surface albedo combined with small solar zenith angle. The relative standard deviation of the zenith-angle-averaged normalized broadband forcing for 15 models-was 8% for particle radius near the maximum in this forcing (approx. 0.2 microns) and at low surface albedo. Somewhat greater model-to-model discrepancies were exhibited at specific solar zenith angles. Still greater discrepancies were exhibited at small particle radii and much greater discrepancies were exhibited at high surface albedos, at which the forcing changes sign; in these situations, however, the normalized forcing is quite small quite small. Discrepancies among the models arise from inaccuracies in Mie calculations, differing treatment of the angular scattering phase function, differing wavelength and angular resolution, and differing treatment of multiple scattering. These results imply the need for standardized radiative transfer methods tailored to the direct aerosol forcing problem. However, the relatively small spread in these results suggests that the uncertainty in forcing arising from the treatment of radiative forcing of a well-characterized aerosol at well-specified surface albedo is smaller than some of the other sources of uncertainty in estimates of direct forcing by anthropogenic sulfate aerosols and anthropogenic aerosols generally.
Boucher, O.↗
BOREAS Aerosol Optical Depth Measurements and Atmospheric Correction
Aerosol optical depth measurements were conducted during all three Intensive Field Campaigns of BOREAS in 1994 by both groundbased and airborne tracking sun photometers. These measurements documented the highly variable aerosol loadings in the BOREAS study areas: very clear days with optical depths at 525 nm of 0.05 alternated with very hazy days (due to smoke from extensive western forest fires) with optical depths greater than 0.5. The airborne sun photometer showed the aerosol layer extended up to 3.5-4 km. Remote sensing missions were largely constrained to clear days, but some occurred under less optimum conditions. The spectral aerosol optical depths were used to derive aerosol size distributions and other aerosol optical properties useful for atmospheric correction of satellite and aircraft remote sensing imagery. Aerosol scattering phase functions and aerosol single scattering albedoes were calculated from Mie scattering theory using reasonable assumptions for the index of refraction for the aersols. Our atmospheric correction procedure Imagecor used the aerosol optical properties to derive surface radiances at each pixel from Landsat Thematic Mapper data of the southern study area on July 25, 1994. Similar efforts under FIFE showed close agreement between atmospherically corrected surface radiances and helicopter measurements of surface radiance of the same sites. Recently we incorporated calculations of the total downwelling irradiance from the 6S radiative transfer program (which vary little over the entire Landsat scene) to derive surface reflectances from the atmospherically corrected surface radiances. Tests using this procedure with both FIFE and HAPEX data sets show good agreement with ground-measured surface reflectances. Surface reflectances derived from the atmospherically corrected radiances of the July 25th Landsat scene will be compared to surface measurements made in BOREAS'southern study area.
Wrigley, R. C.↗
Rainbow Fourier Transform
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Alexandrov, Mikhail D.↗