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Scattering Calculations of none-spherical particles have been carried out in order to explain observed optical properties of cometary dust. We focused on two optical properties of cometary dust sensitive to particle shape.
Volcanic eruptions loft gases and ash particles into the atmosphere and produce effects that are both short term (aircraft hazards, interference with satellite measurements) and long term (atmospheric chemistry, climate). Large (greater than 0.5mm) ash particles fall out in minutes [Rose et al, 1995], but fine ash particles can remain in the atmosphere for many days. This fine volcanic ash is a hazard to modem jet aircraft because the operating temperatures of jet engines are above the solidus temperature of volcanic ash, and because ash causes abrasion of windows and airframe, and disruption of avionics. At large distances(10(exp 2)-10(exp 4) km or more) from their source, drifting ash clouds are increasingly difficult to distinguish from meteorological clouds, both visually and on radar [Rose et al., 1995]. Satellites above the atmosphere are unique platforms for viewing volcanic clouds on a global basis and measuring their constituents and total mass. Until recently, only polar AVHRR and geostationary GOES instruments could be used to determine characteristics of drifting volcanic ash clouds using the 10-12 micron window [Prata 1989; Wen and Rose 1994; Rose and Schneider 1996]. The NASA Total Ozone Mapping Spectrometer (TOMS) instruments aboard the Nimbus-7, Meteor3, ADEOS, and Earth Probe satellites have produced a unique data set of global SO2 volcanic emissions since 1978 (Krueger et al., 1995). Besides SO2, a new technique has been developed which uses the measured spectral contrast of the backscattered radiances in the 330-380nm spectral region (where gaseous absorption is negligible) in conjunction with radiative transfer models to retrieve properties of volcanic ash (Krotkov et al., 1997) and other types of absorbing aerosols (Torres et al., 1998).
Mie theory, which is generally used to describe the scattering behavior of particles at a certain wavelength, is only rigorously correct for spherical particles. Particles found as atmospheric constituents, with the exception of cloud droplets, are, however, decidedly nonspherical. An investigation is, therefore, conducted regarding the significant ways in which the scattering behavior of irregularly shaped particles differs from that of spheres. A systematic method is formulated for treating the real scalar scattering behavior. A description is presented of a new semiempirical theory based on simple physical principles and data obtained in laboratory measurements, which successfully reproduces the single scattering phase function for a wide range of particle shapes, sizes, and refractive indices.
An approximate method is proposed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound x(o) (about 5), Mie theory is used. For x greater than x(o), the interaction is divided into three components: diffraction, external reflection, and transmission. Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third. The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes. Limitations of the theory are also noted.
A large discrepancy exists in current estimates of a mean cirrus particle size appropriate for calculations of the effects of these ice clouds on solar and thermal infrared radiative fluxes. For spheres with large size parameter (x = (2 pi r / lambda) is greater than 30, where r is particle radius), and moderate absorption (n(sup i) x less than 1, where n(sup i) is imaginary index of refraction for ice), the optimal effective particle radius is given by: r(sub e) = integral of r(exp 3)n(r)dr / integral of r(exp 2)n(r)dr. For the remote sensing of cirrus particle size at wavelengths of 0.83, 1.65, and 2.21 mu m, a 50 mu m ice sphere would have a size parameter of about 200, and values of n(sup i) x of 0, 0.045, and 0.06, satisfying the above conditions. However, while r(sub e) is a well-defined parameter for spheres, this cross-section area-weighted particle radius can only be extended to non-spherical particles by defining some equivalent sphere, typically an equivalent volume or equivalent cross-section area sphere. Using equivalent volume spheres, values of r(sub e) obtained over Lake Michigan on October 28, 1986, during FIRE phase I varied from 200 mu m (King Air 2D Imaging probes) to 60 mu m (Landsat reflectances at 0.83, 1.65, and 2.2 mu m), to 25 mu m (HIS spectrometer thermal emission between 8 and 12 mu m). Three major uncertainties were identified in this comparison: small ice particles missed by the 2D-C aircraft probes, uncertain ice refractive index, and uncertainties in the single scatter albedos and scattering phase functions used in the radiative calculations. Since the first FIRE cirrus results, advances have been made in all three areas. The present paper reports on improvements in the radiative modeling of ice particles at 0.83, 1.65, and 2.21 mu m wavelengths appropriate for comparisons to Landsat Thematic Mapper data. The paper also includes new results for Landsat observations of ice clouds in the eastern and western tropical Pacific.
Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.
The atmosphere of Titan is known to contain aerosols, as evidenced by the Voyager observations of at least three haze layers. Such aerosols can have significant effects on the reflection spectrum of Titan and on the chemistry and thermal structure of its atmosphere. To investigate some of these effects laboratory simulations of the chemistry of Titan's atmosphere have been done. The results of these studies show that photolysis of acetylene, ethylene, and hydrogen cyanide, known constituents of Titan's atmosphere, yields sub-micron sized spheres, with mean diameters ranging from 0.4 to 0.8 micron, depending on the pressures of the reactant gases. Most of the spheres are contained in near-linear aggregates. The formation of the aggregates is consistent with models of Titan's reflection spectrum and polarization, which are best fit with non-spherical particles. At room temperature, the particles are very sticky, but their properties at low temperatures on Titan are presently not known.
Multi-angle, multi-spectral remote sensing observations, such as those anticipated from the Earth Observing System (EOS) Multi-angle Imaging SpectroRadiometer (MISR), can distinguish spherical from non-spherical particles over calm ocean for mineral-dust-like particles with the range of sizes and column amounts expected under natural conditions. The ability to make such distinctions is critical if remote sensing of atmospheric aerosol properties is to provide significant new contributions to our understanding of the global-scale, clear-sky solar radiation balance.
Optical scattering from nonspherical randomly aligned polydisperse particles compared to scattering expected from spherical particles
Air-borne radar measurements of thunderstorms were made as part of the CaPE (Convection and Precipitation/Electrification) experiment in Florida in July 1991. The radar has two channels, X-band (10 GHz) and Ka-band (34.5 GHz), and is capable of measuring cross-polarized returns as well as co-polarized returns. In stratiform rain, the cross-polarized components can be observed only at the bright band region and from the surface reflection. The linear depolarization ratios (LDR's) measured at X-band and Ka-band at the bright band are nearly equal. In convective rain, however, the LDR in Ka-band often exceeds the X-band LDR by several dB, and sometimes by more than 10 dB, reaching LDR values of up to -5 dB over heavy convective rain. For randomly oriented hydrometeors, such high LDR values cannot be explained by single scattering from non-spherical scattering particles alone. Because the LDR by single backscatter depends weakly on the wavelength, the difference between the Ka-band and X-band LDR's suggests that multiple scattering effects prevail in the Ka-band LDR. In order to test this inference, the magnitude of the cross-polarized component created by double scattering was calculated using the parameters of the airborne radar, which for both frequencies has beamwidths of 5.1 degrees and pulse widths of 0.5 microsecond. Uniform rain beyond the range of 3 km is assumed.
Multiangle, multispectral remote sensing observations, such as those anticipated from the Earth Observing System (EOS) Multiangle Imaging SpectroRadiometer (MISR), can significantly improve our ability to constrain aerosol properties from space.
A phase/Doppler spray analyzer (P/DSA) and a laser imaging system was used to study the response of a P/DSA to nonspherical particles. Methanol particles with an aspect ratio ranging from 0.7 to 1.4 were used in this investigation. Results indicated that the P/DSA was quite sensitive to particle shape. A Berglund-Liu generator was used to produce particles of 98 microns (volumetric diameter). The P/DSA instrument measured particle sizes ranging from 142 microns for a particle of aspect ratio 0.7, to 84 microns for an aspect ratio of 1.4. Particle diameters based on averaged x and y diameters for the laser imaging system ranged from 95 microns to 92 microns over the same range of aspect ratios.
High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.
Computations of the intensity and linear polarization for single scattering by ice clouds have been made based on the assumption that the particles in ice clouds can be approximated by long circular cylinders which are allowed to be polydispersive as well as arbitrarily oriented in space. The results of two models of optically thin ice clouds are presented and compared with those for polydisperse ice spheres. The two models for ice cylinders are assumed to be either uniformly or randomly oriented in a horizontal plane. Four different wavelengths, 0.7, 3, 3.5 and 6.05 microns, are employed in the light scattering computations. It is found that, compared to ice spheres, long ice cylinders scatter more light in the region with scattering angles near 90 deg, at the expense of scattering in both the forward and backward directions. The glory and cloudbows, which occur in light scattered by spherical particles, are either lost (the glory) or largely reduced and distorted (the cloudbows in the case of cylinders). It is probable that for more irregular particles the cloudbows would also disappear. These differences in scattering by spherical and non-spherical scatterers therefore provide useful information for the differentiation between the ice and liquid phase of cloud particles.
We are engaged in modeling the scattering and emitting properties of irregular particles with the goal of understanding the composition and structure of cometary dust particles.
An evaluation prototype device is described, together with conclusions and several recommendations for follow-on flight hardware. The device detects individual particles crossing an external sensing zone, and produces a histogram displaying the size distribution of particles sensed, over the nominal range of 5 to 50 microns. The output is totally independent of the particle refractive index, and is also largely unaffected by particle shape. The reported diameters are in terms of the equivalent sphere, as judged by the scattered light intercepted by the receiving channels, which develop signals whenever a particle crosses the beam of illumination in the sensing zone. Supporting evidence for the latter assertion is discussed on the basis of experimental test data for non-spherical particulates. Also included is a technical appendix which presents theoretical arguments that provide a firm foundation for this assertion.
Theoretical models that are useful and practical in relating remote sensing data to the important physical parameters characterizing Earth terrain are developed. The development of models that are useful in data analysis and interpretation, scene simulation, and developing new remote sensing approaches and techniques is discussed. Numerous theoretical models that are applicable to the active and passive remote sensing of plowed fields, atmospheric precipitation, vegetation, and snow fields were developed. The radiative transfer theory is used to interpret the active and passive data as a function of rain rate. Both the random medium model and the discrete scatterer model is used to study the remote sensing of vegetation fields. Due to the non-spherical geometry of the scatterers there is strong azimuthal dependence in the observed data. Thus, the anisotropic random medium model and the discrete scatterer model with nonspherical particles was developed. In order to relate the remote sensing data to the actual physical parameters, the scattering of electromagnetic waves from randomly distributed dielectric scatterers was studied. Both the rigorous random discrete scatterer theory and the strong fluctuation theory are used to derive the backscattering cross section in terms of the actual physical parameters and the results agree well with the data obtained from the snow fields.
Cirrus is the most frequently occurring and widely distributed cloud type. The average annual frequency of occurrence for cirrus is 34% and its global coverage is about 20-30% (Warren et al. 1985). It strongly influences weather and climate processes through its effects on the radiation budget of the earth and the atmosphere (Liou 1986). Microphysics of cirrus is a critical component in understanding cloud-climate radiative interactions. For example, ice water content feedback is positive from a 1-D model study. But the feedback is substantially reduced upon the inclusion of small ice crystals (Sinha and Shine 1994). Due to the complexity caused by the non-spherical shape of ice crystals in cirrus, retrievals of cirrus properties are difficult. In recent years, advances have been made both in models and in case studies (e.g., Takano and Liou 1989, Young et al. 1994), but no global scale survey has been conducted. Similar to our previous near-global survey of droplet sizes of liquid water clouds (Han et al. 1994), a survey of cirrus ice crystal sizes is conducted over both continental and oceanic areas. We describe a method for retrieving cirrus particle size information on a near-global scale 50 deg S to 50 deg N using currently available satellite data from ISCCP. To retrieve cirrus particle size, we use a radiative transfer model that includes all major absorbing gases and cloud scattering/absorption to compute synthetic radiances as a function of satellite viewing geometry. Ice crystal shapes are assumed to be hexagonal columns and plates. The model results have been validated against clear sky observations and are consistent with the observed radiance range under cloudy conditions.