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Outline: (1) Signal Physics for Multiple-Scattering Cloud Lidar, (2) SNR Estimation (3) Cloud Property Retrievals (3a) several techniques (3b) application to Lidar-In-space Technology Experiment (LITE) data (3c) relation to O2 A-band
Backscatter lidars are very useful tools in gaining information about the atmosphere. Inversion of backscatter signals can be used to retrieve the spatial distribution of clouds and aerosols, e.g., vertical extensions of clouds and aerosol layers, detection of 'subvisible' cirrus, etc., very accurately compared to passive radiometers. To retrieve extinction coefficient profiles, in general, the so-called lidar equation is solved. This equation describes a laser pulse which propagates through an atmosphere with transmission exp(- integral of sigma(z')dz'), which is scattered singly under 180 degrees towards a receiver, and which is attenuated on its way back again by exp(- integral of sigma(z')dz'). For inversion, further information on optical properties of the scatterers are required (extinction to backscatter ratio). However, it is evident that, at least for optically thick clouds and/or large receiver's field-of-views, this approach may be erroneous because of multiply scattered photons. Several studies were performed to simulate multiple scattering in case of collimated beams or pulses including Monte Carlo, transport, and diffusion theory. Unfortunately, most of the approaches require an enormous amount of computer time. Thus, it is meaningful to elaborate approximate methods, and one such method is discussed. Our method is based on Bissonnett (1988). We have improved the numerical simulation of limited field-of-view detectors, and compared the results to Monte Carlo calculations and an exact model of Altmann (1989).
A method is proposed for the calculation of a multiple-scattering correction to the single-scattering calculation of the radiance of the terrestrial atmosphere resulting from backscattered ultraviolet solar radiation in the spectral region used in the ozone profile inversion. This method uses jointly the usual analytical and Monte Carlo methods. Effects of the lower boundary of the atmosphere, cloud tops, and ground surface are investigated both qualitatively and quantitatively. The ratio of multiple to single scattering is determined, and its importance in ozone profile inversion of backscattered UV solar radiation from the terrestrial atmosphere is evaluated. The polarization of the atmospheric radiance is treated briefly.
The paper examines the multiple scattering of microwaves due to rain and the resulting incoherent intensity for a plane wave incident on a plane-parallel rain region. General formulations of the transfer equation using Stokes parameters are presented, and an extinction matrix which takes into account depolarization effects and nonspherical droplet shape is introduced. Scattering characteristics are calculated for spherical droplets using the Mie solution and the Laws-Parsons distributions. The ratios of incoherent to coherent received powers are calculated at 30 GHz for rain rates of 12.5, 50, 100, and 150 mm/h, rain thicknesses of 3 km and 10 km, and fields of view of 1.5, 5, and 15 deg.
Polarized light multiple scattering in planetary atmospheres, applying extended doubling method to realistic simulations with allowance for radiation polarization and azimuth dependence
Development of camera and instrument simulations for space exploration requires the development of scientifically accurate models of the objects to be studied. Several planned cometary missions have prompted the development of a three dimensional, multi-spectral, anisotropic multiple scattering model of cometary coma.
In this paper we treat the multiple scattering theory of radiative transfer in plane-parallel inhomogeneous atmospheres. The treatment presented here may be adopted to model atmospheres characterized by an optical depth dependent coherent scattering phase function. For the purpose of illustration we consider the semi-infinite medium in which the absorption property of the atmosphere is characterized by an exponential function. The methodology employed here is the extension of the case treated previously by the author for homogeneous atmospheres.
A technique of deriving Hovenier's exit function equation (1978) for multiple scattering, starting with a set of invariant imbedding equations, is presented. The feasibility of the exit function equation as a means to obtain reflection and transmission functions is investigated for isotropic, Rayleigh, and Henyey-Greenstein phase functions with emphasis on the numerical stability, accuracy and timing. It is possible to compute the reflection function rather accurately with an efficiency comparable to that of the standard doubling technique for the same phase functions with moderate anisotropy. The resulting transmission is slightly less accurate than the reflection function, but it may be acceptable for practical purposes.
The Galileo Ultraviolet Spectrometer Experiment (UVS) obtained a map of the celestial sphere from interplanetary Lyman-alpha (IPLA) on 13, 14 December 1990 during the Earth1 encounter. The Galileo spacecraft was near the downwind interstellar axis during the encounter and the map view directions filled the downwind hemisphere. The ratio between the observation and a single scattering model is attributed to a direct measurement of the multiple scattering correction required to model IPLA in the inner solar system. Analysis of this data set, referred to as an antisun map, shows that the solar wind charge exchange rate with interplanetary gas is 25 percent less over the solar poles than in the ecliptic at solar maximum. A model of the interstellar wind based on the antisun map observation exhibits a number density of atomic hydrogen far from the solar system, inside the heliosphere, of 0.16 +/- 0.05/cu cm.
A numerical solution for the multiple light scattering in spherical axisymmetric geometry is applied to the simulation of images of a coma as it would appear to a near-flying satellite such as Giotto. The appearance of symmetric comas and dust jets is examined in detail; the nucleus visibility is studied; the effect of forward scattering is considered; and single and multiple scattering effects are quantified. Attention is given to simulated images of a coma with a hollow cone of dust, as predicted by dust-gas hydrodynamic modeling. The cone's appearance is very similar to the northern area of activity on Comet Halley, observed by the Giotto HMC.
The solution of the generalized two-stream approximation for radiative transfer in homogeneous multiple scattering atmospheres is extended to vertically inhomogeneous atmospheres in a manner which is numerically stable and computationally efficient. It is shown that solar energy deposition rates, photolysis rates, and infrared cooling rates all may be calculated with the simple modifications of a single algorithm. The accuracy of the algorithm is generally better than 10 percent, so that other uncertainties, such as in absorption coefficients, may often dominate the error in calculation of the quantities of interest to atmospheric studies.
Definitions are provided of the basic concepts occurring in the solution of multiple scattering problems involving planetary atmospheres and attention is given to aspects of problem characterization. Approaches are considered for finding the answer to a particular problem without the performance of detailed calculations. The characteristics of albedos are investigated, taking into account semiinfinite atmospheres and finite atmospheres. Questions of surface illumination are discussed along with aspects related to energy deposition in the atmosphere, intensity, and polarization. Precise numerical methods are examined and analytical solutions are presented.
Multiple light scattering solutions accuracy by diffraction peak omission from cloud and haze analytic phase functions compared for optically thick and thin planetary atmospheres
The boundary value problem of plane H-polarized electromagnetic wave multiple scattering by a finite number of unclosed circular cylinders is solved. The solution is obtained by two different methods: the method of successive scattering and the method of partial matrix inversion for simultaneous dual equations. The advantages of the successive scattering method are shown. Computer calculations of the suface currents and the total cross section are presented for the structure of two screens.
A numerical solution has been developed for the anisotropic multiple scattering of light in a spherical shell comet atmosphere. The code has been run for a spherically symmetric coma distribution, benchmarked against past studies, and then run for the conditions of an axisymmetric dust jet at the subsolar point of the comet. The radiant flux impinging on the nucleus surface and the mean intensity of light throughout the coma were investigated.
For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.
Computational results have been obtained for the spherical albedo, global transmission, and global absorption of plane-parallel layers composed of cloud droplets. These computations, obtained using the doubling method for the entire range of single scattering albedos and for optical depths between 0.1 and 100, are compared with corresponding results obtained using selected multiple scattering approximations. The spherical albedo and global absorption computed using asymptotic theory are found to be accurate to better than 5 percent for all values of the single scattering albedo, provided the optical thickness exceeds about 2. The diffuse two-stream approximations have relative accuracies that are much worse than 5 percent for the spherical albedo over most of the parameter space, yet are accurate to within 5 percent in the global absorption when the absorption is significant. The integrated delta-Eddington scheme appears to be the most suitable model over the entire range of variables, generally producing relative errors of less than 5 percent in both the spherical albedo and global absorption.
The ellipticity and the direction of polarization are calculated for radiation that has undergone multiple scattering from plane parallel layers. Both the radiation emerging from the top of the layer and that transmitted through the bottom are considered. Two different phase functions are used for the scattering layer: Rayleigh and haze L. The direction of polarization of the reflected radiation shows little variation as the optical depth of the layer increases, while there is a much larger variation for the transmitted radiation. When the optical thickness is small, the direction of polarization for haze L varies rapidly with zenith angle near those angles at which the single scattered polarization is zero. The ellipticity of the radiation from haze L layers increases at first in direct proportion to the optical thickness of the layer. In general the ellipticity of the transmitted radiation is considerably greater than that of the reflected because of the greater average number of photon collisions in the former case.