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- Author or Editor: J. A. Weinman x
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Abstract
Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).
Abstract
Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).
Abstract
The equation of radiative transfer is applied to the analysis of solar irradiances penetrating into a plant canopy covered by a turbid atmosphere. The method of discrete coordinates is applied to vertically inhomogeneous atmospheres and plant canopies. It is shown that four-point quadrature yields results with an accuracy which is consistent with irradiance measurements.
Abstract
The equation of radiative transfer is applied to the analysis of solar irradiances penetrating into a plant canopy covered by a turbid atmosphere. The method of discrete coordinates is applied to vertically inhomogeneous atmospheres and plant canopies. It is shown that four-point quadrature yields results with an accuracy which is consistent with irradiance measurements.
Abstract
The polarization of 37 GHz microwave radiances emerging from rain clouds above land, rough and calm water surfaces was computed from the equation of radiative transfer. Scattering was assumed to be characterized by a Rayleigh phase matrix. The radiative transfer equation was solved by means of a Neumann solution. It was found that the brightness temperatures of the upward directed radiances emerging from rain clouds were relatively independent of polarization. The weak polarization of radiation emitted by rain clouds can be used to discriminate between cool brightness temperatures emerging from rain clouds and open water. The brightness temperatures of radiances emerging from rain clouds over water can be transformed into a single-valued function of the rainfall rate if polarization effects are considered. A sample of Nimbus 6 data is analyzed in accord with the results of the theoretical analysis.
Abstract
The polarization of 37 GHz microwave radiances emerging from rain clouds above land, rough and calm water surfaces was computed from the equation of radiative transfer. Scattering was assumed to be characterized by a Rayleigh phase matrix. The radiative transfer equation was solved by means of a Neumann solution. It was found that the brightness temperatures of the upward directed radiances emerging from rain clouds were relatively independent of polarization. The weak polarization of radiation emitted by rain clouds can be used to discriminate between cool brightness temperatures emerging from rain clouds and open water. The brightness temperatures of radiances emerging from rain clouds over water can be transformed into a single-valued function of the rainfall rate if polarization effects are considered. A sample of Nimbus 6 data is analyzed in accord with the results of the theoretical analysis.
Abstract
Spaceborne millimeter-wave radiometric measurements offer the potential to observe snowfall at high latitudes. A spaceborne W-band cloud radar on CloudSat has been able to observe snow. There is thus a need for a relatively simple representation of millimeter-wave scattering parameters of snow that can be incorporated into algorithms to retrieve snowfall from remotely sensed millimeter-wave brightness temperature measurements and for computing the millimeter-wave backscatter phase function of randomly oriented aggregates of ice prisms or columns.
The extinction coefficients, asymmetry factors, and backscatter phase functions describing scattering by randomly oriented aggregates of elongated cylinders were computed from the discrete dipole approximation. These parameters were also computed by means of a T-matrix model applied to single blunt cylinders by employing a phase delay that only depended on the frequency and the ratio of the volume to the projected area of the cylindrical aggregates. These scattering parameters were fitted by empirical analytical functions that only depended on that phase delay. This permitted consideration of numerous aggregate shapes with far less computational effort than that required by the discrete dipole approximation.
The results of this analysis were applied to measurements of millimeter-wave extinction, radar reflectivity, and snow size distributions obtained during the SNOW-TWO field experiment conducted by the U.S. Army in 1984. Although the simultaneity of the various measurements was not well documented, the theoretical results fell within the range of measurement uncertainty. Model results of the extinction coefficient and asymmetry factor needed to compute 183-GHz brightness temperatures measured by the NOAA Advanced Microwave Sounding Unit-B (AMSU-B) radiometers are presented in the appendix.
Abstract
Spaceborne millimeter-wave radiometric measurements offer the potential to observe snowfall at high latitudes. A spaceborne W-band cloud radar on CloudSat has been able to observe snow. There is thus a need for a relatively simple representation of millimeter-wave scattering parameters of snow that can be incorporated into algorithms to retrieve snowfall from remotely sensed millimeter-wave brightness temperature measurements and for computing the millimeter-wave backscatter phase function of randomly oriented aggregates of ice prisms or columns.
The extinction coefficients, asymmetry factors, and backscatter phase functions describing scattering by randomly oriented aggregates of elongated cylinders were computed from the discrete dipole approximation. These parameters were also computed by means of a T-matrix model applied to single blunt cylinders by employing a phase delay that only depended on the frequency and the ratio of the volume to the projected area of the cylindrical aggregates. These scattering parameters were fitted by empirical analytical functions that only depended on that phase delay. This permitted consideration of numerous aggregate shapes with far less computational effort than that required by the discrete dipole approximation.
The results of this analysis were applied to measurements of millimeter-wave extinction, radar reflectivity, and snow size distributions obtained during the SNOW-TWO field experiment conducted by the U.S. Army in 1984. Although the simultaneity of the various measurements was not well documented, the theoretical results fell within the range of measurement uncertainty. Model results of the extinction coefficient and asymmetry factor needed to compute 183-GHz brightness temperatures measured by the NOAA Advanced Microwave Sounding Unit-B (AMSU-B) radiometers are presented in the appendix.
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Global precipitation measurements from space-based radars and microwave radiometers have been the subject of numerous studies during the past decade. Rainfall retrievals over land from spaceborne microwave radiometers depend mainly on scattering from frozen hydrometeors. Unfortunately, the relationship between frozen hydrometeors and rainfall varies considerably. The large field of view and related beam filling of microwave radiometer footprints introduce additional difficulties. Some of these problems will be addressed by the improved sensors that will be placed on the Global Precipitation Measurement (GPM) core satellite. Two shuttle missions demonstrated that X-band synthetic aperture radar (X-SAR) could observe rainfall over land. Several X-band SARs that can provide such measurements will be launched in the coming decade. These include four Constellation of Small Satellites for Mediterranean Basin Observations (COSMO-SkyMed), two TerraSAR-X, and a fifth Korea Multipurpose Satellite (KOMPSAT-5) to be launched by the Italian, German, and Korean Space Agencies, respectively. Data from these satellites could augment the information available to the GPM science community. The present study presents computations of normalized radar cross sections (NRCS) that employed a simple, idealized two-layer cloud model that contained both rain and frozen hydrometeors. The modeled spatial distributions of these hydrometeors varied with height and horizontal distance. An exploratory algorithm was developed to retrieve the shape, width, and simple representations of the vertical profiles of frozen hydrometeors and rain from modeled NRCS scans. A discussion of uncertainties in the retrieval is presented.
Abstract
Global precipitation measurements from space-based radars and microwave radiometers have been the subject of numerous studies during the past decade. Rainfall retrievals over land from spaceborne microwave radiometers depend mainly on scattering from frozen hydrometeors. Unfortunately, the relationship between frozen hydrometeors and rainfall varies considerably. The large field of view and related beam filling of microwave radiometer footprints introduce additional difficulties. Some of these problems will be addressed by the improved sensors that will be placed on the Global Precipitation Measurement (GPM) core satellite. Two shuttle missions demonstrated that X-band synthetic aperture radar (X-SAR) could observe rainfall over land. Several X-band SARs that can provide such measurements will be launched in the coming decade. These include four Constellation of Small Satellites for Mediterranean Basin Observations (COSMO-SkyMed), two TerraSAR-X, and a fifth Korea Multipurpose Satellite (KOMPSAT-5) to be launched by the Italian, German, and Korean Space Agencies, respectively. Data from these satellites could augment the information available to the GPM science community. The present study presents computations of normalized radar cross sections (NRCS) that employed a simple, idealized two-layer cloud model that contained both rain and frozen hydrometeors. The modeled spatial distributions of these hydrometeors varied with height and horizontal distance. An exploratory algorithm was developed to retrieve the shape, width, and simple representations of the vertical profiles of frozen hydrometeors and rain from modeled NRCS scans. A discussion of uncertainties in the retrieval is presented.
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Abstract
Eddington's approximation was employed to compute the irradiances passing through atmospheres consisting of several different, albeit internally homogeneous, layers, as a function of solar zenith angle, albedo for single scatering, the asymmetry factor of the phase function, and the albedo of the underlying surface. Results computed for a single layer atmosphere were found to agree with more exact computations within a few percent.
Irradiances within several vertically inhomogeneous three-layer model atmospheres were computed. Effects caused by the vertically inhomogeneous structure are considered. It is noted, for example, that the irradiance within an atmosphere can be greater than that incident upon the atmosphere bemuse radiation may he partially trapped within the atmosphere. The Eddington approximation affords a means to rapidly compute irradiances within realistic inhomogeneous atmospheres with an accuracy of several percent.
Abstract
Eddington's approximation was employed to compute the irradiances passing through atmospheres consisting of several different, albeit internally homogeneous, layers, as a function of solar zenith angle, albedo for single scatering, the asymmetry factor of the phase function, and the albedo of the underlying surface. Results computed for a single layer atmosphere were found to agree with more exact computations within a few percent.
Irradiances within several vertically inhomogeneous three-layer model atmospheres were computed. Effects caused by the vertically inhomogeneous structure are considered. It is noted, for example, that the irradiance within an atmosphere can be greater than that incident upon the atmosphere bemuse radiation may he partially trapped within the atmosphere. The Eddington approximation affords a means to rapidly compute irradiances within realistic inhomogeneous atmospheres with an accuracy of several percent.
