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Y. Takano and K. N. Liou

Abstract

A new Monte Carlo/geometric ray-tracing method has been developed for the computation of the scattering, absorption, and polarization properties of ice crystals with various irregular structure, including hollow columns, bullet rosettes, dendrites, and capped columns. The shapes of these ice crystals are defined by appropriate geometric models and incident coordinate systems. The incident photons are traced with a hit-and-miss Monte Carlo method and followed by geometric reflection and refraction on the crystal boundary. Absorption has been accounted for by means of stochastic procedures. Computation of the phase matrix elements and normalization of the phase function have been carried out using the results derived from rays that undergo reflections and refractions and from Fraunhofer diffraction using projected cross section areas for irregular ice crystals.

Numerical results are presented for visible and near-infrared wavelengths. It is shown that irregular ice crystals scatter more in forward directions than do solid columns and plates and the single scattering albedo becomes larger when a crystal becomes more complex in shape. Results simulated for randomly oriented hollow columns can be used to interpret lidar backscattering observations. Moreover, the authors further illustrate that the computed phase matrix values for randomly oriented dendrites closely match with 1aboratory observed data for plate-type crystals generated in cold chambers. It is also shown that using equal volume or equal projected-area spheres 1eads to significant errors in the computation of scattering, absorption, and polarization properties for irregular ice crystals. The phase functions, the single scattering albedos and their parameterizations, as well as the polarization patterns presented in this paper are significant in terms of the interpretation of radiance and flux observations from the ground, the air, and space in cirrus cloudy conditions and for remote sensing applications.

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Y. Takano, K. N. Liou, and P. Minnis

Abstract

Using a model that combines single-scattering properties for spheroidal and hexagonal ice crystals, the thermal infrared radiative properties of cirrus clouds have been investigated. Infrared scattering and absorption properties for randomly oriented spheroids and hexagons are parameterized based on the anomalous diffraction theory and a geometric ray-tracing method, respectively. Using observed ice crystal size distributions, upwelling radiances at the top of cirrus cloudy atmospheres have been computed. Results show that the presence of small ice crystals can produce significant brightness temperature differences between two infrared wavelengths in the 10-μm window. Theoretical results have been compared with observed brightness temperature differences between 8.35 and 11.16 μm and between 11.16 and 12 μm. The observed values were obtained from the High-Spectral Resolution Interferometer Sounder. It is shown that the use of the present nonspherical model for ice crystals in radiative transfer calculations leads to a significantly better interpretation of the observed data than does the use of the spherical model.

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K. N. Liou, S. C. Ou, Y. Takano, and Q. Liu

Abstract

The delta-four-stream polarized (vector) thermal radiative transfer has been formulated and numerically tested specifically for application to satellite data assimilation in cloudy atmospheres. It is shown that for thermal emission in the earth’s atmosphere, the [I, Q] component of the Stokes vector can be decoupled from the [U, V] component and that the solution of the vector equation set involving the four-stream approximation can be expressed in an analytic form similar to the scalar case. Thus, the computer time requirement can be optimized for the simulation of forward radiances and their derivatives. Computations have been carried out to illustrate the accuracy and efficiency of this method by comparing radiance and polarization results to those computed from the exact doubling method for radiative transfer for a number of thermal infrared and microwave frequencies. Excellent agreement within 1% is shown for the radiance results for all satellite viewing angles and cloud optical depths. For polarization, differences between the two are less than 5% if brightness temperature is used in the analysis. On balance of the computational speed and accuracy, the four-stream approximation for radiative transfer appears to be an attractive means for the simulation of cloudy radiances and polarization for research and data assimilation purposes.

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H. Gerber, Y. Takano, Timothy J. Garrett, and Peter V. Hobbs

Abstract

A new instrument, a cloud integrating nephelometer (CIN), was used on the University of Washington’s CV-580 research aircraft to measure the asymmetry parameter (g), volume scattering coefficient, and backscatter ratio in clouds in situ and in the visible spectrum during the FIRE-ACE/SHEBA field project in the late spring and summer of 1998 in the Arctic. The principle behind the operation of the CIN is described, and error estimates for the measurements are calculated. The average value of g measured with the CIN in all the Arctic clouds was 0.824, which is slightly less than the value expected for the water-containing clouds that dominated the measurements. The average value of g measured in a glaciated cloud, containing mostly large bullet rosette ice crystals, was 0.737. This relatively small value of g is compared to modeled and indirect measurements of g described in the literature, some of which gave similar small values of g.

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K. N. Liou, S. C. Ou, Y. Takano, F. P. J. Valero, and T. P. Ackerman

Abstract

A dual-channel retrieval technique involving the water vapor band at 6.5 μm and the window region at 10.5 gm has been developed to infer the temperature and emissivity of tropical anvils. This technique has been applied to data obtained from the ER-2 narrow field-of-view radiometers during two flights in the field observation of the Stratosphere-Troposphere Exchange Project (STEP) near Damn, Australia, January-February 1987. The retrieved cloud temperatures are between 190 and 240 K, while the cloud emissivities derived from the retrieval algorithm range from about 0.2 to 1. Moreover, the visible optical depths have been obtained from the cloud emissivity through a theoretical parameterization with values of 0.5-10. A significant portion of tropical cirrus clouds are found to have optical depths greater than about 6. Because of the parameterization, the present technique is unable to precisely determine the optical depth values for optically thick cirrus clouds.

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S. C. Ou, K. N. Liou, Y. Takano, and R. L. Slonaker

Abstract

This paper presents a conceptual approach toward the remote sensing of cirrus cloud particle size and optical depth using the degree of polarization and polarized reflectance associated with the first three Stokes parameters, I, Q, and U, for the 0.865- and 2.25-μm wavelengths. A vector line-by-line equivalent radiative transfer program including the full Stokes parameters based on the adding method was developed. The retrieval algorithm employs the steepest-descent method in the form of a series of numerical iteration procedures to search for the simulated polarization parameters that best match the measured values. Sensitivity studies were performed to investigate the behavior of phase-matrix elements as functions of scattering angles for three ice crystal size–shape combinations. Overall, each phase-matrix element shows some sensitivity toward ice crystal shape, size, and surface roughness due to the various optical effects. Synthetic analysis reveals that the retrieval algorithm is highly accurate, while polarimetric and radiometric error sources cause very small retrieval errors. Finally, an illustrative example of applying the retrieval algorithm to airborne Polarization and Directionality of the Earth’s Reflectances (POLDER) data during the European Cloud and Radiation Experiment (EUCREX) is presented.

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S.C. Ou, K.N. Liou, Y. Takano, N.X. Rao, Q. Fu, A.J. Heymsfield, L.M. Miloshevich, B. Baum, and S.A. Kinne

Abstract

Using the data obtained from the Advanced Very High Resolution Radiometer (AVHRR) 3.7-µm and 10.9-µm channels, a retrieval scheme has been developed to simultaneously infer cirrus cloud optical depth and mean effective ice crystal size based on the theory of radiative transfer and parameterizations. A numerical scheme is further developed to remove the solar component in the 3.7-µm radiance for applications to daytime satellite data. This scheme is based on the correlation between the 3.7-µm (solar) and 0.63-µm reflectances. Validation of the algorithm has been performed by using various datasets that were collected during the FIRE-II IFO (Nov-Dec 1991) at Coffeyville, Kansas. We have focused on the 26 November and 5 December cases. The retrieval analysis over a 0.5°×1.0° area is performed around Coffeyville for each case based on AVHRR-HRPT data. For validation the authors analyze the photomicrograph data collected by the balloonborne replicator, determine the microphysical and optical properties of the sampled cirrus clouds, and derive their position at the satellite overpass based on sounding data. It is demonstrated that the retrieved cirrus cloud temperature, mean effective ice crystal size, and optical depth closely match the observed values. Further, the retrieved cirrus cloud properties are applied to the computation of surface radiative fluxes using a radiative transfer program that involves a consistent representation of cirrus cloud fields. The computed values are compared with the data measured from ground-based radiometers, and it is shown that the computed downward surface IR and solar fluxes are within 5 and 10 W m−2 of the measured values, respectively, near the time of satellite overpass.

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