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Biao Wang

1. Introduction The radiative transfer equation (RTE) for plane-parallel atmospheres can be solved through a sequence of decompositions. First, the atmosphere under consideration is divided into a stack of approximately quasi-homogeneous layers. The equation for each of the layers can be solved by, among others, the discrete ordinate method (DOM; e.g., Stamnes et al. 1988b ) or the spherical harmonic method (SHM; e.g., Karp et al. 1980 ), including their low-order approximations (e

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Alan J. Geer, Peter Bauer, and Christopher W. O’Dell

1. Introduction The small-scale variability of cloud and precipitation must be carefully modeled in order to get accurate simulations of atmospheric radiative transfer. For example, the amount of overlap between different cloud layers can strongly affect quantities such as heating rates and the earth’s albedo (e.g., Morcrette and Fouquart 1986 ; Morcrette and Jakob 2000 ). At microwave frequencies, the nonlinear dependence of radiance on hydrometeor amount causes a “beamfilling effect” in

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Qing Yue, K. N. Liou, S. C. Ou, B. H. Kahn, P. Yang, and G. G. Mace

1. Introduction Satellite data assimilation in numerical weather prediction models requires an efficient and accurate radiative transfer model for the computation of radiances and Jacobians. Present thermal infrared radiative transfer models for satellite data assimilation have been developed primarily for clear conditions (i.e., pure absorbing atmospheres). However, many studies have found that a great majority of satellite observations is “contaminated” by clouds. For example, Saunders (2000

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Ming Liu, Jason E. Nachamkin, and Douglas L. Westphal

1. Introduction Solar and thermal infrared radiation is a fundamental mechanism for driving the energy exchange among air mass, clouds, aerosols, and land surface to maintain the thermal and dynamic systems in the atmosphere. The accurate prediction of atmospheric radiative processes, particularly cloud–radiation interaction, highly depends on the accurate calculation of radiative transfer fluxes (i.e., radiative transfer parameterizations). It has been well recognized that radiation modeling

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Hua Yuan, Robert E. Dickinson, Yongjiu Dai, Muhammad J. Shaikh, Liming Zhou, Wei Shangguan, and Duoying Ji

not been translated into simple analytical solutions suitable for climate models. On the other hand, the concepts of gap probability and clumping index ( Nilson 1971 ; Norman and Welles 1983 ; Li and Strahler 1988 ; Chen and Black 1991 ) have been introduced to take into account the 3D effects of canopy, for example, through the geometric optical–radiative transfer (GORT) model ( Li et al. 1995 ), which has been further developed by combining with a two-stream model, such as the Ecological

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Jarred L. Burley, Steven T. Fiorino, Brannon J. Elmore, and Jaclyn E. Schmidt

typical deterministic or “standard” atmospheric type data utilized by many modern radiative transfer models. Thus, AFIT/CDE has produced an atmospheric effects definition and reference, the Laser Environmental Effects Definition and Reference (LEEDR; Fiorino et al. 2008b ), that allows the export of the first-principles atmospheric characterizations. LEEDR contains both an internally consistent line-by-line and correlated- k distribution radiative transfer algorithm capable of assessing path

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Maziar Bani Shahabadi, Mark Buehner, Josep Aparicio, and Louis Garand

) background field to the horizontal location of the observation and use the resulting vertical profile as input to the radiative transfer model to obtain the simulated observation. This approach neglects that the instrument line-of-sight is slanted through the atmosphere for off-nadir observations. For high peaking channels, the standard approach extracts the model information at the wrong horizontal location. For example, for a channel that has sensitivity around an altitude of 15 km and a satellite

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Bingqiang Sun, George W. Kattawar, Ping Yang, and Eli Mlawer

1. Introduction Radiative transfer is a sine qua non for ocean optics, the remote sensing of the atmosphere, and radiative forcing analyses involved in climate science. The radiative transfer equation has been extensively discussed ( Chandrasekhar 1960 ; Liou 2002 ; Mobley 1994 ; Preisendorfer 1965 ; van de Hulst 1980 ). The vector radiative transfer equation (RTE) is an integral–differential equation that can be derived from statistical electromagnetics ( Mishchenko 2002 ). Even though

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Sebastian W. Hoch, C. David Whiteman, and Bernhard Mayer

heating. Recent developments in radiative transfer modeling now allow simulations of the radiative field in complex terrain to be readily made. Photon-tracing models such as the Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres (MYSTIC) now allow for a realistic representation of complex surface terrain ( Mayer 2009 ; Mayer et al. 2010 ). The role of radiative cooling within topography has previously been investigated for real basins ( Kondo et al. 1989 ) and

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Robert Pincus and K. Franklin Evans

1. Computational methods for solving the radiative transfer equation in three spatial dimensions In the fundamental equation describing the transfer of monochromatic unpolarized radiation in the atmosphere the radiation field depends on two angular dimensions (the zenith and azimuthal angles) and three spatial dimensions. In most applications of radiative transfer in the atmospheric sciences this equation is simplified by omitting the two horizontal spatial dimensions so that the radiation

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