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Chris A. McLinden and Adam E. Bourassa

1. Introduction Models that compute the scattered, or diffuse, radiation field often solve the equation of radiative transfer in plane-parallel geometry. A plane-parallel, or flat, atmosphere is one-dimensional and so extends to infinity in the horizontal with the only variation in the vertical. The primary reasons for making such an approximation are the simplified solution and greatly reduced computation requirements over spherical models. For many applications (e.g., simulating nadir

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Yong Chen, Yong Han, Quanhua Liu, Paul Van Delst, and Fuzhong Weng

are formidable problems in simulating the brightness temperature when considering the cell pressure shift in a line-by-line (LBL) radiative transfer (RT) model with global coverage and over the SSU observation periods. An LBL RT model such as LBLRTM ( Clough et al. 2005 ) is computationally expensive because it requires the averaging of multiple monochromatic calculations within a spectral band. When the spectral response functions (SRFs) change, the entire LBL computation has to be recalculated

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Chao Liu, Bin Yao, Vijay Natraj, Fuzhong Weng, Tianhao Le, Run-Lie Shia, and Yuk L. Yung

1. Introduction Radiative transfer (RT) processes not only impact the Earth–atmosphere energy balance but also provide key information relevant to atmospheric remote sensing ( Goody and Yung 1989 ; Liou 2002 ). Therefore, the transfer of radiation in the atmosphere is an essential problem in atmospheric modeling and measurements ( Chandrasekhar 1960 ; Goody and Yung 1989 ; Liou 2002 ), and significant effort has been devoted to solving the RT equation under different circumstances and with

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A. Marshak, Y. Knyazikhin, J. C. Chiu, and W. J. Wiscombe

theoretically explained and numerically simulated using radiative transfer theory ( Knyazikhin et al. 2011 ; Smolander and Stenberg 2005 ). There are three key parameters that characterize the radiative transfer process: the extinction coefficient, scattering phase function, and single scattering albedo. In vegetation, the optical distance between two points within the canopy does not depend on wavelength because the scattering elements are much larger than the wavelength of solar radiation ( Ross 1981

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Chenxi Wang, Ping Yang, and Xu Liu

, and western South America, the occurrence frequencies of aerosol–water overlap approached 20%. Despite the high frequency of overlap between cloud and aerosol (hereafter referred to as scattering layers) in real atmospheres, some widely used cloud–aerosol retrieval algorithms remain restricted to conditions with only one scattering layer ( Hsu et al. 2006 ; Levy 2009 ). For a single-scattering-layer scene, a forward radiative transfer model (RTM) is unnecessary in the operational retrieval

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Feng Zhang, Zhongping Shen, Jiangnan Li, Xiuji Zhou, and Leiming Ma

1. Introduction Radiative transfer is a key issue for climate modeling and remote sensing. The radiative transfer equation is an integro-differential equation. The exact solution of the radiative transfer equation in a scattering and absorbing media is impossible to be obtained in a computationally efficient manner even for the plane-parallel case; thus, approximate methods are necessary. In the last several decades, considerable attention has been paid to find simple and effective methods to

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Feng Zhang, Yi-Ning Shi, Jiangnan Li, Kun Wu, and Hironobu Iwabuchi

1. Introduction Solving the radiative transfer equation (RTE) is a key issue when dealing with radiative processes related to climate simulations. Because RTE is an integro-differential equation, it has no exact solutions. In recent decades, numerous approximation techniques have been proposed to solve RTE (e.g., Liou 1974 ; Liou et al. 1988 ; Shibata and Uchiyama 1992 ; Kylling et al. 1995 ; Li and Ramaswamy 1996 ; Fu et al. 1997 ; Li and Dobbie 1998 ; Thomas and Stamnes 1999 ; Lin et

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Jiangnan Li and Howard W. Barker

1. Introduction Scattering of longwave (LW) radiation within Earth’s atmosphere is very weak relative to that of solar radiation. As such, climate models have treated, and continue to treat, LW radiative transfer with the absorption approximation (AA), which neglects scattering by cloud and aerosol particles. Observations and theoretical calculations show that when LW scattering is ignored, outgoing LW radiation (OLR) is often overestimated by a few watts per square meter ( Fu et al. 1997 ; Li

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Feng Zhang and Jiangnan Li

1. Introduction The radiative transfer equation is an integro-differential equation. The exact solution of the radiative transfer equation in a scattering and absorbing media generally does not exist; thus, the approximate methods are necessary. In the last several decades considerable attention has been paid to find the simple and effective methods for solving the radiative transfer equation ( Liou 1974 ; Liou et al. 1988 ; Shibata and Uchiyama 1992 ; Kylling et al. 1995 ; Li and Ramaswamy

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Haruma Ishida and Shoji Asano

1. Introduction Many satellite observations [e.g., the pioneering study of Ramanathan et al. (1989) ] have shown that clouds have a large effect on the radiation budget of the atmosphere. Numerical simulations also suggest that radiation processes are very important for cloud formation and decay (e.g., Moeng et al. 1999 ; Hartman and Harrington 2005 ). However, radiative transfer within clouds is very complicated and difficult to evaluate because of spatial inhomogeneities, such as the

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