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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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George P. Kablick III, Robert G. Ellingson, Ezra E. Takara, and Jlujing Gu

were treated by the models ( Ellingson et al. 1991 ). Since that time, the Atmospheric Radiation Measurement (ARM) program has been working on validating model calculations against high-quality spectral observations taken at sites around the world ( Stokes and Schwartz 1994 ; Ackerman and Stokes 2003 ). These data have helped develop accurate, line-by-line (LBL) information about atmospheric constituents, from which a line-by-line radiative transfer model (LBLRTM) has been established for model

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Seiji Kato, Norman G. Loeb, Fred G. Rose, David R. Doelling, David A. Rutan, Thomas E. Caldwell, Lisan Yu, and Robert A. Weller

sensible heat fluxes at the surface. Unlike TOA irradiances that can be estimated from broadband radiance observations ( Loeb et al. 2005 ), a global estimate of the irradiance at the surface is only possible through radiative transfer calculations. For example, Zhang et al. (1995 , 2004 ) use satellite-derived cloud properties ( Rossow and Schiffer 1991 , 1999 ) and temperature and humidity as inputs to compute surface irradiances. Pinker et al. (2003) estimate surface shortwave irradiances using

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Dana E. Lane, Kristen Goris, and Richard C. J. Somerville

Wielicki 1984 ; McKee and Klehr 1978 ). Incorporating information about cloud scale and spatial distribution into cloud and radiation modeling has long been recognized as an important step toward an improved understanding of atmospheric radiative transfer (e.g., Plank 1969 ; Kuhn 1978 ; Stephens and Platt 1987 ). A statistical representation of the cloud field such as that used in stochastic theory may be a useful approach to modeling broken or scattered clouds ( Stephens 1988 ; Malvagi and

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Cenlin He, Yoshi Takano, Kuo-Nan Liou, Ping Yang, Qinbin Li, and Fei Chen

radiative transfer schemes, while the other is using empirical parameterizations derived from snow models. Previous studies have developed several parameterizations under different atmospheric conditions by assuming spherical snow grains externally mixed with impurities (e.g., Marshall and Warren 1987 ; Gardner and Sharp 2010 ; Aoki et al. 2011 ; Dang et al. 2015 ), which have been applied into global climate models (GCMs) partly for the consideration of computational efficiency. For example

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G. Alexander Sokolowsky, Eugene E. Clothiaux, Cory F. Baggett, Sukyoung Lee, Steven B. Feldstein, Edwin W. Eloranta, Maria P. Cadeddu, Nitin Bharadwaj, and Karen L. Johnson

climatologies and hydrometeor property parameterizations, Curry and Ebert (1992) showed that low-altitude (below approximately 3 km) ice-water hydrometeors are important in the Arctic winter. Omission of ice-water hydrometeors in their radiative transfer calculations led to underestimates of about 40 W m −2 in the surface downwelling longwave irradiance. In their study, making liquid-water clouds opaque relative to their expected values increased the surface downwelling longwave irradiance by about 25 W

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Norman G. Loeb, Ping Yang, Fred G. Rose, Gang Hong, Sunny Sun-Mack, Patrick Minnis, Seiji Kato, Seung-Hee Ham, William L. Smith Jr., Souichiro Hioki, and Guanglin Tang

, and snow and sea ice maps based on microwave radiometer data. While the TOA radiation budget is most accurately determined directly from accurate broadband radiometer measurements, the surface radiation budget is derived indirectly through radiative transfer model calculations initialized using imager-based cloud and aerosol retrievals and meteorological assimilation data. Because ice cloud particles exhibit a wide range of shapes and sizes that cannot be independently retrieved a priori from

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H. W. Barker, G. L. Stephens, P. T. Partain, J. W. Bergman, B. Bonnel, K. Campana, E. E. Clothiaux, S. Clough, S. Cusack, J. Delamere, J. Edwards, K. F. Evans, Y. Fouquart, S. Freidenreich, V. Galin, Y. Hou, S. Kato, J. Li, E. Mlawer, J.-J. Morcrette, W. O'Hirok, P. Räisänen, V. Ramaswamy, B. Ritter, E. Rozanov, M. Schlesinger, K. Shibata, P. Sporyshev, Z. Sun, M. Wendisch, N. Wood, and F. Yang

modeling unresolved clouds and radiative transfer in LSAMs along with numerical experiments that show that seemingly small systematic changes in cloud properties have significant impacts on simulated regional and global climate (e.g., Senior 1999 ). Moreover, studies that intercompared cloud radiative feedbacks in LSAMs ( Cess et al. 1996 , 1997 ) came to the conclusion that different representations of cloud-related processes in LSAMs may account for much of the uncertainty associated with estimates

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Tarek Ayash, Sunling Gong, and Charles Q. Jia

Energy System (CERES) instruments. The MODIS-based estimates are derived from MODIS retrievals of aerosol optical depth, single-scattering albedo, and phase function that best matches spectral radiances observed at the TOA. These retrieved aerosol optical properties are then used with the CLIRAD–SW radiative transfer model ( Chou 1992 ) to calculate TOA fluxes that best match the observed radiances from which the aerosol direct radiative effect is calculated. The CERES-based estimates are derived

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David M. Romps, Jacob T. Seeley, and Jacob P. Edman

demonstrating the properties that lead to carbon dioxide’s logarithmic forcing, building a simplified analytic model to showcase the underlying processes, and showing that a line-by-line radiative transfer model gives a logarithmic forcing for the same reasons. This will occupy the bulk of paper, from sections 5 to 8 . The reader who wants to quickly learn the basic mechanism may be satisfied with the overview in section 3 and could skip ahead to that section now. 2. Preliminaries To reduce the

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