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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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Ingo Meirold-Mautner, Catherine Prigent, Eric Defer, Juan R. Pardo, Jean-Pierre Chaboureau, Jean-Pierre Pinty, Mario Mech, and Susanne Crewell

1. Introduction A strong need is emerging to have accurate radiative transfer simulations from realistic cloudy and rainy scenes at high microwave frequencies. First, efforts are made to assimilate satellite microwave radiation from cloudy and rainy atmospheres within numerical weather prediction (NWP) models. As a first step, precipitation affected satellite observations at microwave frequencies up to 22 GHz are assimilated in the European Centre for Medium-Range Weather Forecasts (ECMWF

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Laurent Makké, Luc Musson-Genon, Bertrand Carissimo, Pierre Plion, Maya Milliez, and Alexandre Douce

1. Introduction Infrared radiation (IR) is a physical process that plays a prominent role in atmospheric physics—especially through interaction with clouds. It is the most important physical phenomenon that drives radiation fog formation ( Davis 1994 ). To study atmospheric radiation, the question arises whether to adopt a 1D, 2D, or 3D approach to compute radiative transfer (RT). Many sophisticated treatments of the radiative transfer equation (RTE)—Monte Carlo method (MCM) ( Fleck 1961 ) for

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Ming Liu, Young-Joon Kim, and Qingyun Zhao

radiative processes highly depends on the accuracy of radiative transfer (RT) parameterizations, by which solar and thermal infrared (IR) radiative fluxes are generated and radiative heating rates are calculated for atmospheric temperature tendency integration and the surface energy budget. Radiation modeling is critically important in both general circulation models and regional models. Thus, the incorporation of an accurate and efficient RT parameterization into NWP models has become a crucial step to

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Robin J. Hogan

) was the first to propose that, for vertically homogeneous atmospheres, the gaseous mass absorption coefficients k can be “sorted” into a monotonic function that is much more conducive to efficient numerical integration. This was extended to vertically inhomogeneous atmospheres by Lacis et al. (1979) , and the resulting “correlated- k distribution” (CKD) method now forms the basis of most radiative transfer schemes in general circulation models (GCMs). It takes advantage of the fact that in the

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Quanhua Liu, Xingming Liang, Yong Han, Paul van Delst, Yong Chen, Alexander Ignatov, and Fuzhong Weng

1. Introduction The Community Radiative Transfer Model (CRTM) is a sensor-band-based fast radiative transfer model developed at the Joint Center for Satellite Data Assimilation (JCSDA; Han et al. 2006 ). It is a key component in the U.S. data assimilation for weather forecasting at the National Centers for Environmental Prediction (NCEP) of the National Oceanic and Atmospheric Administration (NOAA). It is used in conjunction with the atmospheric and surface data from users of many applications

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Chenxi Wang, Ping Yang, Steven Platnick, Andrew K. Heidinger, Bryan A. Baum, Thomas Greenwald, Zhibo Zhang, and Robert E. Holz

-based optical thickness retrievals are limited to lower values of optical thickness in comparison with solar reflectance–based techniques and require accurate surface temperature and atmospheric state profiles (e.g., Huang et al. 2004 ; Cooper and Garrett 2010 ). Some studies demonstrated that shortwave and IR observations provide complementary information and therefore the combination of the two can provide more consistent retrievals ( Baran and Francis 2004 ). To simulate the radiative transfer (RT) in

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Ulrike Wissmeier, Robert Buras, and Bernhard Mayer

inexpensive one-dimensional radiative transfer solvers. The need of a good radiative transfer scheme that considers three-dimensional effects becomes more and more important when going to higher model resolutions, however. Then, the net radiation flux between neighboring model columns can no longer be neglected. A widely employed method for calculating irradiances in NWP or LES models is the so-called independent column approximation (ICA), also called independent pixel approximation (IPA)—in the

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Christopher Lee and Mark Ian Richardson

Young (1975) developed a relatively simple radiative transfer model (RTM) that included clouds and absorption from carbon dioxide and water and used this model to calculate a radiative–convective temperature that was close to the observed profile and exhibited the familiar “greenhouse” warming ( Ingersoll 1969 ). After the Pioneer Venus mission, Crisp (1986 , 1989) developed a radiation model for the middle and upper atmosphere (above 50 km) that included much of the information that was

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Biao Wang

1. Introduction In Wang (2017 , hereafter Part I ), a unified formulation for radiative transfer in plane-parallel atmospheres based on the generally decomposed radiative transfer equation system (GD-RTES) has been presented, from which some of the established methods, such as the discrete ordinate method (DOM) and the spherical harmonic method (SHM), can be derived when the appropriate bases are prescribed. Following the general procedure described in Part I , a basis prescribed so that it

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