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Hogan, Robin J.; Schäfer, Sophia A. K.; Klinger, Carolin; Chiu, J. Christine and Mayer, Bernhard (2016): Representing 3-D cloud radiation effects in two-stream schemes: 2. Matrix formulation and broadband evaluation. In: Journal of Geophysical Research-Atmospheres, Vol. 121, No. 14: pp. 8583-8599

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Estimating the impact of radiation transport through cloud sides on the global energy budget is hampered by the lack of a fast radiation scheme suitable for use in global atmospheric models that can represent these effects in both the shortwave and longwave. This two-part paper describes the development of such a scheme, which we refer to as the Speedy Algorithm for Radiative Transfer through Cloud Sides (SPARTACUS). The principle of the method is to add extra terms to the two-stream equations to represent lateral transport between clear and cloudy regions, which vary in proportion to the length of cloud edge as a function of height. The present paper describes a robust and accurate method for solving the coupled system of equations in both the shortwave and longwave in terms of matrix exponentials. This solver has been coupled to a correlated-k model for gas absorption. We then confirm the accuracy of SPARTACUS by performing broadband comparisons with fully 3-D radiation calculations by the Monte Carlo model MYSTIC for a cumulus cloud field, examining particularly the percentage change in cloud radiative effect (CRE) when 3-D effects are introduced. In the shortwave, SPARTACUS correctly captures this change to CRE, which varies with solar zenith angle between -25%and +120%. In the longwave, SPARTACUS captures well the increase in radiative cooling of the cloud, although it is only able to correctly simulate the 30% increase in surface CRE (around 4Wm(-2)) if an approximate correction is made for cloud clustering.

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