Representing 3‐D cloud radiation effects in two‐stream schemes: 2. Matrix formulation and broadband evaluation

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 4 W m−2) if an approximate correction is made for cloud clustering. Key Points New broadband radiation scheme captures 3‐D effects efficiently Solves modified two‐stream scheme using matrix exponentials Validated against 3‐D Monte Carlo model in shortwave and longwave