The incorporation of the Tripleclouds concept into the <i>δ</i>-Eddington two-stream radiation scheme: solver characterization and its application to shallow cumulus clouds

Abstract. The treatment of unresolved cloud–radiation interactions in weather and climate models has considerably improved over the recent years, compared to conventional plane-parallel radiation schemes, which previously persisted in these models for multiple decades. One such improvement is the state-of-the-art Tripleclouds radiative solver, which has two cloudy and one cloud-free region in each vertical model layer and is thereby capable of representing cloud horizontal inhomogeneity. Inspired by the Tripleclouds concept, primarily introduced by Shonk and Hogan (2008), we incorporated a second cloudy region into the widely employed δ-Eddington two-stream method with maximum-random overlap assumption for partial cloudiness. The inclusion of another cloudy region in the two-stream framework required an extension of vertical overlap rules. While retaining the maximum-random overlap for the entire layer cloudiness, we additionally assumed the maximum overlap of optically thicker cloudy regions in pairs of adjacent layers. This extended overlap formulation implicitly places the optically thicker region towards the interior of the cloud, which is in agreement with the core-shell model for convective clouds. The method was initially applied on a shallow cumulus cloud field, evaluated against a three-dimensional benchmark radiation computation. Different approaches were used to generate a pair of cloud condensates characterizing the two cloudy regions, testing various condensate distribution assumptions along with global cloud variability estimate. Regardless of the exact condensate setup, the radiative bias in the vast majority of Tripleclouds configurations was considerably reduced compared to the conventional plane-parallel calculation. Whereas previous studies employing the Tripleclouds concept focused on researching the top-of-the-atmosphere radiation budget, the present work pioneeringly applies the Tripleclouds to atmospheric heating rate and net surface flux. The Tripleclouds scheme was implemented in the comprehensive libRadtran radiative transfer package and can be utilized to further address key scientific issues related to unresolved cloud-radiation interplay in coarse-resolution atmospheric models.