The Neighboring Column Approximation (NCA) - A fast approach for the calculation of 3D thermal heating rates in cloud resolving models

Due to computational costs, radiation is usually neglected or solved in plane parallel 1D approximation in today's numerical weather forecast and cloud resolving models. We present a fast and accurate method to calculate 3D heating and cooling rates in the thermal spectral range that can be used in cloud resolving models. The parameterization considers net fluxes across horizontal box boundaries in addition to the top and bottom boundaries. Since the largest heating and cooling rates occur inside the cloud, close to the cloud edge, the method needs in first approximation only the information if a grid box is at the edge of a cloud or not. Therefore, in order to calculate the heating or cooling rates of a specific grid box, only the directly neighboring columns are used. Our so-called Neighboring Column Approximation (NCA) is an analytical consideration of cloud side effects which can be considered a convolution of a 1D radiative transfer result with a kernel or radius of 1 grid-box (5 pt stencil) and which does usually not break the parallelization of a cloud resolving model. The NCA can be easily applied to any cloud resolving model that includes a 1D radiation scheme. Due to the neglect of horizontal transport of radiation further away than one model column, the NCA works best for model resolutions of about 100 m or lager. In this paper we describe the method and show a set of applications of LES cloud field snap shots. Correction terms, gains and restrictions of the NCA are described. Comprehensive comparisons to the 3D Monte Carlo Model MYSTIC and a 1D solution are shown. In realistic cloud fields, the full 3D simulation with MYSTIC shows cooling rates up to -150 K/d (100 m resolution) while the 1D solution shows maximum coolings of only -100 Kid. The NCA is capable of reproducing the larger 3D cooling rates. The spatial distribution of the heating and cooling is improved considerably. Computational costs are only a factor of 1.5-2 higher compared to a 1D solution. (C) 2015 Elsevier Ltd. All rights reserved.