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A Fast Three-Dimensional Approximation for the Calculation of Surface Irradiance in Large-Eddy Simulation Models

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  • 1 Institut für Physik der Atmosphäre, Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen, Germany
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Abstract

Cloud-resolving models—in particular, large-eddy simulation (LES) models—are important tools to improve the understanding of cloud–radiation interactions. A method is presented for accurate, yet fast, three-dimensional calculation of surface shortwave irradiance within an LES model using the tilted independent column approximation with smoothing of the diffuse irradiance. The algorithm calculates a tilted optical thickness for each surface pixel that is then used as input to a one-dimensional radiative transfer code. In a sensitivity analysis, it is shown that this calculation can even be replaced by a simple precalculated lookup table that tabulates surface irradiance as a function of only solar zenith angle and cloud optical thickness. Because the vertical variability of the cloud is of little relevance for the surface irradiance, this approximation introduces little extra uncertainty. In a final step, surface irradiance is smoothed to account for horizontal photon transport between individual columns. The algorithm has been optimized for parallelization, which enhances its applicability in LES models. In this implementation, the total computational time of the LES model increased by only 3% relative to the reference run without radiation. Comparisons between the fast approximation and detailed three-dimensional radiative transfer calculations showed very good agreement for different cloud conditions and several solar zenith and azimuth angles, with a root-mean-square difference of 6%.

* Current affiliation: School of Earth Sciences, The University of Melbourne, Melbourne, Australia.

Corresponding author address: Kathrin Wapler, Deutscher Wetterdienst/German Weather Service, Frankfurterstr. 135, 63067 Offenbach, Germany. Email: kathrin.wapler@dwd.de

Abstract

Cloud-resolving models—in particular, large-eddy simulation (LES) models—are important tools to improve the understanding of cloud–radiation interactions. A method is presented for accurate, yet fast, three-dimensional calculation of surface shortwave irradiance within an LES model using the tilted independent column approximation with smoothing of the diffuse irradiance. The algorithm calculates a tilted optical thickness for each surface pixel that is then used as input to a one-dimensional radiative transfer code. In a sensitivity analysis, it is shown that this calculation can even be replaced by a simple precalculated lookup table that tabulates surface irradiance as a function of only solar zenith angle and cloud optical thickness. Because the vertical variability of the cloud is of little relevance for the surface irradiance, this approximation introduces little extra uncertainty. In a final step, surface irradiance is smoothed to account for horizontal photon transport between individual columns. The algorithm has been optimized for parallelization, which enhances its applicability in LES models. In this implementation, the total computational time of the LES model increased by only 3% relative to the reference run without radiation. Comparisons between the fast approximation and detailed three-dimensional radiative transfer calculations showed very good agreement for different cloud conditions and several solar zenith and azimuth angles, with a root-mean-square difference of 6%.

* Current affiliation: School of Earth Sciences, The University of Melbourne, Melbourne, Australia.

Corresponding author address: Kathrin Wapler, Deutscher Wetterdienst/German Weather Service, Frankfurterstr. 135, 63067 Offenbach, Germany. Email: kathrin.wapler@dwd.de

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