Monte Carlo spectral integration:
A consistent approximation for radiative transfer in large eddy simulations

Robert Pincus and
Bjorn Stevens

Journal of Advances in Modeling Earth Systems, June 2009.
doi:10.3894/JAMES.2009.1.1

Abstract

Large-eddy simulation (LES) refers to a class of calculations in which the large energy-rich eddies are simulated directly and are insensitive to errors in the modeling of sub-grid scale processes. Flows represented by LES are often driven by radiative heating and therefore require the calculation of radiative transfer along with the fluid-dynamical simulation. Current methods for detailed radiation calculations, even those using simple one-dimensional radiative transfer, are far too expensive for routine use, while popular shortcuts are either of limited applicability or run the risk of introducing errors on time and space scales that might affect the overall simulation.

A new approximate method is described that relies on Monte Carlo sampling of the spectral integration in the heating rate calculation and is applicable to any problem. The error introduced when using this method is substantial for individual samples (single columns at single times) but is uncorrelated in time and space and so does not bias the statistics of scales that are well resolved by the LES. The method is evaluated through simulation of two test problems; these behave as expected. A scaling analysis shows that the errors introduced by the method diminish as flow features become well resolved. Errors introduced by the approximation increase with decreasing spatial scale but the spurious energy introduced by the approximation is less than the energy expected in the unperturbed flow, i.e. the energy associated with the spectral cascade from the large scale, even on the grid scale.

This article is published in the open-access Journal of Advances in Modeling Earth Systems. Reproduction and electronic distribution are encouraged under the Creative Commons Attribution 3.0 License