## 1. Introduction: Radiative Transfer in Large-Scale Models

[2] Global weather forecast and climate models predict the evolution of the atmosphere by computing changes in the energy, momentum, and mass budgets at many levels in each of many columns around the globe. One term in the energy budget is the local heating or cooling due to transfers of radiation, which is derived from the radiative fluxes averaged across each model grid cell. Computing these fluxes in a large-scale model (LSM) is in principle a two-part process. The LSM must first determine the state of the atmosphere within each grid cell, including the horizontal and vertical distributions of clouds, aerosols, and optically active gases, then give this description to a radiative transfer solver, which computes fluxes at each level.

[3] The description of clouds in current LSMs is quite simple: Most predict the proportion of each grid cell filled with cloud (the “cloud fraction”) and the mean in-cloud condensate concentration, then prescribe vertical structure using simple, fixed rules known as overlap assumptions. This leads to a relatively small number of possible cloud configurations within each column. In nature, though, domains the size of LSM grid cells often contain clouds with substantial horizontal variability [e.g., *Barker et al.*, 1999; *Pincus et al.*, 1999; *Rossow et al.*, 2002] and complicated vertical structure [e.g., *Hogan and Illingworth*, 2000; *Mace and Benson-Troth*, 2002]. Unresolved subgrid-scale variability impacts radiative fluxes as well as microphysical process rates [*Pincus and Klein*, 2000], so cloud schemes are now emerging that address this structure either parametrically [*Cusack et al.*, 1999; *Tompkins*, 2002] or explicitly [*Grabowski and Smolarkiewicz*, 1999; *Khairoutdinov and Randall*, 2001].

[4] Domain-average fluxes in variable clouds can be determined quite accurately using the plane-parallel independent column approximation (ICA) by averaging the flux computed for each class of cloud in turn [*Cahalan et al.*, 1994; *Barker et al.*, 1999]. Unfortunately, the ICA is far too computationally expensive when the number of cloud states is even moderately large. Radiative transfer is time consuming because fluxes and heating rates are broadband quantities that must be integrated over many spectral intervals: A heating rate profile in a single column is, in fact, the result of many narrowband calculations.

[5] The impracticality of the ICA has inspired a variety of computational shortcuts. Simple representations of overlapping homogeneous clouds, for example, can be treated by weighting clear-and cloudy-sky fluxes [*Morcrette and Fouquart*, 1986]. A variety of methods exist to compute domain-averaged radiative fluxes for internally variable clouds; all invoke restrictive assumptions about the nature of the variability and link layers in the vertical with further ad hoc assumptions [e.g., *Stephens*, 1988; *Oreopoulos and Barker*, 1999; *Cairns et al.*, 2000].

[6] What existing radiative transfer schemes have in common is an intimate coupling between assumptions about cloud structure and methods for computing radiative transfer. This is an unnatural marriage, since cloud structure and radiative transfer are conceptually distinct, and leads to a variety of problems. It is difficult to ensure consistency, for example; radiative fluxes computed using different implementations of the same overlap assumptions may differ substantially from each other and from benchmark calculations [*Barker et al.*, 2003]. More importantly, weaving assumptions about cloud structure into the fabric of radiative transfer solvers makes these codes hard to extend or generalize. Large-scale models that provide estimates of subgrid-scale variability will require accurate, flexible radiative transfer solvers. It seems very unlikely that small modifications to existing, highly particular treatments of clouds and radiation will be up to the task.

[7] This paper describes a computationally efficient technique for computing domain-averaged broadband radiative fluxes in vertically and horizontally variable cloud fields of arbitrary complexity. The method makes random, uncorrelated errors in estimates of radiative quantities, but the expectation value of these estimates is completely unbiased with respect to the ICA. In the sections that follow we describe the method, quantify the noise it produces, and demonstrate that random errors of this magnitude do not affect forecasts made by a large-scale model. Finally, we describe a variety of model formulations in which the technique may be useful.