Accounting for subgrid-scale cloud variability in a multi-layer 1D solar radiative transfer algorithm

A multi-layer, ID solar radiative transfer algorithm that accounts for subgrid-scale cloud variability is presented. This algorithm is efficient and suitable for use in large-scale models such as global climate and weather prediction models. While it is built on the same principles as standard multi-layer 1D codes, there are two major differences. First, it is assumed that for all cloudy layers all the time, frequency distributions of optical depth tau are described by gamma probability density functions p(Gamma)(tau) and characterized by mean optical depth <(tau)over bar> and a variance-related parameter nu. Albedos and transmittances for individual layers are estimated by integrals over all tau of the plane-parallel, homogeneous two-stream approximation equations weighted by p(Gamma)(tau). Thus, the model is referred to as the gamma-weighted two-stream approximation. Second, in an attempt to counteract the use of horizontally homogeneous fluxes, a method was devised that often reduces layer values of <(tau)over bar>. The gamma-weighted two-stream approximation was implemented in a well known broadband column model and the parametrizations upon which it is built were tested using 2D and 3D inhomogeneous cloud fields generated by a bounded cascade model and cloud-resolving models. All fields resolved the lowest 20 km of the atmosphere into at least 30 layers. Reference calculations were obtained by: (i) applying the 1D-plane-parallel, homogeneous model to each column and averaging (the independent column approximation); and (ii) a 3D Monte Carlo algorithm. The gamma-weighted two-stream approximation, the regular plane-parallel, homogeneous, and two other 1D models operated on horizontally-averaged versions of the fields (i.e. ID vectors of cloud fraction, <(tau)over bar>, and nu). For several demanding cases, the gamma-weighted two-stream approximation reduced plane-parallel, homogeneous-biases for TOA albedo and surface irradiance by typically more than 85%. Moreover, its estimates of atmospheric heating rates usually differed from the independent column approximation and Monte Carlo values by less than 10%. This translates into heating rate errors that are four to eight times smaller than those associated with conventional 1D plane-parallel, homogeneous algorithms. In a large-scale model, a multi-layer solar code with the gamma-weighted two-stream approximation should require about twice as much CPU time as its plane-parallel, homogeneous counterpart.