Intercomparison of 3D Radiation Codes.

Iterative cascade models in which the probability of horizontal transfer of liquid water approaches zero at small spatial scales. The simplest such model transfers a fraction f*c^n at the nth cascade step, where the parameter f is typically about 1/2 and c about 4/5. The wavenumber spectrum decreases as a power 1-ln_2(c^2), so that when c = 2^(-1/3) (near 4/5), then the power = 5/3, close to that observed for California marine stratocumulus. Singular cascade models, by contrast, have nonzero transfers even when the spatial scale approaches zero, and as a result generally produce more slowly decreasing wavenumber spectra than observed.

The value of cloud liquid or optical thickness which allows a plane-parallel computation to obtain the correct cloud albedo when the cloud is inhomogeneous. Bounded cascades have an effective liquid water content (or effective thickness) approximately equal to the mean liquid (or thickness) times exp(-s^2/2) where s is the standard deviation of the natural logarithm of the distribution of liquid water (or optical thickness) in the cloud. Observed values of s vary geographically, seasonally, and diurnally.

Computation of the albedo and other radiation properties of individual cloud pixels in a digital scene using only the physical properties of clouds and/or other features within each given pixel, neglecting any influence of the physical properties associated with neighboring pixels, which could influence the given pixel due to horizontal radiative transfer. The IPA requires only knowledge of the one-point probability distribution function (pdf) of the cloud properties, not the two-point function (or equivalent wavenumber spectrum or structure function) or higher-order statistics. However, the higher-order statistics influence corrections to the IPA, and must be estimated to determine when the IPA is valid.

Generalization of the IPA that accounts for influence of nearest-neighbor cells on the albedo and other radiation properties of a given cell. This requires knowledge of the Impulse Response Function of the cloud field, which may be determined from observations of offbeam lidar returns.

The bias in albedo and other radiation properties computed by current climate models, due to the model assumption that clouds are horizontally infinite and uniform at each level of the atmosphere, in other words, that clouds are "plane-parallel". Plane-parallel clouds containing realistic amounts of total liquid water are always too reflective (i.e. the albedo is positively biased). This can be shown to follow from the IPA, and the fact that the cloud albedo increases at a decreasing rate as the cloud liquid increases. There are two types of contributions to the bias: a cloud fraction or geometric bias due to the finite size and arrangement of clouds, and a fractal structure bias due to the internal structure of clouds. They are comparable for a typical cloud fraction near 50%, but the cloud fraction bias dominates for smaller cloud fractions, and the fractal structure bias dominates for larger cloud fractions.