Discrete angle radiative transfer: 3. Numerical results and meteorological applications

Abstract

Additional numerical results are obtained for a simple class of scale invariant (fractal) clouds that arises when modeling the concentration of cloud liquid water into ever smaller regions by advection in turbulent cascades. These so-called random "β models' are (also) characterized by a single fractal dimension. Both open and cyclical horizontal boundary conditions are considered. These and previous results are contrasted with plane-parallel predictions, and measures of systematic error are defined as "packing factors' which are found to diverge algebraically with average optical thickness and are significant even when the scaling behavior is very limited in range. Several meteorological consequences, especially concerning the "albedo paradox' and global climate models, are discussed, and future directions of investigation are outlined. -from Authors