Area-Average Solar Radiative Transfer in Three-Dimensionally Inhomogeneous Clouds: The Independently Scattering Cloudlet Model

Abstract A new conceptual and computational basis is described for renormalizing the single-scatter and extinction properties (optical depth, single-scatter albedo, and scattering phase function or asymmetry parameter) of a three-dimensionally inhomogeneous cloud volume or layer so as to describe a radiatively equivalent homogeneous volume or layer. The renormalization may allow area-averaged fluxes and intensities to be efficiently computed for some inhomogeneous cloud fields using standard homogeneous (e.g., plane parallel) radiative transfer codes. In the Independently Scattering Cloudlet (ISC) model, macroscopic “cloudlets” distributed randomly throughout a volume are treated as discrete scatterers, analogous to individual cloud droplets but with modified single-scatter properties due to internal multiple scattering. If a volume encompasses only cloudlets that are optically thin, the renormalized single-scatter properties for the volume revert to the intrinsic values and the homogeneous case is recove...

[1]  Broken-cloud enhancement of solar radiation absorption , 1996 .

[2]  3D Radiative Transfer in Weakly Inhomogeneous Medium. Part I: Diffusive Approximation , 1998 .

[3]  Robert F. Cahalan,et al.  Marine stratocumulus structure , 1989 .

[4]  J. Lenoble Radiative transfer in scattering and absorbing atmospheres: Standard computational procedures , 1985 .

[5]  Robert F. Cahalan,et al.  Nearest Neighbor Spacing of Fair Weather Cumulus Clouds. , 1990 .

[6]  P. Gabriel,et al.  Simple Radiative Transfer Methods for Calculating Domain-Averaged Solar Fluxes in Inhomogeneous Clouds. , 1996 .

[7]  A. Marshak,et al.  BI-MULTIFRACTAL ANALYSIS AND MULTI-AFFINE MODELING OF NON-STATIONARY GEOPHYSICAL PROCESSES, APPLICATION TO TURBULENCE AND CLOUDS , 1993 .

[8]  Norman G. Loeb,et al.  Inference of Marine Stratus Cloud Optical Depths from Satellite Measurements: Does 1D Theory Apply? , 1998 .

[9]  Si-Chee Tsay,et al.  On the cloud absorption anomaly , 1990 .

[10]  D. Schertzer,et al.  Discrete angle radiative transfer: 3. Numerical results and meteorological applications , 1990 .

[11]  H. Frisch,et al.  Monte-Carlo simulation of a radiative transfer problem in a random medium: Application to a binary mixture , 1993 .

[12]  Jouni I. Peltoniemi,et al.  Radiative transfer in stochastically inhomogeneous media , 1993 .

[13]  J. Morcrette,et al.  Broadband solar fluxes and heating rates for atmospheres with 3D broken clouds , 1998 .

[14]  H. Barker,et al.  Accounting for subgrid‐scale cloud variability in a multi‐layer 1d solar radiative transfer algorithm , 1999 .

[15]  Radiative Transfer in Cloud Fields with Random Geometry , 1995 .

[16]  Roger Davies,et al.  Effect of cloud inhomogeneities on the solar zenith angle dependence of nadir reflectance , 1997 .

[17]  Louis Moreau,et al.  The variable effect of clouds on atmospheric absorption of solar radiation , 1995, Nature.

[18]  G. C. Pomraning,et al.  Renormalized equations for linear transport in stochastic media , 1990 .

[19]  Brian Cairns,et al.  Absorption within inhomogeneous clouds and its parameterization in general circulation models , 2000 .

[20]  V. Galinsky 3D Radiative Transfer in Weakly Inhomogeneous Medium. Part II: Discrete Ordinate Method and Effective Algorithm for Its Inversion , 2000 .

[21]  H. Barker A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer , 1996 .

[22]  C. H. Whitlock,et al.  Absorption of Solar Radiation by Clouds: Observations Versus Models , 1995, Science.

[23]  G. C. Pomraning,et al.  Stochastic radiative transfer in a partially cloudy atmosphere. , 1993 .

[24]  K. Stamnes,et al.  Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. , 1988, Applied optics.

[25]  Georgi A. Titov,et al.  Statistical Description of Radiation Transfer in Clouds. , 1990 .

[26]  Radiative transfer inside clumpy media: the penetration of UV photons inside molecular clouds , 1990 .

[27]  Simple parameterizations of the radiative properties of cloud layers: a review , 1995 .

[28]  Shaun Lovejoy,et al.  Discrete-angle radiative transfer in a multifractal medium , 1991, Optics & Photonics.

[29]  K. Evans,et al.  A general solution for stochastic radiative transfer , 1993 .

[30]  D. Schertzer,et al.  Radiative Transfer in Multifractal Clouds , 1991 .

[31]  Robert F. Cahalan,et al.  Fractal Statistics of Cloud Fields , 1989 .

[32]  Robert F. Cahalan,et al.  Independent Pixel and Monte Carlo Estimates of Stratocumulus Albedo , 1994 .

[33]  Alexander Marshak,et al.  The verisimilitude of the independent pixel approximation used in cloud remote sensing , 1995 .

[34]  Graeme L. Stephens,et al.  The Parameterization of Radiation for Numerical Weather Prediction and Climate Models , 1984 .

[35]  Johannes Schmetz,et al.  On the parameterization of the radiative properties of broken clouds , 1984 .

[36]  W. Rossow,et al.  ISCCP Cloud Data Products , 1991 .

[37]  G. Stephens Radiative Transfer through Arbitrarily Shaped Optical Media. Part II. Group Theory and Simple Closures , 1988 .

[38]  P. Francis,et al.  On the question of enhanced absorption of solar radiation by clouds , 1997 .

[39]  H. Barker,et al.  A Parameterization for Computing Grid-Averaged Solar Fluxes for Inhomogeneous Marine Boundary Layer Clouds. Part II: Validation Using Satellite Data , 1996 .

[40]  Solar radiative fluxes for stochastic, scale-invariant broken cloud fields , 1992 .

[41]  Roger Davies,et al.  Reflected solar radiances from broken cloud scenes and the interpretation of scanner measurements , 1984 .

[42]  Paquita Zuidema,et al.  On the validity of the independent pixel approximation for boundary layer clouds observed during ASTEX , 1998 .

[43]  M. Hobson,et al.  Radiative transfer in a clumpy medium – II. The mega-grains approximation for two-phase models , 1993 .

[44]  A. Marshak,et al.  Multiple Scattering in Clouds: Insights from Three-Dimensional Diffusion/P1 Theory , 2001 .

[45]  M. Hobson,et al.  Radiative transfer in a clumpy medium – I. Analytical Markov-process solution for an N-phase slab , 1993 .

[46]  Joanne Simpson,et al.  Statistical properties of a cloud ensemble - A numerical study , 1987 .

[47]  Analytical Approximations for Calculating the Escape and Absorption of Radiation in Clumpy Dusty Environments , 1999, astro-ph/9905029.