Absorption within inhomogeneous clouds and its parameterization in general circulation models

Abstract The effect on absorption in clouds of having an inhomogeneous distribution of droplets is shown to depend on whether one replaces a homogeneous cloud by an inhomogeneous cloud that has the same mean optical thickness, or one that has the same spherical albedo. For the purposes of general circulation models (GCMs), the more appropriate comparison is between homogeneous and inhomogeneous clouds that have the same spherical albedo, so that the radiation balance of the planet with space is maintained. In this case it is found, using Monte Carlo and independent pixel approximation calculations, that inhomogeneous clouds can absorb more than homogeneous clouds. It is also found that because of the different effects of cloud inhomogeneity on absorption and on the transmission of the direct beam the absorption efficiency of an inhomogeneous cloud may be either greater (for low and high optical depths) or lesser (for intermediate optical depths) than that for a homogeneous cloud of the same mean optical d...

[1]  Dudley A. Williams,et al.  Optical properties of water in the near infrared. , 1974 .

[2]  V. Naroditsky.  Wave Propagation in Random Media , 1989 .

[3]  E. Fradkin.  Application of functional methods in quantum field theory and quantum statistics (II) , 1963 .

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

[5]  M.M.R. Williams.  Effect of random material density on reactor criticality , 1990 .

[6]  John,et al.  Diffusing-wave spectroscopy and multiple scattering of light in correlated random media. , 1989, Physical review. B, Condensed matter.

[7]  S. Rosenbaum,et al.  The Mean Green's Function: A Nonlinear Approximation , 1971 .

[8]  A. Kolmogorov.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

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

[10]  Takahisa Kobayashi,et al.  Effects Due to Cloud Geometry on Biases in the Albedo Derived from Radiance Measurements. , 1993 .

[11]  G. C. Pomraning,et al.  Linear Kinetic Theory and Particle Transport in Stochastic Mixtures , 1991 .

[12]  T. McKee,et al.  Scattering of Visible Radiation by Finite Clouds , 1974 .

[13]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[14]  Dudley H. Williams,et al.  Optical constants of water in the infrared , 1975 .

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

[16]  K. Furutsu,et al.  On the statistical theory of electromagnetic waves in a fluctuating medium (I) , 1963 .

[17]  P. Hignett.  A Study of the Short-Wave Radiative Properties of Marine Stratus: Aircraft Measurements and Model Comparisons , 1987 .

[18]  Howard W. Barker,et al.  Solar Radiative Transfer Through Clouds Possessing Isotropic Variable Extinction Coefficient , 1992 .

[19]  J. Jensen.  Sur les fonctions convexes et les inégalités entre les valeurs moyennes , 1906 .

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

[21]  Radiative transfer in inhomogeneous media , 1984 .

[22]  H. Jeffreys,et al.  Theory of probability , 1896 .

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

[24]  Michael D. King,et al.  Comparative accuracy of selected multiple scattering approximations , 1986 .

[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]  Zones of increased and decreased droplet concentration in stratiform clouds , 1993 .

[28]  Robert F. Cahalan,et al.  The albedo of fractal stratocumulus clouds , 1994 .

[29]  John.  Localization and absorption of waves in a weakly dissipative disordered medium. , 1985, Physical review. B, Condensed matter.

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

[31]  O. Anisimov,et al.  Stochastic radiation in macroheterogeneous random optical media , 1992 .

[32]  G. C. Pomraning.  The Effect of Random Material Density on Reactor Criticality , 1991 .

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

[34]  Harshvardhan,et al.  Comments on ``The Parameterization of Radiation for Numerical Weather Prediction and Climate Models'' , 1985 .

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

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

[37]  D. O'Brien,et al.  Accelerated quasi Monte Carlo integration of the radiative transfer equation , 1992 .

[38]  J. Hansen,et al.  Light scattering in planetary atmospheres , 1974 .

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

[40]  P. Jonas.  On the reflectance of cellular cloud layers , 1994 .

[41]  J. Hansen,et al.  A parameterization for the absorption of solar radiation in the earth's atmosphere , 1974 .

[42]  M. King,et al.  Determination of the Optical Thickness and Effective Particle Radius of Clouds from Reflected Solar Radiation Measurements. Part II: Marine Stratocumulus Observations , 1991 .

[43]  Anthony D. Del Genio,et al.  A Prognostic Cloud Water Parameterization for Global Climate Models , 1996 .

[44]  G. Stephens,et al.  Statistical radiative transport in one-dimensional media and its application to the terrestrial atmosphere , 1991 .

[45]  V. Ramanathan,et al.  Warm Pool Heat Budget and Shortwave Cloud Forcing: A Missing Physics? , 1995, Science.

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

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

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

[49]  Peter H. Stone,et al.  Efficient Three-Dimensional Global Models for Climate Studies: Models I and II , 1983 .

[50]  Uriel Frisch,et al.  WAVE PROPAGATION IN RANDOM MEDIA. , 1970 .

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

[52]  Yu. N. Barabanenkov,et al.  Radiation Transport Equation for Correlated Scatterers , 1967 .

[53]  G. Rybicki,et al.  The searchlight problem with isotropic scattering , 1971 .

[54]  R. A. Silverman,et al.  Methods of Quantum Field Theory in Statistical Physics , 1964 .

[55]  Lagendijk,et al.  Light scattering in strongly scattering media: Multiple scattering and weak localization. , 1988, Physical review. B, Condensed matter.

[56]  Régis Borde,et al.  Radiative transfer in multifractal clouds , 1996 .

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

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

[59]  G. M. Hale,et al.  Optical Constants of Water in the 200-nm to 200-microm Wavelength Region. , 1973, Applied optics.

[60]  Y. Knyazikhin,et al.  Transport theory for a leaf canopy of finite-dimensional scattering centers , 1991 .