Computation of Domain-Averaged Irradiance Using Satellite-Derived Cloud Properties

Abstract The respective errors caused by the gamma-weighted two-stream approximation and the effective thickness approximation for computing the domain-averaged broadband shortwave irradiance are evaluated using cloud optical thicknesses derived from 1 h of radiance measurements by the Moderate Resolution Imaging Spectrometer (MODIS) over footprints of Clouds and the Earth’s Radiant Energy System (CERES) instruments. Domains are CERES footprints of which dimension varies approximately from 20 to 70 km, depending on the viewing zenith angle of the instruments. The average error in the top-of-atmosphere irradiance at a 30° solar zenith angle caused by the gamma-weighted two-stream approximation is 6.1 W m−2 (0.005 albedo bias) with a one-layer overcast cloud where a positive value indicates an overestimate by the approximation compared with the irradiance computed using the independent column approximation. Approximately one-half of the error is due to deviations of optical thickness distributions from a ga...

[1]  B. Barkstrom,et al.  Clouds and the Earth's Radiant Energy System (CERES): An Earth Observing System Experiment , 1996 .

[2]  Andrew A. Lacis,et al.  Calculation of surface and top of atmosphere radiative fluxes from physical quantities based on ISCCP data sets: 1. Method and sensitivity to input data uncertainties , 1995 .

[3]  Patrick Minnis,et al.  Parameterizations of reflectance and effective emittance for satellite remote sensing of cloud properties , 1998 .

[4]  J. Joseph,et al.  The delta-Eddington approximation for radiative flux transfer , 1976 .

[5]  David Durand,et al.  Aids for Fitting the Gamma Distribution by Maximum Likelihood , 1960 .

[6]  Yongxiang Hu,et al.  An Accurate Parameterization of the Radiative Properties of Water Clouds Suitable for Use in Climate Models , 1993 .

[7]  C. Bohren.  Multiple scattering of light and some of its observable consequences , 1987 .

[8]  S. Kato.  Computation of Domain-Averaged Shortwave Irradiance by a One-Dimensional Algorithm Incorporating Correlations between Optical Thickness and Direct Incident Radiation , 2003 .

[9]  R. Davies,et al.  Plane Parallel Albedo Biases from Satellite Observations. Part II: Parameterizations for Bias Removal. , 1998 .

[10]  D. F. Young,et al.  Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Tropical Rainfall Measuring Mission Satellite. Part II; Validation , 2003 .

[11]  J. Morcrette,et al.  A fast, flexible, approximate technique for computing radiative transfer in inhomogeneous cloud fields , 2003 .

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

[13]  E. Clothiaux,et al.  Assessing 1D atmospheric solar radiative transfer models: Interpretation and handling of unresolved clouds , 2003 .

[14]  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 .

[15]  E. Clothiaux,et al.  The k-distribution method and correlated-k approximation for a shortwave radiative transfer model. , 1999 .

[16]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[17]  L. J. Cox.  Optical Properties of the Atmosphere , 1979 .

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

[19]  William B. Rossow,et al.  Calculation of surface and top of atmosphere radiative fluxes from physical quantities based on ISCCP data sets: 2. Validation and first results , 1995 .

[20]  W. Weaver,et al.  Two-Stream Approximations to Radiative Transfer in Planetary Atmospheres: A Unified Description of Existing Methods and a New Improvement , 1980 .

[21]  S. C.,et al.  A NOTE ON THE GAMMA DISTRIBUTION , 1958 .

[22]  D. Doelling,et al.  Clouds and the Earth’s Radiant Energy System (CERES) FluxByCldTyp Edition 4 Data Product , 2022, Journal of Atmospheric and Oceanic Technology.

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

[24]  Q. Fu,et al.  Assessment and Optimization of the Gamma-Weighted Two-Stream Approximation , 2000 .

[25]  W. Paul Menzel,et al.  Remote sensing of cloud, aerosol, and water vapor properties from the moderate resolution imaging spectrometer (MODIS) , 1992, IEEE Trans. Geosci. Remote. Sens..

[26]  Thomas P. Charlock,et al.  The CERES/ARM/GEWEX Experiment (CAGEX) for the Retrieval of Radiative Fluxes with Satellite Data , 1996 .

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

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

[29]  Bruce A. Wielicki,et al.  Inversion methods for satellite studies of the Earth's Radiation Budget: Development of algorithms for the ERBE Mission , 1986 .

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

[31]  Bruce R. Barkstrom,et al.  The Earth Radiation Budget Experiment (ERBE). , 1984 .

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

[33]  Bruce A. Wielicki,et al.  Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Tropical Rainfall Measuring Mission Satellite. Part II; Validation , 2003 .