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The diurnal cycle of outgoing longwave radiation (OLR) from the earth is analyzed by decomposing satellite observations into a set of empirical orthogonal functions (EOFs). The observations are from the Earth Radiation Budget Experiment (ERBE) scanning radiometer aboard the Earth Radiation Budget Satellite, which had a precessing orbit with 57[degrees] inclination. The diurnal cycles of land and ocean differ considerably. The first EOF for land accounts for 73% to 85% of the variance, whereas the first EOF for ocean accounts for only 16% to 20% of the variance, depending on season. The diurnal cycle for land is surprisingly symmetric about local noon for the first EOF, which is approximately a half-sine during day and flat at night. The second EOF describes lead-lag effects due to surface heating and cloud formation. For the ocean, the first EOF and second EOF are similar to that of land, except for spring, when the first ocean EOF is a semidiurnal cycle and the second ocean EOF is the half-sine. The first EOF for land has a daytime peak of about 50 W [m.sup.-2], whereas the first ocean EOF peaks at about 25 W [m.sup.-2]. The geographical and seasonal patterns of OLR diurnal cycle provide insights into the interaction of radiation with the atmosphere and surface and are useful for validating and upgrading circulation models.

An algorithm is developed for the gamma-weighted discrete ordinate two-stream approximation that computes profiles of domain-averaged shortwave irradiances for horizontally inhomogeneous cloudy atmospheres. The algorithm assumes that frequency distributions of cloud optical depth at unresolved scales can be represented by a gamma distribution though it neglects net horizontal transport of radiation. This algorithm is an alternative to the one used in earlier studies that adopted the adding method. At present, only overcast cloudy layers are permitted.

Data from the Earth Radiation Budget Experiment scanning radiometer aboard the NOAA-9 operational meteorological satellite are used to investigate the spatial variability of outgoing longwave radiation (OLR). Daily and monthly radiation maps at 2.5 [degrees] latitude-longitude scale are used as a basis for the study. The regions of greatest variability are in the tropics and subtropics. Storm tracks such as the South Pacific convergence zone appear as regions of high OLR variability. Spatial spectra in longitude show two regimes of OLR. At large scales (wavenumbers less than 6), the spatial spectrum is flat. For wavenumbers greater than 10, the spectra decrease as wavenumber to the -3 power. The spatial spectrum of daily anomalies from the mean is a strong function of latitude and season, with interesting features. Correlations of daily anomalies from the monthly mean decrease exponentially in latitude but have a damped-wave structure in longitude. The spatial variability of the daily maps, as measured by degree variance, have 10 times the power at degree 24 than the monthly maps, but at scales between 1 and 10, the degree variance is practically the same for daily as for monthly.