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Norman G. Loeb and J. A. Coakley Jr.


The validity of plane-parallel (1D) radiative transfer theory for cloudy atmospheres is examined by directly comparing calculated and observed visible reflectances for one month of Global Area Coverage Advanced Very High Resolution Radiometer satellite observations of marine stratus cloud layers off the coasts of California, Peru, and Angola. Marine stratus are an excellent testbed, as they arguably are the closest to plane-parallel found in nature. Optical depths in a 1D radiative transfer model are adjusted so that 1D model reflectances match those observed at nadir on a pixel-by-pixel basis. The 1D cloud optical depth distributions are then used in the plane-parallel model to generate reflectance distributions for different sun–earth–satellite viewing geometries. These reflectance distributions are directly compared with the observations. Separate analyses are performed for overcast and broken cloud layers as identified by the spatial coherence method.

When 1D reflectances are directly compared with observations at different view angles, relative differences are generally small (≲10%) in the backscattering direction for solar zenith angles ≲60° and show no systematic view angle dependence. In contrast, 1D reflectances increase much more rapidly with view angle than the observed reflectances in the forward-scattering direction. Relative differences in the forward-scattering direction are ≈2–3 times larger than in the backscattering direction. At solar zenith angles ≳60°, the 1D model underestimates observed reflectances at nadir by 20%–30% and overestimates reflectances at the most oblique view angles in the forward scattering direction by 15%–20%. Consequently, when inferred on a pixel-by-pixel basis, nadir-derived cloud optical depths show a systematic increase with solar zenith angle, both for overcast and broken cloud layers, and cloud optical depths decrease with view angle in the forward scattering direction. Interestingly, in the case of broken marine stratocumulus, the common practice of assuming that pixels are overcast when they are not mitigates this bias to some extent, thereby confounding its detection. But even for broken clouds, the bias remains.

Because of the nonlinear dependence of cloud albedo on cloud optical depth, errors in cloud optical depth lead to large errors in cloud albedo—and therefore energy budget calculations—regardless of whether cloud layers are overcast or broken. These findings suggest that as a minimum requirement, direct application of the plane-parallel model approximation should be restricted to moderate–high sun elevations and to view angles in the backscattering direction. Based on Monte Carlo simulations, the likely reason for the discrepancies between observed radiances and radiances calculated on the basis of 1D theory is because real clouds have inhomogeneous (i.e., bumpy) tops.

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