Observational evidence of plane parallel model biases: Apparent dependence of cloud optical depth on solar zenith angle

This study directly compares plane parallel model calculations with 1 year of Earth Radiation Budget Satellite shortwave observations at nadir over ocean between 30 degrees S and 30 degrees N. When plane parallel model calculations are matched to the observations on a pixel-by-pixel basis by adjusting cloud fraction and cloud optical depth, the resulting frequency distributions of cloud optical depth show a systematic shift towards larger values with increasing solar zenith angle, regardless of the assumptions made in the calculations. This dependence is weak for thin clouds but gets progressively stronger as the clouds become thicker. For the thinnest 50% of the clouds (optical depths less than or similar to 6), it occurs only at oblique solar zenith angles, whereas it is observed at all solar zenith angles for the thickest 10% of clouds (optical depths greater than or similar to 12). On average, the increase is extremely large for solar zenith angles greater than or similar to 63 degrees. Such behavior is unrealistic since average cloud optical depths from such an extensive data set should be almost independent of solar zenith angle. The cause is traced to a fundamental flaw in plane parallel theory applied to real clouds: the solar zenith angle dependence of model reflectance is opposite to that of the observations. The one-dimensional nadir reflectance remains within 10% of the observed reflectance for solar zenith angles less than or similar to 53 degrees when applied to a general ensemble of real clouds, and for solar zenith angles less than or similar to 63 degrees when applied to the thinnest 50% of such clouds. Uncertainties are found to increase rapidly as the Sun becomes more oblique, easily reaching 30% at the lowest solar elevations. Based on results from theoretical studies, it is concluded that three-dimensional cloud structures not accounted for by plane parallel theory have a statistically important effect on the radiation field. As a minimum requirement, application of one-dimensional theory to the remote sensing of cloud optical thickness from measurements of nadir reflectance should therefore be restricted to thin clouds and small solar zenith angles.