Angular dependence of observed reflectances: A comparison with plane parallel theory

In this study, a direct comparison between plane parallel model calculations and one year of Earth Radiation Budget Satellite (ERBS) shortwave scanner observations over ocean between 30 degrees S and 30 degrees N is performed. Considering only cloud-contaminated pixels, plane parallel model calculations are first normalized to observations at nadir at high Sun elevations on a pixel-by-pixel basis by adjusting cloud fraction and cloud optical depth. These are then used to generate plane parallel model reflectances as a function of view, solar zenith, and relative azimuth angle, which are directly compared with the observations on a statistical basis. At moderate to high solar elevations (theta(0) less than or similar to 63 degrees), the relative view angle dependence of plane parallel reflectances remains, on a statistical basis, within approximate to 10% (relative difference) of that of the observations. For larger solar zenith angles, however, observed and plane parallel reflectances show systematic differences at all view angles that increase with increasing solar zenith angle. Provided atmospheric effects above the cloud are accounted for in the calculations, observed reflectances exceed plane parallel values in the backscattering direction by roughly a constant amount at all view angles for theta(0) greater than or similar to 63 degrees. In the forward scattering direction, observed reflectances generally fall within the range of plane parallel model values (for a range of model assumptions) but show a very different view angle dependence; observed reflectances level off at view angles between 60 degrees and 73 degrees, whereas the calculations increase steadily. When stratified by pixel brightness, the plane parallel model generally provides a better approximation to the observed reflectance dependence on view angle for darker (i.e., optically thinner) pixels than for brighter (optically thicker) pixels. For the brightest pixels, reflectance differences are largest at nadir in the backscattering direction and at oblique view angles in the forward direction. Overall, the relative dependence on azimuthal angle is similar for the observations and plane parallel model, irrespective of cloud thickness. Neglecting pixel area expansion with view angle in the calculations is shown to have only a minor influence. Finally, the marked difference in the reflectance dependence on solar zenith angle between observations and calculations is suggested as the likely reason why the principle of directional reciprocity applied to satellite measurements breaks down at ERBS pixel scales.