Accuracy of the independent pixel approximation for satellite estimates of oceanic boundary layer cloud optical depth

A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on the retrieval of optical depth by remote sensing of visible reflectance. Forty-five Landsat scenes of oceanic boundary layer clouds provide a sampling of real cloud fields, including trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus. The spherical harmonic discrete ordinate method (SHDOM) radiative transfer model is used to calculate two-dimensional reflectances from subsampled cloud strips representing the Landsat scenes. The independent pixel approximation (IPA) is used to retrieve optical depth for comparison to the original input. Results for tau(IPA) versus tau(ref) are presented on scales from the Landsat pixel scale (28.5 m) to an imager pixel scale (6 km) to near mesoscale (60 km). The random error decreases as the averaging scale increases, but error due to inhomogeneity remains. At the 60 km scale the average error is about 6% for high Sun, 2% for low Sun. Individual scenes, however, have retrieved optical depth errors as high as 45% due to horizontal radiative transport. The ability to retrieve higher statistical moments of the frequency distribution of optical depth is also assessed. Sigma, (sigma), the standard deviation of tau, is retrieved quite well up to a point, then is underestimated due to the smoothing effect of horizontal radiative transport. The gamma function parameter nu, another measure of the width of the tau frequency distribution, is retrieved quite well over a wide range but with a systematic bias which varies with solar zenith angle, again due to horizontal radiative transport. A method is sought to reduce the optical depth retrieval error using a simple correction based on remotely sensed cloud properties. Of those considered, cloud physical aspect ratio (computed here from one possible relation which depends on properties obtainable from remote sensing) is found to be the most effective correction parameter. The aspect ratio correction reduces the retrieved optical depth bias error by 50 to 100% and the RMS error by 20 to 50%. Correction coefficients are presented at three solar zenith angles. This work is limited by its consideration of only single-level marine boundary layer clouds, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to two-dimensional radiative transport. Future work will attempt to remove some of these limitations. The Landsat data used are also limited due to radiative smoothing.