Inferring Optical Depth of Broken Clouds from Landsat Data

Optical depths τpp for broken, shallow clouds over ocean were inferred from Landsat cloud reflectances Rcld (0.83 μm) with horizontal resolution of 28.5 m. The values τpp were obtained by applying an inverse, homogeneous, plane-parallel radiance model to each pixel value of Rcld. The primary objective of this study was to estimate optical depth errors incurred by the homogeneous, plane-parallel, independent pixel paradigm. This was achieved by computing reflectances Rmc with a 3D Monte Carlo photon transport algorithm that employed τpp and cloud geometric thicknesses h > 0. A single cloud was isolated for study in which the solar zenith angle was 30° and average τpp was 5.8. This cloud measured about 1.2 km in diameter but h had to be estimated. In the Monte Carlo simulations, h was set to be uniform for the entire cloud. For h between 150 and 300 m, cloud-average reflectance Rmc was about 15% less than Rcld. It was found that use of τpp1/δ(h) in the Monte Carlo algorithm yielded Rmc ≈ Rcld. For h = 225 m, 1/δ(h = 225) ≈ 1.11, and this increased average τpp to ∼8.0, which was a 35% increase. At the pixel level, however, random errors associated with fields of Rmc − Rcld were reduced only slightly when τpp1/δ(h) was used rather than τpp. Finally, τpp1/δ(h) was applied to numerous neighboring clouds. When the aspect (height to width) ratio A of neighboring clouds was assumed to be constant, τpp for each cloud received a unique scaling, and this yielded Landsat mean reflectances to within 4% for A < 0.3. This suggested that grid-averaged τpp was likely about 4 rather than 3, as was the plane-parallel, independent pixel estimate.