A Fractal Dimensional Analysis on the Cloud Shape Parameters of Cumulus over Land

Abstract

High-resolution Landsat thematic mapper image data were employed in the present study to estimate the influence of regional wind systems on the macrophysical properties of cumulus clouds, such as perimeter fractal dimension, orientation angle, and cloud-base height. As a case study, an image of cumulus clouds was chosen in which small- and large-sized clouds prevail over the land in the presence of local winds. Cloud extraction from backgrounds becomes difficult when the background comprises various brightnesses. Furthermore, the surface brightness of a cloud is not uniform when shadows appear on the surface. These effects contribute to errors in cloud extraction only using a simple threshold. To address these problems, technical improvements in processing, including the combination of clustering, dynamic threshold, and edge detection, are presented and shown to produce more accurate cloud outlines seen from the zenith direction. The clouds? statistical area?perimeter relation was shown to confirm that the fractal dimension of the cumuli follows the double power law: two different perimeter fractal dimensions exist for larger clouds and for smaller clouds. Correspondence of the bending point (around 0.7 km2) in the area?perimeter relation with the bending point in the area?major axis relation was also demonstrated. Analysis of cloud orientation showed that larger clouds (>0.7 km2) indicate the approximate direction of the local wind, whereas smaller clouds do not show clear tendencies in their directions, suggesting that there is a difference in formation between larger and smaller clouds. These findings suggest that in the presence of horizontal local wind, larger clouds are likely to be formed by aggregation of smaller cloud cells (unicellular clouds) during the process of alignment to become long- and roll-shaped clouds (multicellular clouds). Uneven distribution of cloud-base height was also demonstrated in this study. Clouds with higher base levels are found to locate along the convergence zones of a sea breeze.