CLUSTERING, RANDOMNESS, AND REGULARITY IN CLOUD FIELDS .2. CUMULUS CLOUD FIELDS

During the last decade a major controversy has been brewing concerning the proper characterization of cumulus convection. The prevailing view hu been that cumulus clouds form in clusters, in which cloud spacing is closer than that found for the overall cloud field and which maintains its identity over many cloud lifetimes. This ''mutual protection hypothesis'' of Randall and Huffman (1980) has been challenged by the inhibition hypothesis'' of Ramirez et al. (1990) which strongly suggests that the spatial distribution of cumuli must tend toward a regular distribution. A dilemma has resulted because observations have been reported to support both hypotheses. The present work reports a detailed analysis of cumulus cloud field spatial distributions based upon Landsat, Advanced Very High Resolution Radiometer, and Skylab data. Both nearest-neighbor and point-to-cloud cumulative distribution function statistics are investigated. The results show unequivocally that when both large and small clouds are included in the cloud field distribution, the cloud field always has a strong clustering signal. The strength of clustering is largest at cloud diameters of about 200-300 m, diminishing with increasing cloud diameter. In many cases, clusters of small clouds are found which are not closely associated with large clouds. As the small clouds are eliminated from consideration, the cloud field typically tends towards regularity. Thus it would appear that the ''inhibition hypothesis'' of Ramirez and Bras (1990) has been verified for the large clouds. However, these results are based upon the analysis of point processes. A more exact analysis also is made which takes into account the cloud size distributions. Since distinct clouds are by definition nonoverlapping, cloud size effects place a restriction upon the possible locations of clouds in the cloud field. The net effect of this analysis is that the large clouds appear to be randomly distributed, with only weak tendencies towards regularity. For clouds less than 1 km in diameter, the average nearest-neighbor distance is equal to 3-7 cloud diameters. For larger clouds, the ratio of cloud nearest-neighbor distance to cloud diameter increases sharply with increasing cloud diameter. This demonstrates that large clouds inhibit the growth of other large clouds in their vicinity. Nevertheless, this leads to random distributions of large clouds, not regularity.