CLUSTERING, RANDOMNESS AND REGULARITY IN CLOUD FIELDS .1. THEORETICAL CONSIDERATIONS

During the last decade, there has been considerable controversy in the literature concerning the nature of cloud distributions. Both theoretical and observational evidence has been presented to support cloud field clustering in some cases and cloud field regularity in other cases. Therefore considerable uncertainty exists. It is essential to resolve this issue since it impacts both cloud dynamical and global cloud radiative forcing issues. In the present investigation, analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics, when applied to a point process consisting of cloud centers, show that (1) the Poisson representation of random point processes is superior to pseudorandom number generated models; (2) pseudorandom number generated models bias the observed nearest-neighbor statistics towards regularity; and (3) an upper bound on the errors caused by edge effects in finite areas is shown to be negligible in certain ranges of cloud number density. Interpretation of this nearest-neighbor statistic is discussed for many cases of superpositions of clustering, randomness, and regularity. This is accomplished by plotting the observed versus random nearest-neighbor cumulative distribution functions. Both the magnitude of the positive or negative deviations from the diagonal are important indicators of clustering and regularity. Alternative point-to-neighbor statistics are found to be useful for identifying the components of combinations of distribution types. Finally, and perhaps most importantly, the nature and magnitude of cloud size effects upon the nearest-neighbor and point-to-neighbor cumulative distribution curves are investigated. It is found that even at only 15% cloud cover, size effects dominate the bias caused by the lack of randomness of pseudorandom number generators or by edge effects. Furthermore, cloud size effects shift the nearest-neighbor cumulative distribution curves to mimic regularity.