Finite domains cause bias in measured and modeled distributions of cloud sizes

Abstract

A significant uncertainty in assessments of the role of clouds in climate is the characterization of the full distribution of their sizes. Order-of-magnitude disagreements exist among observations of key distribution parameters, particularly power law exponents and the range over which they apply. A study by Savre and Craig (2023) suggested that the discrepancies are due in large part to inaccurate fitting methods: they recommended the use of a maximum likelihood estimation technique rather than a linear regression to a logarithmically transformed histogram of cloud sizes. Here, we counter that linear regression is both simpler and equally accurate, provided the simple precaution is followed that bins containing fewer than ∼ 24 counts are omitted from the regression. A much more significant and underappreciated source of error is how to treat clouds that are truncated by the edges of unavoidably finite measurement domains. We offer a simple computational procedure to identify and correct for domain size effects, with potential application to any geometric size distribution of objects, whether physical, ecological, social or mathematical.