06 Feb 2024
 | 06 Feb 2024
Status: this preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).

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

Thomas D. DeWitt and Timothy J. Garrett

Abstract. A significant uncertainty in assessments of the role of clouds in climate is characterization of the full distribution of their sizes. Order-of-magnitude disagreements exist among observations of such key distribution parameters as the power law exponent and the range over which a power law applies. A study by Savre and Craig (2023) proposed this discrepancy owes in large part to inaccurate fitting methods. Rather than linear regression to a logarithmically-transformed histogram of cloud sizes, an alternative method termed Maximum Likelihood Estimation was recommended. Here, we counter that Maximum Likelihood Estimation is ill-suited to measurements of physical objects like clouds, and that the accuracy of linear regression can be improved with the simple remedy that bins containing less than ~24 counts be omitted from the regression. Further, we argue that the unavoidably finite nature of measurement domains is a much more significant source of error than has previously been appreciated. Finite domain effects are sufficient to account for previously observed discrepancies among reported cloud size distributions. We provide a simple procedure to identify and correct finite domain effects that could be applied to any measurement of a geometric size distribution of objects, whether physical, ecological, social or mathematical.

Thomas D. DeWitt and Timothy J. Garrett

Status: open (until 19 Mar 2024)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
Thomas D. DeWitt and Timothy J. Garrett
Thomas D. DeWitt and Timothy J. Garrett


Total article views: 150 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
116 30 4 150 3 3
  • HTML: 116
  • PDF: 30
  • XML: 4
  • Total: 150
  • BibTeX: 3
  • EndNote: 3
Views and downloads (calculated since 06 Feb 2024)
Cumulative views and downloads (calculated since 06 Feb 2024)

Viewed (geographical distribution)

Total article views: 144 (including HTML, PDF, and XML) Thereof 144 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 04 Mar 2024
Short summary
There is considerable disagreement on mathematical parameters that describe the numbers of clouds of different sizes, as well as the size of the largest clouds. Both are key defining characteristics of the Earth's atmosphere. A previous study provided an incorrect explanation for the disagreement. Instead, the disagreements may be explained by prior studies not properly accounting for the size of their measurement domain. We offer recommendations for how the domain size can be accounted for.