Testing universality in critical exponents: The case of rainfall

Area of Science:

• * Geophysics and atmospheric science.
• * Statistical physics and complex systems analysis.

Background:

• * Rainfall event sizes often exhibit power-law distributions, a key indicator for self-organized criticality.
• * The universality of the exponents in these power-law distributions is a significant, yet debated, aspect of rainfall dynamics.

Purpose of the Study:

• * To investigate the universality hypothesis for power-law exponents in rainfall event size distributions.
• * To introduce and validate a novel statistical approach for analyzing power-law exponent universality.

Main Methods:

• * Development of a unique statistic to infer power-law exponent distributions.
• * Application of multiple variations of a permutational test to assess statistical significance.
• * Utilizing data from seven Atmospheric Radiation Measurement (ARM) Program sites.

Main Results:

• * The statistical tests led to the rejection of the universality hypothesis for rainfall event size distributions.
• * Despite observed proximity in exponent values across different sites, universality was not supported.
• * The employed statistical method avoids common pitfalls like multiple testing issues and uncertainty quantification.

Conclusions:

• * Rainfall event size distributions do not universally adhere to the same power-law exponents.
• * The findings suggest that factors beyond self-organized criticality may govern rainfall dynamics.
• * Further research is needed to understand the reasons behind the rejection of the universality hypothesis.