Testing Universality in Critical Exponents: the Case of Rainfall

TL;DR

This study investigates whether rainfall event size distributions follow a universal power-law across different sites, using a novel statistical test that avoids common pitfalls, and finds that universality is rejected.

Contribution

Introduces a new permutation-based statistical method to test universality of critical exponents in rainfall data without requiring precise uncertainty estimates.

Findings

Universality hypothesis is rejected across seven monitored sites.

Exponents are similar but not statistically identical.

New method avoids multiple testing issues.

Abstract

One of the key clues to consider rainfall as a self-organized critical phenomenon is the existence of power-law distributions for rain-event sizes. We have studied the problem of universality in the exponents of these distributions by means of a suitable statistic whose distribution is inferred by several variations of a permutational test. In contrast to more common approaches, our procedure does not suffer from the difficulties of multiple testing and does not require the precise knowledge of the uncertainties associated to the power-law exponents. When applied to seven sites monitored by the Atmospheric Radiation Measurement Program the test lead to the rejection of the universality hypothesis, despite the fact that the exponents are rather close to each other.