Rain: Relaxations in the sky

TL;DR

This paper shows that rain events exhibit scale-free, self-organized criticality-like behavior, with power-law distributions and long-range correlations, similar to earthquakes, indicating universal relaxational processes in nature.

Contribution

It introduces a novel analogy between rain and earthquakes, demonstrating rain's scale-invariant properties and linking it to self-organized criticality in natural systems.

Findings

Rain event sizes follow a power-law distribution with an exponent of 1.4.

Rain intensity exhibits long-range correlations with a Hurst exponent of 0.76.

Rain dynamics are consistent with self-organized criticality theory.

Abstract

We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in Nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the number density of rain events per year is inversely proportional to the released water column raised to the power 1.4. This is the rain-equivalent of the Gutenberg-Richter law for earthquakes. The event durations and the waiting times between events are also characterised by scaling regions, where no typical time scale exists. The Hurst exponent of the rain intensity signal $H = 0.76 > 0.5$. It is valid in the temporal range from minutes up to the full duration of the signal of half a year. All of our findings are consistent with the concept of self-organised criticality, which refers to the tendency of slowly driven non-equilibrium systems towards a state of scale free behaviour.