Extreme event statistics of daily rainfall: Dynamical systems approach

TL;DR

This paper analyzes daily rainfall data using a dynamical systems approach, revealing power-law distributions for rainfall amounts and near-exponential waiting times, with implications for understanding extreme weather events like floods and droughts.

Contribution

It introduces a superstatistical dynamical systems framework to model rainfall distributions and extreme event statistics, connecting empirical data with theoretical models.

Findings

Rainfall amounts follow a q-exponential distribution with q≈1.3.

Waiting times between rainy days are best fitted by a q-exponential with q≈1.05.

Extreme rainfall events follow Frechet distributions, indicating potential for flooding.

Abstract

We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss possible reasons for the emergence of this power law. On the contrary, the waiting time distribution between rainy days is observed to follow a near-exponential distribution. A careful investigation shows that a q-exponential with q=1.05 yields actually the best fit of the data. A Poisson process where the rate fluctuates slightly in a superstatistical way is discussed as a possible model for this. We discuss the extreme value statistics for extreme daily rainfall, which can potentially lead to flooding. This is described by Frechet distributions as the corresponding distributions of the amount of daily rainfall decay with a power law. On the other hand, looking at extreme event statistics of waiting times between rainy days (leading to droughts for very long dry periods) we obtain from the observed near-exponential decay of waiting times an extreme event statistics close to Gumbel distributions. We discuss superstatistical dynamical systems as simple models in this context.