An exactly solvable record model for rainfall

TL;DR

This paper introduces an exactly solvable model for rainfall records, revealing how dry days induce negative correlations between record events and deriving their probability distribution, with implications for understanding rainfall patterns.

Contribution

The authors develop a solvable record model for rainfall data, deriving the full distribution of record counts and analyzing the effects of dry days on record correlations.

Findings

Dry days induce negative correlations between record events.

The record count distribution approximates a Poisson distribution for large n.

The model captures non-monotonic behavior of the Fano factor in empirical data.

Abstract

Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we show that the presence of dry days induces negative correlations between record-breaking precipitation events. The resulting non-monotonic behavior of the Fano factor of the record counting process is recovered in empirical data. We derive the full probability distribution $P(R,n)$ of the number of records $R_n$ up to time $n$, and show that for large $n$, its large deviation form coincides with that of a Poisson distribution with parameter $\ln(p\,n)$. We also study in detail the joint limit $p \to 0$, $n \to \infty$, which yields a random record model in continuous time $t = pn$.