# Archive ouverte HAL – Exactly Solvable Record Model for Rainfall

### Satya N. Majumdar 1 Philipp von BomhardJoachim Krug 2 Satya Majumdar 1

#### Satya N. Majumdar, Philipp von Bomhard, Joachim Krug, Satya Majumdar. Exactly Solvable Record Model for Rainfall. Physical Review Letters, American Physical Society, 2019, 122 (15), ⟨10.1103/PhysRevLett.122.158702⟩. ⟨hal-02291862⟩

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 $t = pn$.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. University of Cologne