An exactly solvable record model for rainfall

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 $\ln (pn)$. We also study in detail the joint limit $p\to 0$, $n\to \infty$, which yields a random record model in continuous time $t=pn$.

11 pages, 2 figures + 13 pages and 2 figures of supplemental material

References in corpus (9)

• Public Perception of Climate Change and the New Climate Dice
• Record statistics of a strongly correlated time series: random walks and Lévy flights
• Record occurrence and record values in daily and monthly temperatures
• Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation
• A record-driven growth process
• Exact persistence exponent for the $2d$-diffusion equation and related Kac polynomials
• Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation
• Statistical Properties of the Final State in One-dimensional Ballistic Aggregation
• Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

Cited by in corpus (12)

• Record statistics for random walks and Lévy flights with resetting
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Time between the maximum and the minimum of a stochastic process
• Distribution of the Time Between Maximum and Minimum of Random Walks
• Universal framework for record ages under restart
• Statistics of the Number of Records for Random Walks and Lévy Flights on a $1D$ Lattice
• Record statistics of bursts signals the onset of acceleration towards failure
• Statistical properties of avalanches via the c-record process
• Extreme value statistics of positive recurrent centrally biased random walks
• Exact and asymptotic properties of $\delta$-records in the linear drift model
• Covariance of the running range of a Brownian trajectory
• Replica approach to the generalized Rosenzweig-Porter model