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Related Experiment Video

Updated: Jan 25, 2026

A Protocol for Conducting Rainfall Simulation to Study Soil Runoff
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Exactly Solvable Record Model for Rainfall.

Satya N Majumdar1, Philipp von Bomhard2, Joachim Krug3

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Summary

Dry days in precipitation data create negative correlations in record-breaking rainfall events. The number of precipitation records up to time n converges to a Poisson distribution, revealing patterns in climate data.

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Area of Science:

  • Hydrology and Climatology
  • Statistical Physics

Background:

  • Daily precipitation time series contain dry days (null entries) and wet days (nonzero rainfall amounts).
  • Understanding the statistical properties of extreme precipitation events is crucial for climate modeling and risk assessment.

Purpose of the Study:

  • To investigate the impact of dry days on correlations between record-breaking precipitation events.
  • To derive and analyze the probability distribution of precipitation records.
  • To explore the limiting behavior of precipitation records under specific conditions.

Main Methods:

  • Modeling wet days using a Bernoulli process with success probability p.
  • Analyzing the Fano factor of the record counting process.
  • Deriving the probability distribution P(R,n) for the number of records R_n up to time n.
  • Investigating the joint limit p→0, n→∞.

Main Results:

  • Dry days induce negative correlations between record-breaking precipitation events.
  • The Fano factor of the record counting process exhibits nonmonotonic behavior, consistent with empirical data.
  • The probability distribution P(R,n) converges to a Poisson distribution with parameter ln(pn) for large n.
  • A random record model in continuous time (t=pn) is obtained in the joint limit.

Conclusions:

  • The presence of dry days significantly influences the statistical properties of precipitation records.
  • The derived Poisson distribution provides a theoretical framework for understanding extreme precipitation event frequency.
  • The study offers insights into the long-term behavior of climate data and extreme value analysis.