Power laws in intra-storm temporal rainfall variability

Hyoungseok Kang, Sanghoon Shin, Kyungrock Paik

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


During a storm event, rainfall intensity rarely remains uniform but rather shows radical temporal variation. Given the time window w within a storm, the maximum rainfall intensity over w, namely iw decreases as w increases. Our analysis of individual storm events using ground measurements of 1-minute temporal resolution reveals that the iw–w relationship follows either a single or broken power law. Such scale-invariance is likely associated with known fractal or multi-fractal characteristics of rainfall structure. In broken power-law events, two power-law exponents of βm (at minute time scale) and βh (at hourly time scale) are fitted for segments separated by the characteristic time τ. Mostly βm < βh, implying the persistence of high rainfall concentration prior to τ. This reflects the characteristics of convective storms, and the range of τ agrees with the known time span of convective storm duration. The more concentrated storm event exhibits the stronger persistence (a smaller βm) prior to τ and the faster moisture depletion (a greater βh) thereafter. The knowledge gained from this study provides important implications to the existing design storm formula, often called the Mononobe formula: observed scale-free intra-storm variability is in accordance with this formula while the scaling transition at sub-hourly time scale explains the known limitations of its practical applications.

Original languageEnglish
Article number125233
JournalJournal of Hydrology
Publication statusPublished - 2020 Nov

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Convective storm
  • Design storm
  • Fractal rainfall
  • Mononobe formula
  • Self-similarity

ASJC Scopus subject areas

  • Water Science and Technology


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