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

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2018R1A2B2005772). Rainfall dataset used in this study are from the website of the Korea Meteorological Administration (http://www.kma.go.kr/weather/climate/past_cal.jsp).

Publisher Copyright:
© 2020 Elsevier B.V.

Copyright 2020 Elsevier B.V., All rights reserved.


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

ASJC Scopus subject areas

  • Water Science and Technology


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