On the frequency of heavy rainfall for the Midwest of the United States

Gabriele Villarini, James A. Smith, Mary Lynn Baeck, Renato Vitolo, David B. Stephenson, Witold F. Krajewski

Research output: Contribution to journalArticlepeer-review

190 Scopus citations


Annual maximum daily rainfall time series from 221 rain gages in the Midwest United States with a record of at least 75. years are used to study extreme rainfall from a regional perspective. The main topics of this study are: (i) seasonality of extreme rainfall; (ii) temporal stationarity and long-term persistence of annual maximum daily rainfall; (iii) frequency analyses of annual maximum daily rainfall based on extreme value theory; and (iv) clustering of heavy rainfall events and impact of climate variables on the frequency of occurrence of heavy rainfall events.Annual maximum daily rainfall in the Midwest US exhibits a marked seasonality, with the largest frequencies concentrated in the period May-August. Non-parametric tests are used to examine the validity of the stationarity assumption in terms of both abrupt and slowly varying temporal changes. About 10% of the stations show a change-point in mean and/or variance. Increasing monotonic patterns are detected at 19 stations. Quantile regression analyses suggest that the number of stations with a significant increasing trend tends to decrease for increasing quantiles. Temporal changes in the annual maximum daily rainfall time series are also examined in terms of long-term persistence. Conclusive statements about the presence of long-term persistence in these records are, however, not possible due to the large uncertainties associated with the estimation of the Hurst exponent from a limited sample. Modeling of annual maximum daily rainfall records with the Generalized Extreme Value (GEV) distribution shows well-defined spatial patterns for the location and scale parameters but not for the shape parameter. Examination of the upper tail properties of the annual maximum daily rainfall records points to a heavy tail behavior for most of the stations considered in this study. The largest values of the 100-year annual maximum daily rainfall are found in the area between eastern Kansas, Iowa, and Missouri. Finally, we use the Poisson regression as a framework for the examination of clustering of heavy rainfall. Our results point to a clustering behavior due to temporal fluctuations in the rate of occurrence of the heavy rainfall events, which is modulated by climatic factors representing the influence of both Atlantic and Pacific Oceans.

Original languageEnglish (US)
Pages (from-to)103-120
Number of pages18
JournalJournal of Hydrology
Issue number1-2
StatePublished - Mar 30 2011

All Science Journal Classification (ASJC) codes

  • Water Science and Technology


  • Extreme rainfall
  • Extreme value statistics
  • Midwest US
  • Poisson regression
  • Quantile regression
  • Stationarity


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