An extreme value model for U.S. hail size

John T. Allen, Michael K. Tippett, Yasir Kaheil, Adam H. Sobel, Chiara Lepore, Shangyao Nong, Andreas Muehlbauer

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


The spatial distribution of return intervals for U.S. hail size is explored within the framework of extreme value theory using observations from the period 1979-2013. The center of the continent has experienced hail in excess of 5 in. (127 mm) during the past 30 yr, whereas hail in excess of 1 in. (25 mm) is more common in other regions, including the West Coast. Observed hail sizes show heavy quantization toward fixed-diameter reference objects and are influenced by spatial and temporal biases similar to those noted for hail occurrence. Recorded hail diameters have been growing in recent decades because of improved reporting. These data limitations motivate exploration of extreme value distributions to represent the return periods for various hail diameters. The parameters of a Gumbel distribution are fit to dithered observed annual maxima on a national 1° × 1° grid at locations with sufficient records. Gridded and kernel-smoothed return sizes and quantiles up to the 200-yr return period are determined for the fitted Gumbel distribution. These results are used to illustrate return levels for hail greater than a given size for at least one location within each 1° × 1° grid box for the United States.

Original languageEnglish
Pages (from-to)4501-4519
Number of pages19
JournalMonthly Weather Review
Issue number11
StatePublished - Nov 1 2017


  • Climatology
  • Hail
  • Risk assessment
  • Severe storms


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