Probability. Hydrologic data series 1.Complete series Use all of the data. DateDepth (cm) 4/28/031.0 6/20/030.1 3/30/041.2 11/11/040.8 9/5/050.4 12/22/050.3.

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Presentation transcript:

Probability

Hydrologic data series 1.Complete series Use all of the data. DateDepth (cm) 4/28/ /20/ /30/ /11/ /5/ /22/050.3

Hydrologic data series 2.Partial duration series Use data above or below a base value. For example, Annual exceedance series Choose base such that # of events = # of years DateDepth (cm) 4/28/ /20/ /30/ /11/ /5/ /22/050.3

Hydrologic data series 3.Extreme value series Use maximum or minimum value for each year DateDepth (cm) 4/28/ /20/ /30/ /11/ /5/ /22/050.3 Which is better—annual maximum or annual exceedance?

Frequency analysis: empirical method Construct frequency curve (CDF, essentially) from the given data. Rank the data. Compute plotting position: DateDepth (cm) 4/28/ /20/ /30/ /11/ /5/ /22/050.3 where m = rank n = # values

Frequency analysis: empirical method DateDepth (cm)RankPosition 3/30/ /28/ /5/

Frequency analysis: empirical method

Extreme value Type I PDF Useful for determining return period of extreme events

Log-Pearson Type III PDF Allows for variable skewness