probability. hydrologic data series 1.complete series use all of the data. datedepth (cm) 4/28/031.0...
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Probability
Hydrologic data series1. Complete series
Use all of the data.Date Depth (cm)
4/28/03 1.0
6/20/03 0.1
3/30/04 1.2
11/11/04 0.8
9/5/05 0.4
12/22/05 0.3
Hydrologic data series2. Partial duration series
Use data above or below a base value. For example,
Annual exceedance series
Choose base such that # of events = # of years
Date Depth (cm)
4/28/03 1.0
6/20/03 0.1
3/30/04 1.2
11/11/04 0.8
9/5/05 0.4
12/22/05 0.3
Hydrologic data series3. Extreme value series
Use maximum or minimum value for each year Date Depth (cm)
4/28/03 1.0
6/20/03 0.1
3/30/04 1.2
11/11/04 0.8
9/5/05 0.4
12/22/05 0.3
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:
Date Depth (cm)
4/28/03 1.0
6/20/03 0.1
3/30/04 1.2
11/11/04 0.8
9/5/05 0.4
12/22/05 0.3
1n
mPm
where m = rank
n = # values
Frequency analysis: empirical method
Date Depth (cm) Rank Position
3/30/04 1.2 1 0.25
4/28/03 1.0 2 0.5
9/5/05 0.4 3 0.75
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