Probability
Hydrologic data series
1. Complete series
Use all of the data.
Date
4/28/03
6/20/03
3/30/04
Depth (cm)
1.0
0.1
1.2
11/11/04
9/5/05
12/22/05
0.8
0.4
0.3
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
Date
4/28/03
6/20/03
3/30/04
Depth (cm)
1.0
0.1
1.2
11/11/04
9/5/05
12/22/05
0.8
0.4
0.3
Hydrologic data series
3. Extreme value series
Use maximum or minimum
value for each year
Date
4/28/03
6/20/03
3/30/04
Depth (cm)
1.0
0.1
1.2
11/11/04
9/5/05
12/22/05
0.8
0.4
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:
m
Pm 
n 1
where m = rank
n = # values
Date
4/28/03
6/20/03
Depth (cm)
1.0
0.1
3/30/04
11/11/04
9/5/05
12/22/05
1.2
0.8
0.4
0.3
Frequency analysis: empirical method
Date
3/30/04
4/28/03
9/5/05
Depth (cm)
1.2
1.0
0.4
Rank
1
2
3
Position
0.25
0.5
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