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