Page 69 - Water and wastewater engineering

2-12 WATER AND WASTEWATER ENGINEERING

The regulatory agency will only permit a withdrawal of 5%. Therefore, the allowable with-
drawal will be
3
3
(0055 98 m /s 0 30 m /s
)(
.
)
.
.
3
This is sufficient to meet the safe yield of 0.25 m /s required for the municipality.
If the determination is made that the 50 percentile allowable withdrawal is less than the
required safe yield, then, even with storage, the safe yield cannot be met. An alternative source
should be investigated. If the determination is made that the allowable withdrawal will be adequate,
then an analysis is performed to determine the need for a storage reservoir for droughts. This
analysis is called an annual series or extreme-value analysis.
Annual Series. Extreme-value analysis is a probability analysis of the largest or smallest values
in a data set. Each of the extreme values is selected from an equal time interval. For example, if
the largest value in each year of record is used, the extreme-value analysis is called an annual
maxima series. If the smallest value is used, it is called an annual minima series.
Because of the climatic effects on most hydrologic phenomena, a water year or hydrologic
year is adopted instead of a calendar year. The U.S. Geological Survey (U.S.G.S.) has adopted
the 12-month period from October 1 to September 30 as the hydrologic year for the United
States. This period was chosen for two reasons: “(1) to break the record during the low-water
period near the end of the summer season, and (2) to avoid breaking the record during the winter,
so as to eliminate computation difficulties during the ice period.” (Boyer, 1964)
The procedure for an annual maxima or minima analysis is as follows:

1. Select the minimum or maximum value in each 12-month interval (October to September)
over the period of record.
2. Rank each value starting with the highest (for annual maxima) or lowest (for annual
minima) as rank number one.
3. Compute a return period using Weibull’s formula (Weibull, 1939):

n 1
T (2-1)
m

where T average return period, y
n number of years of record
m rank of storm or drought
4. Plot the annual maxima or minima series on a special probability paper known as Gumbel
paper. (A blank copy of Gumbel paper may be downloaded from the website: http//www.
mhprofessional.com/wwe .) Although the same paper may be used for annual minima series,
Gumbel recommends a log extremal probability paper (axis of ordinates is log scale) for
droughts (Gumbel, 1954).

From the Gumbel plot, the return period for a flood or drought of any magnitude may be deter-
mined. Conversely, for any magnitude of flood or drought, one may determine how frequently it
will occur.