Low Flow Calculations

1
Low Flow Calculations In NPDES permits the
permitted industry or municipality must meet
certain requirements with regards to the toxicity
of their effluent. The percent of the effluent
being discharged to the receiving stream that
must not be toxic is based on the historically
based low flow conditions of the receiving
system. For example, if under low flow
conditions in freshwater the effluent can occupy
65 of the flow of the stream, in the
biomonitoring toxicity tests (Short-term Chronic,
7-day Ceriodaphnia dubia survival and
reproduction test and the Pimephales promelas
survival and growth test) must reveal that the
effluent is not toxic at a dilution of 65 or
lower. The rationale is that under low flow
conditions the effluent cannot occupy more than
65 of the stream but can constitute that much of
the flow or lower. Therefore, the effluent
cannot be toxic when diluted to 65 by upstream
or laboratory water.
2
Depending on the State and the EPA Region, what
constitutes the historic low flow conditions can
vary. Most often the low flow is based on the
7Q10 flow. In Texas the low flow is based on the
7Q2 flow. The definition of 7Q10 is, the lowest
average discharge over a period of one week with
a recurrence interval of 10 years. Since the
value of N for the 7Q10 is 10 years, there is
only a 10 probability that there will be a lower
flow in any given year. There is a 90
probability that the flow will be greater than
the 7Q10 value. The definition of 7Q2 is the
lowest average discharge over a period of one
week with a recurrence interval of 2 years.
Since the value of N for the 7Q2 is 2 years,
there is a 50 probability that there will be a
lower flow in any given year. Or, in other
words, there is a 50 probability that there will
be a flow greater than the 7Q2 in any given year.

3
Given the following record of stream flow data,
estimate the 7Q10 flow for the stream.
Year Lowest Seven-Day Average Flow,
m3/s 1980 4.4 1981 2.8 1982 4.0 19
83 3.4 1984 5.2 Solution First arrange
the flow data in decreasing order of magnitude
and assign a rank or m value to each flow,
beginning with 1 and increasing sequentially. In
the case of ties assign the tied scores the
average of the tied ranks.
4
For example, the following data 2.6, 3.2, 3.2 3.2
and 4.5 m3/s would be ranked 1 for 4.5, and 3 for
each of the 3.2 values and 5 for the 2.6 value.
Had there only been two 3.2 values the average
rank would have been 2.5 for each of these
values. The probability of observing an equal or
higher flow in any given year is estimated by
dividing the rank m by the number of years of
record plus 1 (n1) in this example n 5. In
formula form the probability P m/(n1). Low
Flow, m3/s Rank Probability 5.2 1 1/60.1
67 4.4 2 2/60.333 4.0 3 3/60.500 3.4
4 4/60.667 2.8 5 5/60.833
5
Plot the data on log probability paper with the
y-axis as the Yearly 7-Consecutive Day Low Flow,
m3/s, and the x-axis as the Probability of a
Larger Flow.
6
(No Transcript)
7
If an industry is discharging 2.5 m3 into the
receiving system represented by the calculations
we just made i.e. a 7Q10 of 2.72 and a 7Q2 of 4.0
m3/sec at what percent effluent does the industry
have to pass the WET requirements in their NPDES
permit? Calculations
7Q10 2.5 m3 2.72 m3 5.22 m3 2.53/5.22 48
under low flow conditions the effluent could not
occupy more than 48 the flow of the receiving
system. 7Q2 2.5 m3 4.0 m3/sec 6.5 m3/sec
2.53/6.5 m3/sec 39 under low flow conditions
the effluent could not occupy more than 39 of
the flow of the receiving system.
8
Using the methodology given above determine both
the 7Q10 and the 7Q2 flow for the data shown in
the Table on the next page. The data represent
the lowest seven-day average flow m3/s for the
year shown. How is this determined?
Generally the USGS defines a water year as the
period from October 1 to September 30. Low flow
calculations (e.g. 7Q10) are calculated based on
data collected between April 1 and March 31.
9
Year Lowest Seven-Day Ave. Flow m3/s
1973 5.6
1974 4.3
1975 2.1
1976 6.7
1977 6.2
1978 6.9
1979 3.1
1980 4.1
1981 5.1
1982 4.9
1983 4.7
1984 3.9
1985 3.1
1986 2.1
1987 2.8
1988 2.1
1989 7.2
1990 7.1
1991 6.4
1992 5.1
1993 4.4
10
Rank High to Low Rank High to Low Rank High to Low
Low Flow m3/s Rank Probability