RIVERS AND STREAMS - Water Quality Engineering in Natural Systems - page 119

curve is derived. The procedure for deriving the LDC is
described below.

the frequency of occurrence of observed flow
rates, with high flow rates exceeded rarely (< 10%
of the time) and low low rates exceeded fre-
quently (>90% of the time). various descriptors of
the flow conditions are used to characterize the
flows within various flow ranges, with classifica-
tions suggested by USEPA shown in Figure 4.12
and quantified as follows (USEPA, 2007)

Step 1: Gather the Data. At the stream section of
interest, specify the applicable water-quality stan-
dard, c std , and obtain a long-term record of average
daily flows. In the United States, records of daily-
averaged flows are collected at thousands of loca-
tions by the U.S. Geological Survey (USGS), and
these records can generally be accessed online. If
the stream section of interest does not have a long
record of flow measurements, then alternate esti-
mation methods, such as rainfall runoff models or
scaling of upstream or downstream flow measure-
ments, might be appropriate; however, these alter-
nate methods will generally compromise the
accuracy of the LDC.
Step 2: Calculate the Flow Duration Curve (FDC).
The FDC expresses the functional relationship
between the flow rate in the stream, and the per-
centage of time that the flow rate is exceeded.
Derivation of the FDC is commonly done by first
ranking the N measured daily flows, where 1 is the
rank of the highest flow and N is the rank of the
lowest flow. For any flow with rank m , the exceed-
ance percentage can be estimated by the Weibull
formula (Weibull, 1939) as

Classification Exceedance Percentage (%)

High flows 0-10

Moist conditions 10-40

Mid-range flows 40-60

Dry conditions 60-80

Low flows 80-100

Step 3: Derive the LDC from the FDC. The LDC is
derived from the flow duration curve (FDC) by
simply multiplying the ordinate of the FDC by
the water-quality standard, c std , of the contaminant
of interest. A typical resulting LDC is shown in
Figure 4.13. Since the product of a flow rate and
c std gives the TMDL for that particular flow rate,
then the LDC is simply the TMDL as a function
of the exceedance percentage of the flow rate. In
unusual cases where the water-quality standard,
c std , varies with flow condition, this variation is
respected in multiplying the FDC ordinates by the
appropriate c std to determine the LDC. Such
adjustments are typical of suspended-sediment
standards.

m
N 1

100 (4.158) exceedance percentage = ×

+

The FDC is then obtained by plotting the flow rate
in the stream versus the exceedance percentage,
where the flow rate is usually plotted on a loga-
rithmic scale. A typical FDC is shown in Figure
4.12. The FDC provides a graphical indication of

In cases where water-quality standards are seasonal
(e.g., summer and winter), separate LDCs for each
season are typically more useful than a single LDC for
the entire year.

high ows

10 4

moist conditions

mid-range ows

10 3

dry conditions

10 2

low ows

10

1

0 20 50 90

10 30 40 60 70 80 100

exceedance percentage (%)

Figure 4.12. Flow duration curve.