Appendix A: A Practical Guide to Effective Discharge Calculations
For ungaged sites on streams with only one gaging station, flow duration curves can be estimated
for ungaged sites provided that the streams are tributaries to rivers where the relation between discharge
and basin area conforms to a known power function. Estimates of the contributing flow to the mainstem can
be obtained from the difference between discharges on the mainstem above and below the tributary
junction. Discharge-basin area relations can then be derived for the tributary given the flow duration curve
at the gaging station and the predicted curve at its confluence with the mainstem. However, this technique
should not be used if there are distinct and abrupt downstream changes in the discharge per unit area for
the watershed, due to tributaries draining different hydrological regions. In this case it would be preferable
to use the regionalized duration curve method described next.
Regionalized Duration Curve Method
An alternative to the use of watershed area to generate a flow duration curve for an ungaged site
is to use a regional-scaling method based on data from watersheds with similar characteristics. For
example, Emmett (1975) and Leopold (1994) suggest using the ratio of discharge to bankfull discharge
(Q/Qb) as a non-dimensional index with which to transfer flow duration relationships between basins with
similar characteristics. However, bankfull discharge does not necessarily have either a consistent duration
or return period (see, for example, Williams, 1978). To get around this problem, a non-dimensional
discharge index was proposed by Watson et al. (1997) using the regionalized 2-year discharge to
normalize discharges (Q/Q2).
For ungaged sites the 2-year discharge may be estimated from regionalized discharge frequency
relationships developed by the USGS (1993) on the basis of regression relationships between the drainage
area, channel slope, and slope length. These relationships are available for most American states. The
dimensionless discharge index (Q/Q2) can be used to transfer a flow duration relationship to an ungaged
site from a nearby, gaged site. The gaged site may either be within the same basin, or an adjacent
watershed. The steps involved in developing a regional flow duration relationship are:
Select several gaging stations and divide the discharge values of the flow duration relationship
for each station by the respective Q2 for that gage.
Plot these ratios on a log-log graph. An example plot is shown in Figure 3, which is based on
combined data for 10 gaging stations in watersheds in Mississippi used in the Demonstration
Erosion Control (DEC) Project (Watson et al., 1997). The regression analysis was
performed assuming that discharges less than 1% of the Q2 and with a probability of less than
1%, are morphologically insignificant and may be ignored.
A flow duration curve for any ungaged site may then be computed by substituting the
regionalized Q2 for that site. Flow frequencies for selected discharge classes may then be
extracted from the flow duration curve for the ungaged site.