Flow Duration Curves
Flow duration curves characterize the flow of streams. They show streamflow rates (often daily mean discharge) that have been exceeded various percentages of the time. They apply to a particular place in a stream (site), and they represent flow during a specified period of time (usually the period of record at the site). An example is shown in Figure 1. To improve the readability, discharge (flow rate) is usually plotted on a logarithmic scale (equal distance between 1, 10, 100, et cetera), as in this figure; but other scales may be used on either axis to accentuate various features of the curve.
Figure 1. Flow duration curve for Little Powder River, Montana, 1948-1972.
In this example, a flow rate of 2 cubic feet per second was exceeded about 84 percent of the time; and a flow rate of 100 cubic feet per second was exceeded only about 8 percent of the time. Flow duration curves like this example are constructed by arranging the streamflow data from a gaged site in descending order, calculating the percent of the data that is greater than each value, and plotting the results. Since the streamflow data are rearranged, the duration curve does not show the chronological sequence of flows. A chronological sequence of flows may be shown by a stream hydrograph, which is a graph of the rate of flow of a stream plotted against time. A stream hydrograph shows the seasonal change better than a flow duration curve.
Shape of Flow Duration Curves
The shape of flow duration curves is influenced by various factors. A curve with a steep slope throughout indicates a highly variable stream whose flow is largely due to quick runoff of rainfall to the stream. A flat slope indicates dominance of groundwater discharging to the stream via springs or diffuse inflow along the length of the stream. A flat slope may also be produced by regulation of streamflow through controlling discharge from reservoirs. Streams whose high flows are produced by quick runoff of the larger rainfall events have a steep slope at the upper end. However, stream banks composed of permeable alluvium reduce the high discharges. This reduction is caused by temporary loss of stream water to the alluvium (bank storage). Streams whose high flows come largely from snowmelt tend to have a flat slope at the upper (high flow) end. Swamp areas can also flatten the slope of high flows. The distribution of the low flows in the middle part of the flow duration curve is controlled chiefly by the topography and geology of the basin; especially the permeability, extent, and distribution of the subsurface materials. The lowest flows can be strongly affected by extraction of water by vegetation (phreatophytes) along the stream banks producing a sharp dip at the lower tail of the duration curve. The drainage basin history can also affect the flow duration curve: such things as construction of reservoirs, changes in irrigation practice, and changes in land use. Flow duration curves can also be affected by the period of the streamflow record used. Short periods can be biased by wet and dry climatic cycles. For a reasonably representative curve, at least 30 years of record has been recommended, but as little as 10 years has been used. A comprehensive quantitative understanding of the relative contribution of all the influences on the shape of flow duration curves has not yet been achieved.
Use of Flow Duration Curves
Flow duration curves are used for many purposes in which the frequency of flows of various magnitudes is important. Often the frequency of low flows, high flows, or flows within certain ranges are related to the risk of failure of a project. The use of flow duration curves may include but is not limited to the following:
Siting hydropower facilities,
Siting water-supply facilities,
Siting facilities that require cooling water,
Sewage disposal plant design,
Water use planning and allocation,
Waste discharge allocation,
Water rights risk analysis,
Flood control structure design,
Water quality management,
Aquatic habitat management,
Erosion and sedimentation studies.
Flow Duration Curves for Ungaged Sites
Flow duration curves may be estimated for ungaged sites on streams. This possibility is important because curves may be needed for sites that are not gaged. The estimates may be made by interpolating, extrapolating, and correlating with curves from gaged sites (analogue sites). Analogue sites should have long periods of record. Uncertainty increases when the flow duration curve is based on sparse data. Analogue sites should meet the following requirements:
Be geographically close to the ungaged site and hence have the same climatic regime,
Have similar geologic characteristics (subsurface materials, topography, et cetera),
Have similar hydrologic characteristics (lakes, swamps, et cetera),
Have flow that is not regulated by control structures (or be amenable to adjustment to a natural flow regime),
Have no significant groundwater abstraction (or be amenable to adjustment for the abstraction),
Have no inflow from sources outside the gaged watershed area,
Be unaffected by land use change.
At least one analogue site is needed, but more than one is better. It is best if the characteristics of the ungaged site are intermediate between those of the analogue sites (watershed size, for example); so that they are interpolated rather than extrapolated. Interpolation results in less uncertainty than extrapolation.
Certain properties of flow duration curves for mean daily discharge reduce the uncertainty of the estimated curves. These properties include the following:
Flow duration curves for unregulated drainage areas with similar geology, vegetation, topography, soil types, alluvial area, and climate tend to be similar,
The area under a flow duration curve plotted with arithmetic scales (equal distance between the units on both axes) must be equal to the average daily flow multiplied by 100, and the median daily flow is the 50 percent value,
If the streamflow rate (mean daily discharge) is divided by the mean annual discharge and plotted as in Figure 2, curves for similar drainage areas will plot close together even though they are not the same size and have correspondingly different mean annual discharge (corollary to the property above),
Th logarithm of the streamflow rate (tends to be normally distributed (follow the typical bell-shaped curve).
Figure 2. Dimensionless flow duration curves for Big Dry Creek (2554 square miles) and Sand Creek (317 square miles), Montana.
The mean annual discharge needed to estimate flow duration curves for ungaged sites may be obtained by developing a correlation with basin size and mean annual precipitation in a region. Also regional studies exist wherein formulas for mean annual discharge at ungaged sites have been developed using more advanced statistical techniques. Regional statistical studies can also be used to develop formulas for percentile points on the flow duration curves of ungaged sites.
Spot flow measurements at the ungaged site may be used to reduce the uncertainty. The measurements are taken at various flow rates and correlated to flow rates at analogue sites. Similarly, the flow duration curve for a site with a short period of record can be adjusted to the period of record of an analogue site.
The accuracy of a flow duration curve for an ungaged site can be checked using a blind experiment. In a blind experiment the curve for a gaged site is blindly estimated using the same method that will be applied to the ungaged site. The blind estimate is then compared to the actual curve. An early (perhaps first) use of this verification technique is described in Dunn (1976). Recently, a less subjective technique called bootstrapping has been used.
An example of developing flow duration curves for ungaged streams using a subjective approach requiring a relatively low level of effort is Dunn (1977).
Revised June 9, 2018