Use of Tracer 

Injections to 

Measure Discharge

and Quantify 

Pollutant Loading

by William P. Carey 

Hydrologist, National Science and

Technology Center

Background

Bureau of Land Management

(BLM) hydrologists are often faced

with the problem of obtaining

stream discharge measurements in

streams where the traditional measurement technique is not appropriate. The traditional technique

(current meter measurement, see

Buchanan and Somers, 1973) is

appropriate when the channel bottom and banks are relatively smooth

and the assumption of a logarithmic

vertical velocity profile is reasonable.

In small streams with large roughness elements like cobbles and boulders, a logarithmic velocity profile

cannot be assumed (Marchand et al.,

1984). Also, in streams with highly

porous beds, some of the water will

be flowing through the bed material

where it cannot be measured by a

current meter (Kimball, 1997).

The traditional current meter technique allows some latitude in

selecting optimal measurement

cross section. In water quality studies where the objective is to quantify several inputs in a stream reach,

the location of measurement cross

sections is severely restricted. If the

hydraulics of the measurement sections do not conform to the

assumptions of the traditional

method, then the resulting inaccuracies may mask the change in discharge due to lateral inflow. In

synoptic water quality studies, there

is usually insufficient time to make a

traditional current meter measurement at each sampling location.

These short comings of the traditional current meter method can

be overcome by injecting a conservative tracer to measure stream discharge. In water quality studies,

the tracer injection is used in conjunction with synoptic water

chemistry sampling to quantify

lateral inputs.

Discussion

The general approach to using tracer injections is to measure the

downstream dilution of the injected

tracer and use this information to

compute stream discharge. Since

the tracer is conservative, the downstream decrease in concentration is

due solely to dilution. There are

two methods of measuring stream

discharge using tracer injections:

slug injection and constant rate

injection (Kilpatrick and Cobb,

1985). The slug injection method

instantaneously injects a known

amount of tracer into the flow. The

method requires that the dilution

of the tracer be accounted for by

the complete measurement of its

mass downstream. The constant

rate injection method requires only

the measurement of the plateau

concentration that results downstream after equilibrium has been

reached. Only the constant rate

method will be considered here.

During a constant rate injection, a

tracer solution (injectate) with a

known concentration (C i ) is

injected into the stream at a known

flow rate (Q i ) (Fig. 1).

After a sufficient amount of time,

the tracer will arrive at each of the

downstream sampling points, and

an equilibrium or plateau concentration will be established (Fig. 2). The

arrival of the tracer at each sampling

point can be used to determine the

time of travel throughout the study

reach. To compute a discharge at the

first measurement site downstream

of the injector, the concentration of

the tracer upstream of the injector

(Co ) and the plateau concentration

of the tracer at the measurement site

(C1 ) must be known (Fig. 1). It is

important that the discharge measurement point be located downstream of the tracer mixing length

(ML ) so that complete lateral mixing is a valid assumption (Fig. 1).

For a discussion of mixing length

computations, see Buchanan and

Somers, 1973.

NO. 47 DATE 04/18/01

Range

Hydrology

Q Ci i

Q C1 1 Q Co o

ML

Figure 1. Variables used to define stream discharge

at the first downstream site.

Time

Concentration at site 1

C1

Figure 2. Tracer concentration over time at the

first measurement site where C1 is the plateau

concentration.
Measurement of discharge at the

first downstream site assumes that

no lateral inflow (tributaries, seeps,

ground water) enters the stream

between the injector and the first

site. Actually, lateral inflow is

allowed if the tracer concentration

in the lateral inflow is zero or if the

tracer concentration in the lateral

inflow is equal to the tracer concentration upstream of the injector

(Co ). Usually the first measurement

site is located such that no tributary

inflow occurs between the injector

and the measurement site.

The flow balance at the first measurement site is given by:

Q1 = Qo + Qi (1)

Where Q 1 is the discharge at the first

measurement site, and Qo is the discharge upstream from the injector.

Mass balance is given by:

Q1C1 = QoCo + Qi

Ci (2)

Equation (1) can be solved for 

Qo (Qo = Q1 - Qi) and substituted

into equation 2 yielding:

Qi(Ci – Co )

Q1 = (3)

C1 - Co

Note that if the upstream concentration of the tracer (Co ) is zero,

equation (3) simplifies to:

Qi(Ci)

Q1 = (4)

C1

For synoptic water quality studies,

the following modification of equation (3) is solved sequentially in the

downstream direction.

Q n - 1(Cn - 1 – CL)

Qn = (5)

Cn - CL

Where CL is the tracer concentration in any lateral inflows (tributaries, seeps, ground water) that

occur between points n and (n-1)

(Fig. 3).

Conclusion

Constant rate injection of a conservative tracer can be used to measure

stream discharge in locations where

traditional current meter measurements are not appropriate. The

downstream increase in discharge

due to lateral inputs is computed by

measuring the dilution of the tracer.

The technique is particularly useful

in quantifying sources of pollutants

that may be entering the stream

from tributaries, seeps, or from

ground water. Multiple discharge

measurements can be obtained by

measuring the tracer concentration

at several points downstream and

repeating the dilution calculation

sequentially from point-to-point.

For multiple discharge measurements the tracer injection technique

represents a considerable time savings compared to making multiple

current meter measurements.

Literature Cited

Buchanan, T.J., and Somers, W.P.,

1973, Discharge measurements at

gaging stations: U.S. Geological

Survey Techniques of WaterResources Investigations, Book 3,

Chapter A8, 65p.

Kilpatrick, F.A., and Cobb, E.D.,

1985, Measurement of discharge

using tracers: U.S. Geological Survey Techniques of Water–Resources

Investigations, Book 3, Chapter

A16, 52p.

Kimball, B.A., 1997, Use of tracer

injections and synoptic sampling to

measure metal loading from acid

mine drainage: U.S. Geological

Survey Fact Sheet FS-245 96, 4p.

Marchand, J.P., Jarrett, R.D., and

Jones, L.L., 1984, Velocity profile,

water surface slope, and bed-material

size for selected streams in Colorado:

U.S. Geological Survey Open-File

Report 84–733, 82p.

Contact

William P. Carey

National Science and Technology

Center ST-133

Denver Federal Center

PO Box 25047

Lakewood, CO 80225-0047

phone (303) 236-0103

fax (303) 236-3508

email bill_carey@blm.gov

Range

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Information in this Resource Note is based on the opinion and

experience of the author and has not been peer-reviewed. Conclusions

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Q Cn n

Q C n-1 n-1

Q CL L

Figure 3. Variables used to define stream discharge

at downstream sites.