Adam N. Wlostowski, Erika M. Smull, Michael N. Gooseff

A quick, simple, and effective way to measure discharge in small headwater streams is to use dilution-gauging methods. Measuring flow with standard wading rod methods can be difficult in small streams, especially under low-flow conditions. With a few kilograms of sodium chloride (NaCl), a bucket, and a conductivity data logger, you’ll be getting accurate discharge measurements in no time!

This post will describe the data collection and data analysis procedure used by our lab group to measure discharge in Alaskan headwater tundra streams. We will begin by outlining the mathematical concepts and methodology needed to measure discharge with conservative tracers. Then, we will illustrate step-by-step field procedures. Finally, we will provide access to an Excel spreadsheet used by our lab group to analyze raw injection data.

1. Background

Measuring the dilution of a known volume of conservative tracer is the basis of dilution-gauging methods. We use a simple “slug injection” of a known mass of dissolved NaCl tracer. A slug is a near instantaneous addition of a highly concentrated conservative tracer solution. As the tracer moves downstream, a concentration-time profile known as a break-through-curve (BTC) is recorded by sampling through time at a single downstream monitoring location.

The discharge measurement is made using the following equation.

where, Q is discharge [M^{3}/T], M is the injectate mass [M], C is concentration [M/L^{3}], and t is time [T].

The denominator term on the right hand side of equation 1 is a simple integration (area under the curve) of the BTC, commonly known as the zeroth moment. Looking only at the units of each term in equation 1, it is easy to see how we arrive at an estimate of discharge [L^{3}/T] (equation 2).

Two large assumptions are made when using equation 1 to estimate discharge from a slug injection. First, we assume that all of the injected mass was recovered at the downstream sampling location. Second, the tracer is completely mixed across the channel when it passes the downstream sampling location. The nature of these two assumptions places emphasis on choosing an acceptable reach length (distance from injection location to sampling location). We don’t want the reach to be too long, where tracer might be removed by flow paths which exit the spatial extent of the reach completely; we also don’t want the reach length to be too short, such that the injection is not well mixed (both laterally and vertically) at the sampling location. We recommend trial and error field experimentation to best establish reach lengths under a particular discharge range.

A far more detailed explanation of the mathematical background can be found in [*Kilpatrick and Cobb*, 1985] http://pubs.usgs.gov/twri/twri3-a16/

2. Field Methods

During June 2012, Erika Smull and I measured discharge at many locations along an arctic headwater stream located just south of Toolik Field Station on Alaska’s North Slope. Let’s go through our step-by-step field procedure.

1. Launch conductivity loggers to continuously sample at the downstram location. By continuously sampling conductivity, we can make a simple conversion to NaCl concentration using a laboratory-established relationship. Our group uses Onset HOBO U24-001 Conductivity Loggers, which can be easily launched and downloaded using HOBOware software installed on a field netbook. Because the reach lengths for the injections are relatively short, we use a fine sampling frequency (2 sec) to best characterize the BTC. It is very important to **sync the time on the data logger to the time on your wristwatch, or vice-versa**.

2. After the logger is launched and logging, tie a bright piece of flagging to the logger (in this case, orange) and position it in the thalwag at the downstream sampling location. Position the logger such that measurements are made at approx 50% of the water depth. **Record the river location of the downstream sampling site! **

3. Once the downstream site is all set, move upstream to the injection location and mix the injectate. Given the small nature of our stream, we dissolved approx 1 kg of NaCl into approximately 3 gallons of stream water. First, we partially fill a 5-gallon bucket with stream water. Then, we pour a pre-measured mass of NaCl into the bucket, being sure to **record the NaCl mass**! Using a small PVC stick, stir the bucket contents until all the NaCl is dissolved.

4. Now we are ready to inject! Inject the dissolved tracer by quickly pouring the bucket’s contents across the width of the stream. Be sure to **record the approximate time of injection.**

5. Immediately after pouring the injectate into the stream, rinse both the bucket and the mixing stick in the stream water. This will ensure all the NaCl mass makes it into the stream.

6. Wait for the injection to completely pass the downstream location and the stream concentration to return to ambient conditions before removing the data logger and downloading its data. Bringing a handheld conductivity logger into the field is an easy way to tell if the stream has returned to ambient conditions following the injection.

Once the data is off the data logger and safely saved, you are ready to return to the lab and process the data. Attached below, you will find an excel spreadsheet, which can be easily used to process raw data and calculate an approximate discharge value.

Citations

Kilpatrick, F. A., and E. D. Cobb (1985), *Techniques of Water-Resources Investigations of the United States Geological Survey: MEASUREMENT OF DISCHARGE*.