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Tracers:
We can use the concept of conservation of mass to develop techniques for using tracers to study environmental systems. Tracers can be used in a variety of ways, such as: 1) "tagging" water or sediment with an identifiable tracer (like dye) to determine how the water or sediment is routed through systems like caves, groundwater aquifers, or glaciers; 2) determining the amount of mass that is "lost" from or "added" to an open system, if the amount of tracer that was added to the system is different from the amount measured leaving the system; and 3) determining the flux of water through a system when there is no mass of the tracer added or lost between the input site and the measurement site.
This last application of tracers is what we used to measure water discharge (Q) of Mill Creek. We used salt as our tracer, although you could also use a dye provided that dye does not adhere to sediment in the channel (we must make sure that all of the dye makes it out of the system). To calculate water discharge, you simply balance the inputs of salt to the stretch of stream that we are monitoring with the outputs of salt.
Inputs: The stream has salts naturally dissolved in the water. These come primarily from dissolving minerals out of the bedrock, with potentially additional salts coming from anthropogenic sources like road salt, fertilizer, etc. To this natural salt concentration C0, we added a known mass of salt Ms dissolved in water. So, the mass inputs are Ms+∑(QC0Δtime). In practice, the background conductivity is actually constrained by measuring the electrical conductivity of the water E0 and then converting that value to conductivity using a conversion factor F (each meter has its own conversion factor): Ms+∑(QE0Δtime)/F.
Outputs: The outputs from the system are measured as a pulse in electrical conductivity of the stream water. The added mass of salt results in a spike in electrical conductivity E above the background level. The outgoing mass is the integral of this curve (i.e., the area under the curve), converted to concentration using the conversion factor F, multiplied by water discharge: ∑(QEΔtime)/F.
Balance the inputs and outputs and solve for water discharge:
Ms+∑(QE0Δtime)/F=∑(QEΔtime)/F
which simplifies to:
Q=Ms*F/[∑(E-E0)Δtime]
This technique works well provided no salt settles out in the channel, the salt is well mixed so that a single measurement of electrical conductivity is representative of the entire channel, and discharge is constant. In practice, this method seems to be much more reliable than the traditional area-velocity approach to measuring water discharge.
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