Illustrating flow proportional sampling

by François Birgand

One of our domains of expertise is the computation of uncertainties on nutrient loads at the outlet of watersheds.  We have published several articles on the subject and will be presenting some more results at the ASABE conference in Dallas, TX at the end of July.  One of them will be the evaluation of the flow proportional sampling method to calculate nutrient loads.

This methods consists in automatically sampling and compositing the samples into one big bottle (usually around 20 L).  The nutrient or material load can be calculated by multiplying the composite concentration by the flow volume corresponding to the period during which the samples were taken.  This system can be set up to measure the nutrient load for just one storm, or set up to measure loads on a longer term basis, including annual periods.  In the latter case, the system is set so that samples are composited over a period corresponding to two consecutive field servicing times.  The system requires an automatic sampler connected to a flow calculating device.  This device computes flow rates and calculates the flow volume accumulated since the last sample.  When the cumulative volume reaches a defined threshold, the device triggers the sampling, usually of a small volume.

The first point we want to illustrate, is the concept of cumulative flow.  Cumulative flow over a given period is the integral under the hydrograph over the same period.  This is illustrated in the video above.  Instantaneous flow rates (hydrograph) are represented in the thin blue line while the cumulative flow volume (in mm) is represented both by the area under the hydrograph and the thick blue line.  The triggering of a sample can thus take place after e.g. 0.5 mm has flowed by.

Lots of hydrologists use the flow proportional composite method, and we believe for the right reasons.  We have noticed that to explain how it works, it often involves hand waving and other less than ideal artifices. For that reason, we have decided to create an illustration in the form of a video, which we hope will provide some help.  Ideally, this video will be used by others in the future.

The video shows the same hydrograph as before and a red dot travels through time.  The vertical bars mark the times at which the sampler is triggered and the water accumulated is illustrated in the bottle.  Notice, and that is the heart of the method here, that the sampler is triggered a lot more often during high flows.  One can show that the concentration in the composite bottle is a very good approximation of the flow weighted concentration over the same period of time, which warrants the use of this method to calculate nutrient and material loads.  There are cases, and in particular for suspended solids where this method may induce some significant error, although much smaller than for any other methods.  This will be discussed at length this summer.