Stream flow measurement

The first method of stream flow measurement we will learn is the velocity-area gauging method (sometimes called the midsection method). Understanding how this method works first requires basic dimensional thinking around hydrologic flux, where the total flow of water in a stream is defined by the product of the downstream flux and the cross-sectional area of the stream (9:04 min).

The velocity-gauging method is just a little bit of spatial complexity added to the idea that flow is flux times area, and for stream channels flux is the same thing as velocity. In this case we recognize that the flux or velocity of the water is not consistent across a natural stream channel, so we have to break it up into a bunch of smaller areas, each with their own velocity as you wade across the stream. Here is where we gradually back into the applications of calculus (integration to be specific), though hopefully in a way that its application is completely logical (8:40 min).

With these fundamentals in mind, let's review the equipment and practices needed to obtain a measurement of flow with velocity-area gauging (10:00 min).

See the preparation materials for the stream flow measurement lab for a detailed description of how to build a spreadsheet for calculating discharge from velocity-area gauging data.

Velocity-area gauging tends to be most accurate in relatively wide streams where a fairly uniform cross-section can be found. In smaller, more tortuous channels, confidence in the velocity-area method should be questioned when a uniform cross-section that satisfies the assumptions of the method is difficult to find.

Dilution gauging tends to be more accurate in smaller, more tortuous streams where the measurements from the velocity-area method are dubious. Dilution gauging is based on the principle that you can estimate a volume if you fully mix a known mass of a solute into that volume and then measure the concentration of the solute (i.e., the degree to which you are diluting the solute gives you an estimate of volume). The only complication is dealing with the fact that the volume of water is moving past you when you are measuring the concentration of the solute. Hence, we need more calculus, and this time we integrate over time rather than space. But again, hopefully the application of the logic in the method is clear, even if you struggle with the general concept of integration (11:07 min).

See the preparation materials for the stream flow measurement lab for a detailed description of how to build a spreadsheet for calculating discharge from dilution gauging data.

Velocity-area or dilution gauging provide a measurement of discharge at one point in time. But to use stream flow as an indicator of watershed output behavior, we need to be able to measure flow relatively continuously over time. Flow is not easy to measure directly on a continuous basis in a stream, though it is relatively easy to measure water depth and relate that depth to flow. The elevation of the water surface in streams and rivers is called the stage, and the key to most continuous gauges is understanding the rating curve, or the stage-discharge relationship, at the location where stage is being monitored (6:47 min).

Understanding the relationship between depth and flow is actually a fundamental field of hydrology associated with open channel hydraulics. Therefore, a basic understanding of the role of friction and slope in determining the depth and velocity of water in the channel is critical to assessing the stability of the rating curve for a stream gauging station. Let's use the Darcy-Weisbach equation to get familiar with the basics of channel hydraulics (14:47 min).

These hydraulics equations are not complicated, but they are often difficult to solve because you need iterative techniques to resolve circular dependencies between the left and right hand sides of the equation. We won't be using these equations to calculate numbers in this class, but we can review the logic of the algebra to understand the physical principles these equations represent. First, here are some thought exercises on that topic (4:25 min).

Hydraulics are wildly important to many applications of hydrology. In particular, they are central to the actuarial calculations necessary for managing flood insurance or any flood risk assessment for low-lying areas around streams and rivers. You can take whole classes just on open channel hydraulics for this purpose. For our purposes, the basics of hydraulics can give us some perspective on why a stream gauge accuracy might shift with time. First, let's cover some detail on the development of rating curves that are critical to the function of a continuous stream gauge (3:56 min).

One of the biggest challenges to maintaining the accuracy of a continuous stream gauge is managing the accuracy of the rating curve.  Channel hydraulics provide perspective on why a rating curve might shift over time. Therefore, the stability of the controls on channel hydraulics are a primary concern in stream gauge design (17:14 min).

You may see multiple alternative formulations for channel hydraulics. For example, one that is very common in applied hydraulics and engineering design is Manning's Equation. These equations may look different, but exploration of the algebra reveals that the underlying concepts are identical. I review a few other formulations and try to clarify why they don't really require any different way of thinking about the role of friction and slope in determining the depth and velocity of flow (3:46 min).

That wraps up the material on stream flow measurement. You should now have a fairly detailed perspective on where the data in a hydrograph is coming from, which is important to confidence in the appropriate interpretation of any data set.

Study guide

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Study guides are designed to summarize the vocabulary, concepts, and mathematics learned in this module.

Readings from Dingman (3rd ed)

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A list of associated readings from Physical Hydrology by S. Lawrence Dingman (3rd edition)

Slides used in velocity-area and dilution gauging videos

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Slides used in continuous stream gauging videos

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The embedded Google viewer below sometimes provides poor renderings of Microsoft files. Use the link above to download the original file with proper formatting. 

Laboratory preparation materials for this module

Link to online laboratory preparation materials

A video with more details on stream tracer experimental techniques

If you are interested in stream tracer experiment techniques like those used in dilution gauging, you might be interested in this video with a more detailed perspective on the method and a more general treatment of how it is used (11:58 min).

A video with a review of the nature of logarithmic scales

Confidence in interpreting logarithmic scales on graphs like those in the rating curve videos will be critical in this class, especially when we get to reading hydrographs. If you need a refresher on log scales, this video from Khan Academy might help (11:14 min).

Links to USGS documentation on stream gauging

Link to USGS web page on river gauging

Link to detailed documentation of USGS gauging protocols

Typical values for Manning's roughness coefficient

Manning's roughness is analogous to the friction factor in the Darcy-Weisbach equation (though they are not directly interchangeable) 

Table of typical values for Manning's roughness on the Engineering Toolbox web page

Report on gauge accuracy at the Tenderfoot Creek Experimental Forest

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Paper on the ecological impacts of using NaCl as an artificial tracer

This paper supports the nearly negligible environmental impacts of using a reasonable amount of salt as a tracer

Wood and Dykes (2002) in Water Research

Disambiguation of Manning's Equation as presented in the Dingman text

Click this link to download the postscript PDF document