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Measuring Stage Height

- and how it's done at BBWM -

(last update: 04 Apr 2013)

#### -Under Construction-

There are a bunch of ways to measure stage height... but what is stage height?

According to the USGS in "Techniques and Methods 3-A7", page 13,

The stage of a stream or lake is the height or elevation of the water surface above an established datum plane. For rivers, lakes, reservoirs, coastal streams, estuaries, and surface-water bodies, the height of the water surface is usually referred to as an elevation measured above the North American Vertical Datum of 1988 (NAVD88), the National Geodetic Vertical Datum of 1929(NGVD29), or some other citable datum.

Hmmm... doesn't help much. Fortunately the USGS goes on to say,

The water-surface elevation for most rivers and streams is measured above an arbitrary or predetermined gage datum and is called the gage height of the river or stream. Gage height is often used interchangeably with the more general term stage, although the term gage height is more appropriate when used with a specific reading on a gage. Stage or gage height is usually expressed in feet and hundredths of a foot, or in meters and hundredths or thousandths of a meter.

So... according to the USGS the stage of a stream is in reference to a specific datum, and the gauge of a stream is with respect to a local reference point. However, it is OK to use the term interchangeably.

But if we do use the terms interchangeably... we better be clear about it.

For our purposes there will be no distinction between stage, and gauge (gage) height. In both cases the reference will be a locally defined reference.

#### How is stage height used?

OK... we have defined what we mean by the height of a stream or river... so what!... what's that good for?

The stage height can be used to not only distinguish how much water is flowing in a stream, it can quantify how much water is flowing in the stream.

If some stream beds have a good deal of water in them, it can be pretty clear that there is a lot of flow. In others it is much harder to tell. The surface of the stream or river my show little activity but the volume of flow may be considerable.

One way to determine flow is to use a "V" notch weir.

At the BBWM site they have these images of the East Bear weir. The weirs at BBWM have a 120 degree included angle.

The angle of the notch is important because that is what allows you to use a relatively simple equation to determine the flow, based on how high the water level is above the apex of the notch.

The equation used at BBWM is based on the USGS document: Measurement and Computation of Streamflow: Volume 1. Measurement of Stage and Discharge by S. E. Rantz et. al.

Q = 4.35 \big(h^{2.5}\big)

If $h$ is in feet, then the result will be in cubic feet per second (cfs), which is a common unit used in the literature.

There are formulations for cubic meters per second. An unchecked version of the equation might be,

Q = 2.3902 \big(h^{2.5}\big)

In this case $h$ must be in meters.

In both of these equations the notch must be a 120 degree notch, since the notch angle is wrapped up in the leading constant.