The USGS Water Science School

# How stream height relates to streamflow

How does the height of water in a stream relate to the amount of water flowing? During a big storm in your town you may have heard a radio announcer say "Drybranch Creek" is at a stage of 3 feet, and by tonight is expected to crest at a flood stage of 4 feet, which translates into a flow of 20,000 cubic feet of water per second (cfs)." What does she mean when she says "3 feet," and why will Drybranch be flooding at 4 feet but not at 3 feet?

The U.S. Geological Survey uses the term "gage height" (measured in feet) when referring to the height of water in streams. We use a number of methods to measure gage height, or stage, but the theory behind it is not that much different from just bolting a measuring rod to a bridge and reading how high the water level is. But determining the amount of water flowing at various gage heights is not so simple.

As this diagram shows, river banks are irregular and tend to be flat at the bottom, have a steeply rising bank near the bottom, and then have flatter banks as they near the surrounding land surface. Since the river banks are irregular, the relation between gage height and stream discharge (flow) is not linear. In other words, when a stream's gage height doubles from 10 feet to 20 feet, the flow can more than just double.

The diagram shows this better than I can explain it. At a gage height of 1 foot, our stream has the amount of water (flow) represented by the blue area. Let's say it rains and the water rises to 2 feet. The additional flow is represented by the green area. Though the gage height doubled from 1 to 2 feet, the total flow, represented by adding the blue and green areas, is more than double the flow at 1 foot (the blue area). This is because the river bank has flattened out as it went up from the bottom of the river bed. Since the river bank continues to flatten, by the time the river's gage height goes to 4 feet, the flow, represented by all the colored areas combined, is many times more than it was at 1 foot. Also, as you can imagine, the speed of the water flowing during a storm is much faster than during low flow - thus, more flow at high water.

Remember our radio announcement—and look at the diagram. The stream at 3 feet was not a flood, but just 1 foot higher and the stream flows out of its banks and can be considered a flood. That is because the volume of water flowing at a gage height of 4 feet could easily be double or triple the flow at a gage height of 3 feet.

The USGS California office has a Web page about floods and flood plains.