Look out the window or walk down the street to nearly any river or stream in Minnesota right now and you are likely to observe two things about the river:

  1. it is getting deeper (or “rising” in relation to the banks); and
  2. it appears to be moving faster.

You can, of course, confirm these observations by investigating reports from gauging stations along these rivers, maintained by the U.S. Geological Survey. (See data for the gauging station serving downtown St. Paul.) But what is really happening?

It may be high and fast...: ...but (as of today) the Mississippi at St. Paul is still in a bankfull state.
It may be high and fast...: ...but (as of today) the Mississippi at St. Paul is still in a bankfull state.Courtesy Liza Pryor

Until a river flows over its banks, it is considered to be in a “bankfull” state. In this state, the water flowing through the river is confined to a relatively fixed channel area. Simply put, floods occur because more water is being introduced into this channel from upstream, due to snowmelt, heavy rains, or a dam breach. As this added volume of water moves through a fixed area, it both increases in velocity and in depth until it overflows the banks, at which point some, but not necessarily a lot, of the volume and velocity moving through the channel are reduced.

Scientists call the rate of flow through a channel “discharge." Discharge is defined as the volume of water passing through a given cross-section of the river channel within a specified period of time.A simple equation for determining discharge is

Q = D x W x V

where Q = discharge, D = channel depth, W = channel width and V = velocity.

Looking at this equation, it is easy to see that if discharge becomes greater and channel width is fixed, then an increase in both volume and depth (or height relative to the banks) is likely to be the cause. Discharge can be measured in cubic feet per second or cubic meters per second, for example.

But is the river flowing at the same rate at the surface as it does along its banks and beds? Understanding this requires investigating some more detailed equations, as the banks and bed introduce friction, which affects the rate of flow.

To learn more about rivers and how they flow, you may want to check out the works of Luna Leopold, and M. Gordon Wolman. In particular:

  • Leopold, Luna B. (2006, reprint). A View of the River. Harvard University Press; and
  • Leopold, Luna B.; Wolman, M. Gordon; and Miller, John P. (1995). Fluvial Processes in Geomorphology. Dover Publications, both classics for understanding how rivers work.

Also, check out our full feature on the 2010 Mississippi River flooding.

Your Comments, Thoughts, Questions, Ideas

ArthurSMM's picture
ArthurSMM says:

Below the equation of Discharge, the word "volume" appears. This is a typo, and should read "velocity."

posted on Wed, 03/17/2010 - 5:10pm
Anonymous's picture
Anonymous says:

If the water is slowly rising, then possibly, earth will become a floating waterball in some 1,000,000,000 years!

posted on Sat, 02/12/2011 - 3:09pm

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