Environmental Geology Spring 2010 – Rivers and Floods

 

Rivers and Floods

 

Basic Components

Active Channel, Levee (natural or man made), floodplain

 

Drainage Basin: area that contributes water to a stream.  We looked at map of U.S. with Mississippi drainage defined including all its tributaries.  We also discussed other major drainage basins for the U.S.

 

Gradient: rise/run = elevation change/horizontal distance

 

Units for gradient [L]/[L] as example ft/ft or ft/mile

 

Velocity = [L]/[T] as example mile/hr or ft/sec

 

Discharge = [L3]/[T] as example ft cubed/sec

 

Discharge = width x depth x velocity

 

Example: w = 100 ft; depth = 1 ft; velocity = 7 ft/sec >>>>> Q = 700 ft3/sec

 

A change to any parameter will result in changes to one or all of the other parameters in the equation that will reflect the new state of dynamic equilibrium.

 

Example: in the example above hold discharge, and depth constant and decrease the width to 50 ft. The velocity must increase to 14 ft3/sec to compensate.

 

Headwater streams tend to be high gradient, deeply incised in narrow V shaped valleys.

 

In downgradient reaches floodplains become broader and the streams do not fill the entire floodplain.

 

Discharge generally increases in a downgradient direction.

 

Average velocity also tends to increase in the downgradient portions of the stream.  This results because frictional losses are reduced as the stream becomes wider and deeper and there is less of the total volume of water in contact with the bed and banks.

 

In upper reaches a tremendous amount of energy is expended as white water and eddies.  While some portions of the stream are very high velocity in these headwater regions, the overall average velocity is generally lower because of the energy dissipation as white water and the dead sections in the pools and eddies.

 

Braided channels reflect a stream that is choked with sediment.

 

Load is the amount of material carried by a stream while competence is a reflection of the size of particles a stream is able to transport as either suspended load or bed load.  The competence of the Buffalo River in the upper reaches is high but the capacity is relatively low.  Conversely, the competence of the Arkansas River near Tulsa is relatively low but the capacity is high (it moves a lot of silt and sand but not big bolders).

 

Floods occur when the stream overtops its levees and the water spills into the flood plain. Remember, this is a totally natural process. The floodplain is so named because its function is to disperse and store water during times of excess precipitation.  So when structures are placed in the floodplain the assumption is that they will be flooded at some point in time.

 

Events causing stream stage increases

 

  • Heavy precipitation

 

  • Rapid snow melt

 

  • Dam failure

 

  • Deforestation

 

  • Urbanization

 

Flood Frequency and Magnitude

 

Magnitude = total discharge at time of flood peak

 

Plot flow on a hydrograph: x axis it time (seconds, minutes, days)  This depends on the size of the watershed.  Y axis is discharge or river stage (see diagram in text).

 

For a storm pulse we define several primary factors:

 

  • Lag time – time between onset of precipitation and flood peak/crest

 

  • Rising limb – portion of hydrograph curve that represent rising water levels/increasing stream discharge

 

  • Peak/Crest – point of maximum water level/maximum discharge

 

  • Recessional limb – portion of hydrograph representing the return to more normal flow conditions.

 

Recurrence Interval = R

 

R = (n + 1)/m

 

Where: n = number of years of record; and m = event magnitude for highest annual maximum discharge

 

Example:

 

10 years of record

 

year                  Q m3/sec                                 magnitude                                 R (years)

1                      30                                            8                                              1.375

2                      200                                          5                                              2.2

3                      500                                          4                                              2.75

4                      50                                            7                                              1.75

5                      70                                            6                                              1.83

6                      700                                          2                                              5.5

7                      10                                            9                                              1.22

8                      1500                                        1                                              11

9                      600                                          3                                              3.67

10                    70                                            6                                              1.83

 

Another way to look at this is to calculate the probability that a flow event will be met or exceeded in any year.  This is the probability of exceedance Pe

 

Pe = 1/R = m/(n+1)

 

From example above if R = 11 years then Pe = 1/11 = 0.09 or a 9% chance of this flow in any year.

 

Extrapolate the data to estimate longer times such as 100 and 500 year floods.  This is done by plotting discharge/stage vs. recurrence interval/probability of exceedance (see text for example graph).

 

Upstream flood vs. downstream floods

 

  • Upstream floods:
  • Upper part of drainage basin (headwaters)
  • Intense rainfall – short duration over small area
  • Local in extent
  • Flood crest dissipates when it joins larger trunk stream
  • Often high death

 

Looked at slides for 1972 Rapid City, South Dakota flood that killed 237 people

 

Downstream floods:

 

Extensive regional flooding

Usually few deaths

Extensive property damage

Result from long duration steady precipitation or heavy regional snow melt

 

Example: 1993 Mississippi River flood

 

Floods on the Mississippi with Peak discharge at St. Louis, Missouri

Peak discharge ft3/sec              Month              Year

1,030,000                                August              1993

1,019,000                                June                 1903

926,500                                   May                 1892

889,300                                   April                 1927

862,800                                   June                 1883