Rivers and Floods Assignment(1)
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University of Arkansas *
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Feb 20, 2024
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LAB 7: RIVERS, FLOODS & RIPARIAN ZONES
100 points
Due at the beginning of the next lab.
LEARNING OUTCOMES
At the end of this lab, you will be able to
1.
Construct a flood frequency curve (hydrograph)
2.
Understand and interpret a hydrograph
3.
Predict the probability of a flood of a certain discharge along a stream
INTRODUCTION
Streams and rivers perform an essential function of runoff integration within a watershed to efficiently remove the water from the drainage basin. Basic components of a stream shown in Figure 1 include the streambed, banks, and levees, which define the active channel and the associated floodplain. Just as the name implies, the floodplain performs a specific essential function by providing space for temporary storage of water during times of excess discharge. Thus, by its very nature and function we know that this area will be periodically under water (flooded).
Because we occupy and utilize the floodplain for homes, businesses, and transportation networks, it is important that we understand how to predict the frequency and magnitude of floods. This allows us to minimize resulting loss of life and damage to property. At least 1,850 people died in twenty-four separate riverine and flash floods in the United States during the 20
th
century. If ice-jam, storm-surge, dam-failure, and mudflow floods are included this number jumps to over 9,000 during this period. Dollar losses associated with floods are in the billions.
Riverine and flash floods are controlled by 1) the amount, timing, type, and distribution of precipitation, and 2) the topographic and geologic character of the drainage basin. Large riverine floods usually involve rapid snow melt or excessive rainfall over the drainage basin. These floods tend to inundate large areas and are of relatively long duration (days, weeks or even months). In contrast, flash floods often result from high intensity precipitation in small watersheds, often in areas of moderate to high topographic relief. These floods tend to impact smaller areas than the riverine floods and are of shorter duration (hours to days). However, flash floods often result in more deaths that the longer lasting riverine floods.
To understand flood frequency and magnitude we must first acquire a basic grasp of terminology. One of the components used to describe stream flow is the hydrograph. The hydrograph is an x-y plot of discharge or stage vs. time. See Figure 2 in question 1 for an example.
Stream Discharge is the volume of water passing a specific point along the stream over a
specific time interval. Discharge is therefore length cubed (L
3
) divided by time (t) or L
3
/t. You will
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often see these units expressed as cubic feet per second (cfs or ft
3
/s) or cubic meters per second (m
3
/s) or gallons per minute (gpm). Discharge is calculated as the wetted cross-sectional
area of flow times the velocity using the following formula:
Q = A * V
Q = discharge (L
3
/t) = (Length
3
/time)
A = cross-sectional area = depth (d) x width (w) = Length
2
(L
2
)
V = velocity (L/t) = Length/time
The frequency of annual peak flows (flood frequency) is expressed as a recurrence
interval. The recurrence interval is the average time interval between the occurrence of two similar peak flows and is calculated as:
T = (n+1)/m
T = recurrence interval in years
n = number of years of record
m = rank or order from greatest (1) to smallest
Recurrence interval can be plotted on semi-log graph paper with the recurrence interval on the x-axis (the log axis) and discharge or stage plotted on the y-axis (arithmetic axis).
Connecting the points on the plot with a “best fit” line provides a mechanism to estimate
the recurrence interval of peak flows other than those for which data are available.
Another term one often encounters is the annual probability of exceedance which is the
reciprocal of T.
P = 1/T
P = probability of exceedance
T = recurrence interval in years
This is the probability that each year the annual maximum discharge will be met or exceeded for any given discharge. An annual peak discharge with recurrence interval of 100 years has a 1 percent chance of occurring in any year.
LAB 7: FLOODING AND RIVERS Name: _____________________________
Section: _____________________________
Answer the following questions [100 pts].
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Figure 1. Hydrograph showing predicted and actual streamflow in response to a storm.
Hydrograph Interpretation 1.
Based on the hydrograph above, what is the lag time between the start of the rain and the peak river stage? (5 points)
2.
At peak river stage how many feet were each of the forecasts off by? Why might the forecasts be inaccurate? (5 points)
3
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3.
If urbanization occurred in this watershed, would the hydrograph have a higher or lower
peak? Will flash floods be more or less likely? (5 points)
Figure 2. Hydrograph showing Discharge vs. Time for Illinois River south of Siloam Springs, AR.
Q = A * V
Q = discharge (ft
3
/s)
A = cross-sectional area (ft
2
) = depth (ft) x width (ft)
V = velocity (ft/s)
4.
Based on the figure and the equation above, calculate the width of the stream at point A assuming an instantaneous velocity of 4 ft/s and a stream depth of 2.4 ft. (Show all work and include units) (5 points)
4
5.
Calculate the velocity of the stream at point B assuming a cross-sectional area of 113 ft
2
(Show all work and include units). (5 points)
6.
What happens to the cross-sectional area of a stream as discharge decreases, but the velocity remains the same? (5 points)
7.
Explain at least two ways that cross-sectional area can change in a natural stream. (5 points)
Flood Magnitude and Frequency
8.
Based on the peak flows shown in Table 1 calculate the rank, recurrence interval, and probability of exceedance for each year in Table 1. (15 points)
T = (n+1)/m
T = recurrence interval in years
n = number of years of record
m = the year’s rank from greatest peak flow (rank 1) to smallest peak flow (rank 5)
P = 1/T
P = probability of exceedance
T = recurrence interval in years
Table 1: Peak Flow Data – Illinois River South of Siloam Springs, AR
Year
Peak Flow (ft
3
/s)
Rank (1 is
Recurrence Interval
Probability of
5
greatest)
Exceedance
1996
25,600
1997
23,300
1998
40,000
1999
29,300
2000
32,200
9.
Plot the recurrence intervals from Table 1 on the log-scale graph below and draw a “best fit” line for this data. (5 points)
Figure 3. Flood frequency curve based on data from Table 1.
10. Based on the best fit line, estimate the discharge for a 100-year storm. (5 points)
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11. What is the recurrence interval for a storm with a peak discharge of 57,500 cfs? (5 points)
12. What is the probability of exceedance for a storm with a peak discharge of 45,000 cfs? (5 points)
Use the following figure to answer the questions.
Figure 4. Gage Height vs. Discharge.
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13. Assuming a gage height of 0 ft is 924 ft above sea level, and the top of the levee is 940 ft above sea level, what is the gage height and discharge when the levee is overtopped?
(5 points)
14. How extensive is flooding within the floodplain once the levee is overtopped? Shade the flooded areas on the topographic map provided below. (5 points)
Figure 5. Topographic map for stream gage on Illinois River south of Siloam Springs, AR. The stream gage is located near the bridge.
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Take a picture of the resulting stream table. In the picture, label the following features if they are visible: main channel, slough, island, upstream, downstream, natural levee, floodplain, groundwater spring, lake/pool, delta, abandoned channel, meander, cutbank, and/or point bar. (10 points)
15. Calculate the sinuosity of the main channel. Use the measuring tape. (5 points)
9
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16. With your group try to maximize the channel sinuosity - whichever group gets the highest sinuosity will earn 5 extra credit points. Your group will have 3 minutes to dig channels and add rocks, vegetation, and pipes. Turn on the water for the next 2 minutes. Once water is flowing, the only thing you have control of is the discharge dial. What was your sinuosity? (5 points + 5 extra credit points for highest sinuosity in your class).
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