Please answer all of the questions on the PDF document attached. The course textbook is called The Introduction to Environmental 5th Edition Studies by Edward A. Keller. Thank you in advance!Name:________________________
GEOL194 Environmental Geology
Homework #4 Flood Analysis
Assignment:
1. Flood frequency information can be determined from knowledge of the peak
discharge (highest discharge of water) in any given year provided enough years worth
of information has been collected. This allows one to relate the expected recurrence
interval for a given discharge, and determine the probability that a flood of a given
(or certain) discharge will occur in any given year. The recurrence interval for a given
discharge can be calculated by first ranking the discharges.
a. In the table below for Taunton River, Massachusetts, fill in the Rank
column. To do this, enter a 1 for the maximum discharge that has
occurred during the 60 years of available data. The second highest
discharge will be given a rank of 2, etc… with the lowest discharge
given a value of 60.
b. After you have filled in the Rank column, you can now calculate the
recurrence interval for each peak discharge. The recurrence interval, R, is
given by the Weibull Equation:
R = (n+1)/m
where n is the number of years over which the data was collected (60
years in this case) and m is the rank of each peak discharge (e.g. 1, 2,
3 etc…). So, a rank, m, of 1 would be R = (60+1)/1, which is 61/1 or 61
years. Use this equation to calculate the recurrence interval for each
peak discharge. Fill in the recurrence interval column.
c. The annual exceedance probability, Pe, is the probability that a given
discharge will occur in a given year. It is calculated as the inverse of the
recurrence interval, R:
Pe = 1/R
d. Thus, the probability that a flood with a ten year recurrence interval
will occur in any year is 1/10 = 0.1 or 10%. What are the probabilities
that a 50 year flood and a 100 year flood will occur in any given year?
Pe (50)=___________ __
1
Pe(100)=_____________
Data Table of Discharge for Taunton River, Massachusetts
Date
Discharge
3
(m /sec)
1930
1,580
1931
2,430
1932
1,920
1933
2,990
1934
2,460
1935
3,060
1936
3,020
1937
2,590
1938
2,480
1939
2,040
1940
2,650
1941
2,080
1942
2,080
1943
1,540
1944
1,430
1945
2,230
1946
3,080
1947
1,550
1948
2,480
1949
1,740
1950
1,250
1951
1,580
1952
2,460
1953
2,320
1954
3,040
1955
4,010
1956
2,860
1957
1,950
1958
2,020
1959
1,760
1960
2,240
1961
2,520
1962
2,940
1963
2,880
1964
2,540
1965
1,380
1966
1,450
1967
2,800
2
Rank, m
Recurrence
Interval, R
1968
4,980
1969
4,080
1970
3,820
1971
2,240
1972
2,450
1973
2,470
1974
3,330
1975
1,850
1976
3,230
1985
795
1986
2,300
1987
3,530
1988
2,040
1997
3,710
1998
3,270
1999
2,300
2000
2,420
2001
3,400
2002
1,490
2003
2,630
2004
2,150
2005
3,170
Taunton River Data
e. Next, use the graph on the following page to plot a graph of discharge (on
the y-axis) versus recurrence interval (on the x-axis). Note that the x-axis is a
logarithmic scale, and thus you should try to estimate as best you can where
the data point will fall between the lines on the graph. Once you have
plotted the points use a ruler to draw the best fit straight line through the
data points (i.e. lay a ruler on the graph and try to draw a line that most
closely approximates all of the data points). Do not draw lines that connect
individual data points. The graph will be curved a little near the origin.
3
Discharge vs. Recurrence Interval
Taunton River, Massachusetts
f. By extrapolating your line on the graph, determine the peak discharge
expected in a flood with a recurrence interval of 50 years and 100 years.
These are the discharges expected in a 50-year flood and a 100-year flood.
Q(50-year):____________________
Q(100-year):___________________
g. What is the probability of a flood with the discharge similar to the 1968 flood
will occur in any given year?
Pe:_________________________%
4

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