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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