GE2341 2023A- HW6

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Worcester Polytechnic Institute *

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2341

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Geology

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Jan 9, 2024

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Geology 2341, A Term 2023 Worcester Polytechnic Institute Homework Assignment 6, Due by 11:59 PM Oct. 9 A flood is any relatively high flow of water over land that is not normally under water. Floods occur at streams and rivers but can also be caused by high rainfall or snowmelt as well as high tides along seashores, high groundwater levels, dam failures, and high water levels in lakes. Floods happen naturally in rivers as a response to hydrologic, meteorological and topographic factors. Dams, levees, channelizing rivers, development of agricultural, urban, and suburban areas, and deforestation also effect floods. In this section of the lab you will become familiar with the nature of river floods, the problems that are created by flooding, and potential solutions. Discharge is defined as the rate of stream flow at a given instant in terms of volume per unit time at a given location. Discharge can be calculated from the equation: Q  A * V where Q= discharge (in cubic feet per second, cfs , or m 3 /s) A = cross-sectional area of the wetted channel (width of the channel at a given location multiplied by the depth of the water at that location) V= velocity of the flow (in ft/s or m/s) Flood frequency (the average occurrence of flooding of a given magnitude, over a period of years) is based on the maximum discharge for the year at a given point. Recurrence intervals or return periods are generally used to characterize flood frequency. A recurrence interval is the average time interval (in years) between the occurrence of two floods with the same water level. It can be calculated from the equation: T = n + 1 m Where: T = Recurrence Interval (years); n = the number of years of record; m = is the order of the annual flood discharges from the greatest (1), to the smallest for the number of years of record. One way to view flood data is to plot it on a flood frequency graph with discharge plotted on the vertical axis and recurrence interval on the horizontal axis. Drawing a best fit line allows you to extrapolate the average number of years that will pass until a given magnitude flood occurs again. The longer the number of years of flood records, the more likely it is that floods with extremely large discharges have been recorded. The annual probability of exceedance is calculated from the recurrence interval as: 1 1

P = 1 / T P is the likelihood that in a single year the annual maximum flood will equal or exceed a given discharge. This means that a flood with a recurrence interval of 10 years has a 10% chance of occurring in any year while a 100 year flood has the probability of occurring 1% chance of occurring in any year. Flood Frequency in Connecticut River The discharge flow data of Connecticut River below are retrieved from U.S. Geological Survey information. During lab, the TA will assign you to calculate flood frequency using just one of the four data sets. Rank Year Peak Flood Discharge (cfs) 32.5 1929 84800 6 1930 57600 19 1931 78100 46 1932 98400 80 1933 153000 74 1934 124000 48.5 1935 100000 82 1936 282000 51.5 1937 103000 80 1938 236000 51 1939 103000 70 1940 121000 3 1941 50000 9 1942 73200 11 1943 75000 11.5 1944 75400 38 1945 95000 12 1946 75800 39 1947 97000 64.5 1948 131000 65 1949 138000 23 1950 84300 46 1951 106000 57 1952 113000 61 1953 131000 21 1954 83500 62 1955 174000 51 1956 110000 2

2 1957 47100 48.5 1958 109000 37 1959 99700 57 1960 156000 12 1961 76400 37.5 1962 101000 25 1963 87200 20 1964 84600 1 1965 41700 3 1966 59200 17 1967 84000 33.5 1968 105000 39 1969 109000 13 1970 78700 11 1971 78400 21 1972 90900 28 1973 100000 27 1974 99400 4 1975 68500 30.5 1976 107000 37.5 1977 114000 4 1978 69600 33 1979 112000 15 1980 86700 32.5 1981 113000 29 1982 108000 13 1983 84800 34 1984 186000 1 1985 50800 17 1986 92300 19 1987 152000 9 1988 78500 3 1989 93900 20 1990 101000 18.5 1991 81300 1 1992 74300 20 1993 107000 10 1994 106000 17.5 1995 55500 6 1996 113000 3

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6 1997 87500 14 1998 111000 4 1999 80800 7 2000 82300 9 2001 106000 10 2002 75900 11 2003 88700 10 2004 96100 5 2005 105000 5 2006 114000 7 2007 111000 7 2008 85700 1 2009 87000 2 2010 96900 4 2011 128000 2 2012 66000 2 2013 75400 3 2014 92500 30 2015 78300 1 2016 91500 3 2017 74600 Use your data set to estimate the likely discharge for a 150-year flood by following these steps: 1.) Rank the peak flood discharges for the data set in order of magnitude. Start with 1 for the largest and end with 89 for the smallest. (Hint: using Excel Rank () function will be convenient) 2.) Use the formula for recurrence interval given above to determine the recurrence interval for each of the 89 floods. 3.) Plot the discharge and recurrence interval for each of your 89 floods on the provided piece of semi-logarithmic graph paper with discharge plotted on the vertical axis and recurrence interval on the horizontal axis. Place the paper so that the logarithmic scale is on the horizontal axis. 4.) Draw a best-fit straight line on your graph that extends to the right hand side of the graph. Questions: 1. What is the predicted discharge (in cfs) for a 150-year flood based on your data (using the regression equation)? Predicted discharge (cfs) = 1000 * (Recurrence interval (years))^0.8 Predicted discharge (cfs) = 1000 * (150)^0.8 4

=16775 cfs 2. What is the flood (i.e., discharge) that has the probability of occurring 8% chance of occurring in any year? Recurrence interval (years) = 1 / Probability of occurring in any year Predicted discharge (cfs) = 1000 * (12.5)^0.8 =7542 cfs 3. What is the probability (%) each year that stream flow in Connecticut river will reach 5,000 m 3 /sec ? Probability (%) = 1 / Recurrence interval (years) 5,000 m3/sec * 35.3147 = 176,574 cfs Recurrence interval (years) = (176,574 cfs / 1000)^0.8 Probability (%) = 1 / 133.75 years =0.75% 5

GE2341 2023A- HW6

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