In this problem, you will be assessing real river data to delermine the probabil

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In this problem, you will be assessing real river data to delermine the probability of a flood, and you will als calculate the recurrence interval (how often it happens) of a certain flood level. Floods are devastating disasters, capable of killing thousands of people in a very short time and causing billions of dollars worth of damage Usually when a major flood occurs it is a combination of unusual factors Newspapers conmonly report that a flood is (or was) a 100-year flood or 500-year flood. Yet in 1979, Houston had three 100-year floods. So how do geologists determine if a flood is in fact a 100-year flood and does the designation have any meaning? Using historical reoords and data from United States Geological Survey (USGS) gaging stations and relying on statistics and probability, the frequency of major floods is predicted In predlicting flood frequency geologists use the recurrence interval (R). This is the average period of time that elapses between events of a given size. Smaller floods occur with higher frequency than larger floods. Using the recurrence interval we can determine the probability of a flood ofthat magnitude ocamng This means that the recarrence merval ofaSod B the-verse ofthe probability of its occurring (/probability that a flood of a particular magnitude will occur). For example if we are considering a very small flood one that is likely lo occur every yen, tk?a10% lillod foccurrng and a recurrence nterval of 1 Aslightly larger flood that migh ocar every ote year (2 years) would have a 50% chance of occurring (1/2-05- 50% probability of occurring, or l05-2-recurrence interval). For relme-pps 481-488 of your tal In this exercise you will use information about rivers and their flow in the Umied States. The United States Geological Survey (USGS) mantai mvet gagng tataas on seven und mer, allow-them to monir tow both for drought and flood ondtuns. Most of this data ts avalable-real tne war now is given two different ways, .s stage (R) or discharge at abic feet per second (d) Stage i, the heght ofthe mer above some datums. If the shape (cross-sectional area) of the river is known, cs can be calculated Stage is also used in tidal rivers because the river height fluctuates with the bdal cycle. And of w e, ?the w r guaging station can be put out of commission by ice. The data we are using is in cs Flood frequency infrmation can be determined from knowledge ofthe pok áchap?(hghet dschrs) n any given year provided enough years of information have boen collectod This allows onc to relate the expected recurrence interval for a given discharge, and determine the probability that a flood ofagíven discharge will ocur in my given yea. The recurrence val fr agmenb hage can be calalted by first ranking the discharges 1a. In the table on the answer sheet, 20 years of data (1990-2009) are given for the maximum peak discharge for the New River near Allisonia VA. In the table, fill in the Ranik column. To do this, enter a 1 for the maximam discharge that has occurred during the 20 years of available data The second highest discharge will be given a rank of 2eic with the lowest discharge gives a vallue of 20. 1b. Now that you have ranked the data, you can calculate the recurrence interval for each pealk discharge. The recurrence interval, R, B tven by the web! EquamR-car Dm where n·s the number of years over which the data was oollected (20 years) and m is the rank of each peak discharge. Use this equation to calculate the recurrence interval for each peak discharge and pur it in the tablie You only noed o show one calculation le Next using the graph m the m et, plot agraph ofdicharge0 s) versus recurrence merval (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 of the graph Onoe you have plotied the points, use a ruler to draw the best-fit straight line throuagh the data points. Id. 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 le. The annual exceedence probability, Pe, is the probahility that a given discharge will occur in a given yeuit is calculated asthe inverse of rearrme- Pe-1/R Thu, probablity but a nod with aten year recurrence m?rval will occur m any year asino-10% whal ue te probabilities that a 50 year flood and a 100 year flood would occur in any girven year? It Flood stags on New River occurs ada harge of35,000ftiec wha Bthe recurrence interval of such a discharge acoording to your graph?

Explanation / Answer

1f.Since the discharge is 35,000 fts/sec we can simply draw a line from 35000 on the discharge axis to the line and find the reoccurrence interval, which in this case is around 1.95-2.0 years.

1g) We can see that the stream is a meandering stream based on its high sinuosity.

A mile downstream the erosion will occur on the north bank. This is because the north bank is the outer bank of the river where the stream velocity is high and hence there is more erosion than the south bank. Along the south bank, the velocity of the stream is lower and there is deposition on this bank.

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