Missouri and Mississippi Rivers routinely reach flood stage in the St. Louis region each year, sometimes causing catastrophic inundation of the surrounding land. The great flood of 1993 was
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1 EPSc 118a ? Geology of National Parks Homework #4 (50 points) Posted on Thursday, March 9, 2023 Due at 5 PM on Tuesday, March 28, 2023 St. Louis Floods In lecture, we learned that the Missouri and Mississippi Rivers routinely reach flood stage in the St. Louis region each year, sometimes causing catastrophic inundation of the surrounding land. The great flood of 1993 was unprecedented and legendary in this regard. However, even more extensive flooding throughout the midcontinent occurred in 2019, as recounted in this NYT article: The Great Flood of 2019: A Complete Picture of a Slow-Motion Disaster https://www.nytimes.com/interactive/2019/09/11/us/midwest-flooding.html A colleague of mine, who is a hydrologist and an expert on floods and the history of the Mississippi River Basin, noted the following in regard to the 2019 flood (quoted in the St. Louis Post-Dispatch): At this time the Mississippi River at St Louis has a stage that is only considered to be ?moderate,? yet it just exceeded 38 feet. This current water level now exceeds that attained during the great flood of 1903, which featured the highest water from the Civil War to WWII, and had an estimated flow approximating that of 1993. Yet the 1993 flood had a level of nearly 49.6 ft., and now a stage of 38 feet hardly makes the ?top 20? list. This is primarily due to river channelization and an overbuilt levee system. Things might get much more interesting in a few weeks; we’ll see.? To add some currency to this exercise, the National Weather Service had issued the following flood warning for the St. Louis region: https://alerts.weather.gov/cap/wwacapget.php?x=NOAA-NWS-ALERTS-MO126194D5C1B0.FloodWarning.1261953E2390MO.LSXFLSLSX.38644ab74f1aac70252cf55fca5f940b So, let us investigate this flooding problem in the following exercisee.
2 Meanders, Channelization, and Levees Shown below is a cross-section of a river floodplain, which is 10-km wide. In this floodplain, a river flows through it? (with apologies to Brad Pitt), which has a circular cross-section with a diameter of 1 km. The flood plain has a depth? of Z? km, which will figure into this exercise later. The figure on the next page shows two versions of this very same river. The drawing on the right-hand side shows a 50-km-long section of the river flowing within its floodplain. The zig-zag pattern is supposed to mimic the meandering form that the river would assume under natural? conditions. The drawing on the left-hand side shows the appearance of the river after it has been straightened and channelized for purposes of navigation. This exercise asks you to calculate and compare the amount of water held in both versions of the river. (a) [20 pts] Calculate the volume of the natural stream. Assume that the channel can be represented by a series of tubes? (5 of them, each having a length of 15 km for a total length of 75 km) with a semicircular cross-section having a diameter of 1 km, as shown by the inset. For ease of calculation, ignore the overlap between adjacent sections of the river and treat each section as a separate 15 km stretch of river. (b) [10 pts] Calculate the volume of the straight stream channel in the left-hand diagram. Assume the identical cross-section. (c) [20 pts] Compare the volume of the natural meandering stream to that of the straight stream. Assuming that the excess water would spill out into the 10-km-wide flood plain, how deep would that flood be?
3 Note: Each stream segment in the right-hand drawing has a length of 15 km (these diagrams are not drawn to scale).
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