4.11 Case Study: Flood Watch

Summary

The name of this CSC is Flood Watch; it is an example of a real application of calculus with real data. Returning to the notion of rainfall data given in section 1, the CSC asks for an analysis of rainfall data for the Gorge River. Rainfall data are collected ten years apart after similar rainstorms. The purpose of the CSC is to determine if the Gorge River has an increased or decreased likelihood of flooding and the reasons why. Such situations are regularly faced by local and regional planners as they make decisions about the environmental impact of proposed construction or land clearing plans.

By the time you complete the CSC, you should know:

What a hydrograph is.
What a centroid is; and the formulas for a centroid.
What the lag time is and how to compute it.
How to use the Food Watch applet to process the data.
How to pose relevant questions, and how to use the applet to get answers to those questions.
How to work with one or more classmates on a team project. (This is not necessary but is encouraged.)
How to write a CSC report, especially the Interpretation and Summary.
This CSC as another example of applying mathematics you have learned to solving a real-world problem.

Examples

Calculate the centroid of the region between the curves f(x) = x² + 2 and g(x) = 2x + 5 for x in the interval [–1, 3].

A certain river has rainfall discharge data and rainfall recorded during and after a storm. Find the base flow of the river, the total volume of rainfall discharge, and the lag time between the rainfall event and the rainfall discharge.

A flower grows at varying rates, measured at the beginning of each month and halfway through each month, according to a chart. What is the approximate height of the flower after three months? Consider a second flower that requires fertilizer to grow, and compute the lag time between the application of fertilizer and the flower's growth.