Analysis of the Rainfall of Tropical Storm Allison

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Analysis of the Rainfall of Tropical Storm Allison

• Creating an Excel Model

2
Applying the Model to Allison

• Now we are ready to use our knowledge of
  functions and computational modeling to help us
  understand the flooding which took place in
  Harris County, June 5-9, 2001 during Tropical
  Storm Allison.
• To use the model , we will be working with
  information from the website Tropical Storm
  Allison Recovery Project - TSARP

Tropical Storm Allison Recovery Project
3
Allison Rainfall Assignment

• Go to the website Tropical Storm Allison Recovery
  Project TSARP and select Watershed from the
  left column.
• Select 2 watersheds to study, other than the
  Buffalo Bayou Watershed which will be our
  example.
• Create an Excel spreadsheet for each watershed
  that you select using the data obtained from the
  bar chart of the rainfall amounts.
• Follow the format of the example which follows on
  the next slide.

4
Sample Spreadsheet

• Remember, a fast way to get your averages is to
• Highlight the 3 rainfall amounts you want to
  average
• Go to Insert, then Function
• Average should be highlighted, so click ok.
• 4. Then be certain that the correct cells to be
  averaged are displayed in the Function Arguments
  Box.. Then click ok.

5
Graphing the Function

• Now highlight the cells that give the average of
  the three measuring stations in the watershed
  over the 3 time periods of 1, 12, and 120 hours.
  (On the example it would be highlighting the 6
  Average Rainfall cells). Be careful to highlight
  the time first and then the rainfall amounts.
  Excel makes the first column highlighted the
  independent variable. Since the amount of
  rainfall depends on how long it rained, time must
  be selected first to have an accurate graph.

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Graphing the Function Continued

• Then go to Insert, Chart, and Chart Wizard
  appears. Under the tab, Standard Types, select XY
  (Scatter), and then click on Next.
• You should see that the time (duration of
  rainfall) is the independent variable (x-axis)
  with a scale of 0-140 hours.
• The dependent variable (y-axis) is the average
  amount of rainfall for the watershed and in the
  sample the scale is 0-18 inches.
• Click Next and you should be at Chart Options.

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Graphing the Function Continued

• At Chart Options under the tab
• Titles Title the graph and label each axis
• Axis Both value (x) axis and value (Y) axis
  should be checked.
• Gridlines Add major and/or minor gridlines for
  each axis, depending on what is needed to be able
  to determine the values on the graph.
• Legends Remove check mark
• Data Labels Check X Value and Y Value, this will
  give the coordinates of your points.
• Click Next and then Finish. This will place the
  graph on your spreadsheet.
• Note If the scale on the x-axis has changed
  during this process, you can change it back by
  resizing the graph to make it longer.

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Writing a Regression Equation

• We want to determine whether the relationship
  between the duration time and the rainfall amount
  is a function.
• To determine this, we are going to use our
  scatterplot.
• Select the graph, go to Chart, then Add
  Trendline.
• Click on the graph which best fits your
  scatterplot, then click on the Options tab.
• Select automatic, display equation on chart, and
  display R-squared value on chart and click OK.
• Your graph should look similar to the one on the
  next slide.
• The R-Squared value helps determine the accuracy
  of the regression equation. The closer the
  R-squared value is to 1, the better the equation
  fits the data.
• Add a Word Art to the graph which identifies the
  function.

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Sample Scatterplot, Trendline, and Regression
Equation
A Logarithmic Function
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Summary of the Results

• The relationship between the duration of the
  rainfall and the average amount of rainfall which
  Buffalo Bayou Watershed experienced is a
  logarithmic function,
• The independent variable is the duration of the
  rainfall and the dependent variable is the amount
  of rainfall.
• The parent logarithmic function translated up
  2.8886 and horizontally stretched by a factor of
  2.6815.
• The domain of the graph is all real numbers
  greater than or equal to 1.
• The range of the graph is all real numbers
  greater than or equal to 2.83.

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Summary of Results Continued

• The regression equation is an accurate model of
  this data because R2 .9998. ( The R2 is a
  statistical indicator. The closer the value is to
  1.0000, the more accurate the equation.)
• This knowledge allows us to calculate the amount
  of rainfall at any time during the storm, by
  merely substituting in the desired time for the
  independent variable in the regression equation.

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Rainfall Assignment Continued

• You should now complete the assignment (begun on
  slide 4) of studying the rainfall amounts of 2
  different watersheds in Harris County during
  Allison.
• Each watershed study must include all of the
  following list. It must then be copied and pasted
  into a Word document and turned in or emailed to
  your teacher.
• 1. A spreadsheet, like slide 5

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Rainfall Assignment Continued

• 2. A scatterplot graph, like slide 10 with
• a. A trendline
• b. A regression equation
• c. An R-squared value (should be between .9 and 1
  to be an accurate model of the data)
• d. The function identified, if there is a
  functional relationship

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Rainfall Assignment Continued

• 3. A brief summary of the results (see slide 11
  for the points to include in the summary)
• a. Describe the function.
• b. Identify the type of function.
• c. Write it in functional notation.
• d. Describe the transformations of the parent
  function.
• e. Give the domain and range of the graph.
• f. Evaluate the accuracy of the regression
  equation.
• g. Apply the results to the situation.

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