Analysis of the Rainfall of Tropical Storm Allison

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					Analysis of the Rainfall of
 Tropical Storm Allison
     Creating an Excel Model
        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
                                    Tropical Storm Allison Recovery Project
    Project - TSARP
     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.
Sample Spreadsheet
             Remember, a fast way to get
                your averages is to
             1. Highlight the 3 rainfall
                amounts you want to
                average
             2. Go to Insert, then
                Function
             3. 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.
          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.
    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.
        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.
             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.
        Sample Scatterplot, Trendline, and
             Regression Equation
                         Buffalo Bayou Watershed's Rainfall during Allison

                      20.00
Average Amount of
 Rainfall in Inches




                      15.00                                                                  120, 15.67

                      10.00            12, 9.67
                                                                        y = 2.6815Ln(x) + 2.8886
                       5.00                                                    2
                                  1, 2.83                                     R = 0.9998
                       0.00
                              0         20        40         60        80          100     120     140
                                                       Time of Duration in Hours
          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,
     f(x)  2.6815ln(x  2.8886
                      )
   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.
    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.
       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
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
    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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