# 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.
Remember, a fast way to get
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
   Click Next and then Finish. This will place the graph on your
   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
 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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