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Introduction similarity which can lead to a

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Introduction

The analysis of past data helps
society to connect past occurrences to future possibilities in multiple
situations. Through analyzing statistics from Hurricane Katrina, possible
impacts can be determined and a correlation between wave height and hurricane wind
speed can be set. This allows for more adequate precaution for future instances
when storms arise.When examining various features of hurricanes is it possible
that wave heights depict a pattern? Do the wave heights of Hurricane Katrina
follow the same correlations as the structure for wave formation based on
increasing wind speed, and if so, can this data allow for estimated future wave
heights during a storm of similar severity in the future?

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            Wave
heights during storms allow for varied intensities and dangerous impacts on
coastal areas and its citizens. Through exploring this topic, I aim to find a
pattern within the wave heights of Hurricanes Katrina through using a sine
function that can help to predict the heights and later compare them to the actual
wave heights from the storm. By comparing the wave heights during the stages of
formation as wind increases, I hope to notice a similarity which can lead to a
prediction for how high waves grew to be during the hurricanes duration.
Through determining a function of prediction I can see if the patterns would
generate a similar wave pattern to the actual recorded wave heights.

            Hurricane
impact is a personal topic to me as I am from a coastal city in South Florida
which experienced detrimental effects after the passing of hurricane Katrina
and currently is recovering from the passing of Hurricane Irma. I viewed
shorelines, coastal nature, homes, and docks being destroyed during and after
the hurricane. If data could have predicted wave heights based on predicted
wind speed then a grasp of the damage could have been reached, possibly many
homes and a good portion of my hometown would not have been as affected. I hope
to depict a correlation between Hurricane Karina’s predicted wave heights based
on wind speed and the actual wave heights. This will help to display a need to
participate in the precautionary principle, and allow for the thought of some
caution to take place the next time a storm is on the horizon. Through having a
collection of past data, there should be no reason for similar results to occur
again and again.

Katrina and Wave Structure

            As hurricanes grow in strength,
their wind patterns grow in intensity. Looking at Hurricane Katrina’s average
wind speed at its category three size, Katrina averaged at least 74 MPH to be
deemed a hurricane. Katrina being a Category three hurricane at landfall
produced average wind speeds of 111-129 MPH. The wind speed itself is what is
set on the Saffir-Simpson Hurricane Wind Scale and is used to determine the predicted
destructivity level of the storm. The relation between wind speed and wave
height is essential in the creation of a wave. Waves form from the energy of
wind hitting the ocean’s surface. Hurricane’s surge from tropical storms
building in intensity out in mid-ocean. As temperature differences, densities,
and tropical depressions all interact wind begins to build up creating a
greater surge on the ocean surface constructing waves.

            A wave has
three basic parts to it: amplitudes (positive/negative), crest, and a trough. A
wave begins on a flat plane of the ocean surface before wind interacts with it.
Once wind energy increases, the wave begins a ripple. The waves amplitudes is
the distance from the top of the first wave or ripple to the ocean’s flat surface.
Using a sine graph to depict a wave, the amplitude is equal in meaning; the
maximum vertical distance from the X-axis (or ocean surface). Amplitudes can be
positive or negative for a wave as when the ripple descends in passses under
the oceans level or passed the X-axis approaching negative X values. The crest
of a wave is the maximum highest distance of a single wave and the trough is
the lowest distance it reaches. A diagram of a wave from crest, trough, to
crest is used to determine wavelength. Wavelength is best compared to the
period of a sine graph.

            Using the
parts of a wave, a sine function can be formed to depict a specific wave at a
certain wind speed. As wind speed changes the wave height or amplitude can
increase. Using a sine function, I will depict varying wind speeds affecting
the wave heights shown through the graph and compare my function’s results with
the actual wave height results of Hurricane Katrina’s waves. I can also then
use my parent function to predict the wave heights of future hurricanes based
on wind speed averaged per category of hurricane. A depiction of the wave
heights can better help to understand possible severity when expecting
approaching hurricanes in the future.

Figure 1. Diagram depicting the structure of waves and their
parts

“Four Grants in Four Days.” Kennesaw
State University | College of Science and Mathematics,
science.kennesaw.edu/. 

In Figure 1, a depiction of a wave is seen. In the model of
a wave, the amplitude can be seen and equated to the amplitude in a sine graph.
The period of the “graph” of the wave can be seen through the wavelength. As
wave height is determined from measuring the height from wave crest to trough,
the wave height will be equal to half of the wavelength, or half of the period of
the sine graph.

Charting Waves

Wave heights during Katrina were looked at through
characteristics of pressure, height, time to develop, and wind speed. Data and
weather trackers recording buoy information collected take significant wave
heights into account as many waves can fail to form or may be to minor and
routine to be significant. Using data for significant wave heights from the
National Data Buoy Center’s (NDBC) buoy stations in the Gulf of Mexico I will
create a chart relating the height of the significant waves in meter to the
time taken to develop (seconds) throughout the period of a day.

Figure 2. Chart Displaying the Significant Wave Heights in
meters of Hurricane Katrina per NDBC’s data from August 27th, 2005.

Hour

Wave Height (meters)

Seconds

0

3.9

7.7

1

2.6

7.5

2

3.5

8

3

5

9.3

4

5.1

9.5

5

6.2

10.5

6

6.1

10.4

7

6.3

10.6

8

7.6

11.3

9

7.1

11

10

7.8

11.7

11

7.7

11.6

12

8.1

12

 

In order to use this information to have a more uniform wave
pattern graphed I take the averages of the wave heights and seconds to find an
average height and span of time in order to construct a Sine function from it.

After adding all the significant wave height data from the
NDBC I received a total of 77 meters in total.

77÷ 12 = 6.41 (rounded to the
nearest tenth place)

6.4 is the average wave height.

To calculate the average seconds it took for
the waves to develop the same practice is followed. After adding all the
seconds I received a total of 131.1 seconds.

131.1 ÷ 12 = 10.925

After rounding to the nearest tenth place my
average for seconds per wave is 10.9.

Once I graph my average wave heights, this
will be my amplitude of my sine graph. The period itself is a total of 10.92
which I am setting equal to ?. To find my B for the equation I took the standard form
of a Sine function: Y= a×Sin (bx + c) + d

and took the middle term of (bx + c) knowing that there is
no phase shift, allowing C to equal zero so that when that term is set equal to
zero, and I have to solve for X I will result with zero. I also know that B
would be 2 because the expression to find a period in a Sine graph is:

Placing my B value of 2 below and solving, I would result
with ? which is my period, allowing me to use 2 for B as it proves this.

Figure 3. A Graph of the Wave Height Sine Equation:

My amplitude within the function shown in Figure 3. is 6.4
per the wave height, and the period is ?, with no phase or vertical shift.

 

 

 

 

Works Cited

“Reports from the National Data Buoy
Center’s Stations in the Gulf of Mexico During the Passage of Hurricane
Katrina.” NDBC – Reports from the
National Data Buoy Center’s Stations in the Gulf of Mexico During the Passage
of Hurricane Katrina, www.ndbc.noaa.gov/hurricanes/2005/katrina/.

 

GFDL
– Geophysical Fluid Dynamics Laboratory, www.gfdl.noaa.gov/global-warming-and-hurricanes/.

 

Fairclough, Caty. “Currents, Waves,
and Tides: The Ocean in Motion.” Ocean
Portal | Smithsonian, Smithsonian’s National Museum of Natural History, 26
Oct. 2017, ocean.si.edu/ocean-news/currents-waves-and-tides-ocean-motion

 

US Department of Commerce, National
Oceanic and Atmospheric Administration. “Currents.” NOAA’s National Ocean Service Education: Currents: Waves, 19 Dec.
2004, oceanservice.noaa.gov/education/kits/currents/03coastal1.html. 

 

 

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