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?

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.