# Introduction similarity which can lead to a

IntroductionThe analysis of past data helpssociety to connect past occurrences to future possibilities in multiplesituations. Through analyzing statistics from Hurricane Katrina, possibleimpacts can be determined and a correlation between wave height and hurricane windspeed can be set. This allows for more adequate precaution for future instanceswhen storms arise.When examining various features of hurricanes is it possiblethat wave heights depict a pattern? Do the wave heights of Hurricane Katrinafollow the same correlations as the structure for wave formation based onincreasing wind speed, and if so, can this data allow for estimated future waveheights during a storm of similar severity in the future? Waveheights during storms allow for varied intensities and dangerous impacts oncoastal areas and its citizens. Through exploring this topic, I aim to find apattern within the wave heights of Hurricanes Katrina through using a sinefunction that can help to predict the heights and later compare them to the actualwave heights from the storm.

By comparing the wave heights during the stages offormation as wind increases, I hope to notice a similarity which can lead to aprediction for how high waves grew to be during the hurricanes duration.Through determining a function of prediction I can see if the patterns wouldgenerate a similar wave pattern to the actual recorded wave heights. Hurricaneimpact is a personal topic to me as I am from a coastal city in South Floridawhich experienced detrimental effects after the passing of hurricane Katrinaand currently is recovering from the passing of Hurricane Irma. I viewedshorelines, coastal nature, homes, and docks being destroyed during and afterthe hurricane. If data could have predicted wave heights based on predictedwind speed then a grasp of the damage could have been reached, possibly manyhomes and a good portion of my hometown would not have been as affected. I hopeto depict a correlation between Hurricane Karina’s predicted wave heights basedon wind speed and the actual wave heights. This will help to display a need toparticipate in the precautionary principle, and allow for the thought of somecaution to take place the next time a storm is on the horizon.

Through having acollection of past data, there should be no reason for similar results to occuragain and again. Katrina and Wave Structure As hurricanes grow in strength,their wind patterns grow in intensity. Looking at Hurricane Katrina’s averagewind speed at its category three size, Katrina averaged at least 74 MPH to bedeemed a hurricane. Katrina being a Category three hurricane at landfallproduced average wind speeds of 111-129 MPH.

The wind speed itself is what isset on the Saffir-Simpson Hurricane Wind Scale and is used to determine the predicteddestructivity level of the storm. The relation between wind speed and waveheight is essential in the creation of a wave. Waves form from the energy ofwind hitting the ocean’s surface. Hurricane’s surge from tropical stormsbuilding in intensity out in mid-ocean.

As temperature differences, densities,and tropical depressions all interact wind begins to build up creating agreater surge on the ocean surface constructing waves. A wave hasthree basic parts to it: amplitudes (positive/negative), crest, and a trough. Awave 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 isthe 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; themaximum vertical distance from the X-axis (or ocean surface). Amplitudes can bepositive or negative for a wave as when the ripple descends in passses underthe oceans level or passed the X-axis approaching negative X values.

The crestof a wave is the maximum highest distance of a single wave and the trough isthe lowest distance it reaches. A diagram of a wave from crest, trough, tocrest is used to determine wavelength. Wavelength is best compared to theperiod of a sine graph.

Using theparts of a wave, a sine function can be formed to depict a specific wave at acertain wind speed. As wind speed changes the wave height or amplitude canincrease. Using a sine function, I will depict varying wind speeds affectingthe wave heights shown through the graph and compare my function’s results withthe actual wave height results of Hurricane Katrina’s waves. I can also thenuse my parent function to predict the wave heights of future hurricanes basedon wind speed averaged per category of hurricane. A depiction of the waveheights can better help to understand possible severity when expectingapproaching hurricanes in the future.

Figure 1. Diagram depicting the structure of waves and theirparts”Four Grants in Four Days.” KennesawState University | College of Science and Mathematics,science.kennesaw.edu/.

In Figure 1, a depiction of a wave is seen. In the model ofa 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. Aswave 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 ofthe sine graph. Charting WavesWave heights during Katrina were looked at throughcharacteristics of pressure, height, time to develop, and wind speed. Data andweather trackers recording buoy information collected take significant waveheights into account as many waves can fail to form or may be to minor androutine to be significant. Using data for significant wave heights from theNational Data Buoy Center’s (NDBC) buoy stations in the Gulf of Mexico I willcreate a chart relating the height of the significant waves in meter to thetime taken to develop (seconds) throughout the period of a day.

Figure 2. Chart Displaying the Significant Wave Heights inmeters 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 wavepattern graphed I take the averages of the wave heights and seconds to find anaverage height and span of time in order to construct a Sine function from it.

After adding all the significant wave height data from theNDBC I received a total of 77 meters in total.77÷ 12 = 6.41 (rounded to thenearest tenth place)6.4 is the average wave height.To calculate the average seconds it took forthe waves to develop the same practice is followed. After adding all theseconds I received a total of 131.1 seconds.

131.1 ÷ 12 = 10.925 After rounding to the nearest tenth place myaverage for seconds per wave is 10.9.Once I graph my average wave heights, thiswill be my amplitude of my sine graph.

The period itself is a total of 10.92which I am setting equal to ?. To find my B for the equation I took the standard formof a Sine function: Y= a×Sin (bx + c) + dand took the middle term of (bx + c) knowing that there isno phase shift, allowing C to equal zero so that when that term is set equal tozero, and I have to solve for X I will result with zero. I also know that Bwould 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 resultwith ? 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 6.4per the wave height, and the period is ?, with no phase or vertical shift. Works Cited”Reports from the National Data BuoyCenter’s Stations in the Gulf of Mexico During the Passage of HurricaneKatrina.” NDBC – Reports from theNational Data Buoy Center’s Stations in the Gulf of Mexico During the Passageof 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.” OceanPortal | Smithsonian, Smithsonian’s National Museum of Natural History, 26Oct. 2017, ocean.si.edu/ocean-news/currents-waves-and-tides-ocean-motion US Department of Commerce, NationalOceanic and Atmospheric Administration.

“Currents.” NOAA’s National Ocean Service Education: Currents: Waves, 19 Dec.2004, oceanservice.noaa.gov/education/kits/currents/03coastal1.html.