Forecasting Hurricane Hazards for the Long Island Area

 

Introduction

Water_line

My family was flooded out of our ranch-style house twice in two years due to Hurricanes Irene and Sandy. While we had a foot and a half of water from Irene in 2011, Sandy brought more than four feet into our home in 2012. We lost everything that we did not take with us when we evacuated, such as furniture, mementos, and pictures, and we were forced to live with my aunt for much of my freshman year and my entire sophomore year. The damage from the two hurricanes was so extensive that my family was forced to sell our home and move. It is difficult to fathom that I will never again live in the house where I grew up, where most of my childhood memories occurred. Sandy destroyed my entire neighborhood, and as I watched families rebuild their homes and lives, I was inspired to help my community. Subsequently, I investigated flooding risks due to hurricanes in the Long Island area and created a novel model for seasonal hurricane prediction in this area.

Hurricanes represent a major hazard for America’s coastal communities, and society’s vulnerability to damage from hurricanes continues to increase due to increasing population and property values near the coastline (Anthes et al. 2006), combined with a continuing increase in global sea level (IPCC 2007). Thus, these hazards must be quantified and mitigated to enable resilient utilization of coastal areas threatened by hurricanes.

This project focuses on prediction of variations in hurricane hazards within a specific, localized area. Past research into the prediction of seasonal hurricane probabilities focused primarily on hurricane risk over the entire Atlantic region for an upcoming season, rather than on hurricane risk for a local area (Gray 1984). While this method shows some skill (Gray 1992), it is difficult for local areas to utilize this type of information.

In consecutive years, the Long Island region of New York was hit by two catastrophic storms: Irene (2011) and Sandy (2012). Irene caused a storm surge of three to six feet in New York City and Long Island, leading to hundreds of millions of dollars in property damage (Avila and Cangialosi 2011). Sandy was even more catastrophic, with even more widespread effects. On Long Island, damage was estimated at more than half a billion dollars, with around 100,000 homes being severely damaged or destroyed, primarily by the storm surge and waves, and more than 2,000 homes deemed uninhabitable (Blake et al. 2013). Prior to Irene, the last major, catastrophic hurricane was the New England Hurricane of 1938, whose economic losses were in excess of all previous hurricanes in that area combined, causing more destruction of property than the destruction caused by any other hurricane in the United States at that time (Tannehill 1938).

In a study of the effects of sea level rise on storm surge risk along the southern shores of Long Island, even before Sandy devastated Long Island in 2012, Shepard et al. (2012) suggested that Long Island is under increased risk of being hit by a hurricane. Those results showed that sea level rise will likely play a major role in increasing risk in most coastal areas, creating risk where it did not exist before. Even a modest and probable sea level rise of 0.5 meter by 2080 vastly increases the number of people (a 47% increase) and level of property loss (a 73% increase) expected to be impacted by storm surges. Studies such as these clearly demonstrate the need for seasonal and long-range predictions on a local scale.

My study examines the degree of predictability for surge hazards in the Long Island area and develops a novel approach for their seasonal prediction. I hypothesized that: (1) the persistence of large-scale oceanic and atmospheric circulation patterns provides an improved quantitative basis for hurricane probabilities within the Long Island area for an upcoming hurricane season, and (2) predicted variations in storm probabilities can be used to estimate upcoming hurricane-generated surge hazards in this area, and (3) a local geographic perspective can provide a better basis to understand and quantify local effects than a global perspective. My study focuses on the first half of this predictive problem: predicting the local hurricane threat for an upcoming year.  

A key component of my work is an analysis of the interacting scales of variability in coupled oceanic-atmospheric characteristics. This leads to a Long Island regional probability model that is developed and tested using the historical database of storms and oceanic atmospheric conditions, focusing on the possible impact of climate variability on hurricane characteristics in the Long Island area and the role of this variability in the prediction of seasonal hurricane probabilities.

 

Methodology

Large-Scale Patterns – Sea Surface Temperature and Atmospheric Circulation Patterns

Since hurricanes represent a synoptic-scale phenomenon, their motions and intensities are influenced by larger scale atmospheric and oceanic circulation phenomena. In this study, large-scale patterns in sea surface temperature (SST) and atmospheric circulation are analyzed to understand the processes controlling the behavior of hurricanes. I hypothesized that the variation in these large-scale oceanic and atmospheric features significantly influences storm probabilities on a yearly and multi-year basis. To establish an oceanographic context for climatological variations in this area, I analyzed sea surface temperature characteristics near the Long Island area over the interval 1854 to 2012, using data from the Extended Reconstructed Sea Surface Temperature (ERSST.v3b) released by the National Oceanic and Atmospheric Administration (NOAA), subsequently smoothed using a five-year running average. The SSTs analyzed include the three-month averages of SST values from August, September, and October of each year.

Characterization of climatological variations in atmospheric circulation is based on monthly mean atmospheric pressure fields (Compo et al. 2011) over the North Atlantic Ocean from 1870 through 2012. These patterns, as well as sea surface temperature variations, form the basis for an analysis of the potential role of oceanic and atmospheric predictors.

In order to analyze atmospheric circulation patterns, I calculated the eigenfunctions using an available computer code to analyze the covariance matrix among all points in the pressure grid, covering an area from 2°N to 60°N and 100°W to 30°E. Eigenfunctions, or principal component analysis (PCA), are multivariate patterns that explain maximum pressure-field variance through time for any given number of functions, and are often used to represent natural patterns. I used the eigenfunctions to investigate and quantify variations in decadal and multidecadal atmospheric circulation patterns. Thirteen vectors, explaining over 93% of the total variance, are included in this analysis. 

Storm Selection

Estimates of storm surge hazards for the Long Island area require either extensive numerical simulations, or the development of a surrogate for the general threat posed by these storms. In this study, I used the two primary storm characteristics affecting local surge levels from Irish and Resio (2010) as this surrogate: landfall proximity and storm intensity. For a storm to be selected for this study, it must have crossed a box defined as 38°N to 41°N and 75.5°W to 72°W. This box provides a sample size of 20 storms since 1870. For tropical storms to produce a significant storm surge, evidence from historical storms suggests that a threshold of 975 mb provides a good limit for identifying storms posing a significant hazard. I retrieved the data for all storms from the National Oceanic and Atmospheric Administration’s HURDAT2 data (Landsea and Franklin 2013). This data is available on the NOAA website.

Quantifying Relationships Between Atmospheric and Oceanic Large-scale Characteristics

Eigenfunctions are uncorrelated with each other. However, correlations between atmospheric and oceanic processes exist due to their coupled roles in transporting energy and momentum around the Earth. Thus, it is necessary to quantify the correlations between the various eigenfunctions and sea surface temperatures. To test the statistical significance of such correlations, I made the null hypothesis that the SSTs and the eigenfunctions are uncorrelated. This correlation determines the strength of coupling between the oceanic and atmospheric systems in this region. I determined the statistical significance of this correlation via a Student’s “t-test” at a level of significance of 0.05.

Relationships Among Storm Frequency and Intensity and Large-scale Atmospheric and Oceanic Circulation Patterns

Storm occurrences represent a categorical variable, with only two discrete possibilities in a given year: either a storm occurs or does not occur in the defined area. Consequently, I used contingency tables to determine the predictability of storms in the Long Island area as a function of large-scale sea surface temperatures and atmospheric characteristics. I made a null hypothesis that there is no relationship between storm occurrence and these characteristics. I set up a 2x2 contingency table using a Fisher’s Exact Test, with the two columns being “Years with No Storms” and “Years with Storms” and the two rows being categories of SSTs or atmospheric circulation characteristics.

 Weightings on the eigenfunctions are defined by the equation,

beatrice formula

where Pkj is the kth point in the pressure grid for the jth sequential observation in time, Eik is the value of the kth point in the ith eigenfunction, and Wij is the weighting of the jth sequential observation in time on the ith eigenfunction. I smoothed weighting data using a five-year running average, over the interval 1872 to 2010. The second and next-to-last years in the total record (1871 and 2011) are estimated from a three-year running average, and the first and last years in the total record (1870 and 2012) use only the data from that individual year.

Prediction of Annual Large-scale Atmospheric Characteristics and SST Values and Related Storm Probabilities

Autocorrelation, also known as “serial correlation,” is the cross-correlation of a signal with itself. In this study, I used autocorrelation to estimate the persistence of the eigenfunctions over time as an indicator of the predictability of these characteristics over a given time interval. Since the eigenfunction weightings represent atmospheric circulation patterns, persistence in weightings suggests an enhanced ability to make autoregressive predictions through time.

I estimated the probability of high hurricane activity in the Long Island area via autoregression, with the term “high hurricane activity” quantified as the expected frequency of hurricane occurrence based on where the estimated values for that year fall relative to selected thresholds in SSTs and atmospheric circulation values. Differences between storm frequencies in the high-activity and low-activity years provide a physical link to the expected hurricane risk in the upcoming year.

The probability of falling into a high hurricane activity category in an upcoming year depends on two factors: (1) the predicted SSTs value relative to the selected threshold (based on the contingency tables analyses) and (2) the uncertainty in that predicted value.

Since I used five-year averages to characterize storm activity in the contingency table analyses in relation to the eigenfunction and SST thresholds, I used multi-year averages in the autoregressive equations for estimating the five-year probabilities. For SST, iterations on the prediction methodology led to a prediction based on the latest possible three-year average SST in August, September, and October, centered at two years before the year for which the prediction is made, added to the single year SST from the previous year, which can be written as:

SSTpredicted = (SSTAv3 (i-2) + SST (i-1)) /2, where the subscript “Av3” is for a 3-year average, defined as SSTAv3 (i-2) = (SST (i-3) + SST (i-2) + SST (i-1)) /3

For the eigenfunctions significantly related to hurricane activity, the prediction method used for the weightings is analogous to that used for sea surface temperature. First, I developed a prediction equation and determined the standard deviation of the predictions. Then, I used the cumulative distribution function of the Normal Distribution to estimate the expected probability of an upcoming year falling into a high hurricane activity category. After iteration, I based the selected autoregressive prediction on the latest possible four-year and two-year weightings on the eigenfunctions:

Wtpredicted (i) = (WtAv4+WtAv2) /2 where

WtAv4 = (Wti-4 + WTi-3 + Wti-2 +Wti-1)/4 and

WtAv2 – (Wti-2 + Wti-1)/2

Since multiple atmospheric and oceanic factors both affect the probability of falling into a high hurricane activity category, I combined probabilities of each estimated factor significantly related to storm activity multiplicatively to obtain a unified estimate of the likelihood of increased probability of hurricane activity in the Long Island area.

 

Results

Large-Scale Patterns – Sea Surface Temperature and Atmospheric Circulation Patterns

I analyzed sea surface temperature characteristics near the Long Island area over the interval 1854 to 2012, using data from NOAA’s Extended Reconstructed Sea Surface Temperature (ERSST.v3b) (Figure 1A). I then smoothed these using a five-year running average (Figure 1B).

Figure_1

Figure 1: Both (A) and (B) show sea surface temperature data from 1854—2012, obtained from ERSST.v3b, with the SSTs in (A) being three-month averages for the months of August, September, and October and SSTs in (B) being smoothed using a five-year running average.


I analyzed Eigenfunctions 1-13, and the percentage of variance explained by each vector is shown in Table 1. Contours for Eigenfunctions 4 and 6 are shown in Figure 2A and Figure 2B as examples of these functions.

Table 1: Percentage of Variance Explained by Eigenfunctions 1-13

Eigenfunction Percentage of Variance Explained
1 25.63%
2 20.29%
3 15.92%
4 8.12%
5 6.79%
6 3.99%
7 3.42%
8 2.54%
9 1.81%
10 1.46%
11 1.22%
12 1.11%
13 0.85%
Total 93.14%

The total variance explained by Eigenfunctions 1-13 is 93.14%, and thus, Eigenfunctions 1-14 explain most of the variance

 

Figure_2

Figure 2: (A) is the contour of Eigen vector 4 and (B) is the contour of Eigen vector 6.


Storm Selection

 Twenty storms since 1870 passed through the defined geographic box south of Long Island. Of these storms, six were considered to be intense (with a central pressure of less than 975 mb): AL131936, AL061938 (New England), AL091985 (Gloria), AL031991 (Bob), AL092011 (Irene), and AL182012 (Sandy). The tracks of these storms are shown in Figure 3. Table 2 contains the list of all 20 storms that pass through the selection box and the year in which they occurred, with the six intense storms highlighted.

Figure_3

Figure 3: Names and years of the 20 storms selected, with the six intense storms highlighted.


 Table 2: Storms Selected

Storm Name Year
AL021879 1879
AL041893 1893
AL041903 1903
AL071934 1934
AL131936 1936
AL061938 (New England Hurricane) 1938
AL111944 1944
AL091971 (Doria) 1971
AL021972 (Agnes) 1972
AL071976 (Belle) 1976
AL091985 (Gloria) 1985
AL051986 (Charley) 1986
AL031991 (Bob) 1991
Al021996 (Bertha) 1996
AL081999 (Floyd) 1999
AL112004 (Jeanne) 2004
AL022007 (Barry) 2007
AL082008 (Hanna) 2008
AL092011 (Irene) 2011
AL182012 (Sandy) 2012

Names and years of the 20 storms selected, with the six intense storms bolded.

 

Quantifying relationships between atmospheric and oceanic large-scale characteristics       

A Student’s t-test of the correlation between sea surface temperature and the eigenfunction weightings shows that all eigenvector weightings are significantly correlated with sea surface temperature, at probability values less than the 0.05 level of significance typically used as a standard, and that three eigenfunctions (2-7 and 9) are correlated at a significance level of less than 0.001. Weightings on these eigenvectors, along with the SST values for the same year, are shown in Figure 4, and the results of all t-tests are shown in Table 3. Thus, I rejected the null hypothesis that the sea surface temperature and eigenfunction weightings are uncorrelated. Even though the analysis of the eigenfunctions was conducted independently from the SST values, the coupling between the atmospheric patterns and SST is very pronounced. It is clear from this figure that the patterns in sea surface temperature and large scale atmospheric circulation have all been varying secularly since 1870, with some marked episodic variations.

Figure_4

Figure 4: On this plot of Eigen vectors 2,4,7 10, and 11 and SST, the SST was found by subtracting the mean (20.5 degrees C) and multiplying by 10. Eigen vectors 2,4,7, and 11 are significantly negatively correlated with SST, and Eigen vector 10 is significantly positively correlated with SST.


 Table 3: Student's t-test Results for Correlations between Eigenfunction Weighting and SST

Eigenvector R t-score p-value
1 -0.204449549 2.45 0.014312
2 -0.413931280 5.32 <.0000001
3 0.297788382 3.58 0.0000304
4 -0.685704291 11.14 <.0000001
5 -0.281917542 3.48 0.000647
6 0.334564716 4.19 0.000044
7 -0.513975501 7.09 <.0000001
8 0.158386782 1.89 0.058845
9 -0.399339497 5.15 0.0000001
10 0.524501562 7.30 <.0000001
11 -0.607231975 9.04 <.0000001
12 0.186258346 2.24 0.025927
13 0.256597191 3.15 0.001978

  Eigenvectors 2, 4,7, 10, and 11 were found to have extremely significant correlation with SST, with their p-values being <.00000001, and the t-scores for the 0.05 and 0.001 levels of significance are 1.97 and 3.39, respectively.

 

Relationships Among Storm Frequencies and Intensities and Large-scale Atmospheric and Oceanic Circulation Patterns

Contingency tables containing the occurrences of hurricanes and SST above and below a threshold of 20.5oC (the mean SST for the time period) are shown in Figure 5A and Figure 5B; both the contingency table using all the storms and the table using only the intense storms have p-values that are statistically significant. I did a similar analysis for the contingency tables using the eigenfunctions. The p-values for the contingency tables using the weightings on the eigenfunctions are shown in Table 4. Only the weightings on Eigenfunctions 6 and 9 were statistically significant at the 0.05 level, so I included only those in the predictive equations.

 

Figure 5: Contingency Tables for SST

A   B
Intense Storms   All Storms
  Years with No Storms Years with Storms     Years with No Storms Years with Storms
SST>20.5°C 63 6   SST>20.5°C 54 15
SST<20.5°C 74 0   SST<20.5°C 69 5
p-value: 0.0112   p-value: 0.0145

A is the contingency table using SST for intense  storms, with the p-value of 0.0112 being significant, and B is the contingency table using SST for all storms, with p-value of 0.0145 being significant. 

 

Table 4: P-values for Contingency Tables Using Eigenfunctions 1-13

Eligenvector P-value for intense storms P-value for all storms
1 1.0000 0.6329
2 0.2395 0.0945
3 0.4147 0.2286
4 0.4190 0.0942
5 0.6888 0.3434
6 0.4010 0.0129
7 1.0000 0.6308
8 0.7003 0.8129
9 0.1023 0.0142
10 0.6978 0.2301
11 0.4292 0.1475
12 0.6915 0.4681
13 0.4414 0.0570

 p-values for the contingency tables using Eigen vectors 1-13, for both intense storms and all storms; the statistically significant p-values for Eigen vectors 6 and 9 for all storms are bolded. 

 

Prediction of Annual Large-scale Atmospheric Characteristics and SST Values and Related Storm Probabilities

As seen in Figure 6, the autocorrelation in many of the eigenfunction weightings, based on unsmoothed annual weighting values, remains quite high over several years. This indicates the presence of substantial multi-year persistence within these atmospheric patterns.

 

Figure_6

Plot of the autocorrelation of Eigen vectors 1-13, with Eigen vectors 4,10, and 11 bolded due to their strong autocorrelation, indicating persistence and possible decadal and/or multi-decadal atmospheric circulation patterns. Eigen vectors 6 and 9 are bolded due to their strong correlation with hurricane activity.


  

Figure 7A shows a comparison of predicted SST values, based on predictive equations described previously, to observed SST in the following year. As can be seen here, the overall pattern of predictions was fairly good, with a slight time shift. The value of the standard deviation of the differences between the predicted and observed SST values is 0.29oC. Estimates of the probability of a given year falling in the high hurricane activity category are shown in Figure 7B. Observed versus predicted values for Eigenfunction 6 are shown in Figure 8A and observed versus predicted values for Eigenfunction 9 are shown in Figure 8B. Estimated standard deviations are 0.23 and 0.24 for the predicted values of weightings on Eigenfunctions 6 and 9, respectively. I obtained the probability of falling in the high hurricane activity category for each Eigenfunction. Combining sea surface temperature, weighting on Eigenfunction 6, and weighting on Eigenfunction 9 probabilities multiplicatively, the estimated probability of falling in the category with high hurricane activity is shown in Figure 9 (red lines indicate years with intense storms).

Figure 7: SST Autoregression Results

Figure_7

A is the plot of the observed vs. predicted SST from the autoregression, with the predicted SST values being fairly accurate. B is the probability curve of storm activity produced, using autoregression with SST alone.


 

 

 

Figure 8: Observed Vs. Predicted Values for Significant Eigenfunctions

Figure_8

A is the plot of the observed vs. predicted values for Eigenfunction 6 from the autoregression. B is the plot of the observed vs. predicted values for Eigenfunction 9 from the autoregression.


 

Figure_9

Figure 9: Probability curve of high hurricane activity produced using the combination of values of SST, Eigenfunction 6, and Eigenfunction 9, with the years with intense hurricanes denoted with a red line.


 

Discussion

Quantifying Relationships Between Atmospheric and Oceanic Large-scale Characteristics

The correlation between the eigenvectors and sea surface temperature is indicative of strong coupling between atmospheric circulation patterns and sea surface temperature. It is evident that both SST variations and eigenfunctions (which represent atmospheric circulation patterns) are linked in their contributions to storm characteristics, exhibiting clear trends from 1870 through 2012 in both the SST and the atmospheric circulation patterns.

Quantifying the Relationships Among Storm Occurrences and Intensities and Large-scale Atmospheric and Oceanic Circulation Patterns

Due to significant p-values for the contingency tables using SST for both all and intense storms, it is evident that storm occurrence is related to a sea surface temperature threshold. Thus, SST is a good predictor for hurricane probability in the Long Island area. Since weightings on the eigenfunctions are highly related to these variations, they cannot be considered independent predictors; however, results here suggest an increased predictive skill when the effects of these shifting atmospheric patterns were included. 

Prediction of Annual Large-scale Atmospheric Characteristics and SST Values and Related Storm Probabilities for an Upcoming Season

 Autocorrelations in the eigenfunction weightings for Vectors 6 and 9 for the upcoming year indicate a clear ability to predict hurricane probabilities one year in advance. The autoregression model I developed appears successful in predicting hurricane probabilities for the following year with good skill. The model has peaks during the years that all six intense storms occurred: 1936, 1938, 1985, 1991, 2011, and 2012. These peaks are denoted by the red lines on Figure 9. These predictions should not be viewed as deterministic, since they are based on probabilities. For example, there is a peak in the 1970s, indicating that one would expect high storm activity during these years even though no intense storms occurred in this interval. The probability curve using only SST is quite successful, although there is no peak in 1991, the year that Hurricane Bob occurred, and a peak in the period from 1940 to 1960. Based on only SST, the model would suggest intense storms should have occurred in the 1950s and 1960s. However, when Eigenfunctions 6 and 9 were included, the estimated probabilities were significantly reduced. It is evident that multiple factors work together to influence high hurricane activity in the Long Island area, not just sea surface temperature. Thus, my hypothesis that persistence in sea surface temperature and large-scale atmospheric circulation patterns produces a useful tool for forecasting local hurricane activity for an upcoming season is supported.

The overall trend in the storm probabilities suggests that the Long Island area is currently in a period of increased hurricane activity, although the risk is perhaps trending downward at the very end of the record. This is somewhat a different (local) perspective on risk than that of Knutson et al. (2010), which is based on an examination of global characteristics. Their results suggest that global warming will cause tropical cyclone intensity around the world to increase (by 2% to 11% by 2100) and that the globally averaged frequency of tropical cyclones will either remain the same or decline by 6% to 34%. It seems evident that hurricane activity can increase in one local area and decline in another, indicating the need for more localized hurricane prediction models. My study suggests that while the frequency of tropical cyclones appears to be declining worldwide, the frequency of hurricanes specifically in the Long Island area may be increasing, emphasizing the need to examine local-scale hurricane frequencies in addition to basin-wide and worldwide frequencies. This finding supports my third hypothesis, that a local basis could provide a better tool for such predictions.

Limitations

The lack of sample size for intense historic hurricanes in the Long Island area was a serious limitation in the statistical analyses used in my study. Also, the autoregressive method I used was based only on persistence. This introduced a lag in the predicted values and the actual values. Additional research, either using information from earlier in the same year (January to May) or using more sophisticated predictive methods, could likely decrease the lag effects in these predictions; however, these were beyond the scope of the present study.  

 

Conclusions

Previous literature in this area focused on the ability to predict seasonal hurricane probabilities for the entire Atlantic Ocean basin. My study is unique since it suggests an ability to predict seasonal hurricane probabilities for a local area, Long Island. As an offshoot of this work, I observed that climatic variability is evident over the entire historic record analyzed and plays a significant role in determining hurricane probabilities for this area. Both sea surface temperature and atmospheric circulation patterns exhibit pronounced secular and episodic variability which significantly affect hurricane characteristics. By using a three-year running average of sea surface temperature from August, September, and October and Eigenfunctions 6 and 9, I predicted hurricane probabilities for the following year in the localized Long Island area relatively well from data ending as early as the November of the previous year. It is evident that in order for a hurricane to hit the Long Island area, a combination of factors is required: (1) a sea surface temperature above a threshold is required for the storm to be intense, and (2) atmospheric circulation patterns are necessary to steer the storm into the area. Even if the sea surface temperature makes it possible for a storm to be intense, the storm will not hit the area if the necessary atmospheric circulation steers the storms away. My research suggests that a method using seasonal hurricane probabilities, such as the one used here, might provide the Long Island area with valuable information for seasonal planning.

My persistence-based autoregression model suggests an overall increase in hurricane activity in the Long Island area in recent years. If current trends persist, hurricane hazards in this area will likely increase. Thus, the Long Island area should carefully monitor the possibility of continuing climate trends and associated increased risk. Such monitoring might help provide improved seasonal warning for events such as Hurricanes Irene and Sandy, which could be used to better prepare communities for hurricanes.

Since eigenfunctions tend to reflect localized atmospheric circulation patterns, their utility for accurate probability predictions in the Long Island area suggests that it is possible that local predictions could have more predictive skill than predictions for the entire North Atlantic, at least in some localized regions. In the future, studies such as this one should be considered for other areas along the East Coast of the United States that are susceptible to storm surges from hurricanes in the Atlantic, as well as for coastal communities worldwide. Factors that influence hurricane activity in those specific regions should be investigated in order to develop optimal methods for predicting seasonal hurricane probabilities.

 

Acknowledgments

I would like to thank Prof. Donald T. Resio at the University of North Florida for his unyielding support and assistance. He provided me with the patient guidance, support, and critique that I needed to complete my research to the best of my abilities. I would also like to thank Liz Orelup and the rest of Oceanweather, Inc. for their support and assistance and for providing me with the instruction and materials needed to complete my research. Finally, I would like to thank my parents and my research teacher, Mrs. Barbara Franklin, for their love and support, which allowed me to persevere and complete my research.

 

References

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