1. Introduction
When a hurricane exists in the Gulf of Mexico, Caribbean Sea, or North Atlantic Ocean, millions of residents of the U.S. coastline pay close attention to all information related to that storm. The possibility of a storm potentially threatening a coastal location has substantial human and economic repercussions. Property valued in the billions of dollars is subject to damage or destruction, and many aspects of daily life, including personal safety, are affected by these seasonal storms. Once a tropical cyclone forms, residents of coastal states have a vested interest in knowing where the storm is headed. The National Hurricane Center (NHC) is the U.S. governmental agency responsible for providing projections and predictions for storm location and intensity. Their forecasts are fundamentally similar to other weather forecasts in that the atmosphere is analyzed using the properties of fluid dynamics (Weber 2003).
Little attention is given to the climatological record when projecting the future track and strength of a storm. Only one of the NHC computer models directly uses climatology to predict future storm movement. The Climatology and Persistence model (CLIPER) considers the historical movement of hurricanes and tropical storms in the Atlantic basin between 1932 and 1970 to estimate future storm positions and intensities (information available online at http://www.nhc.noaa.gov/modelsummary.shtml). The rationale behind CLIPER is analogous to pretelegraph weather forecasting. The simplest method for predicting what the weather will be like today at a given location is to extrapolate the previous day’s conditions; this is the “persistence” method.
Another simple method is to look at the historical record. That is, if the average high temperature for a location is 20°C based on a period of record, then predicting a high temperature of 20°C is a reasonable guess; this is the “climatology” method. These two forecast methods are called “no skill” techniques.
The National Hurricane Center has collected 150+ years of tropical cyclone data for the Atlantic Ocean and Gulf of Mexico. These data are referred to as the Hurricane Database (HURDAT; Jarvinen et al. 1984). Landsea et al. (2004) discuss some of the limitations of this dataset. Especially noteworthy are the lack of landfall observations in sparsely populated states before the twentieth century. Even though the HURDAT dataset has been extensively reviewed, a lack of observers during the early years of the dataset means a number of landfalling storms were never documented. For this reason, data prior to the year 1900 are not used in the analysis.
The purpose of this study is twofold—first, to determine whether spatial patterns exist in the climatological record of Atlantic basin hurricanes; and second, to determine whether probability can indicate the relative likelihood of landfall as a function of storm position. This study intends to take a step back and find out where storms have historically traversed. If, for example, a hurricane is very near the island of Bermuda, residents of southern Texas have very little to worry about. Even without analyzing the NHC forecasts, most people who regularly follow tropical cyclones know that storms never move from Bermuda toward southern Texas. This type of ad hoc analysis is based on anecdotal climatology.
There are many probabilistic relationships in the historical data that can aid the public in preparing for these destructive storms. Most importantly, emergency management officials can utilize this information to gather resources, direct personnel, and initiate evacuation planning when a storm enters a particular location. Currently, the NHC issues forecasts up to 5 days (120 h) in advance (information available online at http://www.nhc.noaa.gov/aboutnhcprod.shtml). If a storm is moving at 5 m s−1, up to 2160 km of storm movement is potentially forecastable. What if a storm is 3000 km away from possible impact to the U.S. coastline? What if a storm is halfway between the Lesser Antilles and the west coast of Africa? The climatological record indicates that certain coastal areas should be more concerned than others.
The danger in using the climatological record for estimating landfall probability should not be disregarded. Probability only analyzes events in the past and extrapolates those relationships to the future. The danger in this is either worrying too much when there is nothing to worry about or worrying too little when there is much to worry about. Meteorological forecasts always take precedent when assessing a storm. However, a climatological perspective significantly helps to assess the historical risk of a location.
2. Background
a. Hurricanes over time
Throughout the entire recorded history of the western Atlantic Ocean, hurricanes have impacted the U.S. coastline (Cline 1926; Dunn and Miller 1960; Simpson 1981). In fact, these great storms affected the expeditions of Christopher Columbus in the late fifteenth century (Ludlum 1963). Unfortunately, the significance of hurricanes to humans over the centuries is highly correlated with the number of deaths and the extent of property damage. If few people died during a storm or few structures were demolished, the storm’s legacy is historically minimal, regardless of the actual properties of the storm. After the development of reliable instruments, a storm’s strength (wind speed or barometric pressure) could be quantified as a separate measurement of intensity. The relationship between storm intensity and storm destructiveness is not always straightforward. However, knowing the patterns of tropical cyclone tracks is important in vulnerability assessment and mitigation.
b. Hurricane frequency and movement
The number or tropical cyclones in the North Atlantic varies from year to year. In 2005, 28 storms reached tropical storm intensity or greater, while only 4 such storms formed in 1983; the long-term average is 10.6 yr−1 (Blake et al. 2005). More than 1300 storms are recorded in the HURDAT dataset (993 storms between 1900 and 2006). Even though some years are more active than others, there is a sufficiently large sample to draw probabilistic conclusions. Figure 1 shows all tropical cyclone tracks between 1900 and 2006.
Several factors affect the movement of storms in the North Atlantic basin (Tannehill 1945; Emanuel 2005). First and foremost are the positions of steering-level winds (4–5 km). These wind regimes are a function of the position of the dominant subtropical high pressure cell in the North Atlantic, the “Azores high.” The clockwise winds around this anticyclone force most storms to move from east to west when they are south of the anticyclone. When storms approach the southwestern portion of the subtropical high pressure cell, or the saddle point weakness between the regions of highest pressure, they typically turn to the northwest, then north, and eventually northeast. A number of storms south of the Azores high begin their poleward movement even before reaching the longitude of the Lesser Antilles. Even though the position of this high pressure cell changes little from day to day, relatively minor position and intensity fluctuations greatly affect the storm tracks. Tropical cyclones in the eastern and central Atlantic almost always travel between due west and west-northwest. In the area of the Greater Antilles, storms generally travel northwesterly. Along the east coast of the United States, most storms travel in a northerly or north-northwesterly direction. Of course, these are only verbal descriptions and many variations exist for individual storms. One of the goals of this study is to add a quantitative dimension to the verbal descriptions.
In addition to the large-scale movement associated with the subtropical high pressure cell, tropical cyclones influence their own movement though several well-known processes. Ancillary vortices (beta gyres) spawned by the tropical cyclone tend to force the storm to move poleward of the steering-level wind regime. The strength of the storm determines the magnitude of this process. Wind shear also exerts a steering influence on storms. If the upper-level winds displace the storm’s upper-level anticyclone, the flow around the anticyclone acts as a steering mechanism affecting the overall storm movement (Emanuel 2005).
c. Probability
The simplest measure of the likelihood of an event occurring is to know how many times in the past (if any) an event occurred (Lucas 1970). The probability of an event is “the ratio of the number of times the event occurs to the total number of opportunities for occurrence of the event” (Kachigan 1991, p. 57). There are two methods for estimating probability—theoretical (a priori) and empirical (a posteriori). This study utilizes the empirical probability approach to assess the relative likelihood of movement of tropical storms and hurricanes based solely on the past movement of storms.
d. Hurricane probability studies
Almost every book discussing tropical cyclones contains a series of storm-track maps. Why is this? A nearly implicit expectation of pattern recognition exists in those storm tracks. The reader is left to make judgments as to what the jumbled sets of lines actually mean. Is there a pattern to those tracks? The professional and research communities recently began analyzing the historical storm tracks in an attempt to decipher trends and develop a comprehensive tropical climatology for the Atlantic basin. The breadth of this research is not as comprehensive as one might expect. More specifically, landfall probability studies looking into the ocean to determine where storms originate are relatively uncommon. This background section discusses the relevant works involving hurricane climatology and probability studies.
e. Spatial hurricane landfall probability studies
The most in-depth, analytical studies of hurricane track climatology were produced by the staff of the National Oceanic and Atmospheric Administration. These studies were primarily conducted during the 1960s and 1970s when computing power limited analytical capabilities.
Several studies used the tropical climatological record to compute average storm motion in the Atlantic basin (Neumann and Pryslak 1981; Neumann 1993). Neumann and Pryslak used a network of points to analyze storm movement within 2.5° × 2.5° squares for the Atlantic basin. Their end result is a map of arrows whose size and orientation reflect the average storm direction and magnitude. Neumann’s (1993) work shows storm motion vectors in all tropical basins and storm density within 140 km of a point for all basins. These studies represent important contributions to the quantification of storm tracks.
A spatial probability study released by Hope and Neumann (1971) contained the first maps of storm tracks and calculated probabilities of eventual landfall for a given location. The authors divided the entire Atlantic basin into 2.5° × 2.5° squares. For each square intersecting the coastline, all landfalling storms were identified. Then, each of 2.5° × 2.5° squares through which a storm had previously passed was tabulated. A summation of those squares yielded a relative likelihood of eventual landfall along the previously identified section of coastline. For example, if 20 storms made landfall in the 2.5° × 2.5° square overlapping southern Texas, and if 14 of those 20 passed through the 2.5° × 2.5° square immediately to the southwest, then that southwestern square has a 70% likelihood (0.7 probability) of contributing a storm to the southern Texas coast. The authors performed this analysis along the entire coast looking at all tropical storms and hurricanes. Elsner and Kara (1999) studied hurricane landfall probability (excluding tropical storms) using the same methodology.
Methodologically, the studies by Hope and Neumann (1971) and Elsner and Kara (1999) suffer from several limitations and differ from this study in important ways. First, 2.5° × 2.5° squares are not all the same size. A 2.5° × 2.5° square between 15° and 17.5°N latitude covers an earth area of approximately 75 019 km2. A 2.5° × 2.5° square between 30° and 32.5°N latitude covers an earth area of approximately 66 801 km2. Therefore, the square at the lower latitude is 12% larger in area. Additionally, using a square disproportionately selects storm tracks that cross a corner of the square. The corner of a square is 1.77° from the center, while the edge of the square due east, west, north, or south of the center is only 1.25° away. This overrepresents storms that are farther away from the center of the square. Ho et al. (1975) addressed the overrepresentation of corners using octagons instead of squares; however, octagons leave portions of the study area unrepresented.
These three studies laid the foundation for this paper. The results of their analyses are a quantification of the contribution zones for landfalling storms. Regions of the Atlantic basin containing storms eventually striking the United States are identified, and patterns are broadly established. However, the methodological issues stated above limit the effectiveness of the analysis.
Today, more and more researchers utilize the HURDAT dataset to analyze and assess tropical cyclone properties and probabilities. Xie et al. (2005) used the HURDAT dataset to identify spatial patterns in hurricane-track density as correlated to large-scale climate oscillations. They utilized 2.0° × 2.0° squares to calculate the storm density values. Jagger et al. (2006) calculated extreme wind potential for landfalling storms using the HURDAT dataset. They divided the Atlantic coast into three landfall regions and statistically estimated maximum wind probabilities using extreme value theory. Emanuel et al. (2006a, b) used the HURDAT dataset as a control variable for validating the hypothetical tracks generated by their hurricane model. The authors assume that if randomly generated hurricane tracks are similar to actual hurricane tracks, the model is successful. A similar study used the HURDAT dataset to initialize and evaluate model-generated hurricanes (Vickery et al. 2000). The authors generated hurricanes over a 20 000-yr period and assessed the relative likelihood of landfall at all coastal locations. Like the previous study, the HURDAT dataset is not evaluated directly; instead, it is used to validate the model storms.
3. Methods
a. Measurement shapes
Several of the studies described previously utilize measurement areas based on rectangular coordinates, that is, latitude and longitude (Hope and Neumann 1971; Ho et al. 1975; Elsner and Kara 1999). Because tropical cyclone positions are reported in latitude and longitude, defining an observation site using rectangular coordinates is somewhat logical. However, as mentioned earlier, using shapes defined by these coordinates results in study areas of different sizes.
The only geometric shapes that completely cover the Atlantic basin without any overlap are squares, triangles, and hexagons. The square is primarily limited by the corner representation. A network of triangles magnifies the corner issue, and also magnifies the orientation issue; that is, the direction the triangle “points” affects the number of storm tracks observed intersecting the triangle.
A hexagon represents the best compromise between overlap and uniformity. As with the square and triangle, a tessellation of hexagons fits together with no area uncovered. Because all interior angles of the hexagon are equal and all sides are of an equal length, the hexagon best approximates the ideal shape of a circle. The area of a hexagon whose maximum extent is 1° × 1° at 10°N is 9223 km2. The area of a hexagon whose maximum extent is 1° × 1° at 40°N is 7130 km2. For the aforementioned reasons, this study utilizes hexagons as the measurement shape for analysis.
b. Creating equal area hexagons
Several options are available to resolve this problem of converging meridians (Kimerling et al. 1999). Spherical harmonics is one method for transforming coordinates for atmospheric calculations (Moses 1974). This technique is unnecessarily complicated for the needs of this study. To solve the map distortion problem, the Atlantic basin is converted from latitude/longitude coordinates to a cylindrical equal area projection using a geographic information system (GIS) and then a tessellation of hexagons is created to cover the entire basin. The sides of each hexagon are 50 000 m long and the angular difference between each side is 120°. Therefore, every hexagon represents the same size on the earth’s surface.
A mosaic of 3375 hexagons covers most of the Atlantic basin. Figure 2 shows the extent of the hexagons. Areas receiving few storms, if any, are not covered by the hexagon tessellation. If an area receives storms very infrequently (such as north of the Cape Verde islands), the storm densities in these regions are too small to be meaningful and therefore are not included.
c. Probability calculations
Each of the 3375 hexagons is systematically evaluated against the complete HURDAT dataset to determine the number of storms passing through that shape. When all storms passing through a hexagon are identified, each storm is followed to determine its eventual path and to determine if landfall occurred in the contiguous United States. A count is made of all of the storms that both do and do not strike the United States. The proportion of storms eventually striking the United States is reported as the a posteriori conditional probability of eventual landfall.
What actually constitutes landfall is not easily extracted from the HURDAT dataset’s individual positions. The HURDAT file indicates the path of a storm as a series of temporally spaced points; however, hurricane or tropical storm conditions are not confined to a point. Tropical cyclone conditions are observed over a wide region. Within the HURDAT dataset, if a hurricane makes landfall in the United States, the landfalling state or states are identified and the strength category is stated. If a storm is below hurricane strength, the landfall is not explicitly identified in the dataset. Therefore, the identified affected states in the HURDAT file are not used. For example, Hurricane Rita officially made landfall in southwestern Louisiana in 2005 near the city of Cameron, slightly east of the Texas state line. Beaumont, Texas, reported sustained winds of 36 m s−1 (information available online at http://www.nhc.noaa.gov/pdf/TCR-AL182005_Rita.pdf). If the HURDAT position data are interpreted literally, only Louisiana received the storm’s impact. Another example from the 2005 tropical season is Hurricane Ophelia. Officially, the hurricane never made landfall, but Cape Lookout, North Carolina, reported sustained winds of 33 m s−1 (information available online at http://www.nhc.noaa.gov/pdf/TCR-AL182005_Ophelia.pdf).
An adjustment factor of 50 km is included to determine whether landfall occurred near a state boundary because the typical radius of a tropical cyclone eye is 20 km, with an eyewall width of 15–20 km (Weatherford and Gray 1988). Using this threshold distance, both Louisiana and Texas are landfall targets of Hurricane Rita and North Carolina is counted as a landfall for Hurricane Ophelia. Ideally, a nonuniform threshold distance would represent a more realistic wind distribution resulting from the effect of forward momentum and friction (Emanuel 2005). However, the high degree of variability of wind radii within storms of similar intensity makes this adjustment problematic.
4. Results and analysis
Between 1900 and 2004, 374 tropical cyclones struck the U.S. coastline from Texas to Maine, according to the HURDAT dataset. In the past, researchers and the general public were left to draw their own conclusions as to where storms typically move by looking at a jumbled set of lines that represent the historical record (Colon 1953; Cry 1965; Alaka 1968; Neumann 1993; Neumann et al. 1999).
The landfall probability maps (Figs. 3, 6 –9) developed from the previously described methodology show 10 categories of historical landfall likelihood. The 3375 hexagons each contain a calculated conditional probability value and are displayed according to the category within which the value falls. The categories are measured as percentages and are as follows: 2–10, 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90, and 90–100. Each category is mutually exclusive so there is no overlap between consecutive groupings.
The geographical unit of landfall for this study is an individual state, because in the United States the state political unit maintains much of the responsibility for protection of its citizens and their property. For demonstrative purposes, four representative states are chosen—Texas, Louisiana, Florida, and North Carolina. Table 1 lists the number of storms directly striking or passing within 50 km of each of these four coastal states.
a. North Atlantic basin landfall probability
Clearly defined patterns exist in the landfall map of the entire Atlantic basin. Figure 3 shows the probability (measured as a percentage) of the entire Atlantic basin for all 374 storms eventually making landfall in the United States. As an example of how to read this map, notice the nearly black hexagon between Cancun, Mexico, and the western tip of Cuba in Fig. 3. Twenty-one storms passed through the area covered by this hexagon between 1900 and 2006. Of those 21 storms, 19 eventually made landfall (or came within 50 km of landfall) in the United States along the Gulf or Atlantic Coasts; therefore, the probability for that hexagon is 90.48% (19/21).
The most notable pattern in Fig. 3 is the high probability of landfall in the Gulf of Mexico and the immediate East Coast and the diminishing probability moving southeast from those high-probability regions. Inspection of Fig. 4 reveals the average movement of all storms, regardless of eventual landfall, within the HURDAT dataset, and Fig. 5 shows the frequency (density) of storms during this period.
b. Texas landfall probability
Figure 6 shows the landfall probability distribution for Texas. Because Texas lies at the western end of the Gulf of Mexico, it is not surprising that Atlantic basin storms affecting Texas pass through this body of water. The southern Gulf is much more likely to contribute a landfalling storm than the eastern or northern Gulf. Inspection of the average storm movement vectors in Fig. 4 shows that storms in the southern Gulf typically move to the northwest, toward Texas.
Between 80° and 60°W longitude (approximately the longitudes of Miami, Florida, and the easternmost Lesser Antilles), storms north of the Greater Antilles generally do not strike Texas. Storms impacting Texas are tightly clustered within a swath of approximately 5° of latitude in this region of the Atlantic basin. A sharp gradient is apparent in the central Caribbean Sea where storms south of the middle Caribbean do not strike Texas, but north of that line the storms have a high likelihood of ultimately impacting Texas.
No storms north of 20°N and east of the Bahamas have ever made landfall in Texas. Only two storms that struck the Florida peninsula from the east later impacted Texas with tropical storm–force winds.
c. Louisiana landfall probability
Louisiana’s landfall probability looks very similar to that of Texas. Figure 7 shows the landfall probability distribution for Louisiana. In the Gulf of Mexico, the highest probability hexagons are shifted slightly east of those for Texas, which is not surprising because Louisiana is due east and northeast of Texas. A notable difference is the north–south orientation of the highest probabilities in the Gulf as opposed to the northwest–southeast orientation for Texas. Also, very few storms existing east of 60°W longitude make landfall in Louisiana. The storm motion vectors in Fig. 4 show that storms impacting Louisiana frequently arrive from the south.
In the Caribbean Sea, a stretch of high probabilities exists from the western tip of Cuba to Aruba. Storms in the northern Lesser Antilles rarely strike Louisiana and a gap exists immediately north of the Greater Antilles, indicating that no storms strike Louisiana from that region. Several storms in the past have traversed the Bahamas, crossed Florida, and struck Louisiana. The most recent examples of this are Hurricane Katrina in 2005 and Hurricane Andrew in 1992. Very few storms existing east of 65°W longitude make landfall in Louisiana.
d. Florida landfall probability
Figure 8 shows the landfall probability distribution for Florida. Unlike Texas and Louisiana, Florida receives tropical cyclones from three different directions—east, south, and west. The landfall probability for the area west of Florida in the Gulf of Mexico decays at a slower rate than the area in the open Atlantic to the east. The southwest Caribbean contributes a much larger proportion of storms to Florida than to either Texas or Louisiana.
Many storms east of 60°W longitude eventually make landfall in Florida. Therefore, the “Cape Verde” storms originating in the extreme eastern Atlantic are more likely to strike Florida than other state. The northern islands of the Lesser Antilles frequently experience storms that make a future landfall in Florida; this is markedly different from the probabilities for Texas and Louisiana.
e. North Carolina landfall probability
The portion of the Atlantic basin immediately east of the North Carolina Outer Banks experiences more tropical cyclones than any other portion of the basin (see Fig. 5). This region marks the intersection of storms affected by the weakness in the subtropical high pressure cell (Tannehill 1945) and storms crossing Florida from the Gulf of Mexico.
The storms impacting North Carolina (Fig. 9 shows the landfall probability distribution for North Carolina) usually move in a northward direction; the landfall probability declines dramatically for hexagons located due east of the state. The average storm vectors shown in Fig. 4 indicate that storms typically move northeast in the vicinity of North Carolina.
The far eastern Atlantic contributes a sizeable proportion of the storms that ultimately strike North Carolina. A corridor of high-probability hexagons exists from the Cape Verde Islands to north of Puerto Rico and east of the Bahamas. A secondary high-probability corridor is in the northeastern Gulf of Mexico and the Florida peninsula between Tampa and Jacksonville.
f. Days until landfall
The National Hurricane Center publishes a 120-h forecast for active tropical cyclones (available online at http://www.nhc.noaa.gov/aboutnhcprod.shtml). Assuming the forecast is accurate, only a fraction of the Atlantic basin is able to contribute a storm to the coast. The remainder of the Atlantic basin is beyond the limit of current forecast ability. The following quote from the NHC (Hurricane Isabel Discussion Number 23; available online at http://www.nhc.noaa.gov/archive/2003/dis/al132003.discus.023.shtml) for Hurricane Isabel illustrates the problem with long-range tropical cyclone forecasts:
The big question continues to be what will happen beyond the 5-day forecast period. It is still impossible to state with any confidence whether a specific area along the U.S. coast will be impacted by Isabel. This will likely depend on the relative strength and positioning of a mid-troposphere ridge near the East Coast and a mid-latitude trough to the west or northwest around the middle of next week. Unfortunately . . . we have little skill in predicting the evolution of steering features at these long ranges.
This forecast discussion was issued 6.75 days prior to landfall on the North Carolina coast, when Hurricane Isabel was still a category 5 storm. Beyond 5 days, initialization problems and model resolution prohibit meaningful forecasts. At some point in the future, numerical forecasts are superceded by climatology. Figure 10 shows the length of time for all storms eventually striking the United States that is required to reach the coast.
For storms within the “<5” category in Fig. 10, forecasts from the NHC should indicate a potential landfall somewhere along the coast, assuming that the storm is moving at a minimum speed threshold and is moving in the direction of the United States. Climatology is important in this region for a variety of reasons. When the atmospheric dynamics are complicated or are not well established, climatology provides an important guide for future movement.
In the region labeled >5 days away from the United States, landfall climatology is the best guide to future landfall potential. In Fig. 10, no distinction is made as to the portion of the coast affected. For example, storms near Puerto Rico making landfall in the contiguous United States generally strike between Florida and North Carolina. The calculated length of time until landfall follows the historical storm tracks. If the storm near Puerto Rico bypassed the Atlantic coast and hit Texas instead, the length of time would increase by several days.
The time until landfall is a function of distance from land and forward speed. The distance from land is dependent on the exact track that a storm follows. For example, a hypothetical storm at the western end of Puerto Rico is 1545 km from Miami. However, the distance to Long Island, New York, is 2500 km and the distance to Galveston, Texas, is 3020 km. Assuming that the storm is moving at 7 m s−1, a trajectory toward Miami implies landfall in 2.55 days, a trajectory toward Long Island implies landfall in 4.13 days, and a trajectory toward Galveston implies a landfall in 5.0 days. Therefore, the average time until landfall (see Fig. 10) for the hypothetical storm near Puerto Rico is highly uncertain.
The other portion of the length-until-landfall equation is the forward speed of the tropical cyclones in different portions of the Atlantic basin. Figure 11 shows the average speed of movement for all tropical cyclones during the historical period (not just landfalling storms). Because storms at higher latitudes generally move faster, the isochrones of equal time until landfall are farther away from the coastline for the New England states than for Texas or Louisiana.
g. Comparison of several recent hurricanes with climatology
A secondary purpose of this study is to add a new measure of tropical cyclone landfall prediction. Numerous hurricanes have impacted the United States in recent years. How do these storms compare to the expected probability patterns described earlier in this study?
To assess the climatological point of view, four landfalling hurricanes from recent years are viewed from the perspective of the states they impacted or were forecast to impact and are compared with their historical landfall probabilities. For example, Hurricane Rita struck the Texas–Louisiana border. Rita’s complete storm track is examined and is compared with the probability values for Texas (Fig. 6). A second assessment is conducted to compare the complete storm track with the probability values for Louisiana (Fig. 7). The two assessments are overlaid on each other.
Figure 12 shows the tracks of the four storms (Hurricanes Isabel, Frances, Katrina, and Rita) used for this assessment. Only the final location of landfall is considered. Therefore, Hurricane Katrina’s landfall in Florida as a category 1 storm is not evaluated.
A surfacing technique (kriging) was applied to the hexagon centroids to create a continuous raster grid of probability values for each of the states assessed in this section (not shown); kriging was used because of specific error-minimization capabilities required for this analysis (Lam 1983). A cross-sectional profile of the raster grid shows the historical landfall probability as a function of distance to landfall. The x axis on the figures represents distance from landfall along the storm’s path, not the straight-line distance. The y axis represents the historical landfall probability (%).
1) Hurricane Isabel (2003) in comparison with climatology
Hurricane Isabel formed in the eastern Atlantic basin in September 2003. The storm moved in a westerly and then northwesterly direction for 12.5 days until landfall near Okracoke Island, North Carolina. The chart in Fig. 13 shows the historical landfall probability during the entire history of Isabel for North Carolina and Florida.
The first 3500 km the storm traveled showed a significant difference in the historical probability between North Carolina and Florida. The Florida probability is below 10% for most of this period, while the North Carolina probability is between 15% and 30% during this time frame. Climatology clearly favors a North Carolina landfall for the storm’s locations over a Florida landfall.
The landfall probability hexagons steadily increase for North Carolina until 1000 km before landfall, when a slight decrease is noted. After this decrease, a gradual increase in historical probability occurs until a sharp increase during the last 200 km before landfall, when the outer bands of Isabel were already impacting the North Carolina coastline. The portion of the ocean immediately southeast of coastal North Carolina is where many storms curve out to sea (see Fig. 4). Therefore, the relatively low historical landfall probability in close proximity to the coast is not unexpected. Only a few instances are observed in which Isabel’s storm track moves over an area for which Florida’s historical landfall probability exceeded 10%.
Figure 13 shows that Isabel traveled in a region of the Atlantic that climatologically favored a future landfall in North Carolina versus a landfall in Florida for nearly the entire history of the storm. The official NHC forecast consistently showed the correct movement during the history of Isabel. Five days before eventual landfall, the NHC forecast position was 400 km south-southeast of the actual location. This corresponds favorably with the 412-km-average 120-h forecast track error for the 2003 season (information available online at http://www.nhc.noaa.gov/verification/pdfs/Verification_2003.pdf).
2) Hurricane Frances (2004) in comparison with climatology
Hurricane Frances formed in the eastern Atlantic basin south of the region where Hurricane Isabel formed in 2003. The storm moved in a westerly and then northwesterly direction for 12.25 days until landfall near Palm Beach, Florida. The chart in Fig. 14 shows the historical landfall probability during the entire history of Frances for North Carolina and Florida.
For nearly 3000 km, Frances traveled in a region of the Atlantic Ocean where the landfall probability was only slightly higher for Florida than North Carolina. Once the storm moved within 2200 km of the coast (along its eventual path, not a straight-line distance), the historical landfall probability is consistently higher for Florida. The analysis therefore provided a benefit for several days before any landfall was forecast.
Five days before eventual landfall, the NHC forecast position was 120 km northwest of the actual location. This corresponds very favorably with the 545-km-average 120-h forecast track error for the 2004 season (information available online at http://www.nhc.noaa.gov/verification/pdfs/Verification_2004.pdf).
3) Hurricane Katrina (2005) in comparison with climatology
Hurricane Katrina formed in the vicinity of the southeastern Bahamas. The storm moved in a northwesterly direction across the Bahamas and then turned westward prior to landfall in southern Florida as a minimal hurricane. Katrina moved southwest upon entering the Gulf of Mexico before turning northwest and then finally northward between 85° and 90°W. The chart in Fig. 15 shows the historical landfall probability for Louisiana, Mississippi, Alabama, and Texas during the entire 6.75-day history of Katrina until landfall.
Katrina formed in a region where few storms ultimately impact either Louisiana or Mississippi. Neither of the landfall probabilities for Louisiana or Mississippi exceeded 20% until the storm was 850 km from the coast in the central Gulf of Mexico. The landfall probability for each state did not match well with the climatology until the last 350 km of Katrina’s track. The west and southwest motion of Katrina during the first 3 days of the storm’s life cycle were somewhat unusual. In fact, Alabama showed the highest historical landfall probability for much of Katrina’s early history. In this instance, the historical landfall >5 days in advance provided little benefit.
Five days before eventual landfall, the NHC forecast position was 600 km northeast of the actual location, well inland in southwest Georgia. A significant poleward bias existed in the models and early forecasts for Hurricane Katrina. The 600-km distance between the actual and forecast position is slightly larger than the 530-km-average 120-h forecast track error for the 2005 season (information available online at http://www.nhc.noaa.gov/verification/pdfs/Verification_2005.pdf).
4) Hurricane Rita (2005) in comparison with climatology
Hurricane Rita formed in an area similar to that of Hurricane Katrina, near the southeastern Bahamas. Rita immediately started on a west-northwest track and did not veer much from that bearing until a northwest turn in the day prior to landfall. The chart in Fig. 16 shows the historical landfall probability for Texas and Louisiana during the entire 6.75-day history of Rita until landfall.
Neither state showed an initial landfall probability as high as 10% during the first 1000 km along the storm’s track. Once the storm moved into the central Gulf of Mexico (about 1750 km prior to landfall), the historical landfall probabilities increased for both states. The Louisiana historical landfall probability started with a low value that increased steadily for the final 1700 km before Rita made landfall. Texas’ landfall probability increased to 25% at 1700 km and oscillated between 20% and 40% for the next 1450 km.
Once Rita moved within 500 km of landfall, the probabilities increased dramatically for both states. Even though the initial landfall probabilities are comparatively low, they are higher for Texas and Louisiana than for any other state (not shown). Climatology performed much better for Hurricane Rita than Hurricane Katrina. Interestingly, the forecasts for Rita, while it was in the eastern and central Gulf of Mexico, were for landfall in central Texas. Climatology suggested that Rita would turn poleward, and it eventually did.
Five days before eventual landfall, the NHC forecast position was 155 km southwest of the actual location, near San Luis Pass, Texas. The 155-km distance between the actual and forecast position is substantially less than the 530-km-average 120-h forecast track error for the 2005 season (information available online at http://www.nhc.noaa.gov/verification/pdfs/Verification_2005.pdf).
5. Conclusions
The maps of landfall probability are intended to provide a supplemental measure of preparedness to individuals and government entities along the Gulf of Mexico and Atlantic Ocean coastline. Contemporaneous forecasts are always superior to the historical record in the Atlantic basin; however, knowing the historical climatology enables a potential landfall assessment beyond the time frame of dynamic forecasts.
a. Assessment of results
A network of 3375 hexagons covering the Atlantic basin enabled a systematic assessment of landfalling tropical cyclones for a 107-yr period. A geographic information system determined the a posteriori conditional probability of landfall based on the presence of storms passing through each of the hexagons.
The combined tracks of 374 landfalling storms (from the 993 unique storms in the database) between 1900 and 2006 allowed for the creation of baseline landfall probabilities. Table 1 shows the number of landfalling storms for each state. The paths these storms traverse is not random. There are known climatological factors influencing storm movement on all time scales. The landfall probability maps clearly show the spatial regions contributing storms to the different coastal states. Storms in various areas of the Atlantic basin move in very predictable paths. The maps quantify these collective patterns.
b. Final thoughts
Each state and region along the Atlantic basin coast is occasionally impacted by tropical storms and hurricanes. Both the region of origin and the portion of the basin that the storms traverse are not spatially unique. Regular and measurable patterns define the historical record of storm tracks. For example, storms near the island of Grenada rarely move up the East Coast; instead, they normally impact some portion of the Gulf Coast. Therefore, should residents of North Carolina pay attention to a storm near Grenada? This study does not attempt to answer that question; instead, it provides a historical perspective allowing people in North Carolina to assess the climatological risk of impact given a current position. More information in the hands of the general public allows for better decisions regarding individual and public safety.
Acknowledgments
The author thanks Richard Dixon, Mark Fonstad, Phil Suckling, Jonathan Herbert, and the anonymous reviewers for their assistance in developing this manuscript.
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All tropical cyclone tracks between 1900 and 2006 in the North Atlantic basin.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Location of 3375 equal area hexagons used for analysis. Hexagons are omitted north of the Cape Verde Islands because of a lack of historical data. Map is in a Platte Carre projection (raw latitude and longitude coordinates), and therefore the hexagons appear to have different sizes. Each hexagon is exactly 6495 km2 in area.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Probability (%) in the North Atlantic basin of storms passing through equal area hexagons eventually striking the United States or coming within 50 km of the United States. Only hexagons containing three or more landfalling storms are considered. The period of record is 1900–2006, and the number of affecting storms is 374.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Speed and direction of movement (m s−1) of all storms in the North Atlantic basin passing through the centroid of equal size hexagons. The arrows point in the direction of storm movement and the arrow sizes represent the forward speed of the storms. The arrow sizes are proportionally scaled according to their forward speeds. The period of record is 1900–2006.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Total number of storms passing through equal area hexagons, that is, storm density. The period of record is 1900–2006.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Probability (%) in the North Atlantic basin of storms passing through equal area hexagons eventually striking Texas or coming within 50 km of Texas. Only hexagons containing two or more landfalling storms are considered. The period of record is 1900–2006, and the number of affecting storms is 86.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
As in Fig. 6, but for Louisiana and the number of affecting storms is 84.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
As in Fig. 6, but for Florida and the number of affecting storms is 165.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
As in Fig. 6, but for North Carolina and the number of affecting storms is 86.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Length of time (days) until landfall of all of the storms in the North Atlantic basin passing through equal area hexagons that eventually made landfall. Only hexagons containing three or more landfalling storms are considered. The period of record is 1900–2006.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Average forward movement of storms passing through equal area hexagons (m s−1). The period of record is 1900–2006.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Four hurricane tracks for comparison with landfall climatology.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Historical landfall probability for Florida and North Carolina along the complete storm track of Hurricane Isabel in 2003.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
As in Fig. 13, but for Hurricane Frances in 2004.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Historical landfall probability for Alabama, Louisiana, Mississippi, and Texas along the complete storm track of Hurricane Katrina in 2005.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Historical landfall probability for Texas and Louisiana along the complete storm track of Hurricane Rita in 2005.
Citation: Journal of Applied Meteorology and Climatology 47, 2; 10.1175/2007JAMC1711.1
Count of landfalling storms by state between 1900 and 2006. The value represents the total number of storms passing within 50 km of the state.
