a. Monthly frequency

Figure 1 shows the number of 6-hourly observations per Julian day, stratified by storm category, for EBT TCs. By multiplying the number of observations by 6, these units can be converted to “TC hours,” a measure of how long each TC category is present. Consistent with Landsea (1993), who studied all TCs from 1886 to 1991, very few TCs occur before 1 June or after 30 November, the dates marking the start and end of the official Atlantic basin hurricane season. Landsea applied a 9-day running mean to his frequency plot (his Fig. 2); a 13-day running mean was required here to obtain a smooth curve because there were significantly less observations in our 15-yr period compared to Landsea's 106-yr period. Landsea compared TSs, minor (H1 and H2), and intense (H3, H4, and H5) hurricanes and found a distinct peak in Atlantic TC activity in mid-September. Figure 1 shows each category separately. Weaker systems (TS and H1) peak earlier (late August) than in Landsea's case. The TSs and H1s show a secondary peak in late September. The reverse is seen for H2s: a peak in late September with a secondary peak in late August. Intense hurricanes (H3, H4, and H5) peak in mid-September, consistent with Landsea (1993). Landsea uses a 106-yr (from 1886 to 1991) dataset instead of just 15 yr. Hence, the dual peaks may be a reflection of a decadal climate variability that did not show up in Landsea's larger multidecadal dataset. To further investigate the dual peaks, the EBT dataset was examined on a year-by-year basis. In the early years of the EBT dataset, from 1988 to 1991 (except for 1990), a mid-September peak similar to Landsea's is seen. In the last 11 yr, from 1992 to 2002 (except for 2001), dual peaks like those in Fig. 1 are seen. These two periods do not coincide with the El Niño–Southern Oscillation (ENSO) or quasi-biennial oscillation (QBO) cycles known to affect Atlantic hurricane frequency (Gray 1984). Another factor that affects TC activity is sea surface temperature (SST), Elsner et al. (1999) report on a 7–10-yr North Atlantic SST oscillation. Shapiro and Goldenberg (1998) note that intense hurricane frequency is not correlated with Atlantic SST fluctuations, in agreement with Fig. 1; the dual peaks are seen only in TS, H1, and H2 storms. It is possible that during the dual-peak period (1992–2002), SSTs warm earlier in the season causing a peak in TS, H1, and H2 activity in late August. Due to this enhanced storm activity, upwelling causes SSTs to temporarily drop. Once SSTs recover, a second peak of TS, H1, and H2 activity occurs in late September. Further investigation of the exact nature of this SST periodicity and its effect on inter- and intraseasonal Atlantic hurricane activity is beyond the scope of the present study.

b. Spatial distribution

Figures 2a–f show the spatial distribution of 6-hourly EBT observations by the maximum category a storm obtained. Note, different symbols are used to represent different TC categories. Clearly visible are the typical track patterns of Atlantic storms, forming from tropical easterly waves in the lower latitudes in the eastern Atlantic and being steered toward the west/west-northwest by the easterly trade winds and the so-called beta effect. As the storms travel far enough northward, they encounter the midlatitude westerlies, recurve, and move toward the northeast. Other systems form in the Gulf of Mexico and move to the north and west. Figure 3 shows the distribution of TCs with latitude for each TC category. Weaker systems (TS, H1, and H2) each have two latitudinal peaks. In the case of TSs (Fig. 2a), the lower-latitude peak (15°–20°N) consists of systems that form in the Caribbean Sea and the Atlantic Ocean. Some of these systems continue to intensify to hurricanes of all categories (Figs. 2b–f) at higher latitudes. The higher-latitude peak (25°–30°N) in TS frequency is mostly due to TSs that form in the Gulf of Mexico and off the eastern seaboard (Figs. 2a,b). These systems may intensify to category-1 or category-2 hurricanes, but not much more. The two peaks in H1 and H2 frequency are caused by systems that form in the lower latitudes (low-latitude peak) and intensify to H3 and H4 status, followed by weakening back to H2 or H1 status and recurvature (high-latitude peak). The H4 and H5 storms have only one peak coinciding with the maximum intensity of the systems either during recurvature between 25° and 30°N (Fig. 2e for H4) or toward the end of an elongated track (Fig. 2f for H5) between 15° and 20°N. Figure 4 shows the longitudinal distribution of each TC category. Weak systems (TS, H1) peak in the 60°–65°W range and do not have a distinct region where they prefer to form (Figs. 2a,b). The reason for the peak at the 60°– 65°W range, therefore, is that this longitude covers the largest latitude range (see Fig. 2) and includes a large number of pre- as well as postrecurving systems. Farther west of the peak, the latitude range decreases and, therefore, so does the number of storms. Farther east, the number of storms in the northern regions drops off as systems decay after recurvature. The peaks for H2s– H5s are less sharp than for weaker systems and have a secondary peak a little farther to the east of their main peak, except for H5s (Fig. 4). The H2s and H4s peak a little farther east than their weaker cousins, while H3s and H5s peak farther west. The main H2 peak (55°– 60°W) is caused by category-2 systems that have intensified from TSs that formed in the mid-Atlantic (Fig. 2c), pre- and postrecurving category-3 storms (Fig. 2d), and postrecurving category-4 storms (Fig. 2e). The secondary H2 peak (45°–50°W) is caused by category-2 systems that intensified from TSs that formed in the eastern Atlantic (Fig. 2c), pre- and postrecurving category-3 storms (Fig. 2d), and prerecurving category-4 storms (Fig. 2e). The primary H3 peak (70°–75°W) is mostly due to category-3 storms that intensified from TSs originating in the mid- to eastern Atlantic (Fig. 2d). Since it takes these systems a while to intensify and move westward, the H3 peak occurs farther west than the H2 peak. The secondary H3 peak (60°–65°W) is due to TSs that formed in the mid- to eastern Atlantic just like the primary peak, but weakening H4s (Fig. 2e) also contribute. The H4s seem to have a distinct preference to form in the eastern Atlantic and to intensify quite rapidly. Therefore, the H4 peak (55°–60°W) is located east of the H3 peak. The H5 peak is due to Hurricanes Mitch (October–November 1998) and Gilbert (September 1988), which remained H5s longer than any of the other category-5 storms and did so in the 80°–85°W region.

c. Temporal distribution

Figure 5 shows the distribution of EBT TC observations across the Atlantic basin by month. Again, it is clear that August and September provide the most observations and that activity tapers off before and after those months, consistent with the findings of Landsea (1993). Neumann et al. (1999) discuss the areas of formation of TCs in the Atlantic. Their description agrees with Fig. 5. June storms (Fig. 5a) are almost entirely confined to the Gulf of Mexico and Caribbean regions. In July, the area of occurrence shifts farther east to include the U.S. Atlantic coast (Fig. 5b). During August and September, systems occur over a broad range extending from the Gulf of Mexico westward to the Cape Verde Islands (Figs. 5c,d). During this time, many TCs form in the southeastern North Atlantic from tropical waves and traverse the entire Atlantic. Late-season storms (Fig. 5f) form in the Caribbean and mid-Atlantic. By October the genesis region has shifted farther west (Fig. 5e), and by November TC activity is once again concentrated in the Caribbean region, with a few occurrences at higher latitudes in the Atlantic possibly forming from cold-core lows associated with midlatitude baroclinic systems (Kimberlain and Elsner 1998).

d. Intensification tendency

The “intensification tendency” of an observation is calculated by subtracting the wind speed of that observation from the wind speed of the next observation, and then dividing by 6 h. A negative result means the storm is weakening, a value of 0 indicates a steady-state storm, and a positive result indicates an intensifying storm. The storm's maximum wind speed (VMAX) rather than psmin is chosen to measure intensity because the size parameters to be discussed in the following sections are based on wind measurements. Additionally, there are no missing VMAX observations in the EBT file. Figure 6 depicts the distribution of weakening, steady-state, and intensifying storms with latitude and longitude. At latitudes below about 18°N, most TCs are intensifying or in a steady state, while at latitudes above around 32°N most storms are weakening or in a steady state (Fig. 6a). This is as expected, since storms form and intensify at lower latitudes in favorable environments and weaken when they encounter unfavorable conditions (cooler SSTs and increased vertical wind shear) as they move into midlatitude regions. The distribution with longitude (Fig. 6b) shows a slight preference for intensifying and steady-state TCs west of about 50°W, which is where storms form from easterly waves. Between 55° and 70°W, a slight preference for weakening and steady-state TCs exists, possibly related to postrecurvature systems. Between 70° and 85°W, a slight preference for intensifying and steady-state TCs occurs, possibly related to strong systems passing from the Atlantic into the Caribbean region. Finally, west of around 85°W, no longitudinal preference for any intensification can be seen; in the Gulf of Mexico an equal number of systems intensify and decay.

Figure 7 shows percentages of weakening, steady-state, and intensifying 6-hourly observations by category. Percentages are shown because in previous sections we saw that the actual number of observations per category differs dramatically (Fig. 1). Mean intensification or weakening rates are shown in parentheses. The vast majority (65.0%) of 6-hourly H5 observations are of weakening H5s, while 20% of all H5 observations intensify, and this happens at a faster rate than H5 weakening. For H2s–H4s, the differences are less extreme, but more time is spent weakening than intensifying, and weakening occurs at a faster rate. The H1s and TSs spend more time intensifying than weakening; H1s do so at almost the same rate, while TSs, on the other hand, intensify at a much slower rate than they weaken. In other words, when systems first form, they take longer to get organized and intensify. On the other hand, when storms have reached the intense H5 stage, they take a long time to spin down due to their high level of structural organization.

a. REYE

Table 3 lists the number and percentages of 6-hourly eye observations by S–S category. For all TCs (TS through H5) and all hurricanes collectively (H1 through H5), the percentages of 6-hourly eye observations are calculated using the numbers in Table 3 and are 18.3% and 39.9%, respectively. The percentage of 6-hourly eye observations for TSs is 0.6% (listed in Table 3). In Weatherford and Gray's (1988b) three-season sample of flight missions into northwest Pacific typhoons, the percentages are 47%, 71%, and 24% for TCs, hurricanes, and TSs, respectively. These percentages are substantially larger than the Atlantic EBT values. The formation of an eye indicates that a TC has reached a high level of organization, and is therefore usually a characteristic of more intense systems (Weatherford and Gray 1988b), which are fewer in number (Fig. 1). This partly explains the low number of eye observations. Table 3 confirms that the more intense a TC, the more likely it is to have an eye. Other reasons for the lack of eye recordings in the EBT dataset are that (i) the value is missing due to recording or instrumental errors; (ii) there is a value in the EBT dataset, but it has been eliminated in this study due to inconsistencies with other size parameters; (iii) the eye may have become obscured by the central dense overcast (CDO) and was difficult to estimate due to lack of data sources; or (iv) the eye may have been poorly defined due to eyewall replacement cycles, in which a small inner eyewall is replaced by a larger outer eyewall (Willoughby et al. 1982). A larger outer eyewall may form from a coalescence of spiral bands. In only 17 out of 3493 records, inconsistent (i.e., RMW < REYE) REYE data were detected. All of these records except one were east of 55°W, where aircraft reconnaissance missions are not flown. The percentages were recalculated for data west of 55°W (i.e., to include aircraft reconnaissance data) and increased slightly (22.6%, 47.4%, and 0.7%) compared to the percentages for the total dataset (18.3%, 39.9%, and 0.6%). Even though aircraft are used west of 55°W, there is not aircraft data for all storms at all times, whereas Weatherford and Gray (1988b) used aircraft data exclusively. Hence, the EBT dataset includes nonaircraft data such as satellite images. Eyes can easily be missed in satellite images due to the presence of a CDO.

The numbers in the previous paragraph refer to 6-hourly observations. It is possible that for a given storm some but not all eye observations during its lifetime are missing. Therefore, if at least one observation is present, the storm is counted as having an eye. In Table 3, an individual storm is counted more than once if it assumes more than one storm category with an eye during its lifetime. If a storm assumes the same category with an eye during more than one time period in its lifetime, it is counted as having an eye in that category only once. As expected, the percentages of eye observations go up if storms are counted instead of 6-hourly observations. All 7 category-5 hurricanes have an eye, but only 9 out of 172 TSs (5.2%) have an eye at least once during their lifetime. Each of these nine TSs (Tropical Storms Joan, October 1988; Fran, August–September 1996; Lili, October 1996; Bret, August 1999; Alberto, August 2000; Isaac, September–October 2000; Humberto, September 2001; Isidore, September 2002) eventually intensified to become hurricanes. This again confirms that the formation of an eye is associated with more organized, intensifying systems (Weatherford and Gray 1988b). Two intense hurricanes did not have any recorded REYEs in the EBT dataset: H4 Opal (September–October 1995) and H3 Isidore (September–October 1996). A satellite image of Hurricane Isidore with an eye was found online (Cooperative Institute for Meteorological Satellite Studies 2003), hence, instrumental or recording errors may explain the missing eye observations in the EBT dataset. Isidore occurred east of 45°W and hence aircraft reconnaissance and radar data were not available. Several online satellite images of Hurricane Opal were viewed, but only one showed a clear eye. This infrared image of Opal at peak intensity (0815 UTC, 4 October 1995) shows a clear eye, shortly before and after this the eye is not easily discernable. Instrumental or recording errors may explain the fact that no eye observation was recorded for Opal at that time. Storms tend to first form eyes at the H1 stage (Table 3), and eyes that form earlier or later tend to be smaller except at the H3 stage. However, only two cases first formed an eye at the H3 stage, both of which were relatively large (see minimum and maximum first eyes in Table 3). No storms first formed an eye at the TD or H5 stage.

The frequency distributions of REYE (a histogram and a boxplot) are shown in Fig. 8. A boxplot is a graphical summary of a frequency distribution based on measures of position known as quartiles. On the boxplot, the ends of the box represent the 25% or first (Q₁) and 75% or third (Q₃) quartiles. The box itself contains the middle 50% of the data and ranges from Q₁ = 13.9 km to Q₃ = 27.8 km (Table 2). At least 25% of the data are at or below the first quartile (REYE ≤ 13.9 km) and at least 75% of the data are at or below the third quartile (REYE ≤ 27.8 km). The line inside the box indicates the median (50% quartile) REYE, and at least 50% of the data fall below the second quartile or median. The difference between the first and third quartiles is known as the interquartile range (IQR = Q₃ − Q₁ = 13.9 km for REYE), and it measures the spread of the data. A longer box indicates that the measurements are spread over a larger range. The bracket below the box identifies the shortest half, that is, the range of the densest 50% of the observations. The diamond in the box is known as the means diamond. The means diamond indicates the sample mean and the 95% confidence interval for the population mean. The lines extending on both sides of the box are known as whiskers. The lower whisker extends to the outermost measurement within Q₁ − 1.5 IQR (=−7.0 km for REYE; or 4.6 in this case because this is the smallest recorded and valid value of REYE), and the upper whisker extends to the outermost measurement within Q₃ + 1.5 IQR (=48.7 km for REYE). Any measurement beyond the whiskers, that is, any measurement smaller than Q₁ − 1.5 IQR or larger than Q₃ + 1.5 IQR, is known as an outlier. An outlier is a measurement that does not conform to the pattern of the rest of the measurements and is identified using an asterisk (*) or a dot ( · ) on the boxplot. In Fig. 8, there are no outliers on the lower end; this is as expected because the end of the whisker value is negative. One outlier was identified on the higher end, that is, storms with REYEs larger than 48.7 km. This storm was Hurricane Georges 1998 (REYE = 50.9 km). The reason for unusually large REYEs may be the occurrence of eyewall replacement cycles, when the larger outer REYE is recorded because it is better defined than the inner radius. Such radii are often observed to contract while the storm temporarily weakens or remains in a steady state (Willoughby et al. 1982). The REYE of Georges did indeed contract with its intensity remaining the same during the 18 h following the 50.9-km observation. A good sense of how a boxplot represents a frequency distribution can be achieved by comparing the boxplot to the histogram in Fig. 8. Boxplots will be used in the remainder of this paper to describe the distributions of various size parameters.

The REYE distribution is right skewed (Fig. 8), which means that there are more observations of smaller than larger REYEs. The median REYE is 18.5 km, and the mean is 21.7 km. A few storms with large eyes have an undue influence on the mean REYE, making it larger. For this reason the median REYE better represents the more common REYE for storms in the EBT sample than does the mean. The minimum reported REYE is 4.6 km, while the maximum is 50.9 km. Weatherford and Gray (1988b) reported 4 and 120 km, respectively, for three seasons of northwest Pacific typhoons, while the mean was 20 km. Comparison of the EBT (Fig. 8) and Weatherford and Gray's (1988b) REYE histograms shows the latter to be more right skewed than the former. This indicates that, even though northwest Pacific storms have a larger REYE maximum, small eyes are more common than in the Atlantic. This is confirmed by Table 4, which uses Weatherford and Gray's (1988b) definitions for small, medium, and large eyes and gives the percentage of storms in each REYE group for both samples. A larger percentage of small eyes can be seen in the northwest Pacific sample. In both samples, eyes between 16 and 30 km are most common.

Figure 9 shows boxplots of REYE distributions stratified by S–S category. The median REYE increases with storm intensity except for H3 and H5 storms. However, H2, H3, and H4 storms have larger REYE medians than weak (TS and H1) or very intense (H5) storms. For most S–S categories, except for H2 and H4 storms, the REYE distributions are right skewed. In other words, most of these storms tend to have smaller eyes, and only a few have large eyes. Mood's median test was applied to compare median REYEs of different categories. The result is significant at the 5% level indicating that median REYEs are different for at least two categories (p < 0.001). The TSs and H5s never obtain eyes larger than 30 km, whereas the other categories do. Eyewall replacement cycles may account for the large variability in eye sizes for those categories. Eyewall replacement cycles do not typically occur in TSs, explaining their smaller range in possible eye sizes. Eyewall replacement cycles cause temporary weakening of hurricanes (Willoughby et al. 1982). Therefore, if a category-5 hurricane undergoes an eyewall replacement cycle, the system may be temporarily downgraded to category-4 status until the larger secondary eyewall has contracted to a smaller size. This may explain why category-5 systems display a small range in eye sizes. The median REYE gets larger from the TS to H1 to H2 stages. This does not mean that the eye grows as a TS intensifies to an H1 and then to an H2. Table 3 shows that eyes that initially form at the TS stage are smaller than those that form at the H1 stage, explaining the apparent eye expansion from TS to H1. Eyes that initially form at the H2 stage are smaller than those that first form at the H1 stage (Table 2). However, only 38 out of 198 H2 observations with eyes (Table 3) are initial eyes. The larger H2 eyes in Fig. 9 may be due to eyewall replacement cycles rather than the size of the initial eye.

The relationship between REYE and intensification tendency is shown in Fig. 10. The REYE distributions are slightly right skewed for weakening and steady-state storms if the outliers are considered. Intensifying storms have no outliers and the REYE distribution is right skewed. In both weakening and steady-state cases, the outliers include observations from Hurricanes Gabrielle (August–September 1989), Luis (August–September 1995), and Alberto (August 2000). Additional outliers for weakening storms (REYE > 36.9 km) are observations from Hurricanes Floyd (1999) and Dennis (1999), and Hurricane Georges (1998) for steady-state storms (REYE > 41.8 km). Figure 10 shows that weakening and intensifying systems have the same REYE median (18.5 km), with the smallest 50% of REYE observations distributed in almost the same range (4.6– 18.5 km). The larger 50% of weakening REYEs is spread over a smaller range than that for intensifying storms (almost half the size), with the exception of the outliers. Steady-state storms have a larger median REYE, and the larger 50% of REYEs spans a fairly large range, from 23.1 to 50.9 km. Mood's median test shows a significant difference between the median eye size of steady-state versus intensifying and weakening systems (p = 0.001). Figure 10 shows that the REYE distributions for intensifying and weakening storms differ at the higher end; the medians are equal (18.5 km), but Q₃ is larger in the intensifying sample (27.8 km) than in the sample of weakening storms (23.1 km). This means that for intensifying storms, 25% of all REYE observations lie between 18.5 and 27.8 km, while in weakening storms they lie between 18.5 and 23.1 km. Observing larger eyes for intensifying storms compared to weakening storms may seem to contradict the well-documented fact that eyewalls contract as hurricanes intensify (e.g., Willoughby et al. 1982). Figure 11 shows that H5s and TSs (which have smaller median eyes, as seen in Fig. 9) do not play a role in this trend due to their small number of eyes (TS) or small number of total observations (H5). Hence, the observed trend is due to H1–H4 storms, whose median REYEs are larger (Fig. 9). However, weakening H1s–H4s predominantly have small eyes (Fig. 11), indicating that they have completed the eyewall contraction process and are now ready to decay. Furthermore, H1, H2, and H3 storms with large eyes are mostly intensifiers, indicating that a secondary contracting eyewall may have just formed. Weakening systems are more intense (median VMAX is 33.4 m s⁻¹), well-organized systems with smaller eyewalls than intensifying storms (median VMAX of 28.3 m s⁻¹). Intensifying storms have larger eyewalls that contract to a smaller size. Once there, the systems become steady or begin to weaken for reasons such as a new outer eyewall takes over, the eyewall collapses as the system makes landfall or encounters lower SSTs, or the system encounters larger vertical wind shear or a hostile atmospheric environment.

A boxplot of REYE versus longitude (not shown) reveals that median REYEs are largest in the 40°–60°W region and comparatively smaller east and west of this region. A boxplot of REYE versus longitude (not shown) shows that there is a slight tendency for REYEs to increase with latitude (correlation coefficient = 0.226, p < 0.0001, N = 643). A logical explanation might be that the occurrence of large REYEs at higher latitudes is related to the weakening of systems as they travel northward and encounter lower SSTs and/or interact with midlatitude synoptic-scale systems. The median latitude for weakening systems is indeed farther north (28.7°N) than for intensifying systems (21.1°N). Figure 3 indicates that north of 40°N, only TSs, H1s, and a few H2s are observed. The TSs do not usually have eyes (Table 3), but H1s have mostly small eyes (Fig. 9). However, Fig. 12 shows that while the overall H1 median REYE is 18.5 km, H1s located between 40° and 50°N have a larger median REYE of 37.0 km. Hence, a predominance of weakening H1s with large eyes is found at higher latitudes, but in the previous section it was found that weakening systems tend to have smaller eyes. This contradictory result is explained by looking at the latitudinal distribution of intensifying and weakening systems with large (greater than 20 km) and small (less than 20 km) eyes (Fig. 13). The cutoff of 20 km equals the median REYE (18.5 km, see Table 2), rounded up to 20 km. First, weakening systems with small eyes are far more common than weakening systems with large eyes at all latitudes except at high latitudes (30°–50°N). Second, at all latitudes except very low latitudes (10°–20°N), intensifying storms with large eyes are more common than intensifying storms with small eyes. There are more weakening storms at 30°– 50°N than intensifying ones (see also Fig. 6a), and weakening storms there tend to have large eyes. This may be a reflection of the fact that TC-weakening processes at high latitudes differ from weakening processes at mid- and low latitudes, that is, encountering cold water after recurvature versus landfall (Fig. 6a).

A boxplot of REYE versus month is shown in Fig. 14. There are no REYE observations in June and December, and there is only a small number in July (18 observations for 2 storms: Hurricane Bertha in 1990 and in 1996) and November (33 observations for 4 storms: Hurricanes Florence, 1994; Lenny, 1999; Michelle, 2001; Olga, 2001). The variation of median REYE with month is statistically significant (p < 0.001; Mood's median test). The smallest median eyes are observed in July, October, and November (18.5 km), and the largest are observed in September (23.1 km). Most July, October, and November storms are TSs (Fig. 1), which generally do not have eyes, or H1s, which possess mostly small eyes (Fig. 9), especially in the early and late season (median REYE = 18.5 km; not shown). The large median REYE in September is explained by the large amount of stronger hurricanes in that month (Fig. 1), which tend to have larger eyes (Fig. 9), and because the median REYE for H1s in that month is higher (23.1 km; not shown). This is possibly explained in Fig. 5, where we see very few “Cape Verde–type” storms (i.e., storms that form near the Cape Verde Islands off Africa) in July, October, and November, as is also stated in Neumann et al. (1999). Furthermore, in August and September, EBT systems form at a median latitude and longitude of 14.3°N, 45.9°W and 14.9°N, 55.2°W, respectively. In other months, systems form at median latitudes north of 18°N and median longitudes west of 65°W. This may indicate that Cape Verde hurricanes may have different size characteristics than hurricanes from nontropical origins.

b. RMW

A boxplot of RMW versus storm category (Fig. 15) shows that the median RMW decreases with increasing storm intensity, from 55.5 km at the TS stage to 27.8 km at the H5 stage (a reduction of 50%). A decreasing spread of RMWs with S–S categories can also be seen. Mood's median test confirms that the differences in median RMWs are significant for at least two storm categories (p < 0.001). Weatherford and Gray (1988a) also found decreasing RMWs with increasing storm intensity for northwest Pacific storms. This is consistent with Willoughby's (1998) theory of intensifying storms: the most rapid pressure falls occur on the inside of the RMW, tightening the pressure gradient and increasing the winds (by gradient wind balance) in that region, thus causing the RMW and eyewall to contract as the storm intensifies.

A map showing the spatial distribution of 25-km RMW bins is presented in Fig. 16. RMWs less than 25 km (dots in Fig. 16a) are not very common and occur mostly in the Gulf of Mexico and Caribbean regions. RMWs between 25 and 75 km are most common (Figs. 16a,b) and are scattered uniformly across the entire Atlantic basin. RMWs larger than 100 km (Fig. 16c) are again not very common and seem to be mostly concentrated off the U.S. and Mexican coastlines. Boxplots of RMW versus 10° latitude–longitude bins (not shown) reveal that there are no differences in RMW medians from 10° to 50°N and from 90° to 10°W, where the median is equal to the sample median of 55.5 km. West of 90°W, the sample median is higher (74.0 km). This difference is significant (p < 0.001), according to Mood's median test, and agrees with the swath of larger RMWs seen in Fig. 16c off the eastern seaboard and across the Gulf of Mexico. The swath coincides with a large concentration of TSs and H1s (Figs. 2a,b), which tend to have large RMWs (Fig. 15), but could also result from the availability of better observational tools [radar, Coastal–Marine Automated Network (C-MAN), buoys, and aircraft reconnaissance] closer to the coast.

The median RMW does not vary from July through November and is equal to the overall sample median of 55.5 km (Fig. 17). The boxplot shows that small RMWs are most common in August, September, and October when 75% of all observations are below 74.0 km. The frequency of intense hurricanes peaks in those months (Fig. 1), and such storms tend to have small RMWs (Fig. 15). Very large RMWs (>200 km) occur in August through November but are not common.

The median RMW does not change with intensification tendency; each median equals the median of the total EBT dataset (55.5 km, see Table 2). A boxplot of RMW versus intensification tendency (Fig. 18) shows that all three distributions are right skewed. The distributions differ in the bottom half, as is shown in Table 5, with a larger percentage of weakening TCs having small RMWs (RMW ≤ 45 km; this value was rounded down from the 25th percentile of the total sample). This is consistent with the predominance of small eye values for weakening storms as compared to intensifying storms (Fig. 10) and the theory of eyewall and RMW contraction during TC intensification (Willoughby 1998), as discussed in the previous section. Figure 19 shows that a larger percentage of intensifying than weakening TCs are TSs and H1s, which have larger RMWs (Fig. 15) and take time to spin up due to their low level of organization. On the other hand, a larger percentage of weakening than intensifying storms are stronger hurricanes (H2s–H5s), which have smaller RMWs (Fig. 15) and intense cores that take time to wind down.

c. Outer-wind radii: R17, R26, and R33

The minimum R17 found in the EBT sample is smaller (46.2 km) than that of Tropical Cyclone Tracy (1974), which had an R17 of 50 km. The two storms (Felix, 1989 and Diana, 1990) were both TSs when this size was recorded, while Tracy was an H4. The smallest H4 in the EBT dataset is 101.8 km, while the maximum R17 (693.8 km) is only slightly larger than half of Supertyphoon Tip's size (1100 km). Weatherford and Gray (1988a) reported a mean R26 of 115 km for northwest Pacific storms, considerably smaller than the current sample mean of 143.2 km. No studies of R33 were found.

The variation in the median R33, R26, and R17 with S–S categories is statistically significant (p < 0.001 in all three cases) according to Mood's median test. A substantial variation in the median size parameters with storm categories exists (Fig. 20). Also shown are the inner- and outer-core boundaries (thin dashed lines at 111 and 278 km) as defined by Weatherford and Gray (1988a). The main difference between a median TS and a median H1 is stronger outer-core wind speeds (larger median VMAX, R26, and R17) in the H1 case. At the H2 stage, the inner- and outer-core wind speeds become stronger, however the size (R17) is almost the same as an H1 storm. The H3s have stronger inner and outer cores and are larger than H2s. The differences between the wind profiles in each successive category, from TS to H2, are illustrated in Fig. 21a for the TS to H1 case. From the H2 to H3 stage, the same changes occur: the outer-wind radii expand (i.e., the inner and outer cores intensify), but additionally the RMW contracts. From the H3 to H4 stage (Fig. 21b), VMAX increases, but the wind speeds in the outer regions of the inner and the outer cores weaken (R33, R26, and R17 in Fig. 20 shrink). The H5s have the smallest of all RMWs, and the inner and outer cores are stronger (larger VMAX and R26) than an H4, but the size (R17) is similar to H4 storms. These results agree with earlier findings (e.g., Weatherford and Gray 1988a) that inner and outer cores behave independently and differently. Figure 20 also indicates that as storms increase in intensity, the VMAX (RMW) moves closer to the inner edge of the eyewall (REYE). It must be emphasized that the above transitions are described in terms of the medians of the size parameters, and includes intensifying, steady-state, and weakening systems. Behavior of inner and outer cores stratified by storm category and intensification tendency will be investigated in a follow-up paper.

The median R33 and R26 both show a tendency to increase with latitude from 10° to 40°N (not shown), with a significant difference between medians in at least two 10° latitude bins (Mood's median test; p < 0.0001 for both parameters). The median R17 increases from 10° to 60°N; clearly visible is a concentration of storms with R17 > 350 km north of 30°N in Figs. 22b,c. Mood's median test indicates that the medians differ significantly in at least two 10° latitude bins between 10° and 60°N (p < 0.0001). Therefore, north of 40°N, the median R26 and R33 decrease, but the median R17 increases, indicating a weakening of the inner and outer cores but an expansion in size as TCs move poleward. The R33 frequency north of 40°N decreases due to TCs decaying below hurricane intensity. Weatherford and Gray (1988a) also found an increase in median R26 with latitude for northwest Pacific TCs.

The largest R17s occur between 50° and 80°W (median = 231.2 km). East of 50°W and in the Gulf of Mexico (west of 80°W), the median R17 is smaller. Similar characteristics are seen for R33 and R26. Gulf systems tend to form in the gulf (median latitude of formation is 20.5°N; median longitude of formation is 82.1°W) instead of moving into this area from the Atlantic. Hence, their incipient systems are likely to be tropical upper-tropospheric trough (TUTT) cells or monsoon trough features from the eastern Pacific (e.g., Hurricane Allison, June 2001) instead of easterly waves from Africa. Mood's median test comparing the medians of the three longitude groups (80°–100°, 50°–80°, and 10°–50°W) indicates that the differences are statistically significant (p < 0.0001) for all three parameters. The smallest storms occur in the extreme southeastern North Atlantic (Fig. 22a), while at high latitudes after recurvature, larger R17s dominate (Figs. 22b,c). These findings are consistent with Merrill's (1984) conclusions that recurving storms expand in size after recurvature. Merrill (1984) used ROCI to measure storm size instead of R17. The spatial distribution of ROCI will be discussed in the next section.

The changes in the medians of the size parameters with storm intensification tendency are shown in Fig. 23. Mood's median test indicates that the differences between the medians of the outer-wind radii are statistically significant (p < 0.001). Compared to weakening TCs, intensifying systems have weaker inner and outer cores and are smaller in size. This makes sense because the sample of weakening storms consists predominantly of TSs and H1s (Fig. 19), which are weak and small systems (Fig. 20). Weakening TCs are large in size because they include many intense hurricanes (Fig. 19), which are large (Fig. 20).

Figure 24 displays the median size parameters as a function of month. The variation of the median with month is statistically significant for R33 and R17 (R33: p < 0.001; R17: p < 0.001) but not for R26 (p = 0.186) according to Mood's median test. Weatherford and Gray (1988a) found little variation in the median R26 from May through October for northwest Pacific TCs and define R26 > 300 km as large. These values can exist in August and September and compose only a small percentage of their total sample. In the current sample of Atlantic TCs, large R26s ranging from 300.6 to 476.5 km (not shown) compose 1% of the total sample and occur from July through November. Hurricanes Gilbert (September 1988), Bertha (July 1990), Felix (August 1995), and Olga (November 2001) are the main contributors, with R26 remaining larger than 300 km for 12 to 24 h. No large R26 storms occur in October, three occur in September, and one occurs in each of the remaining months. Large R26s amount to a large areal coverage of highly damaging winds. The median TC size (R17) peaks in September to coincide with a peak in the frequency of H2s–H5s (Fig. 1), which are larger (Fig. 20). Very large storms (R17 > 550 km, not shown) occur in September, October, and November but are not common (1% of the total sample). Their locations are mostly north of 30°N and west of 60°W, that is, not in the Gulf of Mexico (Fig. 22c). Late-season (September, October, and November) storms tend to be large, while early-season (June and July) storms are small. This is possibly caused by the occurrence of some intense (H3 and above) hurricanes in later months, whereas June and July produce almost exclusively TSs and H1s (Fig. 1). The H1s and TSs are significantly smaller (Fig. 20) than intense hurricanes (H3s–H5s).

d. ROCI

This parameter was used by Merrill (1984) to measure overall TC size. Statistical properties are presented in Table 2 for EBT storms during the years 1988–2002 (mean = 351.9 km ± 122.0 km) and for 1957–77 (mean = 333.0 km ± 155.4 km) from Merrill's (1984) Atlantic TC sample (his statistics were converted to kilometers by assuming that 1° of latitude equals 111 km). A t test was used to compare the mean ROCI for storms during these two time periods. The test results show that storms during the 1988–2002 period had significantly higher ROCIs compared to storms during the 1957–77 period (p = 0.000011). A histogram of the ROCIs for all TCs during the years 1988–2002 is shown in Fig. 25. The shape of the distribution is similar to Merrill's (1984) TC sample. Both distributions peak at an ROCI of 300 km and are slightly right skewed with more observations on the smaller ROCI end. The distribution in Fig. 25 was also compared to a distribution of ROCI observations taken west of 55°W where observations are more reliable due to the availability of aircraft reconnaissance. Table 6 gives the statistical properties of the ROCI distributions west of 55°W; these are not significantly different from those listed in Table 2 for the entire dataset. This provides confidence that the 1988–2002 ROCI values in Table 2 are reliable. There are two possibilities for the differences between the two ROCI distributions from 1957–77 and 1988–2002: 1) decadal climate variability and 2) data quality. North Atlantic seasonal hurricane activity is correlated to ENSO on the decadal time scale (Gray 1984). During the La Niña phase of ENSO, more as well as more intense TCs occur (Gray 1984). These findings are confirmed in the EBT dataset. Figure 26 shows the distribution of S–S categories stratified by ENSO using the EBT dataset [individual years were categorized according to ENSO phase using NOAA (2003)]. During La Niña and neutral years, about 50% of all 6-hourly observations are TSs, while the other 50% or so are hurricanes. During El Niño years, more than 60% of all 6-hourly observations are TSs, which explains the smaller median ROCI of 296 km observed during EBT El Niño years compared to 333 km during EBT La Niña and neutral years. Figure 20 shows that the median ROCI is much smaller for TSs than hurricanes (except for H5s, which are so low in number that their influence is neglible). Perhaps the median ROCI from 1957–77 is smaller than that during the 1988–2003 period because more El Niño years occur in the previous period than the latter. Unfortunately, this was not the case; the earlier (21 yr) period contained 7 El Niños and 5 La Niñas, while the latter (15 yr) period contained 7 El Niños and 3 La Niñas (NOAA 2003), which translates to 9.8 and 4.2, respectively, in 21 yr. It is therefore concluded that the ROCI differences between the two periods are due to improved instrumentation and observational techniques in the latter period. The ROCI data from 1957 to 1977 were obtained from the NHC operational surface analyses (Merrill 1984). During this time, aircraft reconnaissance missions were flown, but it is unknown to the authors how the operational surface analyses were obtained.

There are 143 large (greater than the right whisker in Fig. 25, i.e., 601.3 km) ROCI observations for 20 storms (including the three famous storms: Hurricanes Gilbert, 1988; Hugo, 1989; and Opal, 1995). The increase in the median ROCI with latitude is less pronounced than the increase in the median R17, which almost doubled in size, but is still significant (p < 0.0001) according to Mood's median test. These results are consistent with Merrill's (1984) findings, which detected a large percentage of larger cyclones (ROCI ≥ 444 km) in the 30°–40°N region for his 1957–77 sample of Atlantic storms. From 30° to 40° and 80° to 90°W (Gulf of Mexico), the median ROCI is 323.8 km, while from 40° to 80°W, the median ROCI is 333 km. However, the differences between 10°-longitude groups are not significant at the 5% level (p = 0.2) according to Mood's median test. Figure 25 shows two outliers at the lower end (ROCI < 83.3 km): Hurricanes Iris (1989; ROCI = 55.5 km) and Barry (1989; ROCI = 74.0 km).

The median ROCI increases with the month of the year (Fig. 24). While the ROCI peaks in the late season, the R17 peaks in midseason. Hurricanes have significantly (p < 0.001) larger median ROCIs (Mood's median test) than TSs (Fig. 20). No variation in the median ROCI is seen between intensifying, steady-state, and weakening TCs (Fig. 23).