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i

NASA/TP—2012–217470

Estimating the Length of the North Atlantic 

Basin Hurricane Season

Robert M. Wilson

Marshall Space Flight Center, Huntsville, Alabama

October 2012

National Aeronautics and

Space Administration

Marshall Space Flight Center • Huntsville, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076 –1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov/login/wt/>
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

2. RESULTS ........................................................................................................................... 3

3. CONCLUSION .................................................................................................................. 11

REFERENCES ....................................................................................................................... 13
iv
v

LIST OF FIGURES

1. The annual and 10-yma values of (a) FSD and (b) LSD for the interval 

1945–2011. Excludes FSD33 in 1952 and FSD19 in 1978, both short-lived 

tropical storms and considered statistical outlier events in this study ........................... 3

2. The annual and 10-yma values of LOS for the interval 1945–2011 .............................. 4

3. The scatter plot of annual values of LOS versus FSD ................................................. 6

4. The annual and 10-yma values of (a) <AT>, (b) <AMO>, (c) <AMM>, 

and (d) <ONI> for the interval 1945–2011, and (e) the NENM and NLNM 

during the interval 1950–2011 ...................................................................................... 7

5. Scatter plots of LOS versus (a) <AT>, (b) <AMO>, (c) <AMM>, 

and (d) <ONI> ............................................................................................................ 9
vi

LIST OF ACRONYMS AND ABBREVIATIONS

10-yma 10-year moving average

AMM Atlantic Meridional Mode

AMO Atlantic Multidecadal Oscillation

AT Armagh Observatory surface air temperature

DOY day of year

ENSO El Niño Southern Oscillation

ENY El Niño year

FSD first storm day

HURDAT hurricane data

LNY La Niña year

LOS length of season

LSD last storm day

NENM number of El Niño months

NLNM number of La Niña months

NY neutral year

ONI Oceanic Niño Index

PWS peak wind speed

SST sea surface temperature
vii

NOMENCLATURE

cl confidence level

n+ number of annual values above mean

n– number of annual values below mean

n+r number of annual value positive runs

P probability

r coefficient of correlation

r2 coefficient of determination

sd standard deviation

se standard error of estimate

x independent variable

y dependent variable

z normal deviate of sample
viii
1

TECHNICAL PUBLICATION

ESTIMATING THE LENGTH OF THE NORTH ATLANTIC BASIN HURRICANE SEASON

1. INTRODUCTION

Conventionally, the North Atlantic basin hurricane season spans the 183-day period from 

June 1 to November 30. Of the 67 yr spanning 1945–2011, an interval considered to be the most 

reliable based on the near continuous use of reconnaissance aircraft and especially Earth-orbiting 

satellite imaging (since the 1960s),1–3 only 22 yr had yearly (or seasonal) first or last storm days outside this interval4 where the first storm day (FSD) and the last storm day (LSD) of a season refer, 

respectively, to the first and last days of a yearly hurricane season when tropical cyclones had a 1-min 

sustained peak wind speed (PWS) of at least 34 kt. The yearly length of season (LOS) is defined as 

the elapsed time in days between FSD and LSD for that year.

For the interval 1945–2011, some 734 tropical cyclones formed in the North Atlantic basin, 

including 416 storms that became hurricanes (i.e., those having PWS ≥64 kt), of which 183 storms 

became major or intense hurricanes (i.e., those having PWS ≥96 kt). Of the 734 tropical cyclones, 

712 (or about 97%) originated during the nominal hurricane season of June 1–November 30 with 

the bulk (78%) originating in the months of August (27%), September (34%), and October (17%). 

Of the remaining 22 storms, all but two originated during the months of April (2), May (10), and 

December (8), months immediately adjacent to the nominal hurricane season.4 The two tropical 

cyclones that formed outside the inclusive interval of April 1–December 31 include one each tropical 

cyclone of tropical storm strength only (i.e., 34≤ PWS ≤63 kt) that formed in the months of January 

and February, respectively. For the interval 1945–2011, no tropical cyclone is known to have formed 

in the North Atlantic basin during the month of March. Because the January 1978 and February 

1952 tropical storms were not closely preceded nor followed by additional tropical cyclones, they are 

considered statistical outliers and have been excluded in this study.

Previously, Kossin5 examined the interval 1851–2007 ‘best track’ hurricane record (i.e., the 

HURDAT, available online at <www.nhc.noaa.gov/pastall.shtml>) and suggested that the hurricane 

season is increasing in length due to the occurrences of both earlier and later seasonal storms, attributing the increased lengthening to warming sea surface temperature (SST). His analysis was based 

on the use of quantile regression.6,7

In this analysis, the ‘best track’ hurricane record for 1945–2011 is used to ascertain the exact 

day of year (DOY) for each year’s FSD and LSD, thereby allowing for determination of each year’s 

LOS. Ten-year moving averages (10-yma) are then determined for each parameter. Next, based on 

the annual values, the scatter plot of LOS versus FSD is determined, one that reveals a preferential 
2

inverse correlation between the parameters and that is statistically important at the 0.1% level of 

significance (or >99.9% confidence level, or cl). From the reported FSD for the year 2012 

(i.e., May 19, 2012 or DOY=140), the LOS and LSD for the current hurricane season are estimated 

based on the inferred regression. Lastly, the trend of LOS is compared to trends of various markers of surface-air temperature, SST, and the El Niño Southern Oscillation (ENSO) to ascertain the 

degree of similarity between the parameters. 
3

2. RESULTS

Figure 1 displays the variation of the DOY for FSD (fig. 1(a)) and LSD (fig. 1(b)) during the 

interval 1945–2011, ignoring the two previously described outlier tropical storms. The thin jagged 

line represents the annual values and the thick smoothed line represents the 10-yma values. During the 67-yr interval, the DOY for FSD is found to average about 180.5 (corresponding to about 

July 1), having a standard deviation (sd) of about 33 days and range of 110 to 242, and the 

DOY for LSD is found to average about 310 (corresponding to about November 6), having sd of 

about 23 days and range of 263 to 371. (Recall that eight tropical cyclones formed in the month 

of December with two ending in the following calendar year, including one hurricane spanning 

December 30, 1954 –January 5, 1955 and one tropical storm spanning December 30, 2005–January 6, 

2006. Hence, the LSD for 1954 is 370, and the LSD for 2005 is 371, as indicated in fig. 1(b)).

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Year

250

200

150

100

FSD (DOY)

(a)

mean = 180.5

sd = 33.3

range = 110 to 242

400

350

300

250

LSD (DOY)

(b)

mean = 309.9

sd = 23.3

range = 263 to 371

Figure 1. The annual and 10-yma values of (a) FSD and (b) LSD for the interval 1945–2011. 

Excludes FSD33 in 1952 and FSD19 in 1978, both short-lived tropical storms and 

considered statistical outlier events in this study.
4

Based on the movement of the 10-yma values (used to indicate trend), since about 1987, FSD 

has decreased from about DOY 195 to about DOY 170 (in 1996), a decrease of about 13%, varying 

between DOY=169–174 after 1996 and between DOY=175–190 prior to 1987. The 10-yma values 

of FSD have remained below the long-term mean (DOY=180.5) since about 1990.

Since the early 1960s, LSD has slowly increased from about DOY 297 (in 1960) to about 

DOY 325 (in 2003), an increase of about 9%. The 10-yma values of LSD have been relatively flat 

(about DOY=322–325) between 2000 and 2006, the last available 10-yma value of LSD, and above 

the long-term mean (DOY=310) since about 1997.

Together, these movements in the trends of FSD and LSD suggest that LOS will display 

a preferential upward movement, indicative of a lengthening of the hurricane season. Indeed, as 

shown in figure 2, based on the movement of its 10-yma values, LOS has increased from about 

113 days (in 1979) to about 157 days (in 2003), an increase of about 39%. In terms of annual values, 

LOS is found to average about 130 days, having sd of about 42 days and range of 47 to 235 days. 

Runs-testing8 indicates that the annual values of LOS vary nonrandomly at the 5% level of significance (or cl>95%) based on the observed 33 annual LOS values above the mean (n+), the 34 values 

below the mean (n–), and the 22 positive runs (n+r), which together yields the normal deviate of 

the sample z=2.31, a value suggestive of nonrandom variation. The current interval of higher than 

average 10-yma values of LOS began in 1992 and continues through 2006, now measuring about 

154 days. During the interval 1992–2011, annual values of LOS exceeded the long-term mean in 13 

of 20 yr and fell below the long-term mean in 7 of 20 yr, averaging about 148±43 days (i.e., the ±1 sd

interval). 

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Year

250

100

150

200

50

LOS (Number of Days)

mean = 130.3 days

sd = 42.3 days

range = 47 to 235 days

n+ = 33

n– = 34

n+r = 22

⇒z = 2.31 ⇒ cl >95%

 (nonrandom)

Figure 2. The annual and 10-yma values of LOS for the interval 1945–2011.
5

When one plots the annual values of LOS against FSD, one infers a highly statistically important preferential inverse correlation between the two parameters. Figure 3 displays the scatter plot of 

LOS versus FSD for the interval 1945–2011. The diagonal line is the inferred regression line, indicating an inverse correlation between the two parameters, with delayed FSD indicative of shorter LOS 

and early FSD indicative of longer LOS. Hypothesis testing9 of the slope indicates that the inferred 

regression is statistically important at the 0.1% level of significance (or cl>99.9%). Given in the 

scatter plot is the regression equation, having a coefficient of correlation r=–0.84, a coefficient of 

determination r2=0.7 (meaning that the inferred regression, based on FSD, can explain about 70% 

of the variance in LOS), and a standard error of estimate se=23 days. Also given in the figure is the 

observed 2×2 contingency table, which is determined from the median values of FSD and LOS (the 

thin vertical and horizontal lines in the scatter plot), and the result of Fisher’s exact test for 2×2 

contingency tables,10 which indicates a probability (P) of only 0.002% of obtaining the observed 

table, or one more suggestive of a departure from independence (chance). Hence, a very strong preferential association is found to exist between the two parameters, such that when FSD is less than 

(greater than) DOY=175, LOS is expected to be greater than (less than) 128 days. Because FSD for 

the year 2012 has been reported11 as May 19, 2012 (or DOY=140), one strongly suspects that LOS 

for the year 2012 will be ≥128 days from the 2× 2 contingency table and likely equal to about 173

±23 days (i.e., the ±1 se prediction interval) from the inferred regression. Hence, one surmises 

that there is about a 68% probability that the LSD for the year 2012 will occur about November 8 

±23 days, with only about a 5% chance that it will end either before about September 23, 2012 or 

after about December 24, 2012.
6

100 150 200 250

25 9

⇒ P = 0.002%

7 26

FSD (DOY)

50

100

150

200

250

LOS (Number of Days)

y = 321.847 – 1.061x

r = –0.836, r

2 = 0.699

se = 23.4, cl >99.9%

2012 FSD = 140 ⇒2012 LOS = 173.3 ± 23.4 days

 ⇒2012 LSD = 140 + 173.3 ± 23.4 days

 = 313.3 ± 23.4 days

 = November 8, 2012 ± 23 days

y

As previously noted, the cause of the lengthening of LOS is believed to be warming of the 

SST. Figure 4 displays the annual and 10-yma values of the Armagh Observatory (Northern Ireland) surface-air temperature (<AT>, fig. 4(a)) and the SST anomaly indices associated with the 

Atlantic Multidecadal Oscillation (<AMO>, fig. 4(b)), the Atlantic Meridional Mode (<AMM>, 

fig. 4(c)), and the Oceanic Niño Index (<ONI>, fig. 4(d)). Also included in figure 4 are histograms 

(fig. 4(e)) that delineate the number of El Niño months (NENM) and the number of La Niña months 

(NLNM) during each of the years spanning 1950 –2011, based on monthly values of the ONI. (The 

symbols <> about AT, AMO, AMM, and ONI simply indicate that the values are annual averages 

of the monthly parametric values).

Figure 3. The scatter plot of annual values of LOS versus FSD.
7

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

ENSO Phase

1950–2011 NENM = 202

NLNM = 209

12

9

9

6

6

3

3

0

12

NLNM NENM

Cold Warm

Oceanic Niño Index

1950–2011

–1.5

–1

–0.5

0

0.5

1

1.5

<ONI>

Atlantic Meridional Mode

1948–2011

–5

–2.5

0

2.5

5

<AMM>

mean = 0.01 °C

 sd = 0.60 °C

range = –1.19° to 1.29 °C

mean = 0.17 °C

 sd = 1.95 °C

range = –4.13° to 4.98 °C

Atlantic Multidecadal Oscillation SST Index

1945–2011

(a)

(b)

(c)

(d)

(e)

–0.5

–0.25

0

0.25

0.5

<AMO>

mean = 0.003 °C

 sd = 0.188 °C

range = –0.416° to 0.389 °C

Armagh Observatory Surface-Air Temperature

1945–2011 (54°21.2′N, 6°38.9′W)

8

8.5

9

9.5

10

10.5

11

<AT>

 mean = 9.50 °C

 sd = 0.53 °C

 range = 8.35° to 10.59 °C

Figure 4. The annual and 10-yma values of (a) <AT>, (b) <AMO>, (c) <AMM>, and (d) <ONI> 

for the interval 1945–2011, and (e) the NENM and NLNM during the interval 1950–2011. 
8

The Armagh Observatory surface-air temperature record is one of the longest available for 

study, being continuous from 1844 to the present.12–15 The observatory lies about 1 km northeast 

of the ancient city of Armagh in Northern Ireland at 54°21.2′ N. latitude and 6°38.9′ W. longitude. 

Measurements of temperature are determined daily using minimum and maximum thermometers. 

The AMO is defined as a fluctuation in the detrended SST in the North Atlantic Ocean, north of 

the equator (i.e., 0°–70° N. latitude).16–22 The AMM is part of a broader class of meridional modes 

that is characterized by an anomalous meridional SST gradient across the mean latitude of the intertropical convergence zone.23–26 The ONI is a measure of the SST anomaly in the Niño 3.4 region 

(5° N.–5° S. latitude, 120°–170° W. longitude) based on 3-mo running means of the National Oceanic 

and Atmospheric Administration’s Extended Reconstructed SST, version 3b;27 hence, it serves as 

a useful indicator for monitoring the phase of the ENSO (i.e., the occurrences of warm El Niño and 

cold La Niña events). Monthly values of AT, AMO, AMM, and ONI are readily available online.

A comparison of the 10-yma values of LOS with <AT>, <AMO>, and <AMM> bears strong 

resemblance, at least for the past two decades, with all parameters tracking upward with time. Figure 5 depicts the comparison of 10-yma values of LOS versus <AT> (fig. 5(a)), <AMO> (fig. 5(b)), 

<AMM> (fig. 5(c)), and <ONI> (fig. 5(d)). Prior to the late 1980s, the association between LOS and 

the surface-air and SST anomaly parameters appears rather weak; however, since about 1989, the 

10-yma values appear more tightly coupled, suggesting that the LOS, perhaps, is now being driven 

by warmer temperature in the North Atlantic basin, as previously suggested by Kossin.5 While the 

associations of LOS against <AT>, <AMO>, and <AMM> are strongly positive (r ≥0.97), the association of LOS against <ONI> is negative (r=–0.83). Hence, since at least about 1989, more negative (positive) <ONI>, indicative of cooling (warming) in the Niño 3.4 region, apparently is related 

to warming (cooling) and longer (shorter) LOS in the North Atlantic basin. (The arrows plotted in 

fig. 5 identify the last available 10-yma values: the year 2006. Also, the 1989–2006 values are plotted 

as filled squares, while those prior to 1989 are plotted as filled circles).
9

Figure 5. Scatter plots of LOS versus (a) <AT>, (b) <AMO>, (c) <AMM>, 

and (d) <ONI>. 

–0.25 –0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

<AMM>10-yma

<ONI>10-yma

<AMO>10-yma

<AT>10–yma

(a)

(b)

(c)

(d)

160

100

9 9.5 10 10.5

120

140

160

140

120

100

–0.25 –0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2 0.25

–2 –1.5 –1 –0.5 0 0.5 1 1.5 2

140

120

160

100

100

120

140

160

LOS10-yma LOS10-yma LOS10-yma LOS10-yma

y

1989–2006 = –242.134 + 39.144x

 r = 0.966, r

2 = 0.933

 se = 2.675, cl >99.9%

y

1989–2006 = 145.343 – 73.498x

 r = –0.832, r

2 = 0.692

 se = 5.611, cl >99.9%

y

1989–2006 = 137.482 + 81.434x

 r = 0.976, r

2 = 0.953

 se = 2.181, cl >99.9%

y

1989–2006 = 141.206 + 9.420x

 r = 0.976, r

2 = 0.953

 se = 2.198, cl >99.9%

y

1989–2006

y

1989–2006

y

1989–2006

y

1989–2006
10

Returning to figure 4(e), one finds that in the 62-yr interval 1950 –2011, there have been 

202 NENM and 209 NLNM, inferring 333 ENSO neutral months (i.e., months when the ONI was 

neither representative of El Niño nor La Niña). For convenience, one can call a year an El Niño year 

(ENY) when it has NENM ≥6 and call a year a La Niña year (LNY) when it has NLNM ≥ 6. Doing 

so, one finds that there are 18 yr classified as ENY and 18 yr classified as LNY during the 62-yr 

interval, inferring 26 ENSO neutral years (NY). On average, the DOY of FSD for an ENY, LNY, 

and NY, respectively, is about 182±38, 184±25, and 177±36. Plainly, the differences in the DOY 

of FSD for ENY, LNY, and NY are not statistically important; hence, using the DOY of FSD, one 

cannot differentiate the kind of year 2012 will be (i.e., an ENY, LNY, or NY). Similarly for LOS, 

although the average LNY appears, on average, to be about 15 days longer than the average ENY, the 

difference does not appear to be statistically important. However, the difference in the DOY of LSD 

between ENY and LNY does appear to be statistically important (at cl>95%); on average, the DOY 

of LSD is about 300±20 for an ENY and about 316±21 for an LNY, while for NY, on average, the 

DOY of LSD is about 313±27. Thus, one tends to favor the year 2012 to be a non-ENY, especially 

if the DOY for LSD >320 (i.e., after about November 15, 2012). Presently, although an El Niño is 

anticipated to start either later this year or sometime next year,4,28,29 by definition as employed in 

this study, for the year 2012 to be classified as an ENY, its onset must have occurred by July 2012, 

something that did not happen. Hence, the year 2012 must be considered non-ENY.
11

3. CONCLUSION

This study confirms the results of Kossin5 that the length of the hurricane season has increased 

and that warmer temperatures appear to be the driving force behind the lengthening. The lengthening results because both early season and late season storms have more frequently been reported 

recently. On average, the FSD of a year occurs about DOY=180.5 (about July 1), having sd=33 

and range =110–242, and the LSD about DOY=310 (about November 6), having sd=23 and range 

=263–371. Thus, on average, the mean length of season is about 130 days, having sd=42 days and 

range =47–235 days. While true, the length of season is found to be highly dependent upon when 

the FSD occurs, with the scatter plot of annual values being statistically important at the 0.1% level 

of significance, having r=–0.84 and se=23 days. Because FSD for 2012 occurred on DOY=140 

(May 19), one infers that the 2012 hurricane season likely will have a length of about 173±23 days, 

ending about DOY=313±23 (November 8 ±23 days), with only about a 5% chance of ending either 

before September 23, 2012 or after December 24, 2012. Presently, some 14 tropical cyclones have 

formed in the months of May–September 2012, with at least 2 mo remaining in the nominal hurricane season. (The reader should note that this study used the full HURDAT record for the interval 

1945–2011. As such, the possibility exists that weaker, shorter duration tropical cyclones forming 

farther from land in the open Atlantic could easily have been missed, thereby leading to an underestimate of LOS, especially for the interval prior to the routine use of satellites, which began about the 

mid-1960s.30–34 While true, it must be emphasized that the observed increase in LOS has been shown 

to begin about 1979, subsequent to the routine use of Earth-orbiting satellite imagery. Hence, the 

inferred increase appears real and is highly statistically important. A more detailed study of LOS is 

planned, one incorporating the duration, strength, and geographic region of the tropical cyclones).
12
13

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Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18

Estimating the Length of the North Atlantic Basin Hurricane Season

Robert M. Wilson

George C. Marshall Space Flight Center

Huntsville, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 47

Availability: NASA CASI (443–757–5802)

Prepared by the Science and Research Office, Science and Technology Office

M–1346

Technical Publication

NASA/TP—2012–217470

first storm day, last storm day, length of season, the 2012 hurricane season

01–10–2012

UU 28

NASA

U U U

For the interval 1945–2011, the length of the hurricane season in the North Atlantic basin averages about 130±42 days (the 

±1 standard deviation interval), having a range of 47 to 235 days. Runs-testing reveals that the annual length of season varies 

nonrandomly at the 5% level of significance. In particular, its trend, as described using 10-yr moving averages, generally has been 

upward since about 1979, increasing from about 113 to 157 days (in 2003). Based on annual values, one finds a highly statistically 

important inverse correlation at the 0.1% level of significance between the length of season and the occurrence of the first storm 

day of the season. For the 2012 hurricane season, based on the reported first storm day of May 19, 2012 (i.e., DOY=140), the 

inferred preferential regression predicts that the length of the current season likely will be about 173±23 days, suggesting that 

it will end about November 8 ±23 days, with only about a 5% chance that it will end either before about September 23, 2012 or 

after about December 24, 2012.

STI Help Desk at email: help@sti.nasa.gov

STI Help Desk at: 443–757–5802

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George C. Marshall Space Flight Center

Huntsville, Alabama 35812