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i

NASA/TP—2014–218199

On the Relationship Between the Length

of Season and Tropical Cyclone Activity

in the North Atlantic Basin During

the Weather Satellite Era, 1960–2013

Robert M. Wilson

Marshall Space Flight Center, Huntsville, Alabama

August 2014

National Aeronautics and

Space Administration

Marshall Space Flight Center • Huntsville, Alabama 35812
ii

Available from:

NASA STI Information Desk

Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681–2199, USA

757–864–9658

This report is also available in electronic form at

<http://www.sti.nasa.gov>
iii

TABLE OF CONTENTS

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

2. RESULTS AND DISCUSSION ......................................................................................... 2

3. SUMMARY ........................................................................................................................ 13

REFERENCES ....................................................................................................................... 14
iv

LIST OF FIGURES

1. Variation of yearly (a) LOS, (b) fd(10-yma), and (c) distribution of fd(10-yma) 

for the interval 1960–2013 ......................................................................................... 3

2. Variation of yearly (a) FSD and (b) <MLCO2> for the interval 1960–2013 .............. 4

3. Scatterplots of (a) LOS versus <MLCO2> and (b) LOS versus FSD ........................ 6

4. Variation of yearly (a) D(FSD) and (b) D(<MLCO2>) for the interval 

1960–2013 ................................................................................................................. 7

5. Scatterplots of (a) FSD, (b) LSD, and (c) NTC versus LOS ...................................... 10

6. Scatterplots of (a) total ACE and (b) total NSD versus LOS .................................... 11

7. Scatterplot of NTCA versus LOS .............................................................................. 12

LIST OF TABLES

1. Summary of tropical cyclone statistics against FSD and LOS ................................... 8
v

LIST OF ABBREVIATIONS, ACRONYMS, AND DESIGNATORS

ACE accumulated cyclone energy

<ACE> mean seasonal ACE

AMO Atlantic Multidecadal Oscillation (index)

CO2 carbon dioxide

D(FSD) difference between yearly observed and predicted LOS based on FSD

D(<MLCO2>) difference between yearly observed and predicted LOS based on <MLCO2>

DOY day of year

E El Niño

ENY El Niño year

fd(10-yma) first difference of the 10-year moving average

FSD first storm day 

HISACE Highest Individual Storm Accumulated Cyclone Energy

HISPDI Highest Individual Storm Power Dissipation Index

L La Niña

<LAT> mean seasonal latitude

LISNSD longest individual storm NSD

LNY La Niña year

<LONG> mean seasonal longitude

LOS length of season

LP lowest pressure
vi

LIST OF ABBREVIATIONS, ACRONYMS, AND DESIGNATORS (Continued)

<LP> mean seasonal LP

LSD last storm day

MLCO2 Mauna Loa CO2 (index)

<MLCO2> mean seasonal Mauna Loa CO2

NH number of hurricanes

NHD number of hurricane days

NMH number of major hurricanes

NMHD number of major hurricane days

NSD number of storm days

<NSD> mean seasonal NSD

NTC number of tropical cyclones

NTCA net tropical cyclone activity

NUSLFH number of U.S. land-falling hurricanes

NY neutral year

ONI Oceanic Niño Index

PDI Power Dissipation Index

<PDI> mean seasonal PDI

PWS peak wind speed

<PWS> mean seasonal PWS

U.S. United States
vii

NOMENCLATURE

a y-intercept

b slope

cl confidence level

na number above median

nb number below median

nra number of positive runs

P probability

r coefficient of correlation

r2 coefficient of determination

sd standard deviation 

se standard error of estimate

t t statistic for independent samples

x independent variable

y dependent variable

z normal deviate for the sample results
viii
1

TECHNICAL PUBLICATION

ON THE RELATIONSHIP BETWEEN THE LENGTH OF SEASON 

AND TROPICAL CYCLONE ACTIVITY IN THE NORTH ATLANTIC BASIN 

DURING THE WEATHER SATELLITE ERA, 1960–2013

1. INTRODUCTION

Officially, the North Atlantic basin tropical cyclone season runs from June 1 through November 30 of each year. During this 183-day interval, the vast majority of tropical cyclone onsets are 

found to occur. For example, in a study of the 715 tropical cyclones that occurred in the North 

Atlantic basin during the interval 1945–2010, it was found that about 97% of them had their onsets 

during the conventional hurricane season, with the bulk (78%) having had onset during the late 

summer-early fall months of August, September, and October and with none having had onset in 

the month of March.1 For the 2014 hurricane season, it already has had the onset of its first named 

storm on July 1 (day of year (DOY) 182), Arthur, which formed off the east coast of Florida, rapidly 

growing into a category-2 hurricane with peak 1-minute sustained wind speed of about 90 kt and 

striking the coast of North Carolina as a category-2 hurricane on July 3. Arthur is the first hurricane 

larger than category-1 to strike the United States (U.S.) since the year 2008 when Ike struck Texas as 

a category-2 hurricane and there has not been a major hurricane (category-3 or larger) to strike the 

U.S. since Wilma struck Florida as a category-3 hurricane in 2005. Only two category-1 hurricanes 

struck the U.S. in the year 2012 (Isaac and Sandy, striking Louisiana and New York, respectively) 

and there were no U.S. land-falling hurricanes in 2013 (also true for the years 1962, 1973, 1978, 1981, 

1982, 1990, 1994, 2000, 2001, 2006, 2009, and 2010).2

In recent years it has been argued that the length of season (LOS), determined as the inclusive 

elapsed time between the first storm day (FSD) and the last storm day (LSD) of the yearly hurricane 

season (i.e., when peak 1-minute sustained wind speed of at least 34 kt occurred and the tropical 

cyclone was not classified as ‘extratropical’), has increased in length with the lengthening believed 

to be due to the FSD occurring sooner and the LSD occurring later and with both being related 

to global warming.3–5 In this study, the relationship between the LOS and tropical cyclone activity 

and climate is examined for the weather satellite era, 1960–2013.6–8 Estimates are also given for the 

LOS and LSD, as well as for the expected number of tropical cyclones (NTC), the total number of 

storm days (NSD), the total accumulated cyclone energy (ACE), and the net tropical cyclone activity 

(NTCA) index for the 2014 hurricane season.
2

2. RESULTS AND DISCUSSION

Figure 1 displays the yearly variation of the (a) LOS, (b) first-difference of the 10-year moving average (fd(10-yma)) of the LOS, and (c) distribution of the fd(10-yma) values for the weather 

satellite era, 1960–2013. In figure 1(a), the thin jagged line is the yearly seasonal value of the LOS; 

the thick smoothed line is the 10-yma of the LOS; and the letters E and L simply identify those years 

when the Oceanic Niño Index (ONI) was of value 0.5 oC or higher and –0.5 oC or lower, respectively, 

for at least 6 months of the year, used here as an indicator for classifying the year as being either an 

El Niño year (ENY) or a La Niña year (LNY). Years not identified with an E or L represent El Niño 

neutral years (NYs). The overall mean for the LOS is 133 days, having a standard deviation (sd) 

of 42 days. The longest LOS measures 235 days in 2003, an NY, while the shortest LOS measures 

47 days in 1983, an ENY. Based on the E and L classification as employed in this study, 14 years are 

classified as ENY, 15 years as LNY, and 25 years as NY. On average, the 14 ENYs have a mean LOS 

of 110 days (sd=41 days); the 15 LNYs have a mean LOS of 137 days (sd=25 days); and the 25 NYs 

have a mean of 143 days (sd=48 days). The difference in the means between those years classified as 

ENY and LNY is found to be statistically important (t=–2.16, confidence level cl>95%). Hence, if 

a year is predicted to be an ENY, one probably should expect its LOS to be shorter than the mean LOS 

(=133 days), whereas if a year is predicted to be a non-ENY, one probably should expect its LOS to 

be ≥133 days. For the 14 ENYs, 12 of the 14 years (86%) have had LOS <133 days, with the 2 years 

having LOS ≥133 days being the years 1972 (163 days) and 1997 (139 days). Twenty-five of the forty 

years (63%) not being classified as ENY have LOS ≥133 days.

Concerning the yearly variation of the LOS as described by its 10-yma, one finds that it 

appears to be trending upwards since about 1987, increasing from 118 days in 1987 to 157 days 

in 2008 (the last year having a 10-yma entry). Furthermore, a comparison of the two subintervals 

1960–1994 and 1995–2013 indicates that the mean LOS has increased in length from about 122 days 

during the earlier subinterval to about 152 days in the more recent subinterval, with the difference 

in the means being statistically important (t=–2.60, cl>98%). Hence, the more recent subinterval 

is found to have an LOS about 30 days longer, on average, than the earlier subinterval. For the year 

2013, its LOS measured 186 days. (The division of the overall interval 1960–2013 into two subintervals is predicated on the observation that the more recent subinterval is associated with the return 

of the warm phase as measured by the Atlantic Multidecadal Oscillation (AMO) index, a descriptor 

for the Atlantic Meridional Overturning Circulation, a density-driven, global circulation pattern of 

about 65–70 years in length that involves the movement of warm, salty equatorial waters to higher 

latitudes and the subsequent cooling and sinking of those waters into the deep ocean.9–14)
3

1960 1970 1980 1990 2000 2010 2020

Year

50

0

(a)

(b) (c) fd(10-yma)

100

150

200

250

–5

0

5

E

E

L L

L

L

L

L

L

L

L

L

L

L

L

L L

E

E

E E

E

E

E

E

E

E

E

E

mean=133 days

sd=42 days

1960–1994: mean = 122 

 sd = 39 

1995–2013: mean = 152 

 sd = 43

⇒t = –2.60

cl >98%

ENY (14) ⇒ LOS=110 (41) days

LNY (15) ⇒ LOS=137 (25) days

NY (25) ⇒ LOS=143 (48) days

1960 1970 1980 1990 2000 2010 –5

5

0

Number

10

0 5

Year

fd (±2 )⇒ LOS(10-yma)=157±2

 ⇒ LOS(2014)=176±40 days

fd(10-yma) LOS (days)

F1

30

43 = 70%

Figure 1. Variation of yearly (a) LOS, (b) fd(10-yma), and (c) distribution of fd(10-yma) 

for the interval 1960–2013.

In figure 1, (b) and (c), one observes that the fd(10-yma) values of the LOS has varied between 

fd(10-yma)=–5 and 7, having a central spread of about 0±2 that captures 30 of the 43 yearly 

fd(10-yma) values (70%). Hence, one expects the next fd(10-yma) value for the year 2009 likely to 

be about 157±2 days, which suggests that the LOS for the year 2014 should be expected to be about 

176±40days, or LOS(2014) ≥ 136 days. Only 3 of the 43 years (7%) have had fd(10-yma) ≤ –3. Thus, 

one expects the LSD for the 2014 hurricane season to occur no earlier than DOY 318, or about 

November 14, 2014, based on the distribution of fd(10-yma) values. However, if fd(10-yma)=–3 for 

2009, then the LOS for 2014 equals 176±60 days, or LOS(2014) ≥ 116 days and the LSD would occur 

no earlier than DOY 298, or about October 25, 2014.

Figure 2 depicts the yearly variation of (a) FSD and (b) the Mauna Loa CO2 (<MLCO2>) 

index for the overall interval 1960–2013. These particular parameters have previously been shown to 

have some predictive ability regarding determination of the LOS.4,5,7,8 In figure 2(a), the thin jagged 

line is the yearly seasonal FSD; the thick smoothed line is the 10-yma of the FSD; and the letters 

E and L have the same meanings as in figure 1(a). The overall mean of the FSD is DOY 180 (about 

June 29) and the sd=33 days. The latest FSD occurred in 1967 (DOY 242), an NY, and in 1977 (DOY 

242), an ENY, while the earliest FSD occurred in 2003 (DOY 110), an NY. On average, the years classified as ENY have an FSD occurring about DOY 190 (about July 9), while those years classified as 

LNY or NY have an FSD occurring about DOY 180 (about June 29) or DOY 174 (about June 23), 
4

1960 1970 1980 1990 2000 2010 2020

(a) Year

(b)

100

150

200

250

350

300

400

E

E

L

L

L

L

L

L L

L

L

L

L

L

L

L

L

E

E

E

E

E

E

E

E

E

E

E E

mean = 180 (DOY)

 sd = 33 days

1960 1970 1980 1990 2000 2010 2020

Year

<MLCO2> (ppm) FSD (DOY)

F2

ENY (14) ⇒ FSD (DOY) = 190 (38)

LNY (15) ⇒ FSD (DOY) = 180 (24)

NY (25) ⇒ FSD (DOY) = 174 (35)

396.48

316.91

1960–1994: mean = 185

 sd = 34

1995–2013: mean = 170

 sd = 31

⇒t = 1.60

cl <90%

Figure 2. Variation of yearly (a) FSD and (b) <MLCO2> for the interval 1960–2013.

respectively. Statistically speaking, the difference in the means between ENY and LNY is not statistically important (t=0.85, cl<90%). Also, the difference between the means for the two subintervals 

1960–1994 and 1995–2013 is found not to be statistically important (t=1.60, cl<90%). Hence, while 

the FSD for the more recent subinterval is about 15 days, on average, earlier than that for the earlier 

subinterval, the difference is not statistically meaningful. Also, the mere observation that the FSD 

occurs either later or earlier than the mean provides no definitive information for classifying the 

year as ENY, LNY, or NY, although 25 of the 30 years (83%) having FSD <DOY 180 are noted to 

be classified as non-ENY. (Of the 24 years having FSD≥DOY 180, 9 years were ENY, 7 years were 

LNY, and 8 years were NY; of the 30 years having FSD<DOY 180, 5 years were ENY, 8years were 

LNY, and 17 years were NY.)

Based on the distribution of the fd(10-yma) values of FSD (not shown), one finds that 27 of 

43 years (63%) had fd(10-yma)=0±2 and 36 of 43 years (84%) had fd(10-yma)=0±3, suggesting 

that the 10-yma value of FSD for 2009 should be about DOY 167±2 or 3, respectively, and that the 

FSD for the year 2014 should be about DOY 169±40 or 60, respectively. Arthur, the first named 

storm of the 2014 hurricane season, had its FSD on July 1 (DOY 182), thereby setting the 10-yma 

value of FSD for 2009 to be DOY 168.

Figure 2(b) shows the yearly variation of the <MLCO2>, which is observed to be continually rising from year to year. It measured 316.91 ppm in 1960 and 396.48 ppm in 2013, suggesting 

an average rate of increase in the <MLCO2> of about 1.5 ppm yr–1. However, the rate of increase 

actually has been higher of late than earlier, being about 1.98 ppm yr–1 since 1995 as compared to 
5

about 1.25 ppm yr–1 between 1960 and 1995 (a rate of increase about 58% faster since 1995 than 

before 1995). Hence, one expects the <MLCO2> for 2014 to measure about 398.46 ppm and to 

exceed 400 ppm in 2015. (The Mauna Loa CO2 index is a measure of the amount of atmospheric 

concentration of CO2, as determined by the Mauna Loa Observatory in Hawaii, located in a barren 

lava field of an active volcano at an altitude of 3,397 m above mean sea level.15–21)

Figure 3 depicts the scatterplots of LOS versus (a) <MLCO2> and (b) FSD. From figure 3(a), 

one finds that the LOS is inferred to be directly related to the <MLCO2> as expressed by the linear 

regression y=–76.959+0.598x, having a coefficient of correlation r=0.338, a coefficient of determination r2=0.114 (meaning that about 11.4% of the variance in the LOS can be explained by the 

variation in the <MLCO2> alone), a standard error of estimate se=40 days, and cl>98%. Based 

on Fisher’s exact test for 2×2 contingency tables (where the vertical and horizontal lines in the scatterplot represent the parametric medians), the probability P of obtaining the observed result, or one 

more suggestive of a departure from independence (chance), is P=13.8%. Since the expected value 

of the <MLCO2> for 2014 will be greater than the median <MLCO2> value (348.28 ppm), based 

on the overall interval 1960–2013), one expects the LOS for 2014 likely to be greater than the median 

value for the LOS (131 days). Of the 27 years when the <MLCO2> exceeded 348.28 ppm, 16 years 

had LOS≥ 131 days (59%). Presuming <MLCO2>=398.46 ppm for the year 2014, one infers (from 

the regression) LOS=161±40 days (the ±1 standard error of estimate se prediction interval), or 

LOS≥121 days. (In this scatterplot and all succeeding scatterplots, the years marking the extremes 

for the parameters are identified.)

From figure 3(b), one finds that the LOS is inferred to be inversely related to the FSD as 

given by the linear expression y=321.587– 1.052x, having r=–0.828, r2=0.686, se=24 days, and 

cl>99.9%. Furthermore, based on Fisher’s exact test for 2×2 contingency tables, one finds that the 

probability P of obtaining the observed result, or one more suggestive of a departure from independence, is P=0.045%. Because the FSD is now known for the year 2014, one finds from Fisher’s exact 

test that the LOS is about 3 times more likely to be <131 days (and highly likely to be <167 days) than 

≥131 days. From the regression equation, one infers that LOS=130±24 days (the ±1 se prediction 

interval), or LOS <154 days, for the year 2014 (i.e., the yearly hurricane season for the year 2014 is 

expected to end before December 2).
6

300

100 150

2003

1967

1977 1983

Arthur (2014)

200 250

350 400

(a)

(b)

50

1960

1983

2013

y

2003

0

100

150

200

250

<MLCO2> (ppm)

FSD (DOY)

LOS (days)

50

0

100

150

200

250

LOS (days)

F3

11

11

16

16

⇒ P = 13.8%

Assuming <MLCO2> = 398.46 ppm (2014)

⇒ LOS = 161 ± 40 days

y = –76.959 + 0.598x

r = 0.338, r 2 = 0.114

se = 39.956, cl > 98%

20

20

7

7

⇒ P = 0.045%

y = 321.587 – 1.052x

r = –0.828, r 2 = 0.686

se = 23.929, cl > 99.9%

Arthur formed on July 1, 2014 (DOY = 182)

⇒ LOS = 130 ± 24 days

y

Figure 3. Scatterplots of (a) LOS versus <MLCO2> and (b) LOS versus FSD.
7

Figure 4 shows the yearly variation of (a) the difference (observed minus expected) LOS, 

based on the linear fit of LOS versus FSD, D(FSD) and (b) the difference LOS, based on the linear 

fit of LOS versus <MLCO2>, D(<MLCO2>). Runs-testing yields the normal deviate for the sample 

results z=1.06 and 0.02, respectively, meaning that the differences appear to be distributed randomly. 

Based on FSD, 16 years (30%) have had D(FSD) within ±10 days, 33 years (61%) have had D(FSD) 

within ±20 days, and 45 years (83%) have had D(FSD) within ±30 days. Based on <MLCO2>, 

12 years (22%) have had D(<MLCO2>) within ±10 days, 19 years (35%) have had D(<MLCO2>) 

within ±20 days, and 30 years (56%) have had D(<MLCO2>) within ±30 days. Obviously, knowledge of the FSD for a hurricane season provides the best indicator as to how long one should anticipate the hurricane season to last. (In figure 4, na refers to the number of differences above zero, nb

refers to the number of differences below zero, and nra refers to the number of positive-valued runs.)

60

0

–60

90

0

–90

1960 1970 1980 1990 2000 2010 2020

1960 1970 1980 1990 2000 2010 2020

Year

Year

F4

D(<MLCO2>) D(FSD)

(a)

(b)

na = 27

nb = 27

nra = 16

⇒z = 1.06

na = 29

nb = 25

nra = 14

⇒z= 0.02

Figure 4. Variation of yearly (a) D(FSD) and (b) D(<MLCO2>) for the interval 1960–2013.
8

Table 1 gives the statistics (a, b, r, r2, se, and cl, where a is the y-intercept and b is the slope) 

using FSD and LOS as the independent variables for the prediction of specific tropical cyclone 

parametric values. The listing of parameters,7,8 in addition to those called out in the Introduction, 

includes NH (number of hurricanes), NMH (number of major hurricanes), NUSLFH (number of 

U.S. land-falling hurricanes), <LAT> (mean seasonal latitude), <LONG> (mean seasonal longitude, 

PWS (peak wind speed), <PWS> (mean seasonal PWS), LP (lowest pressure), <LP> (mean seasonal 

LP), <ACE> (mean seasonal ACE), HISACE (highest individual storm ACE), <PDI> (mean seasonal power dissipation index), total PDI, HISPDI (highest individual storm PDI), <NSD> (means 

seasonal NSD), LISNSD (longest individual storm NSD), total NHD (total number of hurricane 

days), and total NMHD (total number of major hurricane days). When the inferred correlation has 

cl>95% it is marked with * and when the inferred correlation has cl>98% it is marked **. Examination of the table reveals that the only correlation involving FSD to be marked * or ** is the one 

between LOS and FSD. Regarding the correlations against LOS, those marked * or ** include FSD, 

LSD, NTC, NH, total ACE, total PDI, total NSD, and NTCA.

Table 1. Summary of tropical cyclone statistics against FSD and LOS.

FSD LOS

Parameter a b r r 2 se cl a b r r 2 se cl

FSD – – – – – – 266.031 –0.652 –0.828 0.686 19.009 >99.9%**

LSD 320.587 –0.052 –0.073 0.005 23.528 <90% 265.031 0.348 0.620 0.384 19.158 >99.9%**

LOS 321.587 –1.052 –0.828 0.686 23.768 >99.9%** – – – – – –

NTC 16.032 –0.026 –0.190 0.036 4.517 <90% 4.851 0.049 0.462 0.213 4.116 >99.9%**

NH 6.834 –0.004 –0.044 0.002 2.861 <90% 3.483 0.020 0.308 0.095 2.711 >95%*

NMH 2.907 –0.003 –0.046 0.002 1.926 <90% 0.973 0.011 0.253 0.064 1.827 >90%

NUSLFH 1.833 –0.002 –0.048 0.002 1.486 <90% 0.258 0.009 0.254 0.065 1.449 >90%

<LAT> 24.147 –0.009 –0.090 0.008 3.359 <90% 22.645 –0.001 –0.010 – 3.432 <90%

<LONG> 67.954 –0.025 –0.144 0.021 5.740 <90% 63.740 –0.002 –0.016 – 5.728 <90%

PWS 107.174 0.095 0.145 0.021 21.818 <90% 119.840 0.033 0.065 0.004 22.091 <90%

<PWS> 67.373 0.031 0.119 0.014 8.596 <90% 72.769 0.001 0.006 – 8.837 <90%

LP 944.825 –0.043 –0.065 0.004 23.580 <90% 949.501 –0.093 –0.179 0.032 21.609 <90%

<LP> 983.629 –0.016 –0.069 0.005 7.934 <90% 981.806 –0.008 –0.044 0.002 8.471 <90%

<ACE> 7.740 0.005 0.043 0.002 3.687 <90% 7.792 0.006 0.070 0.005 3.743 <90%

Total ACE 123.257 –0.127 –0.071 0.005 59.607 <90% 40.092 0.456 0.326 0.106 56.427 >98%**

HISACE 37.208 –0.035 –0.073 0.005 15.222 <90% 22.010 0.067 0.176 0.031 16.007 <90%

<PDI> 6.191 0.004 0.036 0.001 3.946 <90% 5.986 0.007 0.079 0.006 3.933 <90%

Total PDI 98.214 –0.091 –0.054 0.003 56.166 <90% 28.755 0.401 0.304 0.092 53.559 >95%*

HISPDI 36.174 –0.030 –0.049 0.002 20.356 <90% 20.386 0.079 0.165 0.027 20.045 <90%

<NSD> 5.104 –0.001 –0.022 0.001 1.391 <90% 4.544 0.003 0.094 0.009 1.354 <90%

LISNSD 12.481 –0.004 –0.036 0.001 3.770 <90% 10.650 0.008 0.095 0.009 3.840 <90%

Total NSD 80.850 –0.127 –0.130 0.017 32.547 <90% 24.522 0.254 0.330 0.109 30.839 >98%**

Total NHD 23.054 0.004 0.008 – 14.701 <90% 13.714 0.075 0.218 0.048 14.449 <90%

Total NMHD 7.025 –0.008 –0.046 0.002 5.880 <90% 1.223 0.033 0.238 0.057 5.712 >90%

NTCA 135.062 –0.142 –0.078 0.006 61.109 <90% 47.280 0.470 0.328 0.107 57.901 >98%**

 * Means inferred correlation is statistically significant at cl >95%.

** Means inferred correlation is statistically significant at cl >98%.
9

Figure 5 depicts the scatterplots of (a) FSD, (b) LSD, and (c) NTC versus LOS. Figure 5(a) 

is simply a replot of figure 3(b), but now using LOS as the independent variable rather than FSD. 

Clearly, the two parameters are highly correlated (inversely). If one assumes an LOS(2014)=131 

days (the median), one infers that the FSD(2014) should be about DOY 181±19 days, or that it 

would likely occur no earlier than about DOY 162 (about June 11) and no later than about DOY 

200 (about July 19). In actuality, the FSD for the 2014 season is now known to have occurred on 

DOY 182 (July 1).

In figure 5(b), assuming LOS(2014)=131 days, one infers that the LSD(2014) should be 

about DOY 311 (November 7)±19 days, or that it likely will occur no earlier than DOY 292 (October 19) and no later than DOY 330 (November 26). Should the actual LOS(2014) be <131 days, this 

would tend to make the LSD(2014)<DOY 310, while LOS(2014)>131 days would tend to make 

LSD(2014)>DOY 310.

In figure 5(c), assuming LOS(2014)=131 days, one infers that the NTC(2014) should be 

about 11±4, which is essentially the long-term average for the 1960–2013 interval. Based on Poisson statistics, it has been shown7 that the probability of obtaining NTC(2014)=11±4 is about 83%. 

Should the year turn out to be classified as ENY, the probability of obtaining NTC(2014)=9±2 

is about 60%. On the other hand, if the year 2014 turns out to be classified as non-ENY, the probability of obtaining NTC(2014)=13±2 is about 60%. It has also been shown8 (1) that the NTC is 

closely related to the yearly <AMO> index, such that it is about 3 times more likely that the NTC≥11 

when the <AMO> is in its warm (positive) phase, which it now is and has been since about 1995 and 

should remain so for at least another decade or more, and (2) that the NTC is strongly related to the 

<MLCO2>, such that the NTC ≥11 is more than twice as likely when the <MLCO2>≥348.28 ppm, 

which it now is and has been since 1987. (The <MLCO2> is expected to measure about 398.46 ppm 

for the year 2014.)
10

1977 1967

1983

1983

1983

1960

2005

30

25

20

15

10

5

0

2003

2003

y

y

y

Arthur (2014)

250

200

150

100

20

20

7

7

⇒ P = 0.045%

⇒ P = 1.4%

12

9

18

15

⇒ P = 8.5%

y = 266.031 – 0.652x

r = –0.828, r 2 = 0.686

se = 19.009, cl > 99.9%

Assuming LOS(2014) = 131 days (median)

⇒ FSD(2014) = 181 (DOY) ± 19 days

y = 265.031 + 0.348x

r = 0.620, r 2 = 0.384

se = 19.158, cl > 99.9%

Assuming LOS(2014) = 131 days (median)

⇒ LSD(2014) = 311 (DOY) ± 19 days

y = 4.851 + 0.049x

r = 0.462, r 2 = 0.213

se = 4.116, cl > 99.9%

Assuming LOS(2014) = 131 days (median)

⇒ NTC(2014) = 11 ± 4

FSD

(a)

(b)

(c)

2003

LOS

F5

0 50 100 150 200 250

2005

400

350

300

250

LSD NTC

8

8

19

19

Figure 5. Scatterplots of (a) FSD, (b) LSD, and (c) NTC versus LOS.
11

Figure 6 shows the scatterplots of (a) total ACE and (b) total NSD versus LOS. Again, 

assuming an LOS(2014)=131 days, one infers that the total ACE(2014) should be about 99.8±56 

(in units of 104 kt2) and the total NSD(2014) should be about 58±31 days. Based on the <AMO> 

being in the warm (positive) phase, one infers that the total ACE(2014) and total NSD(2014) are 

more than twice as likely to be ≥88 and ≥52 days, respectively. Based on the expected <MLCO2> 

value for the year 2014 (398.46 ppm), one expects the total NSD(2014)=87±29 days, or ≥58 days.

2003

2005

1983

300

250

200

150

100

50

0

⇒ P = 20.7%

y = 40.092 + 0.456x

r = 0.326, r 2 = 0.106

se = 56.427, cl > 98%

Assuming LOS(2014) = 131 days (median)

⇒ Total ACE(2014) = 99.8 ± 56

(a)

LOS

0 50 100 150 200 250

Total ACE

1983

2010

2003

200

150

100

50

0

⇒ P = 29.3%

y = 24.522 + 0.254x

r = 0.330, r 2 = 0.109

se = 30.839, cl > 98%

Assuming LOS(2014) = 131 days (median)

⇒ Total NSD(2014) = 58 ± 31 days

(b)Total NSD

F6

y

y

12

11

16

15

12

12

15

15

Figure 6. Scatterplots of (a) total ACE and (b) total NSD versus LOS.
12

Figure 7 displays the scatterplot of NTCA versus LOS. Assuming LOS(2014)=131 days, the 

NTCA(2014) is estimated to be about 108.9%±57.9%, or ≥51%. Based on <AMO> being in the 

warm (positive) phase, one infers that the NTCA(2014) is more than twice as likely to be ≥98.8%.

2003

2005

1983

300

250

200

150

100

50

0

⇒ P = 13.8%

y = 47.280 + 0.470x

r = 0.328, r 2 = 0.107

se = 57.901, cl > 98%

Assuming LOS(2014) = 131 days (median)

⇒ NTCA(2014) = 108.9 ± 57.9

NTCA

F7

y

LOS

0 50 100 150 200 250

11

11

16

16

Figure 7. Scatterplot of NTCA versus LOS.
13

3. SUMMARY

The LOS of the yearly hurricane season is reckoned inclusively from FSD to LSD, averaging 

about 133 days in length and spanning 47 (1983) to 235 (2003) days during the weather satellite era 

(1960–2013). During the subinterval 1960–1994, the LOS averaged about 122 days, while during the 

more recent subinterval 1995–2013, it has averaged about 152 days. Incorporating the phasing of 

the El Niño-Southern Oscillation, the LOS is found to usually be somewhat shorter during an ENY 

(about 110 days, on average), while being somewhat longer during a non-ENY (about 141 days, on 

average). The LOS is found to correlate strongly against both the <MLCO2> and FSD, especially, 

the latter. For the 2014 North Atlantic basin hurricane season, the increased level of CO2 suggests 

that the LOS might be longer than 133 days (as does the current continuing warm phase of the AMO, 

which began about 1995). In contrast, because the FSD for the 2014 hurricane season occurred on 

July 1 (DOY 182), this suggests that the LOS for the 2014 hurricane season likely will be less than 

133 days (the mean; actually it is likely to be less than the median LOS, which equals 131 days). The 

inferred regression of LOS against FSD (having r=–0.828, se=24 days) suggests that the LOS for 

the 2014 hurricane season likely will be about 130±24 days, inferring that the LSD will come no 

earlier than October 15 (DOY 288) and no later than December 2 (DOY 336).

Presently, the Climate Prediction Center and the International Research Institute for Climate 

and Society are predicting the chance for El Niño forming during the Northern Hemisphere this 

summer to be about 70% and to be about 80% during the fall and early winter.22 If the months of 

July–December each have ONI monthly values of 0.5 oC or more, then following the definition of 

ENY as employed in this study, the year 2014 will be classified as an ENY and would be expected to 

have LOS<133 days (about 110±40 days, inferring LSD no earlier than September 9, or DOY 252, 

and no later than November 28, or DOY 332). (The ONI monthly values for January–May 2014 are 

–0.6, –0.6, –0.5, –0.1, and 0.2 oC, respectively.23)

Assuming that the year 2014 will have LOS<133 days and that it will be classified as ENY, 

one expects LSD before DOY 299±18 days, or before November 13 and after October 8. Also, one 

expects NTC=11±4, probably <11; total ACE=101±56, probably <101; NSD=58±30 days, probably <58 days; and NTCA=110±58%, probably <110%. 
14

REFERENCES

 1. Wilson, R.M.: “Statistical Aspects of Tropical Cyclone Activity in the North Atlantic Basin, 1945-

2010,” NASA/TP–2012–217465, NASA Marshall Space Flight Center, Huntsville, AL, 272 pp., 

August 2012.

 2. Landsea, C.W.: “Chronological List of All Hurricanes which Affected the Continental UnitedStates,” <http://www.aoml.noaa.gov/hrd/tcfaq/E23.html>, July 2014.

 3. Kossin, J.P.: “Is the North Atlantic hurricane season getting longer?” Geophys. Res. Lett., Vol. 35, 

No. 23, 3 pp., doi:10.1029/2008GL036012, December 2008.

 4. Wilson, R.M.: “Estimating the Length of the North Atlantic Basin Hurricane Season,” NASA/

TP—2012–217470, NASA Marshall Space Flight Center, Huntsville, AL, 28 pp., October 2012.

 5. Wilson, R.M.: “On the Current Trend of Tropical Cyclone Activity and the Lengthening of the Tropical Cyclone Season in the North Atlantic Basin,” NASA/TP—2013–217486, NASA Marshall Space 

Flight Center, Huntsville, AL, 60 pp., July 2013.

 6. Davis, G.: “History of the NOAA Satellite Program,” <http://www.osd.noaa.gov/download/

JRS012504-GD.pdf>, 28 pp., June 2011.

 7. Wilson, R.M.: “Statistical Aspects of North Atlantic Basin Tropical Cyclones during the Weather 

Satellite Era, 1960–2013: Part 1,” NASA/TP—2014–218196, NASA Marshall Space Flight Center, 

Huntsville, AL, 82 pp., July 2014.

 8. Wilson, R.M.: “Statistical Aspects of North Atlantic Basin Tropical Cyclones during the Weather 

Satellite Era, 1960–2013: Part 2,” NASA/TP—2014–218198, NASA Marshall Space Flight Center, 

Huntsville, AL, 90 pp., July 2014.

 9. Schlesinger, M.E.; and Ramankutty, N.: “An oscillation in the global climate system of period 65-70 

years,” Nature, Vol. 367, pp. 723–726, doi:10.1038/367723a0, February 1994.

10. Dijkstra, H.A.; Raa, L. te; Schmeits, M.J.; and Gerrits, J.: “On the physics of the Atlantic Multidecadal Oscillation,” Ocean Dyn., Vol. 56, No. 1, pp. 36–50, doi:10.1007/s10236-005-0043-0, May 

2006.

11. Grossmann, I.; and Klotzbach, P.J.: “A review of North Atlantic modes of natural variability and 

their driving mechanisms,” J. Geophys. Res., Vol. 114, No. D24, p. 107, doi:10.1029/

2009JD012728, 27 December 2009.
15

12. Broecker, W.S.: “The Great Ocean Conveyor,” Oceanography, Vol. 4, No. 2, pp. 79–89, 

doi:10.1063/1.41925, 1991.

13. AMO unsmoothed from the Kaplan SST V2, Calculated at NOAA/ESRL/PSD1, <www.esrl.

noaa.gov/psd/data/correlation/amon.us.long.data>, June 2014.

14. Atlantic meridional overturning circulation, The Encyclopedia of Earth, <www.eoearth.org/

view/article/150290/>, May 31, 2012.

15. Keeling, C.D.: “The Concentration and Isotropic Abundances of Carbon Dioxide in the Atmosphere,” Tellus, Vol. 12, No. 2, pp. 200–203, doi:10.1111/j.2153-3490.1960.tb01300.x, May 1960.

16. Bolin, B.; and Keeling, C.D.: “Large-scale atmospheric mixing as deduced from seasonal and meridional variations of carbon dioxide,” J. Geophys. Res., Vol. 68, No. 13, pp. 3899–3920, doi:10.1029/

JZ068i013p03899, 1 July 1963.

17. Pales, J.C.; and Keeling, C.D.: “The concentration of atmospheric carbon dioxide in Hawaii,” 

J. Geophys. Res., Vol. 70, No. 24, pp. 6053–6076, doi:10.1029/JZ070i024p06053, 15 December 

1965.

18. Bolin, B.; and Bischof, W.: “Variations of the carbon dioxide content of the atmosphere in the northern hemisphere,” Tellus, Vol. 22, No. 4, pp. 431–442, doi:10.1111/j.2153-3490.1970.tb00508.x, 

August 1970.

19. Bacastow, R.B.; Keeling, C.D.; and Whorf, T.P.: “Seasonal amplitude increase in atmospheric 

CO2 concentration at Mauna Loa, Hawaii, 1959–1982,” J. Geophys. Res.-Atmos., Vol. 90, No. D6, 

pp. 10,529–10,540, doi:10.1029/JD090iD06p10529, 20 October 1985.

20. Thoning, K.W.; Tans, P.P.; and Komhyr, W.D.: “Atmospheric carbon dioxide at Mauna Loa Observatory: 2. Analysis of the NOAA GMCC data, 1974–1985,” J. Geophys. Res.-Atmos., Vol. 94, No. D6, 

pp. 8549–8565, doi:10.1029/JD094iD06p08549, 20 June 1989.

21. NOAA ESRL Data, <ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_annmean_mlo.txt>, July 

7, 2014.

22. El Niño/Southern Oscillation (ENSO) Diagnostic Discussion, National Weather Service, 

Climate Prediction Center, <http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/enso

_advisory/>, August 9, 2012.

23. Cold & Warm Episodes by Season, National Weather Service, Climate Prediction Center,

<http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml>, July

2014.
16

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On the Relationship Between the Length of Season and Tropical

Cyclone Activity in the North Atlantic Basin During the Weather 

Satellite Era, 1960–2013

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 STI Information Desk (757–864–9658)

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

M–1388

Technical Publication

NASA/TP—2014–218199

tropical cyclones, North Atlantic basin, 2014 tropical cyclone season, climate

01–08–2014

UU 28

NASA

U U U

During the weather satellite era (1960–2013), the yearly length of the hurricane season has increased by about 30 days, from 122 days, 

on average, during the subinterval 1960–1994 to 152 days, on average, during the subinterval 1995–2013. For the overall interval 

1960–2013, the mean length of season is 133 days, having a range of 47 days (1983) to 235 days (2003) and standard deviation of 

42 days, with El Niño years tending to be of shorter average length (110 days, on average) and non-El Niño years tending to be of longer 

average length (141 days, on average). The length of season is inversely correlated with the occurrence of the first storm day, such that 

when the first storm day occurs before (after) day of year (DOY) 177 (about June 26, the median), the length of season is about 3 times 

more likely to be longer (shorter) than 131 days (the median). For the 2014 hurricane season, the first storm day occurred on DOY 182 

(July 1), inferring that the 2014 length of season likely will be about 130±24 days (the ±1 standard error of estimate prediction interval) 

and that the last storm day should occur after DOY 288 (October 15) and before DOY 336 (December 2). 

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

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