1. Statistical Analysis of Sea Surface Temperature
(SST) and Hurricanes in the Atlantic Basin
Bryan Butler
2. Outline of Analysis
• Overview of the sea surface temperature analysis and connection to the
Atlantic Multidecadal Oscillation (AMO).
• View of the time series for the AMO and it’s relationship to hurricane counts.
• Transforming the series to 10-year moving average.
• Developing a model
– Diagnostics
• Forecasts of the AMO
• Using the AMO forecast to forecast hurricane counts.
• Refinements
3. Introduction
• North Atlantic sea surface temperatures for 1871 to present contain a 65 –
80 year cycle called the Atlantic Multidecadal Oscillation (AMO).
• Fluctuates between warmer and cooler phases.
• Often measured as an index relative to the normal.
• Year-to-year fluctuations reflect more volatility and the index is more
commonly shown as a 10-year moving average to smooth out the spikes.
• There is a link between the 10-year moving average of the AMO and the 10-
year average of the total number of Atlantic storms.
• Potential to refine the interaction
– Total events (hurricanes and tropical storms)
– Hurricanes only
– Large hurricanes (CAT 4, CAT 5)
– Landfall hurricanes
4. Comparison of Annual Average to Hurricane
Season Average of AMO
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1871 1876 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001
Season Avg
6. Series Properties
• Annual AMO average and the average during hurricane season (Jun – Sep)
very closely aligned.
• Has long swings away from zero and then crosses back over, persistent
cycle.
• When compared to the hurricane counts, both series move in similar
directions but contain volatility that is difficult to predict.
• Both series show that there is a relationship between past levels on future
levels at one and two year intervals.
7. Granger Tests for Causality
• Granger test is a statistical test that measures how well data in one series can be
used to help forecast another series.
– Measured at different time intervals (1 year, 2 year, 5 year, etc.) called lags.
– Example: performing a 1 lag analysis implies that over the entire series the
previous year of one series helps to predict the next year of another series.
• Tests are bi-directional with two null hypotheses, results are to reject or fail to reject.
– AMO does not help forecast the number of hurricanes (Canes)
– Number of hurricanes does not help forecast the AMO
• In all cases (1 year, 2 year, 5 year) the AMO does help forecast the number of
hurricanes.
– AMO and Hurricane landfall counts do not show granger causality.
– Ex: 2005 had most hurricanes, but below average landfall (4 vs. an avg. of 5).
– Significant for CAT4 & CAT 5 counts.
• There is feedback and at the 1 year and 2 year interval, the number of hurricanes
helps forecast the AMO.
– Series are inter-related, however the impacts of the AMO on the number of
hurricanes is the dominant relationship.
8. Transforming the Series (Using Moving Averages)
• To reduce the noise in the series and reflect the longer term impact and
cycle, the 10-year moving average is often used
– 10 year moving average for hurricanes is also used to maintain the
analysis.
• Aggregating the series does induce some other properties that need to be
taken into consideration.
• When looking at the cross correlations between the two series the
persistence and feedback are evident:
– AMO lags impact hurricane counts for up to 25 years.
– Hurricane count lags affect AMO for about 8 years.
– There is strong persistence and feedback between the 10 year moving
average of the AMO and the 10 year moving average of CAT 4 and
CAT 5 storms.
9. Comparison of AMO Index to Hurricane Counts
-0.4
-0.2
0.0
0.2
0.4
3
4
5
6
7
8
9
1880 1900 1920 1940 1960 1980 2000
AMO10 CANES10
AMOIndex
10YearMovingAverageofHurricanes
10. AMO Index and 10 Year Moving Average of CAT 4
& Cat 5 Hurricanes
-0.4
-0.2
0.0
0.2
0.4
0.0
0.5
1.0
1.5
2.0
2.5
1880 1900 1920 1940 1960 1980 2000
AMO10 AVG45
AMOIndex
MovingAvgofCAT4&5
11. Forecast of AMO Moving Average (10 Year)
Dependent Variable: AMO10
Method: Least Squares
Date: 12/21/05 Time: 10:11
Sample(adjusted): 1882 1995
Included observations: 114 after adjusting endpoints
Convergence achieved after 4 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C -0.016881 0.185720 -0.090892 0.9277
AR(1) 1.415656 0.086995 16.27286 0.0000
AR(2) -0.429409 0.087256 -4.921278 0.0000
R-squared 0.979886 Mean dependent var -0.110193
Adjusted R-squared 0.979524 S.D. dependent var 0.163233
S.E. of regression 0.023358 Akaike info criterion -4.649815
Sum squared resid 0.060560 Schwarz criterion -4.577810
Log likelihood 268.0395 F-statistic 2703.813
Durbin-Watson stat 2.191815 Prob(F-statistic) 0.000000
Inverted AR Roots .98 .44
• Model reflects 1 year and 2 year influence of past years
• High Adjusted R-Squared
• All critical variables are significant
– Constant is essentially zero
• All structure has been removed to the best ability as evidence by the D-W statistic
being close to 2.00.
• Use data to 1995, forecast to 2005 to test model performance against known data.
12. Performance of AMO Model Against Whole Series
-0.4
-0.2
0.0
0.2
0.4
1880 1900 1920 1940 1960 1980 2000 2020
AMO10F1 AMO10
13. Comparison of Forecast to Known Values of AMO
Using 1 Year Increments
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
80 85 90 95 00 05 10 15 20
AMO10F1S AMO10
15. Performance of Combined AMO and Hurricane
Model Forecast on 10 Year Moving Average
4
5
6
7
8
9
65 70 75 80 85 90 95 00 05 10 15 20
CANES10 CANES10F
16. Forecast of Moving Average of Total Number of
Events
8
10
12
14
16
65 70 75 80 85 90 95 00 05 10 15 20
EVENTS10 EVENTS10F
17. Evaluation of Models
• 2005 was a very rare year and reflects a shock to the system that cannot be
forecasted.
• The 10 year moving average of the AMO appears to follow a cycle that is
easier to forecast.
• After forecasting out the AMO, forecasts have been developed for two
additional series.
– 10 Year moving average of hurricanes.
– 10 Year moving average of all events.
• There is less precision in forecasting both hurricanes and events since the
correlation is not direct.
– Correlation is very strong and may be the most dominant factor.
– There are other variables that may impact the number of hurricanes that
are not included in the model.
18. Forecasting CAT 4 & CAT 5 Making Landfall in the
US
0.0
0.5
1.0
1.5
2.0
2.5
65 70 75 80 85 90 95 00 05 10 15 20
AVG45F7ALLS AVG45
22. Composition of FL Hurricanes
• Long run mean indicates that there are currently some imbalances.
– CAT 2 and CAT 3 are behind the long run mean.
– CAT 5 currently ahead of the long run mean.
• CAT 1 and CAT 4 storms are close to long run means.
Period
TS CAT1 CAT2 CAT3 CAT4 CAT5
All Years 2.15 2.59 5.67 4.64 6.95 19.13
1956 - 2005 1.67 2.78 16.67 10.00 7.14 8.33
1906 - 1955 2.38 3.85 7.14 5.00 4.17 4.17
1852 - 1905 2.60 1.86 3.06 2.89 17.33 #DIV/0!
FL Return (Years)
23. Composition of Gulf of Mexico (GoM)
• CAT 2 and CAT 3 storm counts appear out of balance with the long-run mean.
• Due to events of Rita and Katrina, CAT 5 return period is running ahead of the long
run average.
Period
TS CAT1 CAT2 CAT3 CAT4 CAT5
All Years 1.24 2.61 3.35 5.50 8.11 15.40
1952 - 2002 1.04 2.63 16.67 7.14 7.14 6.25
1902 - 1952 1.14 2.27 3.85 4.55 5.56 25.00
1852 - 1902 1.69 3.00 1.80 5.40 18.00 #DIV/0!
Return (Years)
24. Conclusions
• Each year approximately 5 hurricanes (of varying strength) are expected to
form in the basin.
• The average has highs and lows that is correlated to the AMO.
• Complete AMO cycle lasts approximately 50 years.
• Current forecast indicates that we are near a peak and that the AMO should
start to decrease slowly.
– This is the feedback influence of the hurricanes.
• Expect a period of increased hurricane activity due to the increased AMO
and is expected to last until approximately 2017.
• Recent activity has brought the short run (50 year cycle) of large storms
(CAT 4, CAT 5) into closer alignment with the long run average.
• Expect more activity in the CAT 2 and CAT 3 storms for both FL and the
GoM
25. Additional Work
• Improve forecasting of CAT 4 and CAT 5 storms making landfall in the US.
– Link to AMO or other index.
• Develop better forecast.
– Current models forecast moving averages which are difficult to interpret.
• Continue more detailed analyses for other areas of the US.
– Northeast
– Carolinas
