Submitted: June 25, 2001 
Revised: August 9, 2001 
Index Terms: U.S. hurricanes, ENSO, NAO,
teleconnection, Poisson regression
Hurricane variability on the seasonal to decadal time scales impact nature and society. Current seasonal climate forecasts of hurricanes over the Atlantic derive skill from a linkage between the frequency of tropical cyclones and the El NiñoSouthern oscillation (ENSO) [Gray, 1984]. Under the El Niño (or warm) phase of the oscillation, atmospheric convection over the western equatorial Pacific shifts eastward along with warm seasurface temperatures (SSTs). Increased convection over the central equatorial Pacific creates stronger upperlevel winds (200 hPa) and greater vertical shearing over the hurricane genesis and development regions of the tropical Atlantic [Gray, 1984; Goldenberg and Shapiro, 1996; Vitart and Anderson, 2001; Goldenberg et al., 2001]. The shear, combined with increased subsidence, inhibits the growth of prehurricane disturbances in the Atlantic. When these conditions persist there is a reduced threat of a coastal storm [Bove et al. 1998].
Yet the character of ENSO changes over time [Trenberth and Hoar, 1996, 1997; Rajagopalan et al., 1997; Kesten et al., 1998]. Urban et al. [2000], using proxy SST data over the central equatorial Pacific, find the middle 19th century cooler and drier compared with the late 20th century. Even within the 20th century there is a tendency for more El Niño events and fewer La Niña events since the late 1970's [Trenberth and Hoar, 1996]. Moreover, the climate's response to a particular ENSO phase can exhibit large variability [Gershunov and Barnett, 1998], even if the variability is strictly stochastic [Gershunov et al., 2000].
Additionally, factors that control the frequency of hurricanes are not necessarily the same as those that control where they track. During certain time periods the tendency is for hurricanes to track parallel to latitudes between 10^{°}N and 20^{°}N, while during other periods the tendency is for storms to recurve into higher latitudes. To some extent, the degree to which the U.S. coast is vulnerable is related to factors associated with the predominance of straightmoving hurricanes. Thus the probability of a U.S. hurricane strike is a function of the factors that control their frequency as well as a function of the factors that control their movement.
In order to understand factors that might have an influence on hurricane steering, it is useful to first examine changes to the strength of the ENSOhurricane connection. In this work, secular variations to the ENSOU.S. hurricane relationship are studied. The paper is outlined as follows: First a test is performed that fails to reject against annual hurricane counts as a random Poisson process. Then a Poisson regression model is entertained that confirms a strong statistical ENSOU.S. hurricane relationship. Evolutive (moving) regressions in 50year intervals are run. Results show a distinct tendency toward a weaker statistical relationship since the beginning of the 20th century. Finally, sealevel pressure variations over the North Atlantic as measured by a North Atlantic oscillation index are used to explain a portion of the secular variation in the strength of the ENSOU.S. hurricane relationship.
A hurricane is a tropical cyclone with maximum sustained (oneminute) 10 m winds of 33 ms^{1} (65 kt) or greater, with landfall occurring when all or part of the eye wall (the central ring of deep atmospheric convection, heavy rainfall, and strong wind) passes directly over the coast or adjacent barrier island. A U.S. hurricane is a hurricane that makes at least one landfall. A reliable list of the annual counts of U.S. hurricanes back to 1900 is available from the U.S. National Oceanic and Atmospheric Administration [Neumann et al., 1999]. These data represent a blend of historical archives and modern direct measurements, but the annual time series appears stationary over the period [see Elsner and Kara, 1999]. The lagone autocorrelation of annual counts is a negligible 0.02. Thus from a statistical perspective, the annual hurricane count from one season to the next can be considered independent.
We begin by first testing the annual counts of U.S. hurricanes using a c^{2} goodnessoffit over the years 19002000, inclusive. The annual counts include all hurricanes reaching the coast during the June through November period. The test is performed by assuming the distribution of counts is Poisson (null hypothesis) with a rate equal to the sample mean of 1.6 U.S. hurricanes per year. Since the empirical distribution has a minimum of 0 and maximum of 6, we divide the distribution into n=7 parts and find the c^{2} value with n1 degrees of freedom equal to 7.36 giving a pvalue of 0.289. As such there is no evidence against the null hypothesis and we proceed to model the annual counts of U.S. hurricanes using Poisson regression [see also, Parisi and Lund, 2000].
To fit a model to Poisson random responses, generalized linear models should be used instead of linear models. Generalized linear models enlarge the class of linear leastsquares models in two ways: the distribution of Y_{i} for fixed predictors X is assumed to be from the exponential family, which includes distributions such as the binomial, Poisson, exponential, gamma, and the normal. Also, the relationship between E(Y_{i}) = m_{i} and b_{0} + å_{k=1}^{p}b_{k} x_{k} is specified by a link function g(m_{i}), which is required only to be monotonic and differentiable.
The canonical link function given by McCullagh and Nelder, [1989] for the Poisson distribution is g(m_{i}) = log(m_{i}). Note that the climate factors, or covariates (x_{k}'s), could be treated as random variables; in which case log(m_{i}) is a random variable with a mixed Poisson distribution. The analysis based on this scheme is quite complex. A generally used alternative analysis, and the one adopted here, is based on conditional distributions, whereby statistical inferences are made conditioned on the observed values of the covariates.
For the present analysis, let m_{i} = E(Y_{i}). Then
 (1) 
 (2) 
 (3) 
The deviance is a measure of the discrepancy between observed and fitted values. It serves as a generalization of the usual residual sum of squares for nonnormal data [Solow, 1989]. The deviance function is useful for comparing two nested models. Unlike the Pearson X^{2} statistic, the deviance is additive for nested models if maximum likelihood estimates are used [McCullagh and Nelder, 1989]. Consider two models with the second having the covariate omitted, and denote the maximum likelihood estimates in the two models by [^(m)]_{1} and [^(m)]_{2}, respectively. Then the deviance difference {D(y;[^(m)]_{2})D(y;[^(m)]_{1})} is equivalent to the likelihoodratio statistic and has an approximate c^{2} distribution with degrees of freedom equal to the difference between the number of parameters in the two models. For probability distributions in the exponential family, the c^{2} approximation is accurate for deviance differences, even though the c^{2} approximation may be inaccurate for the deviances themselves [McCullagh and Nelder, 1989].
A reliable time record of the Pacific ENSO is obtained by using basinscale equatorial fluctuations of SSTs. Average SST anomalies over the region bounded by 6^{°}N to 6^{°}S latitude and 90^{°}W to 180^{°}W longitude are called the ``cold tongue index" (CTI) [Deser and Wallace, 1990]. Values of CTI are obtained from the Joint Institute for the Study of the Atmosphere and the Oceans web site (www.jisao.washington.edu/science2.html) as monthly anomalies (base period: 195079) in hundredths of a degree Celsius. Monthly values of the CTI are strongly correlated with values from other ENSO SST indices. Since the Atlantic hurricane season runs principally from August through October, a 3month averaged (AugOct) CTI from the data set is used. The relationship between CTI and U.S. hurricanes is shown with box plots in Fig. . The annual count of hurricanes is higher when values of the CTI are lower (La Niña events). Note also that, characteristic of a Poisson distribution, the variance of annual counts increases with decreasing values of the CTI.
Table shows the analysisofdeviance table for a Poisson model of the ENSOU.S. hurricane relationship with CTI as the lone covariate (climate factor). The deviance difference between the null model, log(m_{i}) = b_{0}, and the model in (1) is 20.62 with a pvalue of 5.59×10^{6} using a c^{2} test. The larger the deviance difference, the stronger the bivariate ENSOU.S. hurricane relationship. For comparison the analysis is repeated using August through October averaged values of the Southern oscillation index (SOI) in place of the CTI as the covariate. Monthly values of the SOI are obtained from the Climatic Research Unit's web site (www.cru.uea.ac.uk). The SOI is defined as the normalized pressure difference between Tahiti and Darwin. Normalization is based on the method given by Ropelewski and Jones [1987]. The model is significant with a pvalue of 2.62×10^{3}. The difference in model significance when SOI is used instead of CTI as the covariate is probably due to the fact that the SOI is a less reliable indicator of the state of the ENSO. Intraseasonal (3050 day) oscillations in the tropics [Madden and Julian, 1971] perturb the surface pressure field in the equatorial Pacific which tends to add noise (higher frequency variations) to the monthly SOI values.
Thus it appears, as expected, that the ENSO has a statistically significant influence on the annual numbers of U.S. hurricanes during the 20th century [cf., Bove et al. 1998]. The relationship is strongest when using central equatorial Pacific SSTs as measured by the CTI for the model covariate. When CTI values indicate below normal equatorial SSTs, the probability of a U.S. hurricane increases. To verify the model fit, diagnostic plots are shown Fig. . The absolute deviance residuals show striations due to the discrete nature of hurricane counts; otherwise the plots reveal nothing to suggest a poor fit.
Secular variations to the ENSOU.S. hurricane relationship on long timescales are investigated by applying Poisson regressions on successive 50year overlapping time intervals. The 50year intervals are moved one year at a time through the 101 year record and difference in deviance (deviance difference) values are plotted on a time axis in Fig. . Deviance differences corresponding to pvalues of 0.05 (95% significance level) and 0.01 (99% significance level) are indicated by horizontal lines on the graph.
Results reveal variations in the strength of the ENSOU.S. hurricane relationship. In particular, deviance differences are large and significant for regressions run on data from the earliest 50year intervals, but smaller for regressions run on data from the later intervals. Values are somewhat higher again toward the end of the period indicating a recent return to a stronger relationship. Similar results, showing a decrease in the deviancedifference values through time and a recent slight increase, are obtained using intervals in the range between 20 and 60 years. Similar results are also obtained if linear correlation is used instead of deviance difference with values of the correlation ranging between 0.62 (strongest relationship) and 0.27 (weakest relationship).
A closer examination of the change in the ENSOU.S. hurricane connection can be seen in Fig. . Box plots of the relationship are displayed for two contrasting periods. The periods correspond to the largest (190251) and smallest (193180) deviance values of the Poisson regression as noted in Fig. . The abscissa is labelled in pentads of August through October averaged CTI values, where ``MB" is much below average, ``B" is below average, ``N" is normal, ``A" is above average, and ``MA" is much above average. Notice that even during the period of weakest relationship, above normal values of the CTI (indicative of El Niño conditions) correspond with fewer U.S. hurricanes.
Although much of the variation in the ENSOU.S. hurricane relationship might be attributable to sampling variability, it is instructive to look for physical causes. Physical mechanisms responsible for coastal hurricane strikes can be divided into two factors: (1) Factors that control the quantity of hurricanes that form over the North Atlantic during a given season, and (2) Factors that control where the hurricanes will likely track upon formation. ENSO is responsible for factors that contribute to hurricane formation and development, and thus the overall quantity of storms. When the equatorial Pacific is cooler than normal more hurricanes occur over the Atlantic, which increases the probability that the United States will get hit. Yet climate conditions can be such that the storms that form tend to steer clear of the U.S. coastline. Elsner et al. [2000], using historical and geological data [e.g., Liu and Fearn, 2000; Donnelly et al., 2001], suggest that sealevel pressure variations over the North Atlantic are responsible for routing strong hurricanes. In particular, when the North Atlantic oscillation (NAO) is characterized by an intensified Icelandic low there tends to be a greater threat of a major hurricane along the midAtlantic coast to New England (North Carolina to Maine). An NAO index (NAOI) is defined as the normalized pressure difference between the Azores and Iceland. When NAOI values are positive the North Atlantic subtropical high tends to be stronger and located over the eastern part of the ocean basin allowing hurricanes to recurve northward generally away from the United States. The situation is complicated by the fact that recurving hurricanes will, at times, strike the U.S. northeast.
Values of the NAOI, as calculated from Gibraltar and a station over southwest Iceland [Jones et al., 1997], are obtained from the Climatic Research Unit. The values are first averaged over the pre and earlyhurricane season months of May and June. This is a compromise between signal strength and timing relative to the hurricane season. The signaltonoise ratio in the NAO is largest during the boreal winter and spring, whereas the U.S. hurricane season begins in June. Fiftyyear running means are computed and compared to the deviancedifference values from the running regression (Fig. (a)). There is an obvious outofphase relationship. The nonlinear trend lines indicate that during earlier periods when the NAOI was low the strength of the ENSOhurricane relationship was strong, whereas during later periods when the NAOI was higher the relationship was weaker.
In order to make more meaningful comparisons it is necessary to remove the nonlinear trends in both time series using a local weighted smoother. A scatter plot of the relationship after the trends are removed is shown in Fig. (b). The ordinary leastsquares regression line indicates a significant negative relationship (pvalue on the regression slope = 0.0008). This analysis provides evidence for the NAO as an additional important factor in explaining U.S. hurricane activity on the decadal scale after accounting for ENSO.
The paper examines some statistical aspects of the ENSOU.S. hurricane relationship. The annual count of U.S. hurricanes can be considered a Poisson process. The distribution over the 101year period (19002000) is positively skewed with a median and mean of 1 and 1.6, respectively. The lagone year autocorrelation is 0.02. The relationship between annual counts of U.S. hurricanes and ENSO is well documented. During La Niña (El Niño) years, there is a heightened (reduced) threat of hurricanes along the coast. Yet this is only one part of the picture.
ENSO influences largescale atmospheric conditions over the North Atlantic region that favor or inhibit hurricane formation through variations in upperlevel vertical shear of the horizontal winds. The occurrence of hurricanes on the coast, however, is a function of their frequency and their tracks. While ENSO explains a portion of U.S. hurricane variability associated with hurricane frequency, it appears that the NAO is responsible a portion of the variability associated with their tracks. The physical explanation of the NAOU.S. hurricane connection is based on the positioning of the subtropical high [Elsner et al., 2000]. A negative NAOI is associated with a subtropical high that is weaker and displaced farther to the south and west. Under these conditions, hurricanes that form over the open waters of the North Atlantic get steered westward in the direction of the United States. Westward moving, straight tracking hurricanes are likely to threaten the U.S. south of about 35^{°}N latitude. The correlation between the NAOI and the seasonal number of hurricanes making landfall from Texas to South Carolina is 0.273. The situation for understanding overall U.S. hurricane activity, however, is complicated by the fact that recurving hurricanes under a strong NAO will sometimes make landfall along the midAtlantic states and New England. As an example, during the period of strongest ENSOU.S. relationship (190251), the mean annual number of East coast (North Carolina to Maine) was only 0.24. This compares to a mean of 0.34 (an increase in annual landfall odds of 63%) during the 193180 period of weakest ENSOU.S. hurricane relationship.
Quite reasonably then, climate periods during which atmospheric conditions are favorable for: 1) lowlatitude, straight moving hurricane tracks, and 2) recurving hurricanes remaining offshore, are periods during which the ENSOU.S. hurricane relationship is strongest, as the frequency of U.S. landfalls in this case is primarily related to the overall basinwide occurrence of hurricanes. This apparently was the case during the first two decades of the 20th century, but not since. Results from this research provide another piece to the puzzle of hurricane climate variability.
Acknowledgements. We thank R. Murnane, B. Kocher,
and S. Elsner for discussions on this topic, and T. Jagger for
programming assistance. The study was supported by the National
Science Foundation (ATM0086958) and the Risk Prediction
Initiative of the Bermuda Biological Station for Research
(RPI99001).
deviance  residual  
Terms  difference  d.f.  deviance difference  pvalue 
Null  100  115.587  
CTI  20.622  99  94.966  5.59×10^{6} 




