Model for Seasonal US Hurricane Counts

The autocorrelation function of the seasonal tropical cyclone model residuals is plotted in Fig. 1. The plot shows a relatively high correlation at a 10-year lag, which is unrelated to the covariates in the model. We add a term to the model to account for this lag and find that it is indeed significant (Table 2). In fact, a 10-year lag term is significant in models for basin-wide tropical storms and hurricanes and hurricanes alone. The lag term reduces the model deviance by an additional 4 percentage points for the tropical storm-and-hurricane model and by an additional 7 points for the hurricane-only model. The coefficient value of 0.054 on the lag term in the hurricane-only model indicates an increase of 5.4% per hurricane so if there were 10 hurricanes a decade ago, the rate would be 32% higher than if there were only 4

Fig. 1 Autocorrelation function of the residuals from a generalized linear model of Atlantic tropical cyclone counts. The model response variable is the count of tropical cyclones and hurricanes over the period 1914-2006. The dotted lines are the 95% confidence limits. A pronounced 10-year peak is noted

Fig. 1 Autocorrelation function of the residuals from a generalized linear model of Atlantic tropical cyclone counts. The model response variable is the count of tropical cyclones and hurricanes over the period 1914-2006. The dotted lines are the 95% confidence limits. A pronounced 10-year peak is noted

Table 2 Same a Table 1, except with a 10-year term (LAG) added. Also included is a hurricane-only model

Term

Estimate

S.E.

z value

Pr(>z)

TS + H 1914-2006

NAO

-0.108

0.037

-2.925

0.003

SOI

+0.139

0.041

+3.386

0.001

SST

+0.762

0.142

+5.376

<0.001

LAG

+0.031

0.010

+3.268

0.001

H only 1900-2006

NAO

-0.144

0.045

-3.195

0.001

SOI

+0.161

0.049

+3.261

0.001

SST

+0.609

0.162

+3.745

<0.001

LAG

+0.054

0.018

+2.958

0.003

hurricanes a decade ago. The result suggests the possibility of an additional forcing mechanism for Atlantic hurricanes related to the solar cycle.

To examine this possibility we focus on U.S. hurricanes. Reliable records of U.S. hurricane counts extend back to solar cycle number 10 (1860s). Since the statistical model above includes SST, the missing thermodynamic variable in the heat-engine theory is near-tropospheric temperature. We speculate that an increase in solar UV radiation during periods of strong solar activity will have a negative influence on tropical cyclone intensity as the temperature near the tropopause will warm through absorption of the radiation by ozone possibly modulated by the transport of ozone (Labitzke and van Loon 1988; Rind and Balachandran 1995; Shindell et al. 1999; Crooks and Gray 2005; Salby and Callaghan 2007). This effect will be most pronounced in regions of sufficient oceanic heat content and for stronger tropical cyclones. In fact, an 8-11 year cycle in a 270-year proxy for major Atlantic hurricane activity from coral and marine sediments in the Caribbean has been noted (Nyberg et al. 2007). As upper tropospheric data are not available earlier than about 1940, solar activity serves as a proxy for upper tropospheric temperature.

For solar activity we use the August through October averaged sunspot number (SSN). The sunspot numbers produced by the Solar Influences Data Analysis Center (SIDC), World Data Center for the Sunspot Index, at the Royal Observatory of Belgium are obtained from NOAA.

The model for U.S. hurricane counts using data starting with 1866 shows that SSN is significant (p value = 0.048) after accounting for the NAO, SOI, and SST (Table 3). Average sunspot number, as a predictor is more significant using data beginning with 1878. The sign on the coefficient is negative indicating that the U.S.

Table 3 Same a Table 3, except a model for U.S. hurricanes that also includes a term for the solar cycle: sunspot number (SSN)

Term

Coefficient

S.E.

z value

Pr(>z)

Estimate

US H 1866-2006

NAO

-0.207

0.066

-3.143

0.002

SOI

+0.238

0.068

+3.514

<0.001

SST

+0.508

0.235

+2.164

0.030

SSN

-0.003

0.001

-1.979

0.048

US H 1878-2006

NAO

-0.202

0.069

-2.931

0.003

SOI

+0.272

0.071

+3.829

<0.001

SST

+0.499

0.236

+2.120

0.034

SSN

-0.003

0.002

-2.194

0.028

US H 1900-2006

NAO

-0.214

0.076

-2.820

0.005

SOI

+0.285

0.081

+3.487

<0.001

SST

+0.545

0.252

+2.161

0.031

SSN

-0.003

0.002

-1.992

0.046

hurricane rate decreases with increasing solar activity. The coefficient magnitude indicates that for every additional 100 sunspots, the U.S. hurricane rate is reduced by a factor of 0.74. This is consistent with the heat engine theory and with the notion that increased UV radiation accompanying an active sun raises the temperature in the atmosphere above the hurricane. Correlation between the covariates range in absolute value from 0.05 to 0.19 with the highest occurring between SST and SOI and between SST and SSN.

With a generalized linear model, adequacy is checked by examining the Pearson residuals. Under the null hypothesis that the model provides an adequate fit to the data, the sum of the squared Pearson residuals has a chi square distribution with N-p degrees of freedom, where N is the record length and p is the number of model parameters. For all four seasonal models (data starting at different years) considered, the p-value on the chi square goodness-of-fit test is 0.2 or greater indicating no significant lack of fit.

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