PtY mx b

and the minimization over beta is a consistent estimate of the minimization of this expected value. For the fit we choose a linear model for the regression function of the form p = b0 + b • SSNi where SSN is the daily sunspot count.

Figure 2b shows the upper quantiles of hurricane intensity by categories of daily SSN. The slopes from a quantile regression are negative at the median and above (Q50, Q75, Q90, Q95, and Q99) indicating an inverse relationship between sun-spots and storm intensity. The relationship is generally stronger for the more intense cyclones (Table 4).

Over the western Atlantic including the Carilbrean Sea and Gulf of Mexico where oceanic heat content is sufficiently large, the limiting thermodynamic factor for a tropical cyclone to reach its maximum potential intensity (MPI) is the near-

Table 4 Quantile regression coefficients from a model of storm intensity on daily sunspot number (SSN). The values are estimates of the slope over the western North Atlantic basin (see c). SSN is grouped in 25 count intervals. The slope has units of kt/SSN

Quantile

Estimate

S.E.

t value

Pr(>t)

Q50

0.050

0.012

4.017

<0.001

Q75

0.120

0.025

4.908

<0.001

Q90

0.121

0.028

4.368

<0.001

Q95

0.093

0.027

3.461

0.001

Q99

0.099

0.042

2.342

0.019

troposphere temperature. Since this factor is inversely related to MPI, we note that an active sun warms the lower stratosphere thereby decreasing potential intensity. Indeed, the correlation between seasonally averaged SSN and temperatures near the tropopause over the domain is consistently positive based on atmospheric data over the period 1948-2006. The seasonal averaged (August-October) near-tropospheric (200, 150, 100, and 70 mb) temperatures are obtained from the U.S. NCAR/NCEP re-analysis dataset (Kalnay et al. 1996). These results using a quantile regression model on daily cyclone intensity are in agreement with the results of our seasonal model and thus they add evidential support to the hypothesis of a solar hurricane link.

In marked contrast, the daily SSN is positively correlated with daily averaged tropical cyclone intensity for cyclones over the domain bounded by 30 and 60 degrees W longitude and 5 and 30 degrees N latitude. Figure 2c shows the upper quantiles of hurricane intensity by categories of daily SSN over this eastern part of the Atlantic basin. Here the slopes from a quantile regression are positive at the median and above (Q50, Q75, Q90, Q95, and Q99) indicating an direct relationship between sunspots and storm intensity over the central and eastern Atlantic.

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