Index Terms: North Atlantic hurricanes, geomagnetic variation, baroclinically-initiated hurricanes, Poisson regression
The idea that cosmic ray fluxes, modulated by solar wind, can influence storm intensity has been examined recently [Tinsley and Deen, 1991; Tinsley and Beard, 1997]. The relationship is explained through changes to the rate of freezing of supercooled water droplets by ionization processes occurring in high-level storm clouds [Tinsley and Dean, 1991]. The Tinsley and Dean hypothesis suggests that ``electrofreezing" increases the flux of ice crystals that glaciate clouds which leads to increases in latent heating and subsequent intensification of winter cyclones. Motivated by this hypothesis as well as by previous research on the relationship between extraterrestrial factors and the intensification of winter cyclones, here the possibility of a connection between geomagnetic variation and tropical cyclone intensity changes is examined. Based on earlier work [Elsner and Kara, 1999; Elsner et al., 1999] it is suggested that such a relationship will exist only for a specific type of North Atlantic hurricane that forms generally at higher latitudes.
Hurricanes are mature tropical cyclones. Formed from low pressure areas over the warm oceanic waters, a developing tropical cyclone typically moves with the trade winds from east to west at low latitudes. A tropical cyclone reaches hurricane intensity when the rotational wind speed at 10 m above the ground exceeds 33 m/sec (65 kt) sustained over one minute (maximum sustained wind speed). In a few storms the maximum sustained wind speed can exceed 80 m/sec as hurricane Allen did on August 3rd, 1980. In this case the estimated power surpassed the power of nearly 105 Hiroshima-type bombs. Hurricanes may also develop from disturbances of middle latitude origin [Hebert, 1978; Elsner et al., 1996]. Processes leading to the intensification of these hybrid or baroclinically-initiated hurricanes are less well understood [Hess et al., 1995].
Here all hurricanes over the North Atlantic region are examined at the exclusion of hurricanes or typhoons over other tropical-cyclone basins. The region of interest includes the Gulf of Mexico and Caribbean Sea. North Atlantic hurricanes frequently strike the Caribbean islands, Mexico, and the United States. In the United States hurricanes rank at the top of all natural hazards, rivaling the major earthquake, when measured in terms of past loss of life and property damage. Thus understanding controls on their intensity is important to science and society.
Meteorologists have records of North Atlantic hurricanes that date back through the 19th century. Over the last half-century, these records come from on a wide range of measurements including ship and land reports, upper-air balloon soundings, and aircraft reconnaissance. In the present study, data for all recorded hurricanes from January 1, 1950 till December 31, 1999 were examined. The date on which the tropical cyclone first reached hurricane intensity was of primary concern. Also of importance was the eventual maximum intensity of the hurricane.
Depending on development and origin mechanisms the set of all hurricanes is divided into three basic types [Elsner et al., 1996]. The term ``tropical-only" (TO) is used to describe hurricanes that form from tropical disturbances, such as an easterly wave (a low altitude pressure wave that moves westward at low latitudes). Tropical cyclones with origins from tropical disturbances, but which reach hurricane intensity resulting from favorable middle latitude baroclinic influences are termed ``baroclinically-enhanced" hurricanes. The term ``baroclinic" refers to atmospheric processes that derive energy from thermal gradients on constant pressure surfaces. Tropical cyclones that reach hurricane intensity having originated as a baroclinic disturbance, such as a middle latitude trough, are termed ``baroclinically-initiated" hurricanes. A connection between solar activity and annual counts of baroclinically-initiated hurricanes has already been suggested in Elsner and Kara .
In summary, for the North Atlantic hurricane data we have the following types and the total number of each type over the period of investigation:
Regular solar radiation changes affect the Earth's magnetic field. Irregular current systems produce magnetic field changes caused by the interaction of the solar wind with the magnetosphere, by the magnetosphere itself, by the interactions between the magnetosphere and ionosphere, and by the ionosphere itself. Indices of magnetic activity are designed to describe variation in the geomagnetic field caused by these irregular current systems.
The K-index is quasi-logarithmic local index of the 3-hourly range in magnetic activity relative to an assumed quiet-day curve for a single geomagnetic observatory site. It consists of a single-digit 0 through 9 for each 3-hour interval of the universal time day (UT). The planetary 3-hour index, called the Kp, is the mean standardized K-index from 13 geomagnetic observatories located in two latitude belts between 44° and 60° in the Northern and Southern hemispheres.
The Kp index is widely used in ionospheric and magnetospheric studies and is generally recognized as measuring worldwide geomagnetic activity. The apparent range of the Kp index which varies from 0 to 400 was obtained from GeoForschungs Zentrum, Potsdam as a sum of the eight 3-hourly absolute values each day over the same 50-yr period (1950-1999). The primary interest is the daily Kp index (apparent range) values on days preceding the hurricane. Daily Kp index values are averaged over the 10 days preceding the hurricane and including the day of the hurricane. Since most years have more than one hurricane, annual averages of the maximum hurricane intensity and the 11-day mean Kp index were also computed.
If extraterrestrial factors can intensify a hurricane then we should expect to see a correspondence between the maximum intensity of the hurricane and the Kp index averaged over days prior to the storm reaching hurricane intensity. Figure shows the distribution of the Kp index values versus maximum hurricane intensity for the three hurricane types discussed in the previous section. The horizontal line in the interior of the box is located at the median value of the Kp index. This is an estimate of the center of the distribution. The height of the box is equal to the interquartile distance (IQD), which is the difference between the third quartile of the data and the first quartile. The whiskers (dotted lines extending from the top and bottom of the box) extend to the extreme values of the data or a distance of 1.5×IQD from the center, whichever is less. Data points which fall outside the whiskers are indicated by horizontal lines. Note that for baroclinically-enhanced and baroclinically-initiated hurricanes some of the intensity categories are missing as there were no storms of these types that reached those particular maximum intensities.
The plots indicate no obvious relationship between maximum hurricane intensity and the Kp index for tropical-only hurricanes. In comparison, the plot for baroclinically-enhanced hurricanes suggests a slight positive relationship, with higher intensity hurricanes associated with larger Kp index values. The positive relationship appears strongest for baroclinically-initiated hurricanes. Similar plots are obtained if the daily Kp values are averaged for seven or five days prior to the hurricane.
A closer examination of the relationship between maximum baroclinically-initiated hurricane intensity and Kp index values is shown in Fig. . Here the Kp values are grouped into four equal length intervals (quartiles) over the range of values (the minimum 11-day averaged Kp value over the 71 hurricanes is 9.54, the maximum value is 38.18 and the mean is 19.52), where ``MB" indicates values much below average, ``B" indicates values below average, ``A" indicates values above average, and ``MA" indicates values much above average. Values of the maximum hurricane intensity tend to be higher when values of the Kp index are above normal. Note also that the variance of maximum intensity increases with increasing values of the Kp index, which is characteristic of a Poisson response variable.
To fit a model to Poisson random responses, generalized linear models (GLMs) should be used instead of linear models. GLMs enlarge the class of linear least-squares models in two ways: 1) The distribution of the response (maximum hurricane intensity) for a predictor (Kp index) is assumed to be from the exponential family, which includes the Poisson distribution. 2) The relationship between the expected value of the response and the predictor is specified by a link function which is only required to be monotonic and differentiable. The link function for the Poisson distribution is the natural logarithm of the mean of the response variable.
GLMs are examined by considering the size of the difference between the observations and fitted values through the deviance function [McCullagh and Nelder, 1989], which serves as a generalization of the usual residual sum of squares for non-normal data [Solow, 1989]. Two competing models are compared by taking the difference in their respective deviance values (deviance difference). In the present case the competition is between the null model (no predictor) and a model with the Kp index as the single predictor. A large deviance difference when the Kp index is added to the null model indicates an improved model when maximum likelihood estimates are used to determine model coefficients [McCullagh and Nelder, 1989]. How significant the improvement is determined by a c2 distribution with degrees of freedom equal to the difference in the number of coefficients in the competing models.
Considering only the set of baroclinically-initiated hurricanes and comparing the null model with a model that contains the 11-day averaged Kp index (10 days before plus the day the storm first reached hurricane intensity) as a predictor we find a deviance difference of 23.94 kt with a p-value of 9.95×10-7 using a c2 test. The very small p-value indicates that we should reject the null model. Thus it appears that the average Kp index has a statistically significant relationship to the maximum intensity of the baroclinically-initiated hurricane. When Kp index values are higher, the probability of a stronger hurricane is larger.
The relationship between the geomagnetic index and hurricane intensity is investigated further by grouping the hurricanes by years. The maximum intensity of all baroclinically-initiated hurricanes are averaged for each year. Similarly the corresponding 11-day averaged Kp index values are averaged for the year. Results are plotted in Figs. and . The graphs indicate a firm statistical relationship as the two curves tend to vary in phase over time. Correlation between the annual series' is +0.50. The p-value on the slope of the ordinary least-squares linear regression line in the scatter plot is 0.002, indicative of a statistically significant relationship.
The study is an exploratory analysis of a possible relationship between geomagnetic activity and hurricane intensity changes. The study begins with a look at the bivariate relationship between the Kp index and changes in hurricane intensity, as measured by the maximum sustained 1-minute, 10-m wind speed, for all hurricanes over the North Atlantic during the period 1950-1999. An analysis is performed on the three groups of hurricanes originally outlined in Elsner et al. . As anticipated, based on the investigations of Elsner et al. , a relationship is found for the baroclinic type storms only. In particular, the maximum intensity of the baroclinically-initiated storms have a statistically significant relationship with 11-day averaged (the first day of hurricane intensity plus the 10 prior days) Kp index values when modeled with a Poisson generalized linear model. Similar results are obtained when the data are averaged over all baroclinically-initiated hurricanes during the year.
Factors that cause intensification of baroclinically-initiated tropical cyclones are least understood as they are linked to the transformation of an upper-level cyclonic circulation to one featuring a warm-core anticyclonic circulation. Some cyclones make a complete transformation and intensify as full-fledged hurricanes, whereas others continue as weaker, hybrid systems. From the work of Tinsley , a possible triggering mechanism for condensation and freezing within the convective clouds of the fledgling cyclone is suggested related to the ionization of the upper extent of the storm vortex that leads to additional latent heat release and subsequent warming of the core region of the cyclone. Central-core warming is associated with a lowering of the surface pressures and thus with intensification of the hurricane. Moreover, diabatic heating near the storm center can act to inhibit tilting of the vortex circulation against debilitating vertical shear of the horizontal wind (see e.g., DeMaria ). These processes may be most important for hurricanes that form outside the deep tropics as is often the case with baroclinically-initiated hurricanes. Work is in progress to better understand this intriguing result.