### Lack of landfalls

The U.S. has experienced a "hurricane drought" for the last nine years. No major hurricane (Saffir-Simpson category 3 or higher) has made landfall over the U.S. since hurricane Wilma in 2005 and no hurricane of category 1 or higher has made landfall over Florida. This break in landfalling major hurricanes is the longest on record, as documented in the National Hurricane Center's HURDAT database^{1,2} (Figure 1). Despite this U.S. landfalling dearth, hurricane activity in the wider Atlantic basin has not been unusually low (except for 2013 - Figure 2), nor has the Caribbean been spared from landfalls.

*Figure 1: Waiting time between major hurricanes with wind speeds of Saffir-Simpson category 3 or higher over the U.S. The final bar represents the time between the last event (Wilma in 2005) and 1st June 2015. Note that this plot only includes hurricanes that made landfall at intensity category 3 or higher and excludes major hurricanes that had a reduced intensity before landfall.*

*Source: Aspen Re Research and Development, HURDAT*

*Figure 2: Annual number of major hurricanes in the Atlantic basin 1900-2014.*

*Source: Aspen Re Research and Development, HURDAT*

### Chance: the Individual and the Many

The question naturally arises as to what is the likelihood of such a break occurring purely by chance. The issue can be viewed by characterizing the arrival times of major hurricanes over the U.S. as a random process. Randomness is an unusual property, as it implies that while individual events are by definition unpredictable, the outcome or distribution of many events is known. A series of coin tosses is the simplest example, where individual tosses are unpredictable, but with the expectation that after many tosses half would be heads.

### Homogenous Process

The field of statistics provides a rich variety of tools to address such randomness that defines the world of natural hazards, with the Poisson distribution and Generalized Pareto distribution commonly adopted. Occurrence of such events can be characterized as a homogeneous Poisson process, where the arrival of storms are independent events but with a fixed average rate of arrival. The independence criterion means that the arrival time of an event has no relationship to any other events. With 55 storms in 115 years, it is the same as picking 55 random dates from the 115-year period. Independence also means that, despite having already waited nine years for a major hurricane, the chance of observing one this year is the same as any other year and independent of the waiting time.

A Poisson process can be analysed in several ways: by the number of events per time interval (e.g. years); by the times of the individual events; or by the waiting times between the events. It derives its name from the fact that the probability distribution of the numbers of events per time interval is a Poisson distribution, a distribution formulated in the mid-19th Century by the pioneering French mathematician of the same name.^{3} The Poisson distribution is defined only by a single parameter λ, which is the average rate of arrival of events (Equation 1). There were 55 landfalling major hurricanes over the 115-year period 1900-2014, giving a value of λ of 0.48 events per year, or an expected return period of 2.1 years between events (Figure 3).

*Equation 1: For a Poisson process, the probability of observing k hurricanes in a year is defined by the Poisson distribution. The single parameter λ is the average number of hurricanes per year.*

*Figure 3: Probability of having various numbers of major hurricanes per year with intensity at least category 3 over the U.S. The observations match what is expected from the Poisson distribution, which is also shown along with its 95% confidence interval.*

*Source: Aspen Re Research and Development, HURDAT*