On 16 September 1998, a cluster of thunderstorms within an easterly tropical wave formed Hurricane Georges 3,500km to the east of Puerto Rico. Moving a few degrees to the north of due west, and intensifying to category 4, four days later the hurricane began its path of destruction over the Lesser Antilles islands of Anguilla, Antigua and Barbuda. The storm weakened a little before moving between the northern and southern US Virgin Islands, island-hopped the full length of Puerto Rico and Hispaniola, and crossed the eastern end of Cuba before curving to the north to clip the Florida Keys and make landfall in Mississippi. It eventually stagnated over Alabama, a full two weeks after it was born. In affecting two separate regions of the US, as well as at least six separate Caribbean countries, Georges was as good a manifestation as one can get of ‘clash': the potential for a single catastrophe event to impact multiple territories.
Many hurricanes passing through the Caribbean have then gone on to hit the US, and it would be very easy for a nervous reinsurer to establish a single aggregate limit covering both regions. However, this would be a poor use of capital, as an even larger proportion of Caribbean hurricanes do not cause significant loss in the US at all. Beyond assuming a single aggregate limit, some reinsurers, as well as catastrophe modellers, have employed a form of simple probability matrix for tackling this problem: assigning probabilities that a hurricane that affects Puerto Rico will then go on to affect Florida. However, the problem is in reality a far more complex and subtle one than can be captured by such a simple matrix approach.
In 1998, RMS initiated a research project to provide a comprehensive scientific solution to Caribbean-US clash by creating the ability to generate a full ‘basin-wide' population of stochastic hurricanes, each storm with a complete lifetime. Previous stochastic models had simply modelled hurricanes around the time at which they caused their greatest impact at landfall.
The first step in developing the Basin-Wide Stochastic Model was to recognise that hurricanes comprise a series of distinct geographical sub-species. There are three separate tropical basins in which hurricanes form: the Atlantic, the Caribbean and the Gulf of Mexico. The climatic conditions under which hurricanes form in the different basins vary. Most Atlantic hurricanes form from easterly waves and in consequence start off moving towards the west. In contrast, Caribbean storms are far more erratic in their motion, often heading due north or even, exceptionally, towards the east.
The Atlantic basin was in turn divided into two sub-regions: the main basin to the east of the Caribbean islands and a subsidiary basin at higher latitudes in the vicinity of the Bahamas. The main Atlantic basin storms were further subdivided into storms (like Georges) that move west into the Caribbean, and storms (like Hugo in 1989) that re-curve up the Atlantic seaboard.
The modelling then focused on developing a stochastic population of each of these five separate hurricane types. The principle of the modelling technique employed the mathematical language used to define turbulent flow. Viewed from space, individual hurricane tracks resemble the movement of vortices in a ‘stream' (the great atmospheric equatorial gyre). Overall, these paths show some consistency in their behaviour, yet each individual vortex is unique and follows a distinct path. To characterise turbulence requires understanding the mean behaviour as well as the variance around that mean in every specific location. As an additional dimension of complexity, to define the hurricane's behaviour required two separate ‘turbulent' parameters: the forward speed vector and the rate of change of central pressure. Individual ‘disturbances' (such as hurricanes) possess ‘memory': the behaviour of the recent past continues to influence behaviour into the future. As hurricanes do not (solely) drive their own forward motion, ‘memory' of the forward speed vector chiefly reflects persistence in the large-scale currents in the atmosphere.
The basin-wide methodology first involved determining, for each 2º latitude by 2º longitude cell in the whole North America, Caribbean-Atlantic region, the mean and variance around the mean of the forward speed vector of all hurricanes of that type passing through that cell. For each cell, the mean and variance of the rate of change of central pressure (Delta P) was also determined for that same population of storms. These values had to be smoothed where data became sparse on the margins of the hurricane basin. An investigation was undertaken on the asymmetries in Delta P: as the pressure deepens it becomes increasingly difficult to cause further deepening. The memory affect was also calibrated to determine how rapidly hurricanes ‘forget' their past and revert towards mean behaviour. Then, painstakingly, populations of hurricanes were simulated from their birth in the model, provided with parameters sampled from the key distributions in each cell into which they moved, and then followed throughout their lives.
The project, led by Dr Michael Drayton (formerly a Cambridge post-doctorate in turbulent flow), took two years to complete, and the work would not have been possible without a support team of modellers in the RMS India office in New Delhi. The model proved very tricky to calibrate, since making a change in the turbulent distributions in any one location would have an impact on numerous other distributions far downstream. It was like forcing a huge three-dimensional carpet to perfectly drape an uneven landscape: pushing down a ruck at one point would create a new fold somewhere else.
Eventually each of the stochastic models of the five sub-species of hurricanes was fully calibrated. Now it was possible to generate any number of storms, each completely authentic in its behaviour, each completely unique in its track and central pressure behaviour, while the full population of storms reflected the totality of hurricane hazard at each location both offshore and onshore. Approximately 100,000 hurricanes were simulated of each of the five types to act as a baseline set.
The tracks themselves were remarkable in being both artificial and yet completely natural in their behaviour. One could marvel at strange hurricane tracks that had never yet been witnessed: storms that loop the loop, storms that skip along the eastern US coast, storms that make two landfalls in the vicinity of Miami – they are all there. From the full population one can start to see how the pattern of behaviour affects the hazard distribution. How, for example, there is a shadow zone of reduced hazard to the north of Cuba where intense Caribbean origin hurricanes have been weakened crossing the island, while storms that slip past the western end of Cuba, such as Hurricane Camille in 1969, can arrive on the coast of Louisiana at category 5. The power of the modelling technique was highlighted in November 1999 by a completely novel ‘lefty' storm, Hurricane Lenny, that travelled ‘backwards' (to the east) across the Caribbean. Although without precedent in history, there were numerous examples of storms with tracks of this character in the basin-wide stochastic storm set.
With the aid of this model it is now possible, for the first time, to explore Caribbean-US clash, in all its detail and complexity. From the combined Caribbean-US ‘basin-wide' hurricane model, it is possible to quantify the risk of composite loss in a joint Puerto Rico-South Florida portfolio, or optimise the construction of a well-diversified Caribbean portfolio, or even (to be released in the near future) determine how to manage an offshore platform portfolio in the Gulf of Mexico, along with an onshore energy portfolio in Texas (accompanied by a portfolio of hotels in Dominican Republic).
One could also answer the question: how likely was Hurricane Georges? If one considers the track in terms of five circular areas, each of 200km diameter, drawn around the principal points in its path, the model indicates a return period of over 800 years for a storm to pass through all five of these circles, and therefore that would cause this specific set of clash loss combinations. History shows other famous clash combinations. The great category 4 hurricane of 1928 that was highly destructive in both Puerto Rico and in South Florida also crossed Guadeloupe, St Croix in the USVI, the Turks and Caicos Islands and the Bahamas. The great hurricane of 1780, the most destructive in the history of the Caribbean, made direct hits at category 4 or above on Barbados, St Lucia, Martinique and Puerto Rico. However, neither the 1928 nor 1780 island combinations are likely to be precisely repeated in the next major clash storm to occur through the Caribbean and US. If there is one bet to be made, it is that while the specific combination will be new, a near-identical track will already exist within the full basin-wide model event set.