Stochastic modeling of tropical cyclone track data

A stochastic model prototype for the tracks of tropical cyclones is developed, based on historical tropical cyclone track data from the western North Pacific. The data consists of the location and the maximum wind speed of nearly every typhoon from the period 1945-2004, measured in intervals of 6 hours.

Due to the strong inhomogeneities in the shape of the storm tracks, it is necessary to first separate the tracks into 6 homogeneous classes, which are then considered separately. To match the information reflected in the original data, the storm tracks are modeled as polygonal trajectories. The initial points of the polygons are modeled as inhomogeneous Poisson Point Processes. For these, the intensity fields are estimated from the data using the Generalized Nearest Neighbor technique. From the initial points, the propagation of the storm tracks is modeled by Generalized Random Walks: A density is estimated from the data with Kernel methods for the initial values of the direction and speed of the propagation, as well as for the attained maximum wind speeds on the first segment of the track. The same is done for the changes in theses variables on subsequent track segments, which are considered to be independent and identically distributed. Certain boundary conditions have to be considered. The probability of a storm track ending after a certain segment is modeled according to the current location of the storm.

The model is implemented in the Java programming language, so that large amounts of artificial, but realistic storm tracks can be simulated. An event set for a time period of 10000 years is generated. This event set is then used in combination with a numerical wind field and loss simulation model of the Munich Reinsurance Company to assess storm risks in the region.