Improvements to stochastic simulation of tropical cyclone tracks

Stochastic models for the simulation of the tracks of tropical cyclones, such as those introduced in Emanuel et al. (2006), Hall and Jewson (2007), and Rumpf et al. (2006, 2007), have been developed in order to produce large numbers of synthetic tracks with the same characteristics as the historically observed tracks. One purpose of this approach is a vastly extended dataset as a basis for enhanced hazard assessment in areas affected by tropical cyclones.

We introduce a method to improve the fit of simulated tracks to the historical data using an acceptance-rejection method. After a synthetic track has been simulated, a score is calculated that determines how likely this track is, given the historical data in the vicinity of that track. For this purpose, non-parametric density estimates of characteristics including “wind speed“ and “direction of travel“ are calculated from the historical data on a fine grid on the observation window. These density estimates are then evaluated at the values of the characteristics attained by the simulated track at each point of measurement. The scores of the different characteristics for this track are obtained as the averages of these density estimates over all points of measurement along the simulated track. By finally comparing these scores to those obtained by the historical tracks, a rejection probability is obtained which is higher for synthetic tracks whose characteristics differ more strongly from those of the historical tracks, and lower for those who match the historical tracks more closely. According to this probability, a random decision is made whether the simulated track is accepted as part of the final simulation result or if it is rejected and a new track has to be simulated.

The acceptance-rejection procedure has been implemented in Java and applied to tracks simulated with a version of the model introduced in Rumpf et al. (2006, 2007) that has been transferred and adjusted to the North Atlantic ocean basin. Improvements in comparison to the simulation results from the original model appear to be substantial.

Emanuel K., S. Ravela, E. Vivant, and C. Risi, 2006: A statistical deterministic approach to hurricane risk assessment. Bull. Amer. Meteor. Soc., 87, 299 - 314.

Hall T. M., and S. Jewson, 2007: Statistical modeling of North Atlantic tropical cyclone tracks. Tellus, 59A, 486 - 498.

Rumpf J., E. Rauch, V. Schmidt, and H. Weindl, 2006: Stochastic modeling of tropical cyclone track data. 27th Conference on Hurricanes and Tropical Meteorology, April 24-28, 2006, Monterey, CA.

Rumpf J., H. Weindl, P. Höppe, E. Rauch, and V. Schmidt, 2007: Stochastic modelling of tropical cyclone tracks. Math. Meth. Oper. Res., 66, in press.