A bayesian representation of the storm approach probability based on operational track forecast errors

This study provides a statistical review on the forecast errors of tropical storm tracks and suggests a Bayesian procedure for updating the uncertainty about the error. The forecast track errors are assumed to form an axisymmetric bivariate normal distribution on a two-dimensional surface. The parameters are a mean vector and a covariance matrix, which imply the accuracy and precision of the operational forecast. A Bayesian method improves quantifying the varying parameters in the bivariate normal distribution. A normal-inverse-Wishart distribution is employed to determine the posterior distribution (i.e., the weights on the parameters). Based on the posterior distribution, the predictive probability density of track forecast errors is obtained as the marginal distribution. Here, ‘‘storm approach’’ is defined for any location within a specified radius of a tropical storm. Consequently, the storm approach probability for each location is derived through partial integration of the marginal distribution within the forecast storm radius. The storm approach probability is considered a realistic and effective representation of storm warning for communicating the threat to local residents since the locationspecific interpretation is available on a par with the official track forecast.