Representing the uncertainty of tropical cyclone track forecast through Bayesian approach

As the accuracy of typhoon track forecast has continuously improved with the help of numerical models, people's concern is moving toward the probabilistic forecast rather than deterministic forecast. Under the circumstance, various attempts are being made by forecast agencies over the issue how to represent the uncertainty of typhoon track forecast. Although the representation of the multi-model spread is ideal approach to reflect the real-time uncertainties, it has a limitation of lacking available operational models to yield statistically reliable information. In this study, Bayesian approach is employed to update the distribution of track forecast errors efficiently assigning the weights to the recent observations. Here, the probability distribution of cumulative forecast track error is set to be a prior distribution, and maximum likelihood distribution is estimated using the latest observations. Subsequently, conjugate analysis from the prior Gamma distribution returns the posterior distribution of track forecast errors in another Gamma form. Credible intervals are utilized to update the representation of the probability circle in association with the future forecast. Since the Bayesian inference reflects the recent forecast error tendency, it is considered to be a better scheme for operational use by semi-real-time stochastic interpretation.