Mixture-Based Path Clustering for Synthesis of ECMWF Ensemble Forecasts of Tropical Cyclone Evolution

In this article, three tropical cyclones and their 120-h, 50-member ECMWF Integrated Forecasting System (IFS) ensemble track forecasts at 10 initialization times are considered. The IFS forecast tracks are clustered with a regression mixture model, and two traditional diagnostics (the Bayesian information criterion and a measure of strength of cluster assignment) are used to determine the optimal polynomial order and number of clusters to use in the model. In addition, cross-validation versions of the two diagnostics are formulated and computed to further aid in model selection. Both traditional and cross-validation diagnostics suggest that third-order polynomials and five clusters are effective options although the evidence is less conclusive for the number of clusters than for the polynomial order, and the cross-validation diagnostics favor a smaller number of clusters than the traditional ones. Path clustering of IFS tropical cyclone track forecasts with this third-order polynomial, five-cluster regression mixture model produces interpretable partitions by direction and speed of motion for each of the storms and initialization times considered. Thus, this approach effectively synthesizes the forecast spreads within the IFS into a small number of representative trajectories. Based on how forecasts distribute across clusters, this approach also provides information on the likelihood of each such representative trajectory. If used operationally, this information has the potential to aid forecasters in parsing and quantifying the uncertainty in tropical cyclone track forecasts.