Using Regression Mixture Model Clustering to Partition Tropical Cyclone Track Forecasts from Ensemble Prediction Systems

Ensemble forecasts, such as those from the European Centre for Medium-Range Weather Forecasting (ECMWF) Integrated Forecast System (IFS) and National Center for Environmental Prediction Global Ensemble Forecast System (GEFS) provide a method of accounting for uncertainty in model initial conditions and/or physics in tropical cyclone track forecasts. An ensemble of atmospheric forecasts with slightly different initial conditions and/or varying physics provides a range of plausible future storm tracks (the ensemble spread) and the average track produced by the ensemble (the ensemble mean).

A shortcoming of using the ensemble mean and spread is evident when the ensemble splits into multiple predominant paths. In these cases, the ensemble mean track may take a physically unrealistic path that no ensemble member predicts (e.g. Tropical Storm Debby [2012] track forecasts initialized at 00 UTC 25 June; Fig. 1). In a case such as this, the ensemble mean track is of little use as a consensus forecast.

Clustering of ensemble forecast tracks provides information beyond ensemble mean and spread. Regression mixture-model clustering (Gaffney et al. 2007) provides a “soft” partition (probability of cluster membership between 0 and 1) of track forecasts from one or more ensemble prediction systems (EPSs) into a small number of clusters with distinct mean trajectories (Kuruppumullage Don et al 2016; Kowaleski and Evans 2016). This yields information on potential outcomes (cluster mean trajectories) and an estimate of the probability of each outcome (cluster populations).

We obtain 120-hour tropical and subtropical cyclone track forecasts from the North Atlantic and western North Pacific basins between 2008 and 2015. All forecasts meet the following criteria: (i) storm intensity of at least 17.4 m s^-1(35 kts; tropical storm-strength) at the time of forecast initialization and (ii) persistence of the storm as a tropical or subtropical cyclone for at least 72 hours after the initialization time. Track forecast data are obtained from the University Corporation for Atmospheric Research THORPEX Grand Global Ensemble (TIGGE; Bougeault et al. 2010) database.

As in Kowaleski and Evans (2016), we employ four global EPSs: ECMWF IFS, NCEP GEFS, United Kingdom Met Office Global and Regional Ensemble Prediction System (UKMO MOGREPS), and the Canadian Meteorology Centre (CMC) Global Environmental Prediction System (GEPS). All track forecasts are clustered using the regression mixture-model of Gaffney et al. (2007) employed in Kowaleski and Evans (2016), as modified in Kuruppumullage Don et al. (2016). For the three TCs that Kuruppumullage Don et al. (2016) analyzed, a 5-cluster solution was sufficient to capture 120-hour forecast track variability. However, because of the small dataset that they used, it is not certain whether a 5-cluster solution is generally optimal. Therefore, in this study, we perform clustering using four through six clusters. We then determine which number of clusters is superior across the dataset. For simplicity of analysis, a 3^rdorder polynomial is employed in all clustering.

We also examine whether the inclusion of specific EPSs improves or degrades the clustering solution over the forecast dataset. Therefore, for each mixture-model specification, we perform clustering using the following four EPS combinations: (i) ECMWF only; (ii) ECMWF and UKMO; (iii) ECMWF, UKMO, and NCEP; and (iv) ECMWF, UKMO, NCEP, and CMC. Use of these four combinations allows us to determine whether the inclusion of the UKMO, NCEP, and CMC ensembles each improves or degrades the cluster solutions.

After clustering solutions are obtained for each forecast initialization, using the twelve clustering specifications (four through six clusters with each of the four EPS combinations), we calculate the distributions and values of the following cluster characteristics for all initialization times and for relevant forecast subsets:

1)      Total, along-track, and cross-track error of the mean track of the most populous cluster compared to those of other cluster mean tracks. We also calculate these error statistics as a function of cluster population.

2)      Fraction of forecasts for which the mean track of the most populous cluster has a smaller error than the ensemble mean. This fraction is also calculated for the subset of “dominant” clusters (most populous clusters that have at least 1.5 times the membership of any other cluster).

3)      Distribution of the cluster assignment of the observed track as a function of cluster population. The regression mixture model can posteriorly assign the observed track to a cluster. We can also determine the observed track cluster assignment by computing which cluster mean track has the smallest average error relative to the observed track.

Based on a combination of these metrics, we determine which cluster specifications are optimal for 120-hour tropical cyclone track forecasts. We require specifications in which the most populous cluster mean track has small errors relative to the mean tracks of the other clusters and relative to the ensemble mean. We also seek specifications in which the observed track is assigned to clusters in proportion to their populations.

References

Bougeault, P. and Coauthors, 2010: The THORPEX Interactive Grand Global Ensemble. Bull. Amer. Meteor. Soc., 91, 1059–1072, doi: htpp://dx.doi.org/10.1175/2010BAMS2853.1.

Gaffney, S. J., A. W. Robinson, P. Smith, S. J. Camargo, and M. Ghil, 2007: Probabilistic clustering of extratropical cyclones using regression mixture models. Climate Dynamics, 29, 423-440, doi: http://dx.doi.org/10.1007/s00382-007-0235-z.

Kowaleski, A. M. and J. L. Evans, 2016: Regression mixture model clustering of multi-model ensemble forecasts of Hurricane Sandy: Partition characteristics. Mon. Wea. Rev. (In press).

Kuruppumullage Don, P., J. L. Evans, F. Chiaromonte, and A. M. Kowaleski, 2016: Mixture-based path clustering for synthesis of ECMWF ensemble forecasts of tropical cyclone evolution, Mon. Wea. Rev. (In press).

Figure 1.  ECMWF IFS 120-hour forecasts of Tropical Storm Debby (2012) initialized at 00 UTC 25 June. Individual ensemble-member tracks are in red. The ensemble-mean track is in black. The best track through 12 UTC 27 June (the time that Debby dissipated) is in blue.