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

Prabhani Kuruppumullage Don Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, and Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts

Search for other papers by Prabhani Kuruppumullage Don in
Current site
Google Scholar
PubMed
Close
,
Jenni L. Evans Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Jenni L. Evans in
Current site
Google Scholar
PubMed
Close
,
Francesca Chiaromonte Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Francesca Chiaromonte in
Current site
Google Scholar
PubMed
Close
, and
Alex M. Kowaleski Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Alex M. Kowaleski in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

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.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/MWR-D-15-0214.s1.

Corresponding author address: Jenni L. Evans, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: jle7@psu.edu

Abstract

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.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/MWR-D-15-0214.s1.

Corresponding author address: Jenni L. Evans, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: jle7@psu.edu

Supplementary Materials

    • Supplemental Materials (DOCX 70.63 KB)
Save
  • Arnott, J. M., J. L. Evans, and F. Chiaromonte, 2004: Characterization of extratropical transition using cluster analysis. Mon. Wea. Rev., 132, 29162937, doi:10.1175/MWR2836.1.

    • Search Google Scholar
    • Export Citation
  • Barkmeijer, J., R. Buizza, T. Palmer, K. Puri, and J.-F. Mahouf, 2001: Tropical singular vectors computed with linearized diabatic physics. Quart. J. Roy. Meteor. Soc., 127, 685708, doi:10.1002/qj.49712757221.

    • Search Google Scholar
    • Export Citation
  • Berg, R., 2009: Tropical Cyclone Report Hurricane Ike. Rep. AL092008, National Hurricane Center, 55 pp.

  • Buizza, R., 2006: The ECMWF ensemble prediction system. Predictability of Weather and Climate, T. Palmer and R. Hagedorn, Eds., Cambridge University Press, 455–488.

  • Buizza, R., D. Richardson, and T. Palmer, 2003: Benefits of increased resolution in the ECMWF ensemble system and comparison with poor-man’s ensembles. Quart. J. Roy. Meteor. Soc., 129, 12691288, doi:10.1256/qj.02.92.

    • Search Google Scholar
    • Export Citation
  • Camargo, S. J., A. W. Robertson, S. J. Gaffney, P. Smyth, and M. Ghil, 2007: Cluster analysis of typhoon tracks. Part I: General properties. J. Climate, 20, 36353653, doi:10.1175/JCLI4188.1.

    • Search Google Scholar
    • Export Citation
  • ECMWF, 2015: Operational configurations of the ECMWF Integrated Forecasting System (IFS). European Centre for Medium-Range Weather Forecasting, accessed 23 October 2015. [Available online at http://www.ecmwf.int/en/forecasts/documentation-and-support.]

  • Evans, J. L., and R. E. Hart, 2003: Objective indicators of the life cycle evolution of extratropical transition for Atlantic tropical cyclones. Mon. Wea. Rev., 131, 909925, doi:10.1175/1520-0493(2003)131<0909:OIOTLC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Evans, J. L., J. M. Arnott, and F. Chiaromonte, 2006: Evaluation of operational model cyclone structure forecasts during extratropical transition. Mon. Wea. Rev., 134, 30543072, doi:10.1175/MWR3236.1.

    • Search Google Scholar
    • Export Citation
  • Ferstl, F., K. Burger, and R. Westermann, 2016: Streamline variability plots for characterizing the uncertainty in vector field ensembles. IEEE Trans. Vis. Comput. Graph., 22, 767776, doi:10.1109/TVCG.2015.2467204.

    • Search Google Scholar
    • Export Citation
  • Fraley, C., and A. Raftery, 2009: MCLUST version 3 for R: Normal mixture modeling and model-based clustering. Tech. Rep. 504, University of Washington, Seattle, WA, 57 pp. [Available online at https://www.stat.washington.edu/research/reports/2006/tr504.pdf.]

  • Gaffney, S. J., 2004: Probabilistic curve-aligned clustering and prediction with regression mixture models. Ph.D. thesis, University of California, Irvine, CA, 281 pp. [Available online at http://www.ics.uci.edu/pub/sgaffney/outgoing/sgaffney_thesis.pdf.]

  • 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 Dyn., 29, 423440, doi:10.1007/s00382-007-0235-z.

    • Search Google Scholar
    • Export Citation
  • Harr, P. A., and J. M. Dea, 2009: Downstream development associated with the extratropical transition of tropical cyclones over the western North Pacific. Mon. Wea. Rev., 137, 12951319, doi:10.1175/2008MWR2558.1.

    • Search Google Scholar
    • Export Citation
  • Harr, P. A., D. Anwender, and S. C. Jones, 2008: Predictability associated with the downstream impacts of the extratropical transition of tropical cyclones: Methodology and a case study of Typhoon Nabi (2005). Mon. Wea. Rev., 136, 32053225, doi:10.1175/2008MWR2248.1.

    • Search Google Scholar
    • Export Citation
  • Hart, R. E., 2003: A cyclone phase space derived from thermal wind and thermal asymmetry. Mon. Wea. Rev., 131, 585616, doi:10.1175/1520-0493(2003)131<0585:ACPSDF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hart, R. E., J. L. Evans, and C. Evans, 2006: Synoptic composites of the extratropical transition life cycle of North Atlantic tropical cyclones: Factors determining posttransition evolution. Mon. Wea. Rev., 134, 553578, doi:10.1175/MWR3082.1.

    • Search Google Scholar
    • Export Citation
  • Ieva, F., and A. M. Paganoni, 2013: Depth measures for multivariate functional data. Commun. Stat. Theory Methods, 42, 12651276, doi:10.1080/03610926.2012.746368.

    • Search Google Scholar
    • Export Citation
  • Jones, S. C., and Coauthors, 2003: The extratropical transition of tropical cyclones: Forecast challenges, current understanding, and future directions. Wea. Forecasting, 18, 10521092, doi:10.1175/1520-0434(2003)018<1052:TETOTC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • JTWC, 2015: JTWC western North Pacific best track data. Joint Typhoon Warning Center, accessed 22 October 2015. [Available online at http://www.usno.navy.mil/NOOC/nmfc-ph/RSS/jtwc/best_tracks/wpindex.php.]

  • Keller, J. H., S. C. Jones, J. L. Evans, and P. A. Harr, 2011: Characteristics of the TIGGE multimodel ensemble prediction system in representing forecast variability associated with extratropical transition. Geophys. Res. Lett., 38, L12802, doi:10.1029/2011GL047275.

    • Search Google Scholar
    • Export Citation
  • Keller, J. H., S. C. Jones, and P. A. Harr, 2014: An eddy kinetic energy view of physical and dynamical processes in distinct forecast scenarios for the extratropical transition of two tropical cyclones. Mon. Wea. Rev., 142, 27512771, doi:10.1175/MWR-D-13-00219.1.

    • Search Google Scholar
    • Export Citation
  • Kozar, M. E., M. E. Mann, S. J. Camargo, J. P. Kossin, and J. L. Evans, 2012: Stratified statistical models of North Atlantic basin-wide and regional tropical cyclone counts. J. Geophys. Res., 117, D18103, doi:10.1029/2011JD017170.

    • Search Google Scholar
    • Export Citation
  • Leutbecher, M., and T. N. Palmer, 2008: Ensemble forecasting. J. Comput. Phys., 227, 35153539, doi:10.1016/j.jcp.2007.02.014.

  • López-Pintado, S., and R. Jornsten, 2007: Functional analysis via extensions of the band depth. Lect. Notes Monogr. Ser., 54, 103120, doi:10.1214/074921707000000085.

    • Search Google Scholar
    • Export Citation
  • López-Pintado, S., Y. Sun, J. K. Lin, and M. G. Genton, 2014: Simplicial band depth for multivariate functional data. Adv. Data Anal. Classif., 8, 321338, doi:10.1007/s11634-014-0166-6.

    • Search Google Scholar
    • Export Citation
  • McLachlan, G. J., and K. E. Basford, 1987: Mixture Models: Inference and Applications to Clustering. CRC Press, 272 pp.

  • Mirzargar, M., R. T. Whitaker, and R. M. Kirby, 2014: Curve boxplot: Generalization of boxplot for ensembles of curves. IEEE Trans. Visualization Comput. Graphics, 20, 26542663, doi:10.1109/TVCG.2014.2346455.

    • Search Google Scholar
    • Export Citation
  • NHC, 2015: National Hurricane Center Forecast Verification. National Hurricane Center, accessed 23 October 2015. [Available online at http://www.nhc.noaa.gov/verification/verify5.shtml.]

  • Paliwal, M., and A. Patwardhan, 2013: Identification of clusters in tropical cyclone tracks of North Indian Ocean. Nat. Hazards, 68, 645656, doi:10.1007/s11069-013-0641-y.

    • Search Google Scholar
    • Export Citation
  • Puri, K., J. Barkmeijer, and T. Palmer, 2001: Ensemble prediction of tropical cyclones using targeted diabatic singular vectors. Quart. J. Roy. Meteor. Soc., 127, 709731, doi:10.1002/qj.49712757222.

    • Search Google Scholar
    • Export Citation
  • Veren, D., J. L. Evans, S. Jones, and F. Chiaromonte, 2009: Novel metrics for evaluation of ensemble forecasts of tropical cyclone structure. Mon. Wea. Rev., 137, 28302850, doi:10.1175/2009MWR2655.1.

    • Search Google Scholar
    • Export Citation
  • Whitaker, R. T., M. Mirzargar, and R. M. Kirby, 2013: Contour boxplots: A method for characterizing uncertainty in feature sets from simulation ensembles. IEEE Trans. Visualization Comput. Graphics, 19, 27132722, doi:10.1109/TVCG.2013.143.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 571 134 21
PDF Downloads 314 113 18