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  • Bolton, D., 1980: The computation of equivalent potential temperature. Mon. Wea. Rev., 108, 1046–1053, https://doi.org/10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Browning, K., 1971: Radar measurements of air motion near fronts. Weather, 26, 320–340, https://doi.org/10.1002/j.1477-8696.1971.tb04211.x.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Carlson, T. N., 1980: Airflow through midlatitude cyclones and the comma cloud pattern. Mon. Wea. Rev., 108, 1498–1509, https://doi.org/10.1175/1520-0493(1980)108<1498:ATMCAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Cram, T. A., J. Persing, M. T. Montgomery, and S. A. Braun, 2007: A Lagrangian trajectory view on transport and mixing processes between the eye, eyewall, and environment using a high-resolution simulation of Hurricane Bonnie (1998). J. Atmos. Sci., 64, 1835–1856, https://doi.org/10.1175/JAS3921.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Davis, C. A., S. C. Jones, and M. Riemer, 2008: Hurricane vortex dynamics during Atlantic extratropical transition. J. Atmos. Sci., 65, 714–736, https://doi.org/10.1175/2007JAS2488.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • De Silva, V., and J. B. Tenenbaum, 2004: Sparse multidimensional scaling using landmark points. Tech. Rep., Stanford University, 41 pp.

  • Doms, G., and M. Schättler, 2002: A description of the nonhydrostatic regional model LM. Part I: Dynamics and numerics. Deutscher Wetterdienst, 140 pp., http://www.cosmo-model.org.

  • Doms, G., and Coauthors, 2011: A description of the nonhydrostatic regional COSMO model: Part II: Physical parameterization. Consortium for Small-Scale Modeling Doc., Deutscher Wetterdienst, 161 pp.

  • Eiter, T., and H. Mannila, 1994: Computing discrete Fréchet distance. Tech. Rep. CD-TR 94/64, Information Systems Dept., Technical University of Vienna, 7 pp.

  • Eliassen, A., and E. Kleinschmidt, 1957: Dynamic meteorology. Handbuch der Physik, S. Flügge, Ed., Vol. 48, Springer, 1–154.

    • Crossref
    • Export Citation

  • Euler, C., M. Riemer, T. Kremer, and E. Schömer, 2019: Lagrangian description of air masses associated with latent heat release in Tropical Storm Karl (2016) during extratropical transition. Mon. Wea. Rev., 147, 2657–2676, https://doi.org/10.1175/MWR-D-18-0422.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Evans, C., and Coauthors, 2017: The extratropical transition of tropical cyclones. Part I: Cyclone evolution and direct impacts. Mon. Wea. Rev., 145, 4317–4344, https://doi.org/10.1175/MWR-D-17-0027.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Frank, W. M., and E. A. Ritchie, 2001: Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 129, 2249–2269, https://doi.org/10.1175/1520-0493(2001)129<2249:EOVWSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Fréchet, M. M., 1906: Sur quelques points du calcul fonctionnel. Rend. Circ. Matemat. Palermo, 22, 1–72, https://doi.org/10.1007/BF03018603.

  • Hamilton, R., and J. Archbold, 1945: Meteorology of Nigeria and adjacent territory. Quart. J. Roy. Meteor. Soc., 71, 231–264, https://doi.org/10.1002/qj.49707130905.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hart, N. C. G., S. L. Gray, and P. A. Clark, 2015: Detection of coherent airstreams using cluster analysis: Application to an extratropical cyclone. Mon. Wea. Rev., 143, 3518–3531, https://doi.org/10.1175/MWR-D-14-00382.1.

    • Crossref
    • 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, 1052–1092, https://doi.org/10.1175/1520-0434(2003)018<1052:TETOTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Joos, H., and R. M. Forbes, 2016: Impact of different IFS microphysics on a warm conveyor belt and the downstream flow evolution. Quart. J. Roy. Meteor. Soc., 142, 2727–2739, https://doi.org/10.1002/qj.2863.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kjellsson, J., K. Döös, F. Laliberté, and J. D. Zika, 2014: The atmospheric general circulation in thermodynmaical coordinates. J. Atmos. Sci., 71, 916–928, https://doi.org/10.1175/JAS-D-13-0173.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Klein, P. M., P. A. Harr, and R. L. Elsberry, 2000: Extratropical transition of western North Pacific tropical cyclones: An overview and conceptual model of the transformation stage. Wea. Forecasting, 15, 373–395, https://doi.org/10.1175/1520-0434(2000)015<0373:ETOWNP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kruskal, J. B., 1964: Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115–129, https://doi.org/10.1007/BF02289694 .

  • Kumpf, A., M. Rautenhaus, M. Riemer, and R. Westermann, 2019: Visual analysis of the temporal evolution of ensemble forecast sensitivities. IEEE Trans. Vis. Comput. Graph., 25, 98–108, https://doi.org/10.1109/TVCG.2018.2864901.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Lentink, H. S., C. M. Grams, M. Riemer, and S. C. Jones, 2018: The effects of orography on the extratropical transition of tropical cyclones: A case study of Typhoon Sinlaku (2008). Mon. Wea. Rev., 146, 4231–4246, https://doi.org/10.1175/MWR-D-18-0150.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Molinari, J., D. Vollaro, and K. L. Corbosiero, 2004: Tropical cyclone formation in a sheared environment: A case study. J. Atmos. Sci., 61, 2493–2509, https://doi.org/10.1175/JAS3291.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Okubo, A., 1970: Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Res., 17, 445–454, https://doi.org/10.1016/0011-7471(70)90059-8.

    • Search Google Scholar
    • Export Citation

  • Papritz, L., and S. Schemm, 2013: Development of an idealised downstream cyclone: Eulerian and Lagrangian perspective on the kinetic energy. Tellus, 65A, 19539, https://doi.org/10.3402/tellusa.v65i0.19539.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Pasch, R. J., and D. A. Zelinsky, 2016: Tropical Storm Karl (14–25 September). Tech. Rep. AL122016, NOAA/National Hurricane Center, 17 pp, https://www.nhc.noaa.gov/data/tcr/AL122016_Karl.pdf.

  • Riehl, H., 1954: Tropical Meteorology. McGraw-Hill, 392 pp.

  • Riemer, M., and M. T. Montgomery, 2011: Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear. Atmos. Chem. Phys., 11, 9395–9414, https://doi.org/10.5194/acp-11-9395-2011.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Riemer, M., and F. Laliberté, 2015: Secondary circulation of tropical cyclones in vertical wind shear: Lagrangian diagnostic and pathways of environmental interaction. J. Atmos. Sci., 72, 3517–3536, https://doi.org/10.1175/JAS-D-14-0350.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Riemer, M., M. T. Montgomery, and M. E. Nicholls, 2010: A new paradigm for intensity modification of tropical cyclones: Thermodynamic impact of vertical wind shear on the inflow layer. Atmos. Chem. Phys., 10, 3163–3188, https://doi.org/10.5194/acp-10-3163-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Riemer, M., M. T. Montgomery, and M. E. Nicholls, 2013: Further examination of the thermodynamic modification of the inflow layer of tropical cyclones by vertical wind shear. Atmos. Chem. Phys., 13, 327–346, https://doi.org/10.5194/acp-13-327-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016a: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part I: Katia (2011). J. Atmos. Sci., 73, 71–93, https://doi.org/10.1175/JAS-D-15-0052.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016b: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part II: Ophelia (2011). J. Atmos. Sci., 73, 1555–1575, https://doi.org/10.1175/JAS-D-15-0245.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Rios-Berrios, R., C. A. Davis, and R. D. Torn, 2018: A hypothesis for the intensification of tropical cyclones under moderate vertical wind shear. J. Atmos. Sci., 75, 4149–4173, https://doi.org/10.1175/JAS-D-18-0070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Schäfler, A., and Coauthors, 2018: The North Atlantic waveguide and downstream impact experiment. Bull. Amer. Meteor. Soc., 99, 1607–1637, https://doi.org/10.1175/BAMS-D-17-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Simpson, R., and R. Riehl, 1958: Mid-tropospheric ventilation as a constraint on hurricane development and maintenance. Preprints, Tech. Conf. on Hurricanes, Miami Beach, FL, Amer. Meteor. Soc., D4-1–D4-10.

  • Steppeler, J., G. Doms, U. Schättler, H. W. Bitzer, A. Gassmann, U. Damrath, and G. Gregoric, 2003: Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteor. Atmos. Phys., 82, 75–96, https://doi.org/10.1007/s00703-001-0592-9.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Stern, D. P., and F. Zhang, 2013: How does the eye warm? Part II: Sensitivity to vertical wind shear and a trajectory analysis. J. Atmos. Sci., 70, 1849–1873, https://doi.org/10.1175/JAS-D-12-0258.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Tang, B., and K. Emanuel, 2010: Midlevel ventilation’s constraint on tropical cyclone intensity. J. Atmos. Sci., 67, 1817–1830, https://doi.org/10.1175/2010JAS3318.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Theisel, H., and C. Rössl, 2012: Streamline embedding for 3D vector field exploration. IEEE Trans. Vis. Comput. Graph., 18, 407–420, https://doi.org/10.1109/TVCG.2011.78.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1779–1800, https://doi.org/10.1175/1520-0493(1989)117<1779:ACMFSF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Visvaligam, M., and J. D. Whyatt, 1993: Line generalisation by repeated elimination of points. Cartogr. J., 30, 46–51, https://doi.org/10.1179/caj.1993.30.1.46.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Weiss, J., 1991: The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D, 48, 273–294, https://doi.org/10.1016/0167-2789(91)90088-Q.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Wernli, B. H., and H. C. Davies, 1997: A Lagrangian-based analysis of extratropical cyclones. I: The method and some applications. Quart. J. Roy. Meteor. Soc., 123, 467–489, https://doi.org/10.1002/qj.49712353811.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd ed. International Geophysics Series, Vol. 100, Academic Press, 704 pp.

  • Willoughby, H. E., F. D. Marks, and R. J. Feinberg, 1984: Stationary and moving convective bands in hurricanes. J. Atmos. Sci., 41, 3189–3211, https://doi.org/10.1175/1520-0469(1984)041<3189:SAMCBI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Article Type:
Research Article

Cluster Analysis Tailored to Structure Change of Tropical Cyclones Using a Very Large Number of Trajectories

Tobias Kremer 1 , Elmar Schömer 1 , Christian Euler 2 , and Michael Riemer 2
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  • 1 Institute of Computer Science, Johannes Gutenberg University Mainz, Mainz, Germany
  • 2 Institute for Atmospheric Physics, Johannes Gutenberg University Mainz, Mainz, Germany
Published-online:
28 Sep 2020
Print Publication:
01 Oct 2020
Collections:
Waves to Weather (W2W)
DOI:
https://doi.org/10.1175/MWR-D-19-0408.1
Page(s):
4209–4229
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Abstract

Major airstreams in tropical cyclones (TCs) are rarely described from a Lagrangian perspective. Such a perspective, however, is required to account for asymmetries and time dependence of the TC circulation. We present a procedure that identifies main airstreams in TCs based on trajectory clustering. The procedure takes into account the TC’s large degree of inherent symmetry and is suitable for a very large number of trajectories [O⁡(106)]. A large number of trajectories may be needed to resolve both the TC’s inner-core convection as well as the larger-scale environment. We define similarity of trajectories based on their shape in a storm-relative reference frame, rather than on proximity in physical space, and use Fréchet distance, which emphasizes differences in trajectory shape, as a similarity metric. To make feasible the use of this elaborate metric, data compression is introduced that approximates the shape of trajectories in an optimal sense. To make clustering of large numbers of trajectories computationally feasible, we reduce dimensionality in distance space by so-called landmark multidimensional scaling. Finally, k-means clustering is performed in this low-dimensional space. We investigate the extratropical transition of Tropical Storm Karl (2016) to demonstrate the applicability of our clustering procedure. All identified clusters prove to be physically meaningful and describe distinct flavors of inflow, ascent, outflow, and quasi-horizontal motion in Karl’s vicinity. Importantly, the clusters exhibit gradual temporal evolution, which is most notable because the clustering procedure itself does not impose temporal consistency on the clusters. Finally, TC problems are discussed for which the application of the clustering procedures seems to be most fruitful.

Denotes content that is immediately available upon publication as open access.

This article is included in the Waves to Weather (W2W) Special Collection.

Corresponding author: Michael Riemer, mriemer@uni-mainz.de

Abstract

Major airstreams in tropical cyclones (TCs) are rarely described from a Lagrangian perspective. Such a perspective, however, is required to account for asymmetries and time dependence of the TC circulation. We present a procedure that identifies main airstreams in TCs based on trajectory clustering. The procedure takes into account the TC’s large degree of inherent symmetry and is suitable for a very large number of trajectories [O⁡(106)]. A large number of trajectories may be needed to resolve both the TC’s inner-core convection as well as the larger-scale environment. We define similarity of trajectories based on their shape in a storm-relative reference frame, rather than on proximity in physical space, and use Fréchet distance, which emphasizes differences in trajectory shape, as a similarity metric. To make feasible the use of this elaborate metric, data compression is introduced that approximates the shape of trajectories in an optimal sense. To make clustering of large numbers of trajectories computationally feasible, we reduce dimensionality in distance space by so-called landmark multidimensional scaling. Finally, k-means clustering is performed in this low-dimensional space. We investigate the extratropical transition of Tropical Storm Karl (2016) to demonstrate the applicability of our clustering procedure. All identified clusters prove to be physically meaningful and describe distinct flavors of inflow, ascent, outflow, and quasi-horizontal motion in Karl’s vicinity. Importantly, the clusters exhibit gradual temporal evolution, which is most notable because the clustering procedure itself does not impose temporal consistency on the clusters. Finally, TC problems are discussed for which the application of the clustering procedures seems to be most fruitful.

Denotes content that is immediately available upon publication as open access.

This article is included in the Waves to Weather (W2W) Special Collection.

Corresponding author: Michael Riemer, mriemer@uni-mainz.de
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