A Three-Dimensional Hail Trajectory Clustering Technique

Rebecca D. Adams-Selin aVerisk Atmospheric and Environmental Research, Bellevue, Nebraska

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Abstract

Recent advances in hail trajectory modeling regularly produce datasets containing millions of hail trajectories. Because hail growth within a storm cannot be entirely separated from the structure of the trajectories producing it, a method to condense the multidimensionality of the trajectory information into a discrete number of features analyzable by humans is necessary. This article presents a three-dimensional trajectory clustering technique that is designed to group trajectories that have similar updraft-relative structures and orientations. The new technique is an application of a two-dimensional method common in the data mining field. Hail trajectories (or “parent” trajectories) are partitioned into segments before they are clustered using a modified version of the density-based spatial applications with noise (DBSCAN) method. Parent trajectories with segments that are members of at least two common clusters are then grouped into parent trajectory clusters before output. This multistep method has several advantages. Hail trajectories with structural similarities along only portions of their length, e.g., sourced from different locations around the updraft before converging to a common pathway, can still be grouped. However, the physical information inherent in the full length of the trajectory is retained, unlike methods that cluster trajectory segments alone. The conversion of trajectories to an updraft-relative space also allows trajectories separated in time to be clustered. Once the final output trajectory clusters are identified, a method for calculating a representative trajectory for each cluster is proposed. Cluster distributions of hailstone and environmental characteristics at each time step in the representative trajectory can also be calculated.

Significance Statement

To understand how a storm produces large hail, we need to understand the paths that hailstones take in a storm when growing. We can simulate these paths using computer models. However, the millions of hailstones in a simulated storm create millions of paths, which is hard to analyze. This article describes a machine learning method that groups together hailstone paths based on how similar their three-dimensional structures look. It will let hail scientists analyze hailstone pathways in storms more easily, and therefore better understand how hail growth happens.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Rebecca Adams-Selin, rselin@aer.com

Abstract

Recent advances in hail trajectory modeling regularly produce datasets containing millions of hail trajectories. Because hail growth within a storm cannot be entirely separated from the structure of the trajectories producing it, a method to condense the multidimensionality of the trajectory information into a discrete number of features analyzable by humans is necessary. This article presents a three-dimensional trajectory clustering technique that is designed to group trajectories that have similar updraft-relative structures and orientations. The new technique is an application of a two-dimensional method common in the data mining field. Hail trajectories (or “parent” trajectories) are partitioned into segments before they are clustered using a modified version of the density-based spatial applications with noise (DBSCAN) method. Parent trajectories with segments that are members of at least two common clusters are then grouped into parent trajectory clusters before output. This multistep method has several advantages. Hail trajectories with structural similarities along only portions of their length, e.g., sourced from different locations around the updraft before converging to a common pathway, can still be grouped. However, the physical information inherent in the full length of the trajectory is retained, unlike methods that cluster trajectory segments alone. The conversion of trajectories to an updraft-relative space also allows trajectories separated in time to be clustered. Once the final output trajectory clusters are identified, a method for calculating a representative trajectory for each cluster is proposed. Cluster distributions of hailstone and environmental characteristics at each time step in the representative trajectory can also be calculated.

Significance Statement

To understand how a storm produces large hail, we need to understand the paths that hailstones take in a storm when growing. We can simulate these paths using computer models. However, the millions of hailstones in a simulated storm create millions of paths, which is hard to analyze. This article describes a machine learning method that groups together hailstone paths based on how similar their three-dimensional structures look. It will let hail scientists analyze hailstone pathways in storms more easily, and therefore better understand how hail growth happens.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Rebecca Adams-Selin, rselin@aer.com
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  • Adams-Selin, R. D., and C. L. Ziegler, 2016: Forecasting hail using a one-dimensional hail growth model within WRF. Mon. Wea. Rev., 144, 49194939, https://doi.org/10.1175/MWR-D-16-0027.1.

    • Search Google Scholar
    • Export Citation
  • Adams-Selin, R. D., A. Clark, C. Melick, S. Dembek, I. Jirak, and C. Ziegler, 2019: Evolution of WRF-HAILCAST during the 2014-16 NOAA/Hazardous Weather Testbed Spring Forecasting Experiments. Wea. Forecasting, 34, 6179, https://doi.org/10.1175/WAF-D-18-0024.1.

    • Search Google Scholar
    • Export Citation
  • Adams-Selin, R. D., and Coauthors, 2023: Just what is “good”? Musings on hail forecast verification through evaluation of FV3-HAILCAST hail forecasts. Wea. Forecasting, 38, 371387, https://doi.org/10.1175/WAF-D-22-0087.1.

    • Search Google Scholar
    • Export Citation
  • Aggarwal, C. C., 2015: Data Mining: The Textbook. Vol. 1. Springer, 734 pp.

  • Allwayin, N., M. L. Larsen, A. G. Shaw, and R. A. Shaw, 2022: Automated identification of characteristic droplet size distributions in stratocumulus clouds utilizing a data clustering algorithm. Artif. Intell. Earth Syst., 1, e220003, https://doi.org/10.1175/AIES-D-22-0003.1.

    • Search Google Scholar
    • Export Citation
  • Ankerst, M., M. M. Breunig, H.-P. Kriegel, and J. Sander, 1999: OPTICS: Ordering points to identify the clustering structure. SIGMOD Rec., 28, 4960, https://doi.org/10.1145/304181.304187.

    • Search Google Scholar
    • Export Citation
  • Ayhan, S., and H. Samet, 2015: DICLERGE: Divide-cluster-merge framework for clustering aircraft trajectories. IWCTS’15: Proc. Eighth ACM SIGSPATIAL Int. Workshop on Computational Transportation Science, Seattle, WA, ACM, 7–14, https://doi.org/10.1145/2834882.2834887.

  • Brimelow, J. C., G. W. Reuter, and E. R. Poolman, 2002: Modeling maximum hail size in Alberta thunderstorms. Wea. Forecasting, 17, 10481062, https://doi.org/10.1175/1520-0434(2002)017<1048:MMHSIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, 29172928, https://doi.org/10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chu, X., X. Tan, and W. Zeng, 2022: A clustering ensemble method of aircraft trajectory based on the similarity matrix. Aerospace, 9, 269, https://doi.org/10.3390/aerospace9050269.

    • Search Google Scholar
    • Export Citation
  • Davenport, C. E., C. L. Ziegler, and M. I. Biggerstaff, 2019: Creating a more realistic idealized supercell thunderstorm evolution via incorporation of base-state environmental variability. Mon. Wea. Rev., 147, 41774198, https://doi.org/10.1175/MWR-D-18-0447.1.

    • Search Google Scholar
    • Export Citation
  • DiGangi, E. A., D. R. MacGorman, C. L. Ziegler, D. Betten, M. Biggerstaff, M. Bowlan, and C. K. Potvin, 2016: An overview of the 29 May 2012 Kingfisher supercell during DC3. J. Geophys. Res. Atmos., 121, 14 31614 343, https://doi.org/10.1002/2016JD025690.

    • Search Google Scholar
    • Export Citation
  • Duchon, C. E., 1979: Lanczos filtering in one and two dimensions. J. Appl. Meteor., 18, 10161022, https://doi.org/10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ester, M., H.-P. Kriegel, and X. Xu, 1996: A density-based algorithm for discovering clusters in large spatial databases with noise. KDD’96: Proc. Second Int. Conf. on Knowledge Discovery and Data Mining, Portland, OR, Association for the Advancement of Artificial Intelligence Press, 226–231, https://dl.acm.org/doi/10.5555/3001460.3001507.

  • Fuchs, B. R., E. C. Bruning, S. A. Rutledge, L. D. Carey, P. R. Krehbiel, and W. Rison, 2016: Climatological analyses of LMA data with an open-source lightning flash-clustering algorithm. J. Geophys. Res. Atmos., 121, 86258648, https://doi.org/10.1002/2015JD024663.

    • Search Google Scholar
    • Export Citation
  • Gensini, V. A., C. Converse, W. S. Ashley, and M. Taszarek, 2021: Machine learning classification of significant tornadoes and hail in the United States using ERA5 proximity soundings. Wea. Forecasting, 36, 21432160, https://doi.org/10.1175/WAF-D-21-0056.1.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and J. C. Pflaum, 1985: A quantitative assessment of the accuracy of techniques for calculating graupel growth. J. Atmos. Sci., 42, 22642274, https://doi.org/10.1175/1520-0469(1985)042<2264:AQAOTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and I. M. Giammanco, 2020: A workshop on North American hail and hailstorms: What next? Bull. Amer. Meteor. Soc., 101, E1576E1583, https://doi.org/10.1175/BAMS-D-18-0287.1.

    • Search Google Scholar
    • Export Citation
  • Jewell, R., and J. Brimelow, 2009: Evaluation of Alberta hail growth model using severe hail proximity soundings from the United States. Wea. Forecasting, 24, 15921609, https://doi.org/10.1175/2009WAF2222230.1.

    • Search Google Scholar
    • Export Citation
  • Kumjian, M. R., and K. Lombardo, 2020: A hail growth trajectory model for exploring the environmental controls on hail size: Model physics and idealized tests. J. Atmos. Sci., 77, 27652791, https://doi.org/10.1175/JAS-D-20-0016.1.

    • Search Google Scholar
    • Export Citation
  • Kumjian, M. R., K. Lombardo, and S. Loeffler, 2021: The evolution of hail production in simulated supercell storms. J. Atmos. Sci., 78, 34173440, https://doi.org/10.1175/JAS-D-21-0034.1.

    • Search Google Scholar
    • Export Citation
  • Lee, J.-G., J. Han, and K.-Y. Whang, 2007: Trajectory clustering: A partition-and-group framework. SIGMOD’07: Proc. 2007 ACM SIGMOD Int. Conf. on Management of Data, Beijing, China, Association for Computing Machinery, 593–604, https://doi.org/10.1145/1247480.1247546.

  • Lin, Y., and M. R. Kumjian, 2022: Influences of CAPE on hail production in simulated supercell storms. J. Atmos. Sci., 79, 179204, https://doi.org/10.1175/JAS-D-21-0054.1.

    • Search Google Scholar
    • Export Citation
  • Liu, L., Y. Zhang, Y. Hu, Y. Wang, J. Sun, and X. Dong, 2022: A hybrid-clustering model of ship trajectories for maritime traffic patterns analysis in port area. J. Mar. Sci. Eng., 10, 342, https://doi.org/10.3390/jmse10030342.

    • Search Google Scholar
    • Export Citation
  • Macklin, W. C., 1962: The density and structure of ice formed by accretion. Quart. J. Roy. Meteor. Soc., 88, 3050, https://doi.org/10.1002/qj.49708837504.

    • Search Google Scholar
    • Export Citation
  • Mansell, E. R., and C. L. Ziegler, 2013: Aerosol effects on simulated storm electrification and precipitation in a two-moment bulk microphysics model. J. Atmos. Sci., 70, 20322050, https://doi.org/10.1175/JAS-D-12-0264.1.

    • Search Google Scholar
    • Export Citation
  • Mansell, E. R., C. L. Ziegler, and E. C. Bruning, 2010: Simulated electrification of a small thunderstorm with two-moment bulk microphysics. J. Atmos. Sci., 67, 171194, https://doi.org/10.1175/2009JAS2965.1.

    • Search Google Scholar
    • Export Citation
  • McNicholas, C., and C. F. Mass, 2021: Bias correction, anonymization, and analysis of smartphone pressure observations using machine learning and multiresolution kriging. Wea. Forecasting, 36, 18671889, https://doi.org/10.1175/WAF-D-20-0222.1.

    • Search Google Scholar
    • Export Citation
  • Nelson, S. P., 1983: The influence of storm flow structure on hail growth. J. Atmos. Sci., 40, 19651983, https://doi.org/10.1175/1520-0469(1983)040<1965:TIOSFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nelson, S. P., 1987: The hybrid multicellular–supercellular storm—An efficient hail producer. Part II: General characteristics and implications for hail growth. J. Atmos. Sci., 44, 20602073, https://doi.org/10.1175/1520-0469(1987)044<2060:THMSEH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., and A. J. Heymsfield, 1987a: Melting and shedding of graupel and hail. Part I: Model physics. J. Atmos. Sci., 44, 27542763, https://doi.org/10.1175/1520-0469(1987)044<2754:MASOGA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., and A. J. Heymsfield, 1987b: Melting and shedding of graupel and hail. Part III: Investigation of the role of shed drops as hail embryos in the 1 August CCOPE severe storm. J. Atmos. Sci., 44, 27832803, https://doi.org/10.1175/1520-0469(1987)044<2783:MASOGA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Shannon, C. E., 1948: A mathematical theory of communication. Bell Syst. Tech. J., 27, 379423, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x.

    • Search Google Scholar
    • Export Citation
  • Shedd, L., M. R. Kumjian, I. Giammanco, T. Brown-Giammanco, and B. R. Maiden, 2021: Hailstone shapes. J. Atmos. Sci., 78, 639652, https://doi.org/10.1175/JAS-D-20-0250.1.

    • Search Google Scholar
    • Export Citation
  • Stough, S. M., L. D. Carey, C. J. Schultz, and D. J. Cecil, 2022: Supercell thunderstorm charge structure variability and influences on spatial lightning flash relationships with the updraft. Mon. Wea. Rev., 150, 843861, https://doi.org/10.1175/MWR-D-21-0071.1.

    • Search Google Scholar
    • Export Citation
  • Tuel, A., and O. Martius, 2022: Subseasonal temporal clustering of extreme precipitation in the Northern Hemisphere: Regionalization and physical drivers. J. Climate, 35, 35373555, https://doi.org/10.1175/JCLI-D-21-0562.1.

    • Search Google Scholar
    • Export Citation
  • Zhou, X., F. Miao, H. Ma, H. Zhang, and H. Gong, 2018: A trajectory regression clustering technique combining a novel fuzzy C-means clustering algorithm with the least squares method. ISPRS Int. J. Geoinfo., 7, 164, https://doi.org/10.3390/ijgi7050164

    • Search Google Scholar
    • Export Citation
  • Ziegler, C. L., 2013: NSSL MGAUS Oklahoma-Texas sounding data, version 1.0. UCAR/NCAR–Earth Observing Laboratory, accessed 4 May 2023, http://data.eol.ucar.edu/dataset/353.105.

  • Ziegler, C. L., P. S. Ray, and N. C. Knight, 1983: Hail growth in an Oklahoma multicell storm. J. Atmos. Sci., 40, 17681791, https://doi.org/10.1175/1520-0469(1983)040<1768:HGIAOM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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