A Three-Dimensional Trajectory Model with Advection Correction for Tropical Cyclones: Algorithm Description and Tests for Accuracy

William Miller Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

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Da-Lin Zhang Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

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https://orcid.org/0000-0003-1725-283X
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Abstract

When computing trajectories from model output, gridded winds are often temporally interpolated to a time step shorter than model output intervals to satisfy computational stability constraints. This study investigates whether trajectory accuracy may be improved for tropical cyclone (TC) applications by interpolating the model winds using advection correction (AC) instead of the traditional linear interpolation in time (LI) method. Originally developed for Doppler radar processing, AC algorithms interpolate data in a reference frame that moves with the pattern translation, or advective flow velocity. A previously developed trajectory AC implementation is modified here by extending it to three-dimensional (3D) flows, and the advective flows are defined in cylindrical rather than Cartesian coordinates. This AC algorithm is tested on two model-simulated TC cases, Hurricanes Joaquin (2015) and Wilma (2005). Several variations of the AC algorithm are compared to LI on a sample of 10 201 backward trajectories computed from the modeled 5-min output data, using reference trajectories computed from 1-min output to quantify position errors. Results show that AC of 3D wind vectors using advective flows defined as local gridpoint averages improves the accuracy of most trajectories, with more substantial improvements being found in the inner eyewall where the horizontal flows are dominated by rotating cyclonic wind perturbations. Furthermore, AC eliminates oscillations in vertical velocity along LI backward trajectories run through deep convective updrafts, leading to a ~2.5-km correction in parcel height after 20 min of integration.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Da-Lin Zhang, dalin@umd.edu

Abstract

When computing trajectories from model output, gridded winds are often temporally interpolated to a time step shorter than model output intervals to satisfy computational stability constraints. This study investigates whether trajectory accuracy may be improved for tropical cyclone (TC) applications by interpolating the model winds using advection correction (AC) instead of the traditional linear interpolation in time (LI) method. Originally developed for Doppler radar processing, AC algorithms interpolate data in a reference frame that moves with the pattern translation, or advective flow velocity. A previously developed trajectory AC implementation is modified here by extending it to three-dimensional (3D) flows, and the advective flows are defined in cylindrical rather than Cartesian coordinates. This AC algorithm is tested on two model-simulated TC cases, Hurricanes Joaquin (2015) and Wilma (2005). Several variations of the AC algorithm are compared to LI on a sample of 10 201 backward trajectories computed from the modeled 5-min output data, using reference trajectories computed from 1-min output to quantify position errors. Results show that AC of 3D wind vectors using advective flows defined as local gridpoint averages improves the accuracy of most trajectories, with more substantial improvements being found in the inner eyewall where the horizontal flows are dominated by rotating cyclonic wind perturbations. Furthermore, AC eliminates oscillations in vertical velocity along LI backward trajectories run through deep convective updrafts, leading to a ~2.5-km correction in parcel height after 20 min of integration.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Da-Lin Zhang, dalin@umd.edu
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  • Baker, J., 2010: Cluster analysis of long range air transport pathways and associated pollutant concentrations within the UK. Atmos. Environ., 44, 563571, https://doi.org/10.1016/j.atmosenv.2009.10.030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berg, R., 2016: National Hurricane Center tropical cyclone report: Hurricane Joaquin (28 September–7 October 2015). National Hurricane Center Tech. Rep. AL112015, 36 pp., https://www.nhc.noaa.gov/data/tcr/AL112015_Joaquin.pdf.

  • Bowman, K. P., J. C. Lin, A. Stohl, R. Draxler, P. Konopka, A. Andrews, and D. Brunner, 2013: Input data requirements for Lagrangian trajectory models. Bull. Amer. Meteor. Soc., 94, 10511058, https://doi.org/10.1175/BAMS-D-12-00076.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brankov, E., S. T. Rao, and P. S. Porter, 1998: A trajectory-clustering-correlation methodology for examining the long-range transport of air pollutants. Atmos. Environ., 32, 15251534, https://doi.org/10.1016/S1352-2310(97)00388-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Braun, S. A., 2002: A cloud-resolving simulation of Hurricane Bob (1991): Storm structure and eyewall buoyancy. Mon. Wea. Rev., 130, 15731592, https://doi.org/10.1175/1520-0493(2002)130<1573:ACRSOH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Braun, S. A., M. T. Montgomery, and X. Pu, 2006: High-resolution simulation of Hurricane Bonnie (1998). Part I: The organization of eyewall vertical motion. J. Atmos. Sci., 63, 1942, https://doi.org/10.1175/JAS3598.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cavallo, S. M., R. D. Torn, C. Snyder, W. Wang, and J. Done, 2013: Evaluation of the Advanced Hurricane WRF data assimilation system for the 2009 Atlantic hurricane season. Mon. Wea. Rev., 141, 523541, https://doi.org/10.1175/MWR-D-12-00139.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, H., and D.-L. Zhang, 2013: On the rapid intensification of Hurricane Wilma (2005). Part II: Convective bursts and the upper-level warm core. J. Atmos. Sci., 70, 146162, https://doi.org/10.1175/JAS-D-12-062.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, H., D.-L. Zhang, J. Carton, and R. Atlas, 2011: On the rapid intensification of Hurricane Wilma (2005). Part I: Model prediction and structural changes. Wea. Forecasting, 26, 885901, https://doi.org/10.1175/WAF-D-11-00001.1.

    • 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, 18351856, https://doi.org/10.1175/JAS3921.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dahl, J. M. L., M. D. Parker, and L. J. Wicker, 2012: Uncertainties in trajectory calculations within near-surface mesocyclones of simulated supercells. Mon. Wea. Rev., 140, 29592966, https://doi.org/10.1175/MWR-D-12-00131.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., and H. B. Bluestein, 2002: The 8 June 1995 McLean, Texas, storm. Part I: Observations of cyclic tornadogenesis. Mon. Wea. Rev., 130, 26262648, https://doi.org/10.1175/1520-0493(2002)130<2626:TJMTSP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and Coauthors, 2017: A view of tropical cyclones from above: The Tropical Cyclone Intensity (TCI) Experiment. Bull. Amer. Meteor. Soc., 98, 21132134, https://doi.org/10.1175/BAMS-D-16-0055.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585604, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fierro, A. O., J. Simpson, M. A. LeMone, J. M. Straka, and B. F. Smull, 2009: On how hot towers fuel the Hadley cell: An observational and modeling study of line-organized convection in the equatorial trough from TOGA COARE. J. Atmos. Sci., 66, 27302746, https://doi.org/10.1175/2009JAS3017.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fierro, A. O., E. J. Zipser, M. A. LeMone, J. M. Straka, and J. Simpson, 2012: Tropical oceanic hot towers: Need they be undilute to transport energy from the boundary layer to the upper troposphere effectively? An answer based on trajectory analysis of a simulated TOGA COARE convective system. J. Atmos. Sci., 69, 195213, https://doi.org/10.1175/JAS-D-11-0147.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gal-Chen, T., 1982: Errors in fixed and moving frame of references: Applications for conventional and Doppler radar analysis. J. Atmos. Sci., 39, 22792300, https://doi.org/10.1175/1520-0469(1982)039<2279:EIFAMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gradshteyn, I. S., and I. M. Ryzhik, 2007: Table of Integrals, Series, and Products. 7th ed. Academic Press, 1171 pp.

  • Guimond, S. R., G. H. Heymsfield, and F. J. Turk, 2010: Multiscale observations of Hurricane Dennis (2005): The effects of hot towers on rapid intensification. J. Atmos. Sci., 67, 633654, https://doi.org/10.1175/2009JAS3119.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, G. M., J. B. Halverson, J. Simpson, L. Tian, and T. P. Bui, 2001: ER-2 Doppler radar investigations of the eyewall of Hurricane Bonnie during the Convection and Moisture Experiment-3. J. Appl. Meteor., 40, 13101330, https://doi.org/10.1175/1520-0450(2001)040<1310:EDRIOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Homeyer, C. R., K. P. Bowman, L. L. Pan, E. L. Atlas, R.-S. Gao, and T. L. Campos, 2011: Dynamical and chemical characteristics of tropospheric intrusions observed during START08. J. Geophys. Res., 116, D06111, https://doi.org/10.1029/2010JD015098.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the north Atlantic basin. Wea. Forecasting, 18, 10931108, https://doi.org/10.1175/1520-0434(2003)018<1093:LCORIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kristiansen, N. I., and Coauthors, 2012: Performance assessment of a volcanic ash transport model mini-ensemble used for inverse modeling of the 2010 Eyjafjallajökull eruption. J. Geophys. Res., 117, D00U11, https://doi.org/10.1029/2011JD016844.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuo, Y.-H., M. Skumanich, P. L. Haagenson, and J. S. Chang, 1985: The accuracy of trajectory models as revealed by the observing system simulation experiments. Mon. Wea. Rev., 113, 18521867, https://doi.org/10.1175/1520-0493(1985)113<1852:TAOTMA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, Y., D.-L. Zhang, and M. K. Yau, 1999: A multiscale numerical study of Hurricane Andrew (1992). Part II: Kinematics and inner-core structures. Mon. Wea. Rev., 127, 25972616, https://doi.org/10.1175/1520-0493(1999)127<2597:AMNSOH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miller, W., and D.-L. Zhang, 2019: Understanding the unusual looping track of Hurricane Joaquin (2015) and its forecast errors. Mon. Wea. Rev., 147, 22312259, https://doi.org/10.1175/MWR-D-18-0331.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miller, W., H. Chen, and D.-L. Zhang, 2015: On the rapid intensification of Hurricane Wilma (2005). Part III: Effects of latent heat of fusion. J. Atmos. Sci., 72, 38293849, https://doi.org/10.1175/JAS-D-14-0386.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and R. K. Smith, 2014: Paradigms for tropical cyclone intensification. Aust. Meteor. Oceanogr. J., 64, 37–66.

    • Crossref
    • Export Citation
  • Onderlinde, M. J., and D. S. Nolan, 2016: Tropical cyclone–relative environmental helicity and the pathways to intensification in shear. J. Atmos. Sci., 73, 869890, https://doi.org/10.1175/JAS-D-15-0261.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pasch, R. J., E. S. Blake, H. D. Cobb III, and D. P. Roberts, 2006: Tropical cyclone report: Hurricane Wilma, 15–25 October 2005. NOAA/NHC Tech. Rep. AL252005, 27 pp., https://www.nhc.noaa.gov/data/tcr/AL252005_Wilma.pdf.

  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes in Fortran: The Art of Scientific Computing.Vol 1. 2nd ed. Cambridge University Press, 933 pp.

  • Qin, N., D.-L. Zhang, W. Miller, and C. Q. Kieu, 2018: On the rapid intensification of Hurricane Wilma (2005). Part IV: Inner-core dynamics during the steady RMW stage. Quart. J. Roy. Meteor. Soc., 144, 25082523, https://doi.org/10.1002/qj.3339.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R. F., P. D. Reasor, and J. A. Zhang, 2015: Multiscale structure and evolution of Hurricane Earl (2010) during rapid intensification. Mon. Wea. Rev., 143, 536562, https://doi.org/10.1175/MWR-D-14-00175.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rössler, C. E., T. Paccagnella, and St. Tibaldi, 1992: A three-dimensional atmospheric trajectory model: Application to a case study of Alpine lee cyclogenesis. Meteor. Atmos. Phys., 50, 211229, https://doi.org/10.1007/BF01026018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shapiro, A., K. M. Willingham, and C. K. Potvin, 2010: Spatially variable advection correction of radar data. Part I: Theoretical considerations. J. Atmos. Sci., 67, 34453456, https://doi.org/10.1175/2010JAS3465.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shapiro, A., S. Rahimi, C. K. Potvin, and L. Orf, 2015: On the use of advection correction in trajectory calculations. J. Atmos. Sci., 72, 42614280, https://doi.org/10.1175/JAS-D-15-0095.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

    • Crossref
    • 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, 18491873, https://doi.org/10.1175/JAS-D-12-0258.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stewart, J., 1999: Multivariable Calculus. 4th ed. Brooks/Cole, 511 pp.

  • Stoelinga, M. T., 2009: A users’ guide to RIP version 4.7: A program for visualizing mesoscale model output. UCAR, accessed 29 July 2019, http://www2.mmm.ucar.edu/wrf/users/docs/ripug.htm.

  • Stohl, A., 1996: Trajectory statistics—A new method to establish source-receptor relationships of air pollutants and its application to the transport of particulate sulfate in Europe. Atmos. Environ., 30, 579587, https://doi.org/10.1016/1352-2310(95)00314-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stohl, A., and H. Kromp-Kolb, 1994: Origin of ozone in Vienna and surroundings, Austria. Atmos. Environ., 28, 12551266, https://doi.org/10.1016/1352-2310(94)90272-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stohl, A., G. Wotawa, P. Seibert, and H. Kromp-Kolb, 1995: Interpolation errors in wind fields as a function of spatial and temporal resolution and their impact on different types of kinematic trajectories. J. Appl. Meteor., 34, 21492165, https://doi.org/10.1175/1520-0450(1995)034<2149:IEIWFA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1938: The spectrum of turbulence. Proc. Roy. Soc. London, 164A, 476490, https://doi.org/10.1098/rspa.1938.0032.

  • Taylor, G. I., and A. E. Green, 1937: Mechanism of the production of small eddies from large ones. Proc. Roy. Soc. London, 158A, 499521, https://www.jstor.org/stable/96892.

    • Search Google Scholar
    • Export Citation
  • Zhang, D.-L., Y. Liu, and M. K. Yau, 2001: A multiscale numerical study of Hurricane Andrew (1992). Part IV: Unbalanced flows. Mon. Wea. Rev., 129, 92107, https://doi.org/10.1175/1520-0493(2001)129<0092:AMNSOH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, J., and T. Gal-Chen, 1996: Single-Doppler wind retrieval in the moving frame of reference. J. Atmos. Sci., 53, 26092623, https://doi.org/10.1175/1520-0469(1996)053<2609:SDWRIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
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