• Anwender, D., , P. A. Harr, , and S. C. Jones, 2008: Predictability associated with the downstream impacts of the extratropical transition of tropical cyclones: Case studies. Mon. Wea. Rev., 136, 32263247.

    • Search Google Scholar
    • Export Citation
  • Barkmeijer, J., , R. Buizza, , T. N. Palmer, , K. Puri, , and J.-F. Mahfouf, 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
  • Buizza, R., , and A. Montani, 1999: Targeting observations using singular vectors. J. Atmos. Sci., 56, 29652985.

  • Chen, J.-H., , M. S. Peng, , C. A. Reynolds, , and C.-C. Wu, 2009: Interpretation of tropical cyclone forecast sensitivity from the singular vector perspective. J. Atmos. Sci., 66, 33833400.

    • Search Google Scholar
    • Export Citation
  • Diaconescu, E. P., , and R. Laprise, 2012: Singular vectors in atmospheric sciences: A review. Earth-Sci. Rev., 113 (34), 161175, doi:10.1016/j.earscirev.2012.05.005.

    • Search Google Scholar
    • Export Citation
  • Errico, R. M., 1997: What is an adjoint model? Bull. Amer. Meteor. Soc., 78, 25772591.

  • Fiorino, M., , and R. L. Elsberry, 1989: Some aspects of vortex structure related to tropical cyclone motion. J. Atmos. Sci., 46, 975990.

    • Search Google Scholar
    • Export Citation
  • Giering, R., , and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24, 437474.

  • Harnisch, F., , and M. Weissmann, 2010: Sensitivity of typhoon forecasts to different subsets of targeted dropsonde observations. Mon. Wea. Rev., 138, 26642680.

    • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 364 pp.

  • Kim, H. M., , and B.-J. Jung, 2009: Singular vector structure and evolution of a recurving tropical cyclone. Mon. Wea. Rev., 137, 505524.

    • Search Google Scholar
    • Export Citation
  • Kloosterziel, R., , and G. van Heijst, 1991: An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech., 223, 124.

    • Search Google Scholar
    • Export Citation
  • Komori, T., , and T. Kadowaki, 2010: Resolution dependence of singular vectors computed for Typhoon Sinlaku. SOLA, 6, 4548.

  • Kuo, H.-C., , R. T. Williams, , and J.-H. Chen, 1999: A possible mechanism for the eye rotation of Typhoon Herb. J. Atmos. Sci., 56, 16591673.

    • Search Google Scholar
    • Export Citation
  • Lang, S. T. K., , S. C. Jones, , M. Leutbecher, , M. S. Peng, , and C. A. Reynolds, 2012: Sensitivity, structure, and dynamics of singular vectors associated with Hurricane Helene (2006). J. Atmos. Sci., 69, 675694.

    • 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.

  • Nolan, D. S., , and B. F. Farrell, 1999: Generalized stability analyses of asymmetric disturbances in one- and two-celled vortices maintained by radial inflow. J. Atmos. Sci., 56, 12821307.

    • Search Google Scholar
    • Export Citation
  • Orr, W. M., 1907: Stability or instability of the steady motions of a perfect liquid. Proc. Roy. Irish Acad., 27, 969.

  • Palmer, T. N., , R. Gelaro, , J. Barkmeijer, , and R. Buizza, 1998: Singular vectors, metrics, and adaptive observations. J. Atmos. Sci., 55, 633653.

    • Search Google Scholar
    • Export Citation
  • Peng, J., , T. Li, , M. S. Peng, , and X. Ge, 2009: Barotropic instability in the tropical cyclone outer region. Quart. J. Roy. Meteor. Soc., 135, 851864.

    • Search Google Scholar
    • Export Citation
  • Peng, M. S., , and C. A. Reynolds, 2006: Sensitivity of tropical cyclone forecasts as revealed by singular vectors. J. Atmos. Sci., 63, 25082528.

    • Search Google Scholar
    • Export Citation
  • Puri, K., , J. Barkmeijer, , and T. N. 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
  • Reasor, P. D., , M. T. Montgomery, , F. D. Marks, , and J. F. Gamache, 2000: Low-wavenumber structure and evolution of the hurricane inner core observed by airborne dual-Doppler radar. Mon. Wea. Rev., 128, 16531680.

    • Search Google Scholar
    • Export Citation
  • Reynolds, C. A., , M. S. Peng, , and J.-H. Chen, 2009: Recurving tropical cyclones: Singular vector sensitivity and downstream impacts. Mon. Wea. Rev., 137, 13201337.

    • Search Google Scholar
    • Export Citation
  • Riemer, M., , and S. C. Jones, 2010: The downstream impact of tropical cyclones on a developing baroclinic wave in idealized scenarios of extratropical transition. Quart. J. Roy. Meteor. Soc., 136, 617637, doi:10.1002/qj.605.

    • Search Google Scholar
    • Export Citation
  • Riemer, M., , S. C. Jones, , and C. A. Davis, 2008: The impact of extratropical transition on the downstream flow: An idealized modelling study with a straight jet. Quart. J. Roy. Meteor. Soc., 134, 6991, doi:10.1002/qj.189.

    • Search Google Scholar
    • Export Citation
  • Ritchie, E. A., , and R. L. Elsberry, 2007: Simulations of the extratropical transition of tropical cyclones: Phasing between the upper-level trough and tropical cyclones. Mon. Wea. Rev., 135, 862–876.

    • Search Google Scholar
    • Export Citation
  • Rutherford, B., , G. Dangelmayr, , and M. T. Montgomery, 2012: Lagrangian coherent structures in tropical cyclone intensification. Atmos. Chem. Phys., 12, 54835507, doi:10.5194/acp-12-5483-2012.

    • Search Google Scholar
    • Export Citation
  • Sapsis, T., , and G. Haller, 2009: Inertial particle dynamics in a hurricane. J. Atmos. Sci., 66, 24812492.

  • Scheck, L., , S. C. Jones, , and M. Juckes, 2011a: The resonant interaction of a tropical cyclone and a tropopause front in a barotropic model. Part I: Zonally oriented front. J. Atmos. Sci., 68, 405419.

    • Search Google Scholar
    • Export Citation
  • Scheck, L., , S. C. Jones, , and M. Juckes, 2011b: The resonant interaction of a tropical cyclone and a tropopause front in a barotropic model. Part II: Frontal waves. J. Atmos. Sci., 68, 420429.

    • Search Google Scholar
    • Export Citation
  • van Heijst, G. J. F., , and R. C. Kloosterziel, 1989: Tripolar vortices in a rotating fluid. Nature, 338, 569571.

  • Weber, H. C., , and R. K. Smith, 1993: The stability of barotropic vortices: Implications for tropical cyclone motion. Geophys. Astrophys. Fluid Dyn., 70 (1–4), 130, doi:10.1080/03091929308203584.

    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., , R. Sakai, , M. Kyoda, , T. Komori, , and T. Kadowaki, 2009: Typhoon Ensemble Prediction System developed at the Japan Meteorological Agency. Mon. Wea. Rev., 137, 25922604.

    • Search Google Scholar
    • Export Citation
  • Yamaguchi, M., , D. S. Nolan, , M. Iskandarani, , S. J. Majumdar, , M. S. Peng, , and C. A. Reynolds, 2011: Singular vectors for tropical cyclone-like vortices in a nondivergent barotropic framework. J. Atmos. Sci., 68, 2273–2291.

    • Search Google Scholar
    • Export Citation
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Singular Vectors for Barotropic, Hurricane-Like Vortices in Horizontal Shear: Structure and Perturbation Growth Mechanisms

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  • 1 Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Karlsruhe, Germany
  • | 2 Deutscher Wetterdienst, Offenbach, Germany
  • | 3 Engineering Mathematics and Computing Lab, Karlsruhe Institute of Technology, Karlsruhe, Germany
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Abstract

In this study the structure and evolution of singular vectors (SVs) for stable and unstable hurricane-like vortices in background flows with horizontal shear are investigated on f and β planes using a nondivergent barotropic model. With increasing shear strength, the singular values for stable vortices increase and the sensitive regions extend farther away from the vortex. The formation of β gyres leads to significant changes in the SV structure but has only weak influence on the singular values. For sufficiently strong anticyclonic shear, the initial SVs are aligned with streamlines connected to stagnation points. The evolved SVs are dominated by dipole structures, indicating a displacement of the vortex. The displacement is caused by the circulation associated with the initial SV perturbation outside of the vortex core, which grows by untilting and unshielding. This process is strongly enhanced by anticyclonic background shear. For both cyclonic and anticyclonic shear, the displacement by the perturbation circulation causes an additional displacement that is proportional to the shear strength. The shear-enhanced barotropic growth mechanism in stable vortices results in singular values that are comparable to those for unstable vortices without background shear. Perturbation growth involving the normal mode in barotropically unstable vortices suffers from background shear. The shear-induced modifications of the outer vortex regions cause a strong decrease of the singular value with increasing shear. For sufficiently strong shear, the SVs for unstable vortices grow by the same mechanism as for stable vortices.

Current affiliation: Hans-Ertel-Centre for Weather Research, Ludwig-Maximilians-Universität München, Munich, Germany.

Current affiliation: Engineering Mathematics and Computing Lab, Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany.

Corresponding author address: Leonhard Scheck, Karlsruher Institut für Technologie, Institut für Meteorologie und Klimaforschung, Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany. E-mail: leonhard.scheck@kit.edu

Abstract

In this study the structure and evolution of singular vectors (SVs) for stable and unstable hurricane-like vortices in background flows with horizontal shear are investigated on f and β planes using a nondivergent barotropic model. With increasing shear strength, the singular values for stable vortices increase and the sensitive regions extend farther away from the vortex. The formation of β gyres leads to significant changes in the SV structure but has only weak influence on the singular values. For sufficiently strong anticyclonic shear, the initial SVs are aligned with streamlines connected to stagnation points. The evolved SVs are dominated by dipole structures, indicating a displacement of the vortex. The displacement is caused by the circulation associated with the initial SV perturbation outside of the vortex core, which grows by untilting and unshielding. This process is strongly enhanced by anticyclonic background shear. For both cyclonic and anticyclonic shear, the displacement by the perturbation circulation causes an additional displacement that is proportional to the shear strength. The shear-enhanced barotropic growth mechanism in stable vortices results in singular values that are comparable to those for unstable vortices without background shear. Perturbation growth involving the normal mode in barotropically unstable vortices suffers from background shear. The shear-induced modifications of the outer vortex regions cause a strong decrease of the singular value with increasing shear. For sufficiently strong shear, the SVs for unstable vortices grow by the same mechanism as for stable vortices.

Current affiliation: Hans-Ertel-Centre for Weather Research, Ludwig-Maximilians-Universität München, Munich, Germany.

Current affiliation: Engineering Mathematics and Computing Lab, Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany.

Corresponding author address: Leonhard Scheck, Karlsruher Institut für Technologie, Institut für Meteorologie und Klimaforschung, Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany. E-mail: leonhard.scheck@kit.edu
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