Assimilating Vortex Position with an Ensemble Kalman Filter

Yongsheng Chen National Center for Atmospheric Research,* Boulder, Colorado

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Chris Snyder National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

Observations of hurricane position, which in practice might be available from satellite or radar imagery, can be easily assimilated with an ensemble Kalman filter (EnKF) given an operator that computes the position of the vortex in the background forecast. The simple linear updating scheme used in the EnKF is effective for small displacements of forecasted vortices from the true position; this situation is operationally relevant since hurricane position is often available frequently in time. When displacements of the forecasted vortices are comparable to the vortex size, non-Gaussian effects become significant and the EnKF’s linear update begins to degrade. Simulations using a simple two-dimensional barotropic model demonstrate the potential of the technique and show that the track forecast initialized with the EnKF analysis is improved. The assimilation of observations of the vortex shape and intensity, along with position, extends the technique’s effectiveness to larger displacements of the forecasted vortices than when assimilating position alone.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Dr. Yongsheng Chen, NCAR, P.O. Box 3000, Boulder, CO 80307-3000. Email: yochen@ucar.edu

Abstract

Observations of hurricane position, which in practice might be available from satellite or radar imagery, can be easily assimilated with an ensemble Kalman filter (EnKF) given an operator that computes the position of the vortex in the background forecast. The simple linear updating scheme used in the EnKF is effective for small displacements of forecasted vortices from the true position; this situation is operationally relevant since hurricane position is often available frequently in time. When displacements of the forecasted vortices are comparable to the vortex size, non-Gaussian effects become significant and the EnKF’s linear update begins to degrade. Simulations using a simple two-dimensional barotropic model demonstrate the potential of the technique and show that the track forecast initialized with the EnKF analysis is improved. The assimilation of observations of the vortex shape and intensity, along with position, extends the technique’s effectiveness to larger displacements of the forecasted vortices than when assimilating position alone.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Dr. Yongsheng Chen, NCAR, P.O. Box 3000, Boulder, CO 80307-3000. Email: yochen@ucar.edu

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  • Aberson, S. D., and M. DeMaria, 1994: Verification of a nested barotropic hurricane track forecast model (VICBAR). Mon. Wea. Rev., 122 , 28042815.

    • Search Google Scholar
    • Export Citation
  • Aberson, S. D., M. A. Bender, and R. E. Tuleya, 1998: Ensemble forecasting of tropical cyclone tracks. Preprints, 12th Conf. on Numerical Weather Prediction, Phoenix, AZ, Amer. Meteor. Soc., 290–292.

  • Anderson, J. L., B. Wyman, S. Zhang, and T. Hoar, 2005: Assimilation of surface pressure observations using an ensemble filter in an idealized global atmospheric prediction system. J. Atmos. Sci., 62 , 29252938.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., R. J. Ross, R. E. Tuleya, and Y. Kurihara, 1993: Improvements in tropical cyclone track and intensity forecasts using the GFDL initialization system. Mon. Wea. Rev., 121 , 20462061.

    • Search Google Scholar
    • Export Citation
  • Burpee, R. W., S. D. Aberson, J. L. Franklin, S. J. Lord, and R. E. Tuleya, 1996: The impact of Omega dropwindsondes on operational hurricane track forecast models. Bull. Amer. Meteor. Soc., 77 , 925933.

    • Search Google Scholar
    • Export Citation
  • Carr III, L. E., and R. T. Williams, 1989: Barotropic vortex stability to perturbations from axisymmetry. J. Atmos. Sci., 46 , 31773191.

    • Search Google Scholar
    • Export Citation
  • Chan, J. C., and R. T. Williams, 1987: Analytical and numerical studies of the beta-effect in tropical cyclone motion. Part I: Zero mean flow. J. Atmos. Sci., 44 , 12571265.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., and M. K. Yau, 2003: Asymmetric structures in a simulated landfalling hurricane. J. Atmos. Sci., 60 , 22942312.

  • Chen, Y., G. Brunet, and M. K. Yau, 2003: Spiral bands in a simulated hurricane. Part II: Wave activity diagnostics. J. Atmos. Sci., 60 , 12391256.

    • Search Google Scholar
    • Export Citation
  • Cheung, K. K. W., and J. C. L. Chan, 1999a: Ensemble forecasting of tropical cyclone motion using a barotropic model. Part I: Perturbations of the environment. Mon. Wea. Rev., 127 , 12291243.

    • Search Google Scholar
    • Export Citation
  • Cheung, K. K. W., and J. C. L. Chan, 1999b: Ensemble forecasting of tropical cyclone motion using a barotropic model. Part II: Perturbations of the vortex. Mon. Wea. Rev., 127 , 26172640.

    • Search Google Scholar
    • Export Citation
  • Davidson, N. E., and H. C. Weber, 2000: The BMRC high-resolution tropical cyclone prediction system: TC-LAPS. Mon. Wea. Rev., 128 , 12451265.

    • Search Google Scholar
    • Export Citation
  • DeMaria, M., S. D. Aberson, K. V. Ooyama, and S. J. Lord, 1992: A nested spectral model for hurricane track forecasting. Mon. Wea. Rev., 120 , 16281643.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., F. Zhang, L. J. Wicker, C. Snyder, and N. A. Crook, 2004: Wind and thermodynamic retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132 , 19822005.

    • Search Google Scholar
    • Export Citation
  • Dvorak, V. F., 1975: Tropical cyclone intensity analysis and forecasting from satellite imagery. Mon. Wea. Rev., 103 , 420430.

  • Dvorak, V. F., 1984: Tropical cyclone intensity analysis using satellite data. NOAA Tech. Rep. NESDIS 11, 47 pp.

  • Elsberry, R., 1995: Tropical cyclone motion. Global Perspective on Tropical Cyclones, WMO/TD 693, R. Elsberry, Ed., WMO, 160–197.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 , 1014310162.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53 , 343367.

  • Franklin, J. L., C. J. McAdie, and M. B. Lawrence, 2003: Trends in track forecasting for tropical cyclones threatening the United States, 1970–2001. Bull. Amer. Meteor. Soc., 84 , 11971203.

    • Search Google Scholar
    • Export Citation
  • Gray, W. M., C. Neumann, and T. L. Tsui, 1991: Assessment of the role of aircraft reconnaissance on tropical cyclone analysis and forecasting. Bull. Amer. Meteor. Soc., 72 , 18671883.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter–3D variational analysis scheme. Mon. Wea. Rev., 128 , 29052919.

  • Heming, J. T., S. Robinson, C. Woolcock, and K. Mylne, 2004: Tropical cyclone ensemble forecast product development and verification at the Met Office. Preprints, 26th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 158–159.

  • Hoffman, B. N., Z. Liu, J-F. Louis, and C. Grassotti, 1995: Distortion representation of forecast errors. Mon. Wea. Rev., 123 , 27582770.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and H. L. Mitchell, 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 126 , 796811.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner, M. Charron, L. Spacek, and B. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133 , 604620.

    • Search Google Scholar
    • Export Citation
  • Kalman, R. E., 1960: A new approach to linear filtering and prediction problems. J. Basic Eng., 82D , 3545.

  • Kalman, R. E., and R. S. Bucy, 1961: New results in linear filtering and prediction theory. J. Basic Eng., 83D , 95108.

  • Krishnamurti, T. N., R. Correa-Torres, G. Rohaly, and D. Oosterhof, 1997: Physical initialization and hurricane ensemble forecasts. Wea. Forecasting, 12 , 503514.

    • Search Google Scholar
    • Export Citation
  • Kuhl, F. P., and C. R. Giardina, 1982: Elliptic Fourier features of a closed contour. Comput. Graphics Image Process., 18 , 236258.

  • Kurihara, Y., M. A. Bender, and R. J. Ross, 1993: An initialization scheme of hurricane models by vortex specification. Mon. Wea. Rev., 121 , 20302045.

    • Search Google Scholar
    • Export Citation
  • Kurihara, Y., R. E. Tuleya, and M. A. Bender, 1998: The GFDL hurricane prediction system and its performance in the 1995 hurricane season. Mon. Wea. Rev., 126 , 13061322.

    • Search Google Scholar
    • Export Citation
  • Lawson, G. W., and J. A. Hansen, 2005: Alignment error models and ensemble-based data assimilation. Mon. Wea. Rev., 133 , 16871709.

  • Leidner, S. M., L. Isaksen, and R. N. Hoffman, 2003: Impact of NSCAT winds on tropical cyclones in the ECMWF 4DVAR assimilation system. Mon. Wea. Rev., 131 , 326.

    • Search Google Scholar
    • Export Citation
  • Leslie, L. M., and G. J. Holland, 1995: On the bogussing of tropical cyclones in numerical models: A comparison of vortex profiles. Meteor. Atmos. Phys., 56 , 101110.

    • Search Google Scholar
    • Export Citation
  • Liu, Q., T. Marchok, H-L. Pan, M. Bender, and S. Lord, 2002: Improvements in hurricane initialization and forecasting at NCEP with global and regional (GFDL) models. Tech. Procedures Bull. 472, NCEP/EMC Tech. Rep., 7 pp.

  • Liu, Y., D-L. Zhang, and M. K. Yau, 1997: A multiscale numerical study of Hurricane Andrew (1992). Part I: Explicit simulation and verification. Mon. Wea. Rev., 125 , 30733093.

    • Search Google Scholar
    • Export Citation
  • Lord, S. J., 1991: A bogusing system for vortex circulations in the National Meteorological Center global forecast model. Preprints, 19th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 328–330.

  • Marchok, T. P., Z. Toth, and Q. Liu, 2002: Use of the NCEP global ensemble for tropical cyclone track forecasting. Preprints, 25th Conf. on Hurricanes and Tropical Meteorology, San Diego, CA, Amer. Meteor. Soc., 176–177.

  • Melander, M. V., J. C. McWilliams, and N. J. Zabusky, 1987: Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation. J. Fluid Mech., 178 , 137159.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., P. L. Houtekamer, and G. Pelerin, 2002: Ensemble size, balance, and model-error representation in an ensemble Kalman filter. Mon. Wea. Rev., 130 , 27912808.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and R. J. Kallenbach, 1997: A theory for vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes. Quart. J. Roy. Meteor. Soc., 123 , 435465.

    • Search Google Scholar
    • Export Citation
  • Morss, R. E., K. A. Emanuel, and C. Snyder, 2001: Idealized adaptive observation strategies for improving numerical weather prediction. J. Atmos. Sci., 58 , 210232.

    • Search Google Scholar
    • Export Citation
  • Pu, Z., and S. A. Braun, 2001: Evaluation of bogus vortex techniques with four-dimensional variational data assimilation. Mon. Wea. Rev., 129 , 20232039.

    • Search Google Scholar
    • Export Citation
  • Ravela, S., K. Emanuel, and D. McLaughlin, 2004: Data assimilation by field alignment for coherent structures. Preprints, 26th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 560–561.

  • Serrano, E., and P. Undén, 1994: Evaluation of a tropical cyclone bogusing method in data assimilation and forecasting. Mon. Wea. Rev., 122 , 15231547.

    • Search Google Scholar
    • Export Citation
  • Smith, G. B., and M. T. Montgomery, 1995: Vortex axisymmetrization: Dependence on azimuthal wavenumber or asymmetric radial structure changes. Quart. J. Roy. Meteor. Soc., 121 , 16151650.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., 1991: An analytic theory of tropical-cyclone motion in a barotropic shear flow. Quart. J. Roy. Meteor. Soc., 117 , 685714.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., W. Ulrich, and G. Dietachmayer, 1990: A numerical study of tropical cyclone motion using a barotropic model. Part I: The role of vortex asymmetries. Quart. J. Roy. Meteor. Soc., 116 , 337362.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131 , 16631677.

    • Search Google Scholar
    • Export Citation
  • Sutyrin, G. G., 1989: Azimuthal waves and symmetrization of an intense vortex. Sov. Phys. Dokl., 34 , 104106.

  • Vigh, J., 2004: Evaluation of a kilo-member ensemble for track forecasting. Preprints, 26th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 160–161.

  • Wang, Y., 2002: Vortex Rossby waves in a numerically simulated tropical cyclone. Part II: The role in tropical cyclone structure and intensity change. J. Atmos. Sci., 59 , 12391262.

    • Search Google Scholar
    • Export Citation
  • Weber, H., 2003: Hurricane track prediction using a statistical ensemble of numerical models. Mon. Wea. Rev., 131 , 749770.

  • Whitaker, J., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130 , 19131924.

  • Xiao, Q., X. Zou, and B. Wang, 2000: Initialization and simulation of a landfalling hurricane using a variational bogus data assimilation scheme. Mon. Wea. Rev., 128 , 22522269.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132 , 12381253.

    • Search Google Scholar
    • Export Citation
  • Zhang, Z., and T. N. Krishnamurti, 1997: Ensemble forecasting of hurricane tracks. Bull. Amer. Meteor. Soc., 78 , 27852795.

  • Zhang, Z., and T. N. Krishnamurti, 1999: A perturbation method for hurricane ensemble predictions. Mon. Wea. Rev., 127 , 447469.

  • Zhu, T., D-L. Zhang, and F. Weng, 2002: Impact of the Advanced Microwave Sounding Unit measurements on hurricane prediction. Mon. Wea. Rev., 130 , 24162432.

    • Search Google Scholar
    • Export Citation
  • Zou, X., and Q. Xiao, 2000: Studies on the initialization and simulation of a mature hurricane using a variational bogus data assimilation scheme. J. Atmos. Sci., 57 , 836860.

    • Search Google Scholar
    • Export Citation
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