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Advances in Meteorology
Volume 2010 (2010), Article ID 432160, 10 pages
http://dx.doi.org/10.1155/2010/432160
Review Article

Beating the Uncertainties: Ensemble Forecasting and Ensemble-Based Data Assimilation in Modern Numerical Weather Prediction

Department of Atmospheric Sciences, University of Utah, 135 S 1460 E, Rm. 819, Salt Lake City, UT 84112, USA

Received 1 January 2010; Revised 31 March 2010; Accepted 3 June 2010

Academic Editor: Hann-Ming Henry Juang

Copyright © 2010 Hailing Zhang and Zhaoxia Pu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Bjerknes, Dynamic Meteorology and Hydrography. Part II. Kinematics, Carnegie Institute, Gibson Bros, New York, USA, 1911.
  2. J. G. Charney, R. Fjörtoft, and J. V. Neumann, “Numerical integration of the barotropic vorticity equation,” Tellus, vol. 2, pp. 237–254, 1950.
  3. P. Thompson, Numerical Weather Analysis and Prediction, The Macmillan Company, New York, NY, USA, 1961.
  4. G. J. Haltine, Numerical Weather Prediction, John Wiley & Sons, New York, NY, USA, 1971.
  5. E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, Cambridge, UK, 2003.
  6. E. N. Lorenz, “The predictability of hydrodynamics flow,” Transactions of the New York Academy of Sciences Series II, vol. 25, no. 4, pp. 409–432, 1963.
  7. E. N. Lorenz, “A study of the predictability of a 28-variable atmospheric model,” Tellus, vol. 12, pp. 321–333, 1965.
  8. T. N. Palmer, “Predictability of weather and climate: from theory to practice,” in Predictability of Weather and Climate, chapter 1, pp. 1–29, Cambridge University Press, Cambridge, UK, 2006.
  9. E. S. Epstein, “Stochastic dynamic prediction,” Tellus, vol. 6, pp. 739–759, 1969.
  10. Z. Toth and E. Kalnay, “Ensemble forecasting at NCEP: the generation of perturbations,” Bulletin of the American Meteorological Society, vol. 74, pp. 2371–2330, 1993.
  11. Z. Toth and E. Kalnay, “Ensemble forecasting at NCEP and the breeding method,” Monthly Weather Review, vol. 125, no. 12, pp. 3297–3319, 1997. View at Scopus
  12. R. Buizza and T. N. Palmer, “The singular-vector structure of the atmospheric global circulation,” Journal of the Atmospheric Sciences, vol. 52, no. 9, pp. 1434–1456, 1995. View at Scopus
  13. F. Molteni, R. Buizza, T. N. Palmer, and T. Petroliagis, “The ECMWF Ensemble prediction system: methodology and validation,” Quarterly Journal of the Royal Meteorological Society, vol. 122, no. 529, pp. 73–119, 1996. View at Scopus
  14. M. Ehrendorfer and J. J. Tribbia, “Optimal prediction of forecast error covariances through singular vectors,” Journal of the Atmospheric Sciences, vol. 54, no. 2, pp. 286–313, 1997. View at Scopus
  15. P. L. Houtekamer, L. Lefaivre, J. Derome, H. Ritchie, and H. L. Mitchell, “A system simulation approach to Ensemble prediction,” Monthly Weather Review, vol. 124, no. 6, pp. 1225–1242, 1996. View at Scopus
  16. J. L. Anderson, “The impact of dynamical constraints on the selection of initial conditions for Ensemble predictions: low-order perfect model results,” Monthly Weather Review, vol. 125, no. 11, pp. 2969–2983, 1997. View at Scopus
  17. C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the Ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review, vol. 129, no. 3, pp. 420–436, 2001. View at Scopus
  18. M. Wei, Z. Toth, R. Wobus, and Y. Zhu, “Initial perturbations based on the Ensemble transform (ET) technique in the NCEP global operational forecast system,” Tellus, vol. 60, no. 1, pp. 62–79, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. T. N. Krishnamurti, C. M. Kishtawal, Z. Zhang et al., “Multimodel Ensemble forecasts for weather and seasonal climate,” Journal of Climate, vol. 13, no. 23, pp. 4196–4216, 2000. View at Scopus
  20. V. V. Kharin and F. W. Zwiers, “Climate predictions with multimodel Ensembles,” Journal of Climate, vol. 15, no. 7, pp. 793–799, 2002. View at Scopus
  21. R. Buizza, M. Miller, and T. N. Palmer, “Stochastic representation of model uncertainties in the ECMWF Ensemble prediction system,” Quarterly Journal of the Royal Meteorological Society, vol. 125, no. 560, pp. 2887–2908, 1999. View at Scopus
  22. G. Shutts and T. N. Palmer, “The use of high-resolution numerical simulations of tropical circulation to calibrate stochastic physics schemes,” in Proceedings of the Simulation and Prediction of Intra-seasonal Variability with Emphasis on the MJO (ECMWF/CLIVAR '04), pp. 83–102, European Centre for Medium-Range Weather Forecasts, Reading, UK, 2004.
  23. C. A. Reynolds, J. Teixeira, and J. G. McLay, “Impact of stochastic convection on the Ensemble transform,” Monthly Weather Review, vol. 136, no. 11, pp. 4517–4526, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. T. N. Palmer, “A nonlinear dynamical perspective model error: a proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models,” Quarterly Journal of the Royal Meteorological Society, vol. 127, no. 572, pp. 279–304, 2001. View at Publisher · View at Google Scholar · View at Scopus
  25. G. Shutts, “A kinetic energy backscatter algorithm for use in Ensemble prediction systems,” Quarterly Journal of the Royal Meteorological Society, vol. 131, no. 612, pp. 3079–3102, 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. J. Teixeira, C. A. Reynolds, and K. Judd, “Time step sensitivity of nonlinear atmospheric models: numerical convergence, truncation error growth, and Ensemble design,” Journal of the Atmospheric Sciences, vol. 64, no. 1, pp. 175–189, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. P. L. Houtekamer, L. Lefaivre, J. Derome, H. Ritchie, and H. L. Mitchell, “A system simulation approach to Ensemble prediction,” Monthly Weather Review, vol. 124, no. 6, pp. 1225–1242, 1996. View at Scopus
  28. M. S. Tracton and E. Kalnay, “Operational Ensemble prediction at the National Meteorological Center: practical aspects,” Weather & Forecasting, vol. 8, no. 3, pp. 379–398, 1993. View at Scopus
  29. Z.-X. Pu and E. Kalnay, “Targeting observations with the quasi-inverse linear and adjoint NCEP global models: performance during FASTEX,” Quarterly Journal of the Royal Meteorological Society, vol. 125, no. 561, pp. 3329–3337, 1999. View at Scopus
  30. A. C. Lorenc, “Analysis methods for numerical weather prediction,” Quarterly Journal of the Royal Meteorological Society, vol. 112, pp. 1177–1194, 1986.
  31. T. M. Hamill, “Ensemble-based atmospheric data assimilation,” in Predictability of Weather and Climate, pp. 124–156, Cambridge University Press, Cambridge, UK, 2006.
  32. J. L. Anderson, “Data assimilation research testbed tutorial note,” 2006, http://www.image.ucar.edu/DAReS/DART/DART_Documentation.php#tutorial_simple.
  33. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Transactions of the ASME: Journal of Basic Engineering, Series D, vol. 82, pp. 35–45, 1960.
  34. R. E. Kalman and R. Bucy, “New results in linear filtering and prediction theory,” Transactions of the ASME: Journal of Basic Engineering, Series D, vol. 83, pp. 95–108, 1961.
  35. G. Evensen, “The Ensemble Kalman filter: theoretical formulation and practical implementation,” Ocean Dynamics, vol. 53, pp. 343–367, 2003.
  36. G. Evensen, “Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model,” Journal of Geophysical Research, vol. 97, no. 11, pp. 17905–17924, 1992. View at Scopus
  37. G. Evensen, “Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,” Journal of Geophysical Research, vol. 99, no. 5, pp. 143–162, 1994. View at Scopus
  38. G. Evensen and P. J. van Leeuwen, “Assimilation of geosat altimeter data for the agulhas current using the Ensemble kalman filter with a quasigeostrophic model,” Monthly Weather Review, vol. 124, no. 1, pp. 85–96, 1996. View at Scopus
  39. P. L. Houtekamer and H. L. Mitchell, “Data assimilation using an Ensemble Kalman filter technique,” Monthly Weather Review, vol. 126, no. 3, pp. 796–811, 1998. View at Scopus
  40. J. L. Anderson, “An Ensemble adjustment Kalman filter for data assimilation,” Monthly Weather Review, vol. 129, no. 12, pp. 2884–2903, 2001. View at Scopus
  41. S.-J. Baek, B. R. Hunt, E. Kalnay, E. Oott, and I. Szunyogh, “Local Ensemble Kalman filtering in the presence of model bias,” Tellus, vol. 58, no. 3, pp. 293–306, 2006. View at Publisher · View at Google Scholar · View at Scopus
  42. M. Corazza, E. Kalnay, and S. C. Yang, “An implementation of the Local Ensemble Kalman Filter in a quasigeostrophic model and comparison with 3D-Var,” Nonlinear Processes in Geophysics, vol. 14, no. 1, pp. 89–101, 2007. View at Scopus
  43. B. R. Hunt, E. J. Kostelich, and I. Szunyogh, “Efficient data assimilation for spatiotemporal chaos: a Local Ensemble transform Kalman filter,” Physica D, vol. 230, no. 1-2, pp. 112–126, 2007. View at Publisher · View at Google Scholar · View at Scopus
  44. T. Miyoshi and S. Yamane, “Local Ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution,” Monthly Weather Review, vol. 135, no. 11, pp. 3841–3861, 2007. View at Publisher · View at Google Scholar · View at Scopus
  45. J. Harlim and B. R. Hunt, “Four-dimensional local Ensemble transform Kalman filter: numerical experiments with a global circulation model,” Tellus, vol. 59, no. 5, pp. 731–748, 2007. View at Publisher · View at Google Scholar · View at Scopus
  46. S.-C. Yang, E. Kalnay, B. Hunt, and N. E. Bowler, “Weight interpolation for efficient data assimilation with the Local Ensemble Transfom Kalman filter,” Quarterly Journal of the Royal Meteorological Society, vol. 135, no. 638, pp. 251–262, 2009. View at Publisher · View at Google Scholar · View at Scopus
  47. J. S. Whitaker and T. M. Hamill, “Ensemble data assimilation without perturbed observations,” Monthly Weather Review, vol. 130, no. 7, pp. 1913–1924, 2002. View at Scopus
  48. C. Köpken, G. Kelly, and J.-N. Thépaut, “Assimilation of Meteosat radiance data within the 4D-Var system at ECMWF: assimilation experiments and forecasts impact,” Quarterly Journal of the Royal Meteorological Society, vol. 130, no. 601, pp. 2277–2292, 2004. View at Publisher · View at Google Scholar · View at Scopus
  49. J.-F. Mahfouf, P. Bauer, and V. Marécal, “The assimilation of SSM/I and TMI rainfall rates in the ECMWF 4D-Var system,” Quarterly Journal of the Royal Meteorological Society, vol. 131, no. 606, pp. 437–458, 2005. View at Publisher · View at Google Scholar · View at Scopus
  50. P. Bauer, P. Lopez, A. Benedetti, D. Salmond, and E. Moreau, “Implementation of 1D+4D-Var assimilation of precipitation-affected microwave radiances at ECMWF. I: 1D-Var,” Quarterly Journal of the Royal Meteorological Society, vol. 132, no. 620, pp. 2277–2306, 2006. View at Publisher · View at Google Scholar · View at Scopus
  51. E. Kalnay, H. Li, T. Miyoshi, S.-C. Yang, and J. Ballabrera-Poy, “4-D-Var or Ensemble Kalman filter?” Tellus, vol. 59, no. 5, pp. 758–773, 2007. View at Publisher · View at Google Scholar · View at Scopus
  52. A. C. Lorenc, “The potential of the Ensemble Kalman filter for NWP—a comparison with 4D-Var,” Quarterly Journal of the Royal Meteorological Society, vol. 129, no. 595, pp. 3183–3203, 2003. View at Publisher · View at Google Scholar · View at Scopus
  53. E. J. Fertig, J. Harlim, and B. R. Hunt, “A comparative study of 4D-VAR and a 4D Ensemble Kalman filter: perfect model simulations with Lorenz-96,” Tellus, vol. 59, no. 1, pp. 96–100, 2007. View at Publisher · View at Google Scholar · View at Scopus
  54. E. N. Lorenz, “Predictability—a problem partly solved,” in Proceedings of the Seminar on Predictability, ECMWF, September 1996.
  55. S.-C. Yang, M. Corazza, A. Carrassi, E. Kalnay, and T. Miyoshi, “Comparison of Ensemble-based and variational-based data assimilation schemes in a quasi-geostrophic model,” in Proceedings of the 10th Symposium on Integrated Observing and Assimilation Systems for the Atmosphere, Oceans, and Land Surface, 2007, http://ams.confex.com/ams/pdfpapers/101581.pdf.
  56. M. Buehner, C. Charente, B. He, et al., “Intercomparison of 4-DVar and EnKF systems for operational deterministic NWP,” 2008, http://4dvarenkf.cima.fcen.uba.ar/Download/Session_7/Intercomparison_4D-Var_EnKF_Buehner.pdf.
  57. T. M. Hamill and C. Snyder, “A hybrid Ensemble Kalman filter-3D variational analysis scheme,” Monthly Weather Review, vol. 128, no. 8, pp. 2905–2919, 2000. View at Scopus
  58. Z. Pu and J. Hacker, “Ensemble-based Kalman filters in strongly nonlinear dynamics,” Advances in Atmospheric Sciences, vol. 26, pp. 373–380, 2009.
  59. P. J. Van Leeuwen, “A variance-minimizing filter for large-scale applications,” Monthly Weather Review, vol. 131, no. 9, pp. 2071–2084, 2003. View at Publisher · View at Google Scholar · View at Scopus
  60. I. Hoteit, D.-T. Pham, G. Korres, and G. Triantafyllou, “Particle Kalman filtering for data assimilation in meteorology and oceanography,” in Proceedings of the 3rd International Conference on Reanalysis (WCRP '08), p. 6, Tokyo, Japan, 2008.
  61. S.-C. Yang and E. Kalnay, “Handling nonlinearity and non-Gaussianity in Ensemble Kalman filter: Experiments with the three-variable Lorenz model,” 2010, http://www.atmos.umd.edu/~ekalnay/YangKalnay2010Rev.pdf.
  62. J. Du, S. L. Mullen, and F. Sanders, “Short-range Ensemble forecasting of quantitative precipitation,” Monthly Weather Review, vol. 125, no. 10, pp. 2427–2459, 1997. View at Scopus
  63. S. L. Mullen, J. Du, and F. Sanders, “The dependence of Ensemble dispersion on analysis-forecast systems: implications to short-range Ensemble forecasting of precipitation,” Monthly Weather Review, vol. 127, no. 7, pp. 1674–1686, 1999. View at Scopus
  64. H. Yuan, S. L. Mullen, X. Gao, S. Sorooshian, J. Du, and H.-M. H. Juang, “Verification of probabilistic quantitative precipitation forecasts over the southwest United States during winter 2002/03 by the RSM Ensemble system,” Monthly Weather Review, vol. 133, no. 1, pp. 279–294, 2005. View at Publisher · View at Google Scholar · View at Scopus
  65. J. Du and M.S. Tracton, “Implementation of a real time short-range Ensemble forecasting system at NCEP: an update,” in Proceedings of the 9th conference on Mesoscale processed, pp. 355–356, American Meteorological Society, Fort Lauderdale, Fla, USA, 2001.
  66. J. Du, J. McQueen, G. DiMego, et al., “New dimension of NCEP short-range Ensemble forecasting (SREF) system: inclusion of WRF members,” WMO Expert Team Meeting on Ensemble Prediction System, Exeter, UK, February 2006, 5 pages, http://www.emc.ncep.noaa.gov/mmb/SREF/reference.html, Preprint.
  67. H. Yuan, S. L. Mullen, X. Gao, S. Sorooshian, J. Du, and H.-M. H. Juang, “Verification of probabilistic quantitative precipitation forecasts over the southwest United States during winter 2002/03 by the RSM Ensemble system,” Monthly Weather Review, vol. 133, no. 1, pp. 279–294, 2005. View at Publisher · View at Google Scholar · View at Scopus
  68. Z. Zhang and T. N. Krishnamurti, “Ensemble forecasting of hurricane tracks,” Bulletin of the American Meteorological Society, vol. 78, no. 12, pp. 2785–2795, 1997. View at Scopus
  69. S. D. Aberson, M. A. Bender, and R. E. Tuleya, “Ensemble forecasting of tropical cyclone tracks,” in Proceedings of the 12th Conference on Numerical Weather Prediction, pp. 290–292, American Meteorological Society, Phoenix, Ariz, USA, 1998.
  70. B. P. Mackey and T. N. Krishnamurti, “Ensemble forecast of a typhoon flood event,” Weather & Forecasting, vol. 16, no. 4, pp. 399–415, 2001. View at Scopus
  71. F. Zhang, Y. Weng, J. A. Sippel, Z. Meng, and C. H. Bishop, “Cloud-resolving hurricane initialization and prediction through assimilation of doppler radar observations with an Ensemble Kalman filter,” Monthly Weather Review, vol. 137, no. 7, pp. 2105–2125, 2009. View at Publisher · View at Google Scholar · View at Scopus
  72. M. Tong and M. Xue, “Simultaneous estimation of microphysical parameters and atmospheric state with simulated radar data and Ensemble square root Kalman filter. Part II: parameter estimation experiments,” Monthly Weather Review, vol. 136, no. 5, pp. 1649–1668, 2008. View at Publisher · View at Google Scholar · View at Scopus
  73. M. Xue, M. Tong, and G. Zhang, “Simultaneous state estimation and attenuation correction for thunderstorms with radar data using an Ensemble Kalman filter: tests with simulated data,” Quarterly Journal of the Royal Meteorological Society, vol. 135, no. 643, pp. 1409–1423, 2009. View at Publisher · View at Google Scholar · View at Scopus