Advances in Atmospheric Sciences

, Volume 36, Issue 2, pp 231–247 | Cite as

Ensemble Forecasts of Tropical Cyclone Track with Orthogonal Conditional Nonlinear Optimal Perturbations

  • Zhenhua Huo
  • Wansuo DuanEmail author
  • Feifan Zhou
Original Paper


This paper preliminarily investigates the application of the orthogonal conditional nonlinear optimal perturbations (CNOPs)–based ensemble forecast technique in MM5 (Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model). The results show that the ensemble forecast members generated by the orthogonal CNOPs present large spreads but tend to be located on the two sides of real tropical cyclone (TC) tracks and have good agreements between ensemble spreads and ensemble-mean forecast errors for TC tracks. Subsequently, these members reflect more reasonable forecast uncertainties and enhance the orthogonal CNOPs–based ensemble-mean forecasts to obtain higher skill for TC tracks than the orthogonal SVs (singular vectors)–, BVs (bred vectors)–and RPs (random perturbations)–based ones. The results indicate that orthogonal CNOPs of smaller magnitudes should be adopted to construct the initial ensemble perturbations for short lead–time forecasts, but those of larger magnitudes should be used for longer lead–time forecasts due to the effects of nonlinearities. The performance of the orthogonal CNOPs–based ensemble-mean forecasts is case-dependent, which encourages evaluating statistically the forecast skill with more TC cases. Finally, the results show that the ensemble forecasts with only initial perturbations in this work do not increase the forecast skill of TC intensity, which may be related with both the coarse model horizontal resolution and the model error.

Key words

ensemble forecast initial perturbation conditional nonlinear optimal perturbation tropical cyclone 

摘 要

基于MM5模式(Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model), 探讨了正交条件非线性最优扰动(conditional nonlinear optimal perturbations, CNOPs)-集合预报方法在热带气旋路径预报中的应用. 结果表明, 正交CNOPs-集合预报产生的集合成员具有较大的离散度, 合理地位于热带气旋(tropical cyclone, TC)实况路径的两侧, 且较好地呈现了集合离散度和集合平均预报误差近似相等的关系; 与正交奇异向量(singular vectors, SVs), 繁殖向量(bred vectors, BVs), 和随机扰动(random perturbations, RPs)-集合预报方法相比, 正交CNOPs在TC路径预报中具有更高的预报技巧. 此外, 结果还表明, 较小振幅的正交CNOPs, 线性近似的有效性决定了它在TC预报时间较短时具有更高预报技巧, 而对于较大振幅的正交CNOPs, 因为其更多地包含了非线性物理过程的影响, 从而使得其在预报时间较长时产生更高预报技巧.


集合预报 初始扰动 条件非线性最优扰动 热带气旋 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, J. L., 1997: The impact of dynamical constraints on the selection of initial conditions for ensemble predictions: Low-order perfect model results. Mon. Wea. Rev., 125(11), 2969–2983,<2969:TIODCO>2.0.CO;2.CrossRefGoogle Scholar
  2. Birgin, E. G., J. M. Martinez, and M. Raydan, 2000: Nonmonotone spectral projected gradient methods on convex sets. SIAM Journal on Optimization, 10, 1196–1211, Scholar
  3. Brankovic, C., T. N. Palmer, F. Molteni, S. Tibaldi, and U. Cubasch, 1990: Extended-range predictions with ECMWF models: Time-lagged ensemble forecasting. Quart. J. Roy. Meteor. Soc., 116, 867–912, 49711649405.CrossRefGoogle Scholar
  4. Buckingham, C., T. Marchok, I. Ginis, L. Rothstein, and D. Rowe, 2010: Short-and medium-range prediction of tropical and transitioning cyclone tracks within the NCEP global ensemble forecasting system. Wea. Forecasting, 25(6), 1736–1754, Scholar
  5. Buizza, R., P. L. Houtekamer, G. Pellerin, Z. Toth, Y. Zhu, and M. Wei, 2005: A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems. Mon. Wea. Rev., 133, 1076–1097, Scholar
  6. Cheung, K. K.W., 2001: Ensemble forecasting of tropical cyclone motion: Comparison between regional bred modes and random perturbations. Meteor. Atmos. Phys., 78, 23–34, Scholar
  7. Chien, F. C., and B. J. D. Jou, 2004: MM5 ensemble mean precipitation forecasts in the Taiwan area for three early summer convective (Mei-Yu) seasons. Wea. Forecasting, 19, 735–750, <0735:MEMPFI>2.0.CO;2.CrossRefGoogle Scholar
  8. Duan, W. S., and M. Mu, 2009: Conditional nonlinear optimal perturbation: Applications to stability, sensitivity, and predictability. Science in China Series D: Earth Sciences, 52(7), 883–906, Scholar
  9. Duan, W. S., and F. F. Zhou, 2013: Non-linear forcing singular vector of a two-dimensional quasi-geostrophic model. Tellus A, 65, 18452, Scholar
  10. Duan, W. S., and P. Zhao, 2015: Revealing the most disturbing tendency error of Zebiak–Cane model associated with El Ni˜no predictions by nonlinear forcing singular vector approach. Climate Dyn., 44, 2351–2367, Scholar
  11. Duan, W. S., and Z. H. Huo, 2016: An approach to generating mutually independent initial perturbations for ensemble forecasts: orthogonal conditional nonlinear optimal perturbations. J. Atmos. Sci., 73, 997–1014, Scholar
  12. Duan, W. S., M. Mu, and B. Wang, 2004: Conditional nonlinear optimal perturbations as the optimal precursors for El Nino-Southern Oscillation events. J. Geophys. Res., 109, D23105, Scholar
  13. Dudhia, J., 1993: A nonhydrostatic version of the Penn state-NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121, 1493–1513, 121<1493:ANVOTP>2.0.CO;2.CrossRefGoogle Scholar
  14. Eckel, F. A., and C. F. Mass, 2005: Aspects of effective mesoscale, short-range ensemble forecasting. Wea. Forecasting, 20(3), 328–350, Scholar
  15. Eom, H. S., and S. Myoung-Seok, 2011: Seasonal and diurnal variations of stability indices and environmental parameters using NCEP FNL data over East Asia. Asia-Pacific Journal of Atmospheric Sciences, 47(2), 181–192, Scholar
  16. General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Standardization Administration of the People’s Republic of China, 2006: GB/T 19201–2006 Grade of tropical cyclones. Standards Press of China, Beijing [Available online at http://tcdata. std.pdf]. (in Chinese)Google Scholar
  17. Gilmour, I., and L. A. Smith, 1998: Enlightenment in shadows. Nonlinear Dynamics and Stochastic Systems near the Millennium. AIP Conference Proceedings, J. B. Kadtke and A. Bulsara, Eds., American Institute of Physics, 335–340.Google Scholar
  18. Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Technical Note NCAR/TN-398+STR, 138pp, Scholar
  19. Hou, D. C., E. Kalnay, and K. K. Droegemeier, 2001: Objective verification of the SAMEX’98 ensemble forecasts. Mon.Wea. Rev., 129, 73–91, 129<0073:OVOTSE>2.0.CO;2.CrossRefGoogle Scholar
  20. Hsiao, L. F., M. S. Peng, D. S. Chen, K. N. Huang, and T. C. Yeh, 2009: Sensitivity of typhoon track predictions in a regional prediction system to initial and lateral boundary conditions. Journal of Applied Meteorology and Climatology, 48(9), 1913–1928, Scholar
  21. Hwang, S., W. Graham, J. L. Hernandez, C. Martinez, J. W. Jones, and A. Adams, 2011: Quantitative spatiotemporal evaluation of dynamically downscaled mm5 precipitation predictions over the Tampa bay region, Florida. Journal of Hydrometeorology, 12, 1447–1464, 1309.1.CrossRefGoogle Scholar
  22. Jiang, Z. N., and M. Mu, 2009: A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction. Adv. Atmos. Sci., 26, 465–470, Scholar
  23. Jiang, Z. N., and D. H. Wang, 2012: Conditional nonlinear optimal perturbations: Behaviour during the evolution of cold vortices over northeast China. Quart. J. Roy. Meteor. Soc., 138, 198–208, Scholar
  24. Langland, R. H., M. A. Shapiro, and R. Gelaro, 2002: Initial condition sensitivity and error growth in forecasts of the 25 January 2000 East Coast Snowstorm. Mon.Wea. Rev., 130, 957–974,<0957: ICSAEG>2.0.CO;2.CrossRefGoogle Scholar
  25. Leith, C. E., 1974: Theoretical skill of monte Carlo forecasts. Mon. Wea. Rev., 38, 97–110,<0409:TSOMCF>2.0.CO;2.Google Scholar
  26. Leutbecher, M., and T. N. Palmer, 2008: Ensemble forecasting. J. Comput. Phys., 227, 3515–3539, Scholar
  27. Li, H. L., J. X. Peng, and Y. X. Zhang, 2014: Analysis on the role of various observation data in LAPS mesoscale analysis fields. Torrential Rain and Disasters, 33(3), 273–280, (in Chinese)Google Scholar
  28. Liang, X. D., B. Wang, J. C. Chan, Y. H. Duan, D. L. Wang, Z. H. Zeng, and M. Leiming, 2007: Tropical cyclone forecasting with model-constrained 3D-Var. II: Improved cyclone track forecasting using AMSU-A, QuikSCAT and cloud-drift wind data. Quart. J. Roy. Meteor. Soc., 133, 155–165, Scholar
  29. Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 131–141, 020<0130:DNF>2.0.CO;2.Google Scholar
  30. Lorenz, E. N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus, 17, 321–333, Scholar
  31. Lorenz, E. N., 1995: Predictability: A problem partly solved. Proc. Workshop on Predictability, Shinfield Park, Reading, ECMWF, 18pp.Google Scholar
  32. Molteni, F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc., 122, 73–119, Scholar
  33. Mu, M., and Z. Y. Zhang, 2006: Conditional nonlinear optimal perturbations of a two-dimensional Quasigeostrophic model. J. Atmos. Sci., 63, 1587–1604, Scholar
  34. Mu, M., and Z. N. Jiang, 2008: A new approach to the generation of initial perturbations for ensemble prediction: Conditional nonlinear optimal perturbation. Chinese Science Bulletin, 53(13), 2062–2068, Scholar
  35. Mu, M., W. S. Duan, and B. Wang, 2003: Conditional nonlinear optimal perturbation and its applications. Nonlinear Processes in Geophysics, 10, 493–501, Scholar
  36. Mu, M., F. F. Zhou, and H. L. Wang, 2009: A method for identifying the sensitive areas in targeted observations for tropical cyclone prediction: Conditional nonlinear optimal perturbation. Mon. Wea. Rev., 137, 1623–1639, Scholar
  37. Mu, M., F. F. Zhou, X. H. Qin, and B. Y. Chen, 2014: The application of conditional nonlinear optimal perturbation to targeted observations for tropical cyclone prediction. Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics, Ge et al., Eds, World Scientific, 291–325, 0018.Google Scholar
  38. Mureau, R., F. Molteni, and T. N. Palmer, 1993: Ensemble prediction using dynamically conditioned perturbations. Quart. J. Roy. Meteor. Soc., 119, 299–323, 49711951005.CrossRefGoogle Scholar
  39. Pessi, A. T., and S. Businger, 2009: The impact of lightning data assimilation on a winter storm simulation over the North Pacific Ocean. Mon. Wea. Rev., 137, 3177–3195, Scholar
  40. Pu, Z. X., E. Kalnay, D. Parrish, W. S. Wu, and Z. Toth, 1997: The use of bred vectors in the NCEP global 3D Variational analysis system. Wea. Forecasting, 12, 689–695,<0689:TUOBVI>2.0.CO;2.CrossRefGoogle Scholar
  41. Qin, X. H., and M. Mu, 2011: A study on the reduction of forecast error variance by three adaptive observation approaches for tropical cyclone prediction. Mon. Wea. Rev., 139, 2218–2232, Scholar
  42. Qin, X. H., W. S. Duan, and M. Mu, 2013: Conditions under which CNOP sensitivity is valid for tropical cyclone adaptive observations. Quart. J. Roy. Meteor. Soc., 139, 1544–1554, Scholar
  43. Simon, H. D., 1984: The Lanczos algorithm with partial reorthogonalization. Mathematics of Computation, 165(42), 115–142, Scholar
  44. Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang, and J. G. Powers, 2005: A description of the advanced research WRF version 2. NCAR Technical Note NCAR/TN-468+STR, 88 pp.Google Scholar
  45. Stensrud, D. J., J. W. Bao, and T. T. Warner, 2000: Using initial condition and model physics perturbations in short-range ensemble simulations of mesoscale convective systems. Mon. Wea. Rev., 128, 2077–2107,<2077:UICAMP>2.0.CO;2.CrossRefGoogle Scholar
  46. Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: the generation of perturbations. Bull. Amer. Meteor. Soc., 74, 2317–2330, <2317:EFANTG>2.0.CO;2.CrossRefGoogle Scholar
  47. Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125, 3297–3319,<3297: EFANAT>2.0.CO;2.CrossRefGoogle Scholar
  48. Tracton, M. S., J. Du, Z. Toth, and H. Juang, 1998: Short-range ensemble forecasting (SREF) at NCEP/EMC. Preprints of 12th Conference on Numerical Weather Prediction, Phoenix, AZ, Amer. Meteor. Soc., 269–272.Google Scholar
  49. Wei, C. C., 2012: Wavelet support vector machines for forecasting precipitation in tropical cyclones: Comparisons with GSVM, regression, and MM5. Wea. Forecasting, 27, 438–450, Scholar
  50. 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, 2592–2604, Scholar
  51. Yamaguchi, M., T. Nakazawa, and K. Aonashi, 2012: Tropical cyclone track forecasts using JMA model with ECMWF and JMA initial conditions. Geophys. Res. Lett., 39, L09801, Scholar
  52. Yang, L., D. X. Wang, and S. Q. Peng, 2012: Comparison between MM5 simulations and satellite measurements during Typhoon Chanchu (2006) in the South China Sea. Acta Oceanologica Sinica, 31(2), 33–44, Scholar
  53. Ying, M., W. Zhang, H. Yu, X. Q. Lu, J. X. Feng, Y. X. Fan, Y. T. Zhu, and D. Q. Chen, 2014: An overview of the China meteorological administration tropical cyclone database. J. Atmos. Oceanic Technol., 31, 287–301, Scholar
  54. Yu, H. Z., H. L. Wang, Z. Y. Meng, M. Mu, X. Y. Huang, and X. Zhang, 2017: A WRF-Based tool for forecast sensitivity to the initial perturbation: The conditional nonlinear optimal perturbations versus the first singular vector method and comparison to MM5. J. Atmos. Oceanic Technol., 34, 187–206, Scholar
  55. Zhang, Z., and T. N. Krishnamurti, 1997: Ensemble forecasting of hurricane tracks. Bull. Amer. Meteor. Soc., 78(12), 2785–2796,<2785: EFOHT>2.0.CO;2.CrossRefGoogle Scholar
  56. Zhao, Y., and B. Wang, 2008: Numerical experiments for typhoon Dan incorporating AMSU-A retrieved data with 3DVM. Adv. Atmos. Sci., 25(4), 692–703, Scholar
  57. Zhao, Y., B. Wang, and Y. Wang, 2007: Initialization and simulation of a landfalling typhoon using a variational bogus mapped data assimilation (BMDA). Meteor. Atmos. Phys., 98, 269–282, Scholar
  58. Zhao, Y., B. Wang, and J. J. Liu, 2012: A DRP-4DVar data assimilation scheme for typhoon initialization using sea level pressure data. Mon. Wea. Rev., 140, 1191–1203, Scholar
  59. Zhou, F. F., and M. Mu, 2011: The impact of verification area design on tropical cyclone targeted observations based on the CNOP method. Adv. Atmos. Sci., 28(5), 997–1010, Scholar
  60. Zhou, F. F., and M. Mu, 2012: The impact of horizontal resolution on the CNOP and on its identified sensitive areas for tropical cyclone predictions. Adv. Atmos. Sci., 29(1), 36–46, Scholar
  61. Zhou, F. F., M. Yamaguchi, and X. H. Qin, 2016: Possible sources of forecast errors generated by the global/regional assimilation and prediction system for landfalling tropical cyclones. Part I: Initial uncertainties. Adv. Atmos. Sci., 33(7), 841–851, Scholar
  62. Zou, X., F. Vandenberghe, M. Pondeca, and Y. H. Kuo, 1997: Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Technical Note NCAR/TN-435+STR, 117 pp, Scholar

Copyright information

© Chinese National Committee for International Association of Meteorology and Atmospheric Sciences, Institute of Atmospheric Physics, Science Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Meteorological CenterChina Meteorological AdministrationBeijingChina
  2. 2.State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina
  4. 4.Laboratory of Cloud-Precipitation Physics and Severe Storms, Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina

Personalised recommendations