Advertisement

Science China Earth Sciences

, Volume 62, Issue 2, pp 376–388 | Cite as

The application of the orthogonal conditional nonlinear optimal perturbations method to typhoon track ensemble forecasts

  • Zhenhua Huo
  • Wansuo DuanEmail author
Research Paper
First Online:
  • 18 Downloads

Abstract

The orthogonal conditional nonlinear optimal perturbations (CNOPs) method, orthogonal singular vectors (SVs) method and CNOP+SVs method, which is similar to the orthogonal SVs method but replaces the leading SV (LSV) with the first CNOP, are adopted in both the Lorenz-96 model and Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Fifth-Generation Mesoscale Model (MM5) for ensemble forecasts. Using the MM5, typhoon track ensemble forecasting experiments are conducted for strong Typhoon Matsa in 2005. The results of the Lorenz-96 model show that the CNOP+SVs method has a higher ensemble forecast skill than the orthogonal SVs method, but ensemble forecasts using the orthogonal CNOPs method have the highest forecast skill. The results from the MM5 show that orthogonal CNOPs have a wider horizontal distribution and better describe the forecast uncertainties compared with SVs. When generating the ensemble mean forecast, equally averaging the ensemble members in addition to the anomalously perturbed forecast members may contribute to a higher forecast skill than equally averaging all of the ensemble members. Furthermore, for given initial perturbation amplitudes, the CNOP+SVs method may not have an ensemble forecast skill greater than that of the orthogonal SVs method, but the orthogonal CNOPs method is likely to have the highest forecast skill. Compared with SVs, orthogonal CNOPs fully consider the influence of nonlinear physical processes on the forecast results; therefore, considering the influence of nonlinearity may be important when generating fast-growing initial ensemble perturbations. All of the results show that the orthogonal CNOP method may be a potential new approach for ensemble forecasting.

Keywords

Ensemble forecasts Initial perturbation Conditional nonlinear optimal perturbation Singular vector Typhoon track 
Download to read the full article text

Notes

Acknowledgements

The FNL data used in this study can be obtained from http://rda.ucar.edu/datasets/ds083.2/. The historical tropical cyclone data are available at http://tcdata.typhoon.org.cn/en/zjljsjj_zlhq.html. This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 41525017 & 41475100), the National Programme on Global Change and Air-Sea Interaction (Grant No. GASI-IPOVAI-06), and the GRAPES Development Program of China Meteorological Administration (Grant No. GRAPES-FZZX-2018).

References

  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 Weather Rev, 125: 2969–2983CrossRefGoogle Scholar
  2. Barkmeijer J, Buizza R, Palmer T N, Puri K, Mahfouf J F. 2001. Tropical singular vectors computed with linearized diabatic physics. Q J R Meteorol Soc, 127: 685–708CrossRefGoogle Scholar
  3. Basnarkov L, Kocarev L. 2012. Forecast improvement in Lorenz 96 system. Nonlin Processes Geophys, 19: 569–575CrossRefGoogle Scholar
  4. Buizza R, Gelaro R, Molteni F, Palmer T N. 1997. The impact of increased resolution on predictability studies with singular vectors. Q J R Meteorol Soc, 123: 1007–1033CrossRefGoogle Scholar
  5. Cheung K K W. 2001. Ensemble forecasting of tropical cyclone motion: Comparisonbetween regional bred modes and random perturbations. Meteorol Atmos Phys, 78: 23–34CrossRefGoogle Scholar
  6. Chou K H, Wu C C, Lin P H, Aberson S D, Weissmann M, Harnisch F, Nakazawa T. 2011. The impact of dropwindsonde observations on typhoon track forecasts in DOTSTAR and T–PARC. Mon Weather Rev, 139: 1728–1743CrossRefGoogle Scholar
  7. Descamps L, Talagrand O. 2007. On some aspects of the definition of initial conditions for ensemble prediction. Mon Weather Rev, 135: 3260–3272CrossRefGoogle Scholar
  8. Ding R Q, Li J P, Li B S. 2017. Determining the spectrum of the nonlinear local Lyapunov exponents in a multidimensional chaotic system. Adv Atmos Sci, 34: 1027–1034CrossRefGoogle Scholar
  9. Duan M K, Wang P X. 2006. A new weighted method on ensemble mean forecasting (in Chinese). J Appl Meteorol, 17: 488–493Google Scholar
  10. Duan W S, Huo Z H. 2016. An approach to generating mutually independent initial perturbations for ensemble forecasts: Orthogonal conditional nonlinear optimal perturbations. J Atmos Sci, 73: 997–1014CrossRefGoogle Scholar
  11. Duan W S, Mu M, Wang B. 2004. Conditional nonlinear optimal perturbations as the optimal precursors for El Nino–Southern Oscillation events. J Geophys Res, 109: D23105CrossRefGoogle Scholar
  12. Duan W S, Mu M. 2009. Conditional nonlinear optimal perturbation: Applications to stability, sensitivity, and predictability. Sci China Ser DEarth Sci, 52: 883–906CrossRefGoogle 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 Weather Rev, 121: 1493–1513CrossRefGoogle Scholar
  14. Ehrendorfer M, Tribbia J J. 1997. Optimal prediction of forecast error covariances through singular vectors. J Atmos Sci, 54: 286–313CrossRefGoogle Scholar
  15. Elsberry R L, Hughes J R, Boothe M A. 2008. Weighted position and motion vector consensus of tropical cyclone track prediction in the western north pacific. Mon Weather Rev, 136: 2478–2487CrossRefGoogle Scholar
  16. Epstein E S. 1969. Stochastic dynamic predictions. Tellus, 21: 739–759CrossRefGoogle Scholar
  17. Evensen G. 1994. Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res, 99: 10143–10162CrossRefGoogle Scholar
  18. Feng J, Ding R Q, Liu D Q, Li J P. 2014. The application of nonlinear local Lyapunov vectors to ensemble predictions in lorenz systems. J Atmos Sci, 71: 3554–3567CrossRefGoogle Scholar
  19. Gelaro R, Rosmond T, Daley R. 2002. Singular vector calculations with an analysis error variance metric. Mon Weather Rev, 130: 1166–1186CrossRefGoogle Scholar
  20. Gilmour I, Smith L A. 1997. Enlightenment in Shadows. In: Kadtke J B, Bulsara A, eds. Applied Nonlinear Dynamics and Stochastic Systems near the Millennium. American Institute of Physics. 335–340Google Scholar
  21. Hamill T M, Snyder C, Whitaker J S. 2003. Ensemble forecasts and the properties of flow–dependent analysis–error covariance singular vectors. Mon Weather Rev, 131: 1741–1758CrossRefGoogle Scholar
  22. Hao S F, Cui X P, Pan J S. 2007. Ensemble prediction experiments of tracks of tropical cyclones by using multiple cumulus parameterizations schemes (in Chinese). J Trop Meteorol, 23: 569–574Google Scholar
  23. Jiang Z N, Mu M. 2009. A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction. Adv Atmos Sci, 26: 465–470CrossRefGoogle Scholar
  24. Jiang Z N, Wang H L, Zhou F F, Mu M. 2009. Applications of conditional nonlinear optimal perturbations to ensemble prediction and adaptive observation. Springer Verlag Berlin Heidelberg. 231–252Google Scholar
  25. Leith C E. 1974. Theoretical skill of monte carlo forecasts. Mon Weather Rev, 102: 409–418CrossRefGoogle Scholar
  26. Leutbecher M, Palmer T N. 2008. Ensemble forecasting. J Comput Phys, 227: 3515–3539CrossRefGoogle Scholar
  27. Li S, Rong X Y, Liu Y, Liu Z Y, Fraedrich K. 2013. Dynamic analogue initialization for ensemble forecasting. Adv Atmos Sci, 30: 1406–1420CrossRefGoogle Scholar
  28. Li Z J, Navon I M, Hussaini M Y. 2005. Analysis of the singular vectors of the full–physics Florida State University Global Spectral Model. Tellus Ser A–Dyn Meteorol Oceanol, 57: 560–574CrossRefGoogle Scholar
  29. Lorenz E N. 1965. A study of the predictability of a 28–variable model. Tellus, 17: 321–333CrossRefGoogle Scholar
  30. Lorenz E N. 1996. Predictability: A problem partly solved. In: Proc. Workshop on Predictability, Vol. 1. Reading, United Kingdom, ECMWF. 1–18Google Scholar
  31. Molteni F, Buizza R, Palmer T N, Petroliagis T. 1996. The ECMWF ensemble prediction system: Methodology and validation. Q J R Meteorol Soc, 122: 73–119CrossRefGoogle Scholar
  32. Mu M, Zhou F F, Wang H L. 2009. A method for identifying the sensitive areas in targeted observations for tropical cyclone prediction: Conditional nonlinear optimal perturbation. Mon Weather Rev, 137: 1623–1639CrossRefGoogle Scholar
  33. Mu M, Zhou F F, Qin X H, Chen B Y. 2014. The application of conditional nonlinear optimal perturbation to targeted observations for tropical cyclone prediction. In: Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics. 291–325Google Scholar
  34. Mu M, Duan W S, Wang B. 2003. Conditional nonlinear optimal perturbation and its applications. Nonlin Processes Geophys, 10: 493–501CrossRefGoogle Scholar
  35. Mu M, Jiang Z N. 2008. A new approach to the generation of initial perturbations for ensemble prediction: Conditional nonlinear optimal perturbation. Chin Sci Bull, 53: 2062–2068Google Scholar
  36. Mu M, Zhang Z Y. 2006. Conditional nonlinear optimal perturbations of a two–dimensional quasigeostrophic model. J Atmos Sci, 63: 1587–1604CrossRefGoogle Scholar
  37. Mureau R, Molteni F, Palmer T N. 1993. Ensemble prediction using dynamically conditioned perturbations. Q J R Meteorol Soc, 119: 299–323CrossRefGoogle Scholar
  38. Palmer T N, Gelaro R, Barkmeijer J, Buizza R. 1998. Singular vectors, metrics, and adaptive observations. J Atmos Sci, 55: 633–653CrossRefGoogle Scholar
  39. Qin X H, Duan W S, Mu M. 2013. Conditions under which CNOP sensitivity is valid for tropical cyclone adaptive observations. Q J R Meteorol Soc, 139: 1544–1554CrossRefGoogle Scholar
  40. Revelli J A, Rodríguez M A, Wio H S. 2010. The use of rank histograms and MVL diagrams to characterize ensemble evolution in weather forecasting. Adv Atmos Sci, 27: 1425–1437CrossRefGoogle Scholar
  41. Reynolds C A, Peng M S, Chen J H. 2009. Recurving tropical cyclones: Singular vector sensitivity and downstream impacts. Mon Weather Rev, 137: 1320–1337CrossRefGoogle Scholar
  42. Roulston M S, Smith L A. 2003. Combining dynamical and statistical ensembles. Tellus A, 55: 16–30CrossRefGoogle Scholar
  43. Toth Z, Kalnay E. 1993. Ensemble forecasting at NMC: The generation of perturbations. Bull Amer Meteorol Soc, 74: 2317–2330CrossRefGoogle Scholar
  44. Toth Z, Zhu Y J, Marchok T. 2001. The use of ensembles to identify forecasts with small and large uncertainty. Weather Forecast, 16: 463–477CrossRefGoogle Scholar
  45. Wang C X, Liang X D. 2007. Ensemble prediction experiments of tropical cyclone track (in Chinese). J Appl Meteorol, 18: 586–593Google Scholar
  46. Wang H L, Mu M, Huang X Y. 2011. Application of conditional non–linear optimal perturbations to tropical cyclone adaptive observation using the weather research forecasting (WRF) model. Tellus A–Dynamic Meteor Oceanography, 63: 939–957CrossRefGoogle Scholar
  47. Ying M, Zhang W, Yu H, Lu X, Feng J, Fan Y, Zhu Y, Chen D. 2014. An overview of the China meteorological administration tropical cyclone database. J Atmos Ocean Technol, 31: 287–301CrossRefGoogle Scholar
  48. Yu H Z, Wang H L, Meng Z Y, Mu M, Huang X Y, Zhang X. 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 Ocean Technol, 34: 187–206CrossRefGoogle Scholar
  49. Yu J H, Tang J X, Dai Y H, Yu B Y. 2012. Analyses in Errors and Their Causes of Chinese Typhoon Track Operational Forecasts (in Chinese). Meteorol Monthly, 38: 695–700Google Scholar
  50. Zhang Z, Krishnamurti T N. 1997. Ensemble forecasting of hurricane tracks. Bull Amer Meteorol Soc, 78: 2785–2795CrossRefGoogle Scholar
  51. Zhou F F, Mu M. 2011. The impact of verification area design on tropical cyclone targeted observations based on the CNOP method. Adv Atmos Sci, 28: 997–1010CrossRefGoogle Scholar
  52. Zou X, Vandenberghe F, Pondeca M, Kuo Y. 1997. Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Technical Note, NCAR/TN–435–STR, 107Google Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

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

Personalised recommendations