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Comparison of nonlinear local Lyapunov vectors with bred vectors, random perturbations and ensemble transform Kalman filter strategies in a barotropic model

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Abstract

The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors (BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector (NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram–Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than the BVs.

In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random perturbation (RP) technique, and the BV method, as well as its improved version—the ensemble transform Kalman filter (ETKF) method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.

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Authors and Affiliations

  1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

    Jie Feng, Ruiqiang Ding & Deqiang Liu

  2. College of Earth Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Jie Feng & Deqiang Liu

  3. Global Systems Division, Earth System Research Laboratory/Oceanic and Atmospheric Research/National Oceanic and Atmospheric Administration, Boulder, CO, 80305, USA

    Jie Feng

  4. Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, Chengdu University of Information Technology, Chengdu, 610225, China

    Ruiqiang Ding

  5. College of Global Change and Earth System Sciences, Beijing Normal University, Beijing, 100875, China

    Jianping Li

  6. Joint Center for Global Change Studies, Beijing, 100875, China

    Jianping Li

  7. Fujian Meteorological Observatory, Fuzhou, 350001, China

    Deqiang Liu

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  1. Jie Feng
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  2. Ruiqiang Ding
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Correspondence to Jianping Li.

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Feng, J., Ding, R., Li, J. et al. Comparison of nonlinear local Lyapunov vectors with bred vectors, random perturbations and ensemble transform Kalman filter strategies in a barotropic model. Adv. Atmos. Sci. 33, 1036–1046 (2016). https://doi.org/10.1007/s00376-016-6003-4

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  • DOI: https://doi.org/10.1007/s00376-016-6003-4

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