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Mean absolute growth of model error which is used to describe the initial error growth for chaos system, is employed in this paper to investigate the model error growth, and some meaningful conclusions are drew from it. It is found that the mean absolute growth of model error is initially exponential with a growth rate which has no direct relationship with the largest Lyapunov exponent. Afterwards model error growth enters into a nonlinear phase with a decreasing growth rate, and finally reaches a saturation value. If the difference between the attractor of real system and that of the model system is very small, the model error saturation level is consistent with the initial error saturation level of real system. With these conclusions one can obtain the predictability limit of a model easily, which is meaningful for weather prediction models. Also the predictability limit of model can be used for model comparison. The exacter model has a higher predictability limit which is useful for new model development.
- PACS:
05.50.-a [1] Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617
[2] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[3] Sano M, Sawada Y 1985 Phys. Rev. Lett. 55 1082
[4] Kantz H, Schreiber T 2004 Nonlinear Time Series Analysis, Cambridge University. Press, Cambridge
[5] Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[6] Anderson J 2001 Mon. Wea. Rev. 129 2884
[7] Whitaker J, T. Hamill 2002 Mon. Wea. Rev. 130 1913
[8] Lorenz E N 1963 J. Atmos. Sci. 20 130
[9] Orrell D, Smith L, Barkmeijer J 2001 Nonlinear Processes in Geophysics 8 357
[10] Orrell D 2005 J. Atmos. Sci. 62 1652
[11] Nicolis C 2003 J. Atmos. Sci. 60 2208
[12] Nicolis C 2004 J. Atmos. Sci. 61 1740
[13] Ding R Q, Li J P 2008 Acta Phys. Sin. 57 7494 (in Chinese) [丁瑞强, 李建平 2008 物理学报 57 7494]
[14] 杨锦辉 宋君强 2012 物理学报 17 61
[15] Lorenz E N 1963 J. Atmos. Sci. 20 130
[16] Lorenz E N 1995 Proceedings of a Seminar Held at ECMWF on Predictability (Reading: ECMWF) p1
[17] Orrell D 2003 J. Atmos. Sci. 60 2219
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[1] Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617
[2] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[3] Sano M, Sawada Y 1985 Phys. Rev. Lett. 55 1082
[4] Kantz H, Schreiber T 2004 Nonlinear Time Series Analysis, Cambridge University. Press, Cambridge
[5] Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[6] Anderson J 2001 Mon. Wea. Rev. 129 2884
[7] Whitaker J, T. Hamill 2002 Mon. Wea. Rev. 130 1913
[8] Lorenz E N 1963 J. Atmos. Sci. 20 130
[9] Orrell D, Smith L, Barkmeijer J 2001 Nonlinear Processes in Geophysics 8 357
[10] Orrell D 2005 J. Atmos. Sci. 62 1652
[11] Nicolis C 2003 J. Atmos. Sci. 60 2208
[12] Nicolis C 2004 J. Atmos. Sci. 61 1740
[13] Ding R Q, Li J P 2008 Acta Phys. Sin. 57 7494 (in Chinese) [丁瑞强, 李建平 2008 物理学报 57 7494]
[14] 杨锦辉 宋君强 2012 物理学报 17 61
[15] Lorenz E N 1963 J. Atmos. Sci. 20 130
[16] Lorenz E N 1995 Proceedings of a Seminar Held at ECMWF on Predictability (Reading: ECMWF) p1
[17] Orrell D 2003 J. Atmos. Sci. 60 2219
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