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The influence of external forcing on chaotic character, Lorenz map structure and the predictability is studied with the Lorenz system which has a forcing term, and the atmospheric predictability forced by sea surface temperature (SST) is also analyzed. The chaotic attractors are related to the forcing term that changes the moving rules of system and makes randomicity of attractors reduce. The probability distribution function of Lorenz system in the x-y plane has a bimodal structure with two clearly separated peaks. In the absence of forcing, both peaks are equally likely. When an external forcing introduced, the probability of state moving around two Lorenz attractors is changed, and it makes the two peaks asymmetric. It is found that the single cusp of Lorenz map obtained in the absence of forcing splits into two cusps that represent two branches of the Lorenz attractor when the forcing is introduced. On Lorenz map, the moving directions of two cusps and the difference between two cusps and single cusp are determined by the sign and the magnitude of forcing term. The predictability of Lorenz system is also deeply affected by external forcing. The predictability is increased by introducing forcing, and especially the range of increasing is larger when the absolute value of forcing term is bigger. It is also found that the higher potential predictability is obtained by forcing with the stronger SST which causes the larger external variance.
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Keywords:
- Lorenz system /
- external forcing /
- Lorenz map /
- predictability
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Evans E N, Bhatti J K, Pann L, Pena M, Yang S C, Kalnay E, Hansen J 2004 Bull. Amer. Meteor. Soc. 85 520
[3] Palmer T N 1993 Bull. Amer. Meteor. Soc. 74 49
[4] Tsonis A A 1992 Chaos: From Theory to Applications (New York: Plenum press) p274
[5] Palmer T N 1999 J. Clim. 12 575
[6] Yadav R S, Dwivedi S, Mittal A K 2005 J. Atmos. Sci. 62 2316
[7] Sikka D R, Gadgil S 1980 Mon. Wea. Rev. 108 1840
[8] Christiansen B 2003 J. Clim. 16 3681
[9] Shukla J 1998 Science 282 728
[10] Palmer T N 1994 Ind. Natl. Sci. Acad. 60 57
[11] Pal P K, Shan S 1999 Ind. J. Radio Space Phys. 28 271
[12] Mittal A K, Dwivedi S, Pandey A C 2003 Ind. J. Radio Space Phys. 32 209
[13] Mittal A K, Dwivedi S, Pandey A C 2005 Nonlin. Pro. Geophy. 12 707
[14] Dwivedi S, Mittal A K, Pandey A C 2007 Atmoshpere-Ocean 45 71
[15] He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 969 (in Chinese) [何文平, 封国林, 董文杰, 李建平 2006 55 969]
[16] He W P, Feng G L, Gao X Q, Chou J F 2006 Acta Phys. Sin. 55 3175 (in Chinese) [何文平, 封国林, 高新全, 丑纪范 2006 55 3175]
[17] Ding R Q, Li J P 2007 Chin. J. Atmos. Sci. 31 571 (in Chinese) [丁瑞强, 李建平 2007 大气科学 31 571]
[18] Chen B H, Li J P, Ding R Q 2006 Sci. Chin. D 36 1068 (in Chinese) [陈宝花, 李建平, 丁瑞强 2008 中国科学(D辑) 36 1068]
[19] Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[20] Ding R Q, Li J P 2008 Chin. J. Geophy. 51 1007 (in Chinese) [丁瑞强, 李建平 2008 地球 51 1007]
[21] Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 241 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 241]
[22] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[23] Shukla J, Gutzler D S 1983 Mon. Wea. Rev. 111 1273
[24] Trenberth K E 1984 Mon. Wea. Rev. 112 2369
[25] Wang J, Guo Y F 2004 J. Appl. Meteor. Sci. 15 291 (in Chinese) [王嘉, 郭裕福 2004 应用气象学报 15 291]
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Evans E N, Bhatti J K, Pann L, Pena M, Yang S C, Kalnay E, Hansen J 2004 Bull. Amer. Meteor. Soc. 85 520
[3] Palmer T N 1993 Bull. Amer. Meteor. Soc. 74 49
[4] Tsonis A A 1992 Chaos: From Theory to Applications (New York: Plenum press) p274
[5] Palmer T N 1999 J. Clim. 12 575
[6] Yadav R S, Dwivedi S, Mittal A K 2005 J. Atmos. Sci. 62 2316
[7] Sikka D R, Gadgil S 1980 Mon. Wea. Rev. 108 1840
[8] Christiansen B 2003 J. Clim. 16 3681
[9] Shukla J 1998 Science 282 728
[10] Palmer T N 1994 Ind. Natl. Sci. Acad. 60 57
[11] Pal P K, Shan S 1999 Ind. J. Radio Space Phys. 28 271
[12] Mittal A K, Dwivedi S, Pandey A C 2003 Ind. J. Radio Space Phys. 32 209
[13] Mittal A K, Dwivedi S, Pandey A C 2005 Nonlin. Pro. Geophy. 12 707
[14] Dwivedi S, Mittal A K, Pandey A C 2007 Atmoshpere-Ocean 45 71
[15] He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 969 (in Chinese) [何文平, 封国林, 董文杰, 李建平 2006 55 969]
[16] He W P, Feng G L, Gao X Q, Chou J F 2006 Acta Phys. Sin. 55 3175 (in Chinese) [何文平, 封国林, 高新全, 丑纪范 2006 55 3175]
[17] Ding R Q, Li J P 2007 Chin. J. Atmos. Sci. 31 571 (in Chinese) [丁瑞强, 李建平 2007 大气科学 31 571]
[18] Chen B H, Li J P, Ding R Q 2006 Sci. Chin. D 36 1068 (in Chinese) [陈宝花, 李建平, 丁瑞强 2008 中国科学(D辑) 36 1068]
[19] Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[20] Ding R Q, Li J P 2008 Chin. J. Geophy. 51 1007 (in Chinese) [丁瑞强, 李建平 2008 地球 51 1007]
[21] Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 241 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 241]
[22] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[23] Shukla J, Gutzler D S 1983 Mon. Wea. Rev. 111 1273
[24] Trenberth K E 1984 Mon. Wea. Rev. 112 2369
[25] Wang J, Guo Y F 2004 J. Appl. Meteor. Sci. 15 291 (in Chinese) [王嘉, 郭裕福 2004 应用气象学报 15 291]
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