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In this paper a method is presented to estimate the unknown parameters of nonlinear El Nio/La Nio-Southern Oscillation model based on the variational principle. Firstly, the equation of the coupled air-sea model is included into the objective functional. Secondly, the formulas of the adjoint equation and the functional gradient for unknown parameters are derived using the variational method. Finally, the algorithm to estimate unknown parameters of air-sea oscillator system is designed according to the above formulas. The numerical simulation results show that the proposed method is very effective and feasible to estimate the unknown parameters of nonlinear air-sea coupled dynamical system.
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Keywords:
- air-sea coupled model /
- parameter estimation /
- limit cycle /
- variational method
[1] Philander S G H 1984 J. Atmos. Sci. 41 604
[2] [3] Suarez M J, Schopf P S 1988 J. Atmos. Sci. 45 3283
[4] McCreay J P, Anderson D J L 1984 Mon. Wea. Rev. 112 934
[5] [6] Zebiak S E, Cane M A 1987 Mon. Wea. Rev. 115 2262
[7] [8] [9] Wang B, Barcilon A, Fang Z 1999 J. Atmos. Sci. 56 5
[10] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[11] [12] [13] Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 50 606]
[14] [15] Feng G L, Dong W J 2005 Acta Meteo. Sin. 63 864 (in Chinese) [封国林, 董文杰 2005 气象学报 63 864]
[16] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 3245 (in Chinese) [莫嘉琪, 林万涛 2004 53 3245]
[17] [18] [19] Mo J Q, Lin W T 2005 Acta Phys. Sin. 54 1081 (in Chinese) [莫嘉琪, 林万涛 2005 54 1081]
[20] [21] Mo J Q, Wang H, Lin W T 2006 Acta Phys. Sin. 55 6 (in Chinese) [莫嘉琪, 王辉, 林万涛 2006 55 6]
[22] [23] Mo J Q, Lin W T, Zhu J 2006 Adv. Math. 35 232
[24] He J H 1999 Int. J. Nonl. Mech. 34 699
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[28] [29] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Publisher) pp129--141 (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法(郑州: 河南科学技术出版社) 第129---141页]
[30] He J H 1999 Comp. Meth. Appl. Mech. Eng. 178 257
[31] [32] [33] He J H 2000 Int. J. Nonl. Mech. 35 37
[34] Campbell E P 2004 Technical Report 139 18
[35] [36] [37] Burgers G, Jin F F, van Oldenborgh G J 2005 Geophy. Res. Lett. 32 13
[38] Du H D, Huang S X, Cai Q F 2007 Journal of Nanjing Institute of Meteorology 30 444 (in Chinese) [杜华栋, 黄思训, 蔡其发 2007 南京气象学院学报 30 444]
[39] [40] [41] Du H D, Huang S X, Cai Q F 2009 Mar. Sci. Bull. 11 13
[42] [43] Huang S X, Wu R S 2001 Mathematical Physics Problems in Atmosphere Science (Beijing: Meteorology Press) pp460--468 (in Chinese) [黄思训, 伍荣生 2001 大气科学中的数学物理问题 (北京: 气象出版社) 第460--468页]
[44] He J H 2008 Int. J. Modern. Phys. B 22 3487
[45] [46] He J H 2000 Appl. Math. Mech. 21 797
[47] [48] He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309
[49] [50] [51] He J H, Lee E W M 2009 Phys. Lett. A 373 1644
[52] Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1369
[53] [54] Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1523
[55] -
[1] Philander S G H 1984 J. Atmos. Sci. 41 604
[2] [3] Suarez M J, Schopf P S 1988 J. Atmos. Sci. 45 3283
[4] McCreay J P, Anderson D J L 1984 Mon. Wea. Rev. 112 934
[5] [6] Zebiak S E, Cane M A 1987 Mon. Wea. Rev. 115 2262
[7] [8] [9] Wang B, Barcilon A, Fang Z 1999 J. Atmos. Sci. 56 5
[10] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[11] [12] [13] Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 50 606]
[14] [15] Feng G L, Dong W J 2005 Acta Meteo. Sin. 63 864 (in Chinese) [封国林, 董文杰 2005 气象学报 63 864]
[16] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 3245 (in Chinese) [莫嘉琪, 林万涛 2004 53 3245]
[17] [18] [19] Mo J Q, Lin W T 2005 Acta Phys. Sin. 54 1081 (in Chinese) [莫嘉琪, 林万涛 2005 54 1081]
[20] [21] Mo J Q, Wang H, Lin W T 2006 Acta Phys. Sin. 55 6 (in Chinese) [莫嘉琪, 王辉, 林万涛 2006 55 6]
[22] [23] Mo J Q, Lin W T, Zhu J 2006 Adv. Math. 35 232
[24] He J H 1999 Int. J. Nonl. Mech. 34 699
[25] [26] [27] He J H 1998 Comp. Meth. Appl. Mech. Eng. 167 57
[28] [29] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Publisher) pp129--141 (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法(郑州: 河南科学技术出版社) 第129---141页]
[30] He J H 1999 Comp. Meth. Appl. Mech. Eng. 178 257
[31] [32] [33] He J H 2000 Int. J. Nonl. Mech. 35 37
[34] Campbell E P 2004 Technical Report 139 18
[35] [36] [37] Burgers G, Jin F F, van Oldenborgh G J 2005 Geophy. Res. Lett. 32 13
[38] Du H D, Huang S X, Cai Q F 2007 Journal of Nanjing Institute of Meteorology 30 444 (in Chinese) [杜华栋, 黄思训, 蔡其发 2007 南京气象学院学报 30 444]
[39] [40] [41] Du H D, Huang S X, Cai Q F 2009 Mar. Sci. Bull. 11 13
[42] [43] Huang S X, Wu R S 2001 Mathematical Physics Problems in Atmosphere Science (Beijing: Meteorology Press) pp460--468 (in Chinese) [黄思训, 伍荣生 2001 大气科学中的数学物理问题 (北京: 气象出版社) 第460--468页]
[44] He J H 2008 Int. J. Modern. Phys. B 22 3487
[45] [46] He J H 2000 Appl. Math. Mech. 21 797
[47] [48] He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309
[49] [50] [51] He J H, Lee E W M 2009 Phys. Lett. A 373 1644
[52] Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1369
[53] [54] Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1523
[55]
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