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Vorticity and divergence can be calculated using wind field in numerical forecast. The issue involves the problem of calculating differentiation using observation data, and it is ill-posed in mathematics. In a limited domain, the one-dimensional numerical differentiation can be used to calculate vorticity and divergence, but the method requires that the data along the boundary be accurate. This paper suggests a new method of calculating vorticity and divergence using the periodical function's one-dimensional numerical differentiation algorithm, and comparison is made with usually used difference method. The stream function and velocity potential are calculated using vorticity and divergence, and the initial wind field is reconstructed using the stream function and velocity potential. Results show that the algorithm proposed in this paper is stable, feasible, and its accuracy is superior to the difference method. It provides a new idea that the method mag be used in global meteorology data diagnosis analysis and forecast.
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Keywords:
- wind field /
- vorticity /
- divergence /
- numerical differentiation
[1] Gao S T, Zhou Y S, Lei T, Sun J H 2005 Sci. China Earth Sci. 35 107 (in Chinese)[高守亭, 周玉淑, 雷霆, 孙建华 2005 中国科学:地球科学 35 107]
[2] Jia M, Lou C, Lou S Y 2006 Chin. Phys. Lett. 23 2878
[3] [4] [5] Zhou Y S, Cao J, Gao S T 2008 Acta Phys. Sin. 57 6654 (in Chinese)[周玉淑, 曹洁, 高守亭 2008 57 6654]
[6] Gao S T, Zhou F F 2008 Chin. Phys. Lett. 25 3830
[7] [8] [9] Ran L K, Chu Y L 2009 Acta Physi. Sin. 58 8094 (in Chinese)[冉令坤, 楚艳丽 2009 58 8094]
[10] Zhou Y S, Cao J 2010 Acta Phys. Sin. 59 2898 (in Chinese)[周玉淑, 曹洁 2010 59 2898]
[11] [12] Qin Xu, Cao Jie, Gao S T 2011 Adv. Atmos. Sci. 28 1433
[13] [14] Cao Jie, Qin Xu 2011 Adv. Atmos. Sci. 28 1445
[15] [16] Luo Z X, Sun Z A, Ping F 2011 Chin. Phys. B 20 049201
[17] [18] [19] Groetsch C W 1991 Amer. Math. Monthly 98 847
[20] Hanke M, Scherzer O 2001 Amer. Math. Monthly 108 512
[21] [22] Groetsch C W 1992 J. Optimiz. Theory App. 74 373
[23] [24] Murio D A 1987 Comput. Math. Appl. 13 381
[25] [26] Vasin V V 1973 USSR Comp. Math. Math. Phys. 13 161
[27] [28] [29] Locker J, Prenter P M 1980 J. Mathanal. Appl. 74 504
[30] Wang Y B, Jia X Z, Cheng J 2002 Inverse Probl. 18 1461
[31] [32] [33] Tikhonov A N, Arsenin V Y 1977 Solutions of ill-posed problems, Winston and Sons, Washington, USA
[34] Zhao X F, Huang S X 2011 Acta Phys. Sin. 60 119203 (in Chinese)[赵小峰, 黄思训 2011 60 119203]
[35] [36] [37] X Zhao, S Huang 2012 J. Atmos. Sci. 69 2808
[38] [39] He R, Huang S X, Zhou C T, Jiang Z H 2012 Acta Physi. Sin. 61 049201 (in Chinese)[何然, 黄思训, 周晨腾, 姜祝辉 2012 61 049201]
[40] [41] Cai Q F, Huang S X, Gao S T, Zhong K, Li Z Q 2008 Acta Physi. Sin. 57 3912 (in Chinese)[蔡其发, 黄思训, 高守亭, 钟科, 李自强 2008 57 3912]
[42] [43] Yang G F, Ye Y Z, Wang S Z 2004 Journal of Fudan University (Natural Science) 43 315 (in Chinese)[杨古帆, 叶予璋, 王盛章 2004 复旦学报 (自然科学版) 43 315]
[44] Bourke W 1972 Mon. Wea. Rev. 100 683
[45] -
[1] Gao S T, Zhou Y S, Lei T, Sun J H 2005 Sci. China Earth Sci. 35 107 (in Chinese)[高守亭, 周玉淑, 雷霆, 孙建华 2005 中国科学:地球科学 35 107]
[2] Jia M, Lou C, Lou S Y 2006 Chin. Phys. Lett. 23 2878
[3] [4] [5] Zhou Y S, Cao J, Gao S T 2008 Acta Phys. Sin. 57 6654 (in Chinese)[周玉淑, 曹洁, 高守亭 2008 57 6654]
[6] Gao S T, Zhou F F 2008 Chin. Phys. Lett. 25 3830
[7] [8] [9] Ran L K, Chu Y L 2009 Acta Physi. Sin. 58 8094 (in Chinese)[冉令坤, 楚艳丽 2009 58 8094]
[10] Zhou Y S, Cao J 2010 Acta Phys. Sin. 59 2898 (in Chinese)[周玉淑, 曹洁 2010 59 2898]
[11] [12] Qin Xu, Cao Jie, Gao S T 2011 Adv. Atmos. Sci. 28 1433
[13] [14] Cao Jie, Qin Xu 2011 Adv. Atmos. Sci. 28 1445
[15] [16] Luo Z X, Sun Z A, Ping F 2011 Chin. Phys. B 20 049201
[17] [18] [19] Groetsch C W 1991 Amer. Math. Monthly 98 847
[20] Hanke M, Scherzer O 2001 Amer. Math. Monthly 108 512
[21] [22] Groetsch C W 1992 J. Optimiz. Theory App. 74 373
[23] [24] Murio D A 1987 Comput. Math. Appl. 13 381
[25] [26] Vasin V V 1973 USSR Comp. Math. Math. Phys. 13 161
[27] [28] [29] Locker J, Prenter P M 1980 J. Mathanal. Appl. 74 504
[30] Wang Y B, Jia X Z, Cheng J 2002 Inverse Probl. 18 1461
[31] [32] [33] Tikhonov A N, Arsenin V Y 1977 Solutions of ill-posed problems, Winston and Sons, Washington, USA
[34] Zhao X F, Huang S X 2011 Acta Phys. Sin. 60 119203 (in Chinese)[赵小峰, 黄思训 2011 60 119203]
[35] [36] [37] X Zhao, S Huang 2012 J. Atmos. Sci. 69 2808
[38] [39] He R, Huang S X, Zhou C T, Jiang Z H 2012 Acta Physi. Sin. 61 049201 (in Chinese)[何然, 黄思训, 周晨腾, 姜祝辉 2012 61 049201]
[40] [41] Cai Q F, Huang S X, Gao S T, Zhong K, Li Z Q 2008 Acta Physi. Sin. 57 3912 (in Chinese)[蔡其发, 黄思训, 高守亭, 钟科, 李自强 2008 57 3912]
[42] [43] Yang G F, Ye Y Z, Wang S Z 2004 Journal of Fudan University (Natural Science) 43 315 (in Chinese)[杨古帆, 叶予璋, 王盛章 2004 复旦学报 (自然科学版) 43 315]
[44] Bourke W 1972 Mon. Wea. Rev. 100 683
[45]
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