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Meteorological observation data have observational errors inevitably. It is an ill-posed inverse problem to perform the derivation of discrete data with observation errors. In order to solve the perplexing problem, this paper puts forward the new algorithm which reconstructs the first-order partial derivatives of the two-dimensional observation data in the rectangular region， which is based on the idea of Tikhonov regularization . We test the performance of the algorithm with a series of simulating observation data, the results show that the algorithm is effective and has higher accuracy. It is feasible to analyze meteorological observation data with the algorithm and can enhance the recognizing ability for the small-scale weather systems.
[1] ［1］ Kalnay E 2005 Atmospheic Modeling, Data Assimilation and Predictability ( Beijing: China Meteorological Press) p6 (in Chinese) ［Kalnay E 2005 大气模式、资料同化和可预报性(中译本)（北京:气象出版社） 第6页］
[2] ［2］ Liao D X 1996 J. Appl. Meteor. Sci. 7 238 (in Chinese)［廖洞贤 1996 应用气象学报 7 238］
[3] ［3］ 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］
[4] ［4］ Cao J, Gao S T, Zhou Y S 2008 Acta Phys. Sin. 57 2600 (in Chinese)［曹洁、高守亭、周玉淑 2008 57 2600］
[5] ［5］ Vasin V V 1973 USSR Comput. Maths. Math. Phys. 13 16
[6] ［6］ Locker J, Prenter P M 1980 J. Math. Anal. Appl. 74 504
[7] ［7］ Locker J, Prenter P M 1980 SIAM J. Numer. Anal. 17 247
[8] ［8］ Murio D A 1987 Comput. Math. Appl. 13 381
[9] ［9］ Groetsch C W 1998 Am. Math. Mon. 105 320
[10] ］ Groetsch C W 1992 J. Optim. Theory Appl. 74 373
[11] ］ Groetsch C W, Scherzer O 1993 Electron. J. Diff. Eqns. 1993(4) 1
[12] ］ Anderssen R, Hegland M 1999 Math. Comput. 68 1121
[13] ］ Wang Y B, Jia X Z, Cheng J 2002 Inv. Prob. 18 1461
[14] ］ Cai Q F, Huang S X, Gao S T, Zhong K, Li Z Q 2008 Acta Phys. Sin. 57 3912 (in Chinese)［蔡其发、黄思训、高守亭、钟科、李自强 2008 57 3912］
[15] ］ Wang Y B, Wei T 2005 J. Math. Anal. Appl. 312 121
[16] ］ Gong Z Q, Feng G L 2007 Acta Phys. Sin. 56 3619 (in Chinese)［龚志强、封国林 2007 56 3619］
[17] ］ Zhang W， He W P, Zou M W, Feng G L 2007 Acta Phys. Sin. 56 6150 (in Chinese)［张文、何文平、邹明玮、封国林 2007 56 6150］
[18] ］ Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese)［王启光、张增平 2008 57 1976］
[19] ］ Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 1984 (in Chinese)［曹小群、黄思训、杜华栋 2008 57 1984］
[20] ］ Huang S X, Sheng Z 2006 Acta Phys. Sin. 55 6720 (in Chinese)［黄思训、盛铮 2006 55 6720］
[21] ］ Zhang X, Wang B, Ji Z Z, Lin W T 2002 Prog. Nat. Sci. 12 445
[22] ］ Wang G Z, Chen J B, Wu C O 2002 J. Liaoning Norm. Univ. 25 233(in Chinese)［王桂芝、陈纪波、吴诚鸥 2002 辽宁师范大学学报 25 233］
[23] ］ Xu G Q, Shen T L,Tan D N 2002 J. Nanjing Instit. Meteor. 25 764(in Chinese)［徐国强、沈桐立、覃丹宁 2002 南京气象学院学报 25 764］
[24] ］ Zhu J, Wang H, Zhou G Q 2002 Chin. Sci. Bull. 47 2010
[25] ］ Cressman G P 1959 Mon. Wea. Rev. 87 367
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[1] ［1］ Kalnay E 2005 Atmospheic Modeling, Data Assimilation and Predictability ( Beijing: China Meteorological Press) p6 (in Chinese) ［Kalnay E 2005 大气模式、资料同化和可预报性(中译本)（北京:气象出版社） 第6页］
[2] ［2］ Liao D X 1996 J. Appl. Meteor. Sci. 7 238 (in Chinese)［廖洞贤 1996 应用气象学报 7 238］
[3] ［3］ 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］
[4] ［4］ Cao J, Gao S T, Zhou Y S 2008 Acta Phys. Sin. 57 2600 (in Chinese)［曹洁、高守亭、周玉淑 2008 57 2600］
[5] ［5］ Vasin V V 1973 USSR Comput. Maths. Math. Phys. 13 16
[6] ［6］ Locker J, Prenter P M 1980 J. Math. Anal. Appl. 74 504
[7] ［7］ Locker J, Prenter P M 1980 SIAM J. Numer. Anal. 17 247
[8] ［8］ Murio D A 1987 Comput. Math. Appl. 13 381
[9] ［9］ Groetsch C W 1998 Am. Math. Mon. 105 320
[10] ］ Groetsch C W 1992 J. Optim. Theory Appl. 74 373
[11] ］ Groetsch C W, Scherzer O 1993 Electron. J. Diff. Eqns. 1993(4) 1
[12] ］ Anderssen R, Hegland M 1999 Math. Comput. 68 1121
[13] ］ Wang Y B, Jia X Z, Cheng J 2002 Inv. Prob. 18 1461
[14] ］ Cai Q F, Huang S X, Gao S T, Zhong K, Li Z Q 2008 Acta Phys. Sin. 57 3912 (in Chinese)［蔡其发、黄思训、高守亭、钟科、李自强 2008 57 3912］
[15] ］ Wang Y B, Wei T 2005 J. Math. Anal. Appl. 312 121
[16] ］ Gong Z Q, Feng G L 2007 Acta Phys. Sin. 56 3619 (in Chinese)［龚志强、封国林 2007 56 3619］
[17] ］ Zhang W， He W P, Zou M W, Feng G L 2007 Acta Phys. Sin. 56 6150 (in Chinese)［张文、何文平、邹明玮、封国林 2007 56 6150］
[18] ］ Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese)［王启光、张增平 2008 57 1976］
[19] ］ Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 1984 (in Chinese)［曹小群、黄思训、杜华栋 2008 57 1984］
[20] ］ Huang S X, Sheng Z 2006 Acta Phys. Sin. 55 6720 (in Chinese)［黄思训、盛铮 2006 55 6720］
[21] ］ Zhang X, Wang B, Ji Z Z, Lin W T 2002 Prog. Nat. Sci. 12 445
[22] ］ Wang G Z, Chen J B, Wu C O 2002 J. Liaoning Norm. Univ. 25 233(in Chinese)［王桂芝、陈纪波、吴诚鸥 2002 辽宁师范大学学报 25 233］
[23] ］ Xu G Q, Shen T L,Tan D N 2002 J. Nanjing Instit. Meteor. 25 764(in Chinese)［徐国强、沈桐立、覃丹宁 2002 南京气象学院学报 25 764］
[24] ］ Zhu J, Wang H, Zhou G Q 2002 Chin. Sci. Bull. 47 2010
[25] ］ Cressman G P 1959 Mon. Wea. Rev. 87 367
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