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Initial error and model error are key factors restricting the accuracy of numerical weather prediction (NWP). The purpose of the present study is to estimate the errors of spatiotemporal evolution model by using recent observations. By considering the continuous evolution of atmosphere, the observed data (ignoring the measurement error) can be viewed as a series of solutions of accurate model governing the actual atmosphere, and the model errors can be objectively assumed to be an unknown functional term (a missing forcing term) of the numerical model, thus the NWP can be considered as an inverse problem to uncover the unknown model error term by using the long periods of observed data. In this study, we first construct an inverse problem model with its optimization problem, which is constrained by the numerical model, to estimate the errors of spatiotemporal evolution model, then we present a derivative-free optimization (DFO) method to find the minimum solution of the optimization problem by running the numerical model with an external forcing term. The DFO method does not need to compute the gradient of the objective functional and the tangent linear model or adjoint model of the original numerical model. The numerical study of Burgers equation indicates that the presented methods can effectively uncover the model errors from the past data and evidently improve the numerical prediction. The precedures described in this paper open up possibilities for utilizing the past observation data to extract useful information about model errors and enhance the prediction efficiency in the operational models.
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Keywords:
- model error /
- past data /
- inverse problem /
- derivative-free optimization
[1] Toth Z, Kalnay E 1993 Bull. Amer. Meteor. Soc. 74 2317
[2] Molteni F, Buizza R, Palmer T N, Petroliagis T 1996 Quart. J. Roy. Meteor. Soc. 122 73
[3] Zheng Z H, Feng G L, Huang J P, Chou J F 2012 Acta Phys. Sin. 61 199203 (in Chinese) [郑志海, 封国林, 黄建平, 丑纪范 2012 61 199203]
[4] Dong W J, Feng G L 2003 Acta Phys. Sin. 52 2347 (in Chinese) [董文杰, 封国林 2003 52 2347]
[5] Mu M, Jiang Z N 2007 Chin. Sci. Bull. 52 1457 (in Chinese) [穆穆, 姜智娜 2007 科学通报 52 1457]
[6] Duan W S, Mu M 2009 Sci. China Ser. D 52 884
[7] Mu M, Duan W S, Wang Q, Zhang R 2010 Nonlin. Process. Geophys. 17 211
[8] Du Q, Shen T L 2007 J. Trop. Meteor. 23 182 (in Chinese) [杜钦, 沈桐立 2007 热带气象学报 23 182]
[9] Gu Z C 1958 Acta Meteor. Sin. 29 176 (in Chinese) [顾震潮 1958 气象学报 29 176]
[10] Chou J F 2007 Acta Meteor. Sin. 65 673 (in Chinese) [丑纪范 2007 气象学报 65 673]
[11] Huang J P, Yi Y H, Wang S H, Chou J F 1993 Quart. J. Roy. Meteor. Soc. 119 547
[12] Xiong K G, Zhao J H, Feng G L, Huang J P, Hu J G 2012 Acta Phys. Sin. 61 149204 (in Chinese) [熊开国, 赵俊虎, 封国林, 黄建平, 胡经国 2012 61 149204]
[13] Ren H L, Chou J F 2005 Acta Meteor. Sin. 63 988 (in Chinese) [任红利, 丑纪范 2005 气象学报 63 988]
[14] Bao M, Ni Y Q, Chou J F 2004 Chin. Sci. Bull. 49 1296
[15] Sasaki Y 1970 Mon. Wea. Rev. 98 875
[16] Carrassi A, Vannitsem S 2010 Mon. Wea. Rev. 138 3369
[17] Zhong J, Fei J F, Huang S X, Du H D 2012 Acta Phys. Sin. 14 149203 (in Chinese) [钟剑, 费建芳, 黄思训, 杜华栋 2012 14 149203]
[18] Huang J P, Yi Y H 1991 Sci. China Ser. B 34 1246
[19] Zhang Z S, Gong Z Q, Zhi R, Feng G L, Hu J G 2011 Chin. Phys. B 20 019201
[20] Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[21] Xue H L, Shen X S, Chou J F 2013 Adv. Atmos. Sci. 30 1249
[22] Adrian D, Thomas T, Franz S 2010 Numerical Regularization for Atmospheric Inverse Problem (Berlin: Springer-Verlag) pp163-217
[23] Jorge N, Stephen W 2006 Numerical Optimization (Berlin: Springer-Verlag) pp220-244
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[1] Toth Z, Kalnay E 1993 Bull. Amer. Meteor. Soc. 74 2317
[2] Molteni F, Buizza R, Palmer T N, Petroliagis T 1996 Quart. J. Roy. Meteor. Soc. 122 73
[3] Zheng Z H, Feng G L, Huang J P, Chou J F 2012 Acta Phys. Sin. 61 199203 (in Chinese) [郑志海, 封国林, 黄建平, 丑纪范 2012 61 199203]
[4] Dong W J, Feng G L 2003 Acta Phys. Sin. 52 2347 (in Chinese) [董文杰, 封国林 2003 52 2347]
[5] Mu M, Jiang Z N 2007 Chin. Sci. Bull. 52 1457 (in Chinese) [穆穆, 姜智娜 2007 科学通报 52 1457]
[6] Duan W S, Mu M 2009 Sci. China Ser. D 52 884
[7] Mu M, Duan W S, Wang Q, Zhang R 2010 Nonlin. Process. Geophys. 17 211
[8] Du Q, Shen T L 2007 J. Trop. Meteor. 23 182 (in Chinese) [杜钦, 沈桐立 2007 热带气象学报 23 182]
[9] Gu Z C 1958 Acta Meteor. Sin. 29 176 (in Chinese) [顾震潮 1958 气象学报 29 176]
[10] Chou J F 2007 Acta Meteor. Sin. 65 673 (in Chinese) [丑纪范 2007 气象学报 65 673]
[11] Huang J P, Yi Y H, Wang S H, Chou J F 1993 Quart. J. Roy. Meteor. Soc. 119 547
[12] Xiong K G, Zhao J H, Feng G L, Huang J P, Hu J G 2012 Acta Phys. Sin. 61 149204 (in Chinese) [熊开国, 赵俊虎, 封国林, 黄建平, 胡经国 2012 61 149204]
[13] Ren H L, Chou J F 2005 Acta Meteor. Sin. 63 988 (in Chinese) [任红利, 丑纪范 2005 气象学报 63 988]
[14] Bao M, Ni Y Q, Chou J F 2004 Chin. Sci. Bull. 49 1296
[15] Sasaki Y 1970 Mon. Wea. Rev. 98 875
[16] Carrassi A, Vannitsem S 2010 Mon. Wea. Rev. 138 3369
[17] Zhong J, Fei J F, Huang S X, Du H D 2012 Acta Phys. Sin. 14 149203 (in Chinese) [钟剑, 费建芳, 黄思训, 杜华栋 2012 14 149203]
[18] Huang J P, Yi Y H 1991 Sci. China Ser. B 34 1246
[19] Zhang Z S, Gong Z Q, Zhi R, Feng G L, Hu J G 2011 Chin. Phys. B 20 019201
[20] Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[21] Xue H L, Shen X S, Chou J F 2013 Adv. Atmos. Sci. 30 1249
[22] Adrian D, Thomas T, Franz S 2010 Numerical Regularization for Atmospheric Inverse Problem (Berlin: Springer-Verlag) pp163-217
[23] Jorge N, Stephen W 2006 Numerical Optimization (Berlin: Springer-Verlag) pp220-244
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