Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

SUN Guodong; MU Mu; ZHANG Yale

doi:10.1007/s00376-010-9088-1

Impact Factor: 5.8

Volume 27 Issue 6

Nov. 2010

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Article > ADVANCES IN ATMOSPHERIC SCIENCES > 2010 > 27(6): 1311-1321

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

1.
The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology,Chinese Academy of Sciences, Qingdao 266071, The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, Graduate University of the Chinese Academy of Sciences, Beijing 100049

doi: 10.1007/s00376-010-9088-1

Abstract
References
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Abstract:
The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.
- conditional nonlinear optimal perturbation,
- constrained optimization problem,
- unconstrained optimization problem
References

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[2]	JIANG Zhina, 2006: Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 775-783. doi: 10.1007/s00376-006-0775-x
[3]	WANG Qiang, MU Mu, Henk A. DIJKSTRA, 2012: Application of the Conditional Nonlinear Optimal Perturbation Method to the Predictability Study of the Kuroshio Large Meander, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 118-134. doi: 10.1007/s00376-011-0199-0
[4]	QIN Xiaohao, MU Mu, 2014: Can Adaptive Observations Improve Tropical Cyclone Intensity Forecasts?, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 252-262. doi: 10.1007/s00376-013-3008-0
[5]	Zhenhua HUO, Wansuo DUAN, Feifan ZHOU, 2019: Ensemble Forecasts of Tropical Cyclone Track with Orthogonal Conditional Nonlinear Optimal Perturbations, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 231-247. doi: 10.1007/s00376-018-8001-1
[6]	SUN Guodong, MU Mu, 2012: Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 79-90. doi: 10.1007/s00376-011-0226-1
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Manuscript History

Manuscript received: 10 November 2010

Manuscript revised: 10 November 2010

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

1. The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology,Chinese Academy of Sciences, Qingdao 266071, The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, Graduate University of the Chinese Academy of Sciences, Beijing 100049

Manuscript received: 2010-11-10
Manuscript revised: 2010-11-10

Abstract: The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

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