Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP) |
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Authors: | SUN Guodong MU Mu and ZHANG Yale |
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Institution: | 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 |
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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. |
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Keywords: | conditional nonlinear optimal perturbation constrained optimization problem unconstrained optimization problem |
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