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A nonlinear least-squares-based ensemble method with a penalty strategy for computing the conditional nonlinear optimal perturbations

Authors:

Xiangjun Tian1,2 and Xiaobing Feng3

1 ICCES, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

2 Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, China

3 Department of Mathematics, The University of Tennessee, Knoxville, USA

 

Abstract:

Since the conditional nonlinear optimal perturbations (CNOPs) are formulated mathematically as a constrained minimization problem, the existing numerical methods for computing the CNOPs were designed to solve the original constrained optimization problems by directly adapting some (constrained) optimization algorithms. Although such an approach is natural and convenient, it often results in inefficient and expensive numerical methods for computing the CNOPs. In this article we propose an alternative approach which is based on the idea of first transforming the original CNOP problem into a special unconstrained optimization problem (known as a nonlinear least-squares problem) using a penalty strategy and then utilizing a more efficient Gauss–Newton iterative method, to solve the transformed (unconstrained) nonlinear least-squares problem. Compared with the existing numerical methods, the proposed Gauss–Newton iterative method has some desired advantages: it is easy to implement and portable because it does not rely on any existing constrained optimization package; it is also fast, and highly efficient. These advantages and potential merits of the proposed method are demonstrated by several sets of evaluation experiments based on the viscous Burgers equation, theT21L3 quasi-geostrophic model and the shallow-water equation model, respectively.

 

Key Words:

CNOP, constrained and unconstrained optimization, penalty strategy, nonlinear least squares, Gauss-Newton method

 




Citation:

Xiangjun Tian and Xiaobing Feng, 2017: A nonlinear least-squares-based ensemblemethod with a penalty strategy for computing the conditional nonlinear optimal perturbations. Q. J. R. Meteorol. Soc. 143: 641–649, January 2017 B DOI:10.1002/qj.2946. 


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