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A New Strategy for Solving a Class of Constrained Nonlinear Optimization Problems Related to Weather and Climate Predictability


doi: 10.1007/s00376-009-9141-0

  • There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems: the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly efficient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly efficient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally efficient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.
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    [2] BEI Naifang, Fuqing ZHANG, 2014: Mesoscale Predictability of Moist Baroclinic Waves: Variable and Scale-dependent Error Growth, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 995-1008.  doi: 10.1007/s00376-014-3191-7
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    [6] MU Mu, DUAN Wansuo, XU Hui, WANG Bo, 2006: Applications of Conditional Nonlinear Optimal Perturbation in Predictability Study and Sensitivity Analysis of Weather and Climate, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 992-1002.  doi: 10.1007/s00376-006-0992-3
    [7] 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
    [8] WANG Huijun, FAN Ke, SUN Jianqi, LI Shuanglin, LIN Zhaohui, ZHOU Guangqing, CHEN Lijuan, LANG Xianmei, LI Fang, ZHU Yali, CHEN Hong, ZHENG Fei, 2015: A Review of Seasonal Climate Prediction Research in China, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 149-168.  doi: 10.1007/s00376-014-0016-7
    [9] Yunyun LIU, Zeng-Zhen HU, Renguang WU, Xing YUAN, 2022: Causes and Predictability of the 2021 Spring Southwestern China Severe Drought, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 1766-1776.  doi: 10.1007/s00376-022-1428-4
    [10] Zhiyong MENG, Eugene E. CLOTHIAUX, 2022: Contributions of Fuqing ZHANG to Predictability, Data Assimilation, and Dynamics of High Impact Weather: A Tribute, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 676-683.  doi: 10.1007/s00376-021-1362-x
    [11] Wang Zhiren, Wu Dexing, Chen Dake, Wu Huiding, Song Xuejia, Zhang Zhanhai, 2002: Critical Time Span and Nonlinear Action Structure of Climatic Atmosphere and Ocean, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 741-756.  doi: 10.1007/s00376-002-0013-0
    [12] DING Ruiqiang, FENG Guolin, LIU Shida, LIU Shikuo, HUANG Sixun, FU Zuntao, 2007: Nonlinear Atmospheric and Climate Dynamics in China (2003--2006): A Review, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 1077-1085.  doi: 10.1007/s00376-007-1077-7
    [13] DUAN Wansuo, JIANG Zhina, XU Hui, 2007: Progress in Predictability Studies in China (2003--2006), ADVANCES IN ATMOSPHERIC SCIENCES, 24, 1086-1098.  doi: 10.1007/s00376-007-1086-6
    [14] ZHU Benlu, LIN Wantao, ZHANG Yun, 2010: Analysis Study on Perturbation Energy and Predictability of Heavy Precipitation in South China, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 382-392.  doi: 10.1007/s00376-009-8164-x
    [15] WU Duochang, MENG Zhiyong, YAN Dachun, 2013: The Predictability of a Squall Line in South China on 23 April 2007, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 485-502.  doi: 10.1007/s00376-012-2076-x
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    [17] Guokun DAI, Chunxiang LI, Zhe HAN, Dehai LUO, Yao YAO, 2022: The Nature and Predictability of the East Asian Extreme Cold Events of 2020/21, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 566-575.  doi: 10.1007/s00376-021-1057-3
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Manuscript History

Manuscript received: 10 July 2010
Manuscript revised: 10 July 2010
通讯作者: 陈斌, bchen63@163.com
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A New Strategy for Solving a Class of Constrained Nonlinear Optimization Problems Related to Weather and Climate Predictability

  • 1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Training Center, China Meteorological Administration, Beijing 100081

Abstract: There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems: the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly efficient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly efficient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally efficient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.

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