Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models

SUN Guodong; MU Mu

doi:10.1007/s00376-011-0226-1

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Volume 29 Issue 1

Jan. 2012

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Article > ADVANCES IN ATMOSPHERIC SCIENCES > 2012 > 29(1): 79-90

Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models

SUN Guodong,
MU Mu

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

SUN Guodong,
MU Mu

doi: 10.1007/s00376-011-0226-1

Abstract
References
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Abstract:
Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects: abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.
- conditional nonlinear optimal perturbation,
- initial perturbation,
- parameter perturbation,
- grassland ecosystem
References

[1]	SUN Guodong, MU Mu, 2011: Response of a Grassland Ecosystem to Climate Change in a Theoretical Model, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1266-1278. doi: 10.1007/s00376-011-0169-6
[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]	SUN Guodong, MU Mu, ZHANG Yale, 2010: Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP), ADVANCES IN ATMOSPHERIC SCIENCES, 27, 1311-1321. doi: 10.1007/s00376-010-9088-1
[4]	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
[5]	Xin LIU, Jing CHEN, Yongzhu LIU, Zhenhua HUO, Zhizhen XU, Fajing CHEN, Jing WANG, Yanan MA, Yumeng HAN, 2024: An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction, ADVANCES IN ATMOSPHERIC SCIENCES, 41, 545-563. doi: 10.1007/s00376-023-3035-4
[6]	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
[7]	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
[8]	ZHENG Qin, SHA Jianxin, SHU Hang, and LU Xiaoqing, 2014: A Variant Constrained Genetic Algorithm for Solving Conditional Nonlinear Optimal Perturbations, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 219-229. doi: 10.1007/s00376-013-2253-6*
[9]	SUN Guodong, MU Mu, 2013: Using the Lund-Potsdam-Jena Model to Understand the Different Responses of Three Woody Plants to Land Use in China, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 515-524. doi: 10.1007/s00376-012-2011-1
[10]	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
[11]	CHEN Boyu, MU Mu, 2012: The Roles of Spatial Locations and Patterns of Initial Errors in the Uncertainties of Tropical Cyclone Forecasts, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 63-78. doi: 10.1007/s00376-011-0201-x
[12]	WANG Bo, and HUO Zhenhua, 2013: Extended application of the conditional nonlinear optimal parameter perturbation method in the Common Land Model, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1213-1223. doi: 10.1007/s00376-012-2025-8
[13]	Xing ZHANG, Mu MU, Qiang WANG, Stefano PIERINI, 2017: Optimal Precursors Triggering the Kuroshio Extension State Transition Obtained by the Conditional Nonlinear Optimal Perturbation Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 685-699. doi: 10.1007/s00376-017-6263-7
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Manuscript History

Manuscript received: 10 January 2012

Manuscript revised: 10 January 2012

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

Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models

SUN Guodong,
MU Mu

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

Manuscript received: 2012-01-10
Manuscript revised: 2012-01-10

Abstract: Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects: abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.

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