The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial pert...The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition. The results indicate that the valid time period of TLM, during which TLM can be utilized to approximate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double—periodic condition the valid period of the TLM is shorter than that with the rigid—boundary condition. Key words Nonlinear stability and instability - Tangent linear model (TLM) - Validity This work was supported by the National Key Basic Research Project “Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters in China” (No.G1998040910) and the National Natural Science Foundation of China (No.49775262 and No.49823002).展开更多
The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this paper.The relationship between the limit of the validity time of the TLM and initial perturbations ...The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this paper.The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method.A new error function between the nonlinear and the linear evolution of the perturbations is proposed.Furthermore,numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM,such as the initial perturbation,the prediction time,the time step size and so on,by the method of mathematical statistics.展开更多
The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows lon...The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.展开更多
伴随方法是一种高效的敏感性分析方法,在大型非线性复杂系统的敏感性计算中有着显著的优势。依据伴随理论,基于大气化学模式GRAPES-CUACE(global-regional assimilation and prediction system coupled with the CMA unified atmospheri...伴随方法是一种高效的敏感性分析方法,在大型非线性复杂系统的敏感性计算中有着显著的优势。依据伴随理论,基于大气化学模式GRAPES-CUACE(global-regional assimilation and prediction system coupled with the CMA unified atmospheric chemistry environment forecasting system),建立了气溶胶模块和气体模块的伴随模式,并对其进行了正确性测试。结合黑碳气溶胶(black carbon aerosol,BC)及臭氧(O3)浓度观测数据,分别利用气溶胶和气体伴随模块进行了数值模拟及源-浓度的敏感性实验。结果表明:CUACE模式能较好地模拟BC浓度的日变化过程。利用气溶胶伴随模式模拟分析了目标函数(观测浓度与模拟浓度差值)关于BC排放源的敏感性,发现敏感性与浓度差值成正比关系。气体伴随模型的敏感性分析表明,若要减小2015年7月7日08:00至8日07:00北京顺义站O3模拟浓度与观测浓度的差异,需要对NOx和VOCs排放源分布进行调整,即在当前状态减小区域内的NOx排放源以及增大对应网格点的VOCs排放源,再结合优化算法即可得到合理的排放源分布。本文开发的GRAPES-CUACE气溶胶伴随和气体伴随模块能够有效地针对气溶胶和气体进行敏感性分析,为下一步构建完整的GRAPES-CUACE大气化学四维变分同化系统以及污染源反演工作奠定了基础。展开更多
In this study we extend the dimension-reduced projection-four dimensional variational data assimilation （DRP-4DVar） approach to allow the analysis time to be tunable, so that the intervals between analysis time and ...In this study we extend the dimension-reduced projection-four dimensional variational data assimilation （DRP-4DVar） approach to allow the analysis time to be tunable, so that the intervals between analysis time and observation times can be shortened. Due to the limits of the perfect-model assumption and the tangentlinear hypothesis, the analysis-time tuning is expected to have the potential to further improve analyses and forecasts. Various sensitivity experiments using the Lorenz-96 model are conducted to test the impact of analysistime tuning on the performance of the new approach under perfect and imperfect model scenarios, respectively. Comparing three DRP-4DVar schemes having the analysis time at the start, middle, and end of the assimilation window, respectively, it is found that the scheme with the analysis time in the middle of the window outperforms the others, on the whole. Moreover, the advantage of this scheme is more pronounced when a longer assimilation window is adopted or more observations are assimilated.展开更多
The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and deca...The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.展开更多
文摘The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition. The results indicate that the valid time period of TLM, during which TLM can be utilized to approximate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double—periodic condition the valid period of the TLM is shorter than that with the rigid—boundary condition. Key words Nonlinear stability and instability - Tangent linear model (TLM) - Validity This work was supported by the National Key Basic Research Project “Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters in China” (No.G1998040910) and the National Natural Science Foundation of China (No.49775262 and No.49823002).
基金This project is Supported by the National Natural Science Foundation of China(Grant Nos.11471166 and 11426134)the Natural Science Foundation of Jiangsu Province(Grant No.BK20141443).
文摘The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this paper.The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method.A new error function between the nonlinear and the linear evolution of the perturbations is proposed.Furthermore,numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM,such as the initial perturbation,the prediction time,the time step size and so on,by the method of mathematical statistics.
基金Acknowledgments. The authors would like to thank Prof. Z. Yuan for her numerous suggestions in the writing of this paper. This work is supported by the National Natural Science Foundation of China (Grant No.40176009), the National Key Programme for Devel
文摘The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.
文摘伴随方法是一种高效的敏感性分析方法,在大型非线性复杂系统的敏感性计算中有着显著的优势。依据伴随理论,基于大气化学模式GRAPES-CUACE(global-regional assimilation and prediction system coupled with the CMA unified atmospheric chemistry environment forecasting system),建立了气溶胶模块和气体模块的伴随模式,并对其进行了正确性测试。结合黑碳气溶胶(black carbon aerosol,BC)及臭氧(O3)浓度观测数据,分别利用气溶胶和气体伴随模块进行了数值模拟及源-浓度的敏感性实验。结果表明:CUACE模式能较好地模拟BC浓度的日变化过程。利用气溶胶伴随模式模拟分析了目标函数(观测浓度与模拟浓度差值)关于BC排放源的敏感性,发现敏感性与浓度差值成正比关系。气体伴随模型的敏感性分析表明,若要减小2015年7月7日08:00至8日07:00北京顺义站O3模拟浓度与观测浓度的差异,需要对NOx和VOCs排放源分布进行调整,即在当前状态减小区域内的NOx排放源以及增大对应网格点的VOCs排放源,再结合优化算法即可得到合理的排放源分布。本文开发的GRAPES-CUACE气溶胶伴随和气体伴随模块能够有效地针对气溶胶和气体进行敏感性分析,为下一步构建完整的GRAPES-CUACE大气化学四维变分同化系统以及污染源反演工作奠定了基础。
基金supported by the Special Project of the Meteorological Sector program Grant No GYHY(QX) 200906011the 973 project (Grant No 2004CB418304)
文摘In this study we extend the dimension-reduced projection-four dimensional variational data assimilation （DRP-4DVar） approach to allow the analysis time to be tunable, so that the intervals between analysis time and observation times can be shortened. Due to the limits of the perfect-model assumption and the tangentlinear hypothesis, the analysis-time tuning is expected to have the potential to further improve analyses and forecasts. Various sensitivity experiments using the Lorenz-96 model are conducted to test the impact of analysistime tuning on the performance of the new approach under perfect and imperfect model scenarios, respectively. Comparing three DRP-4DVar schemes having the analysis time at the start, middle, and end of the assimilation window, respectively, it is found that the scheme with the analysis time in the middle of the window outperforms the others, on the whole. Moreover, the advantage of this scheme is more pronounced when a longer assimilation window is adopted or more observations are assimilated.
文摘The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.
