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Relationships between the Limit of Predictability and initial error in the Uncoupled and Coupled Lorenz Models

Advances in Atmospheric Sciences 2012年第5期29卷 1078-1088页

作者：丁瑞强李建平 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of Sciences

In this study, the relationship between the limit of predictability and initial error was investigated using two simple chaotic systems： the Lorenz model, which possesses a single characteristic time scale, and the coupled Lorenz model, which possesses two different characteristic time scales. The limit of predictability is defined here as the time at which the error reaches 95% of its saturation level; nonlinear behaviors of the error growth are therefore involved in the definition of the limit of predictability. Our results show that the logarithmic function performs well in describing the relationship between the limit of predictability and initial error in both models, although the coefficients in the logarithmic function were not constant across the examined range of initial errors. Compared with the Lorenz model, in the coupled Lorenz model in which the slow dynamics and the fast dynamics interact with each other--there is a more complex relationship between the limit of predictability and initial error. The limit of predictability of the Lorenz model is unbounded as the initial error becomes infinitesimally small; therefore, the limit of predictability of the Lorenz model may be extended by reducing the amplitude of the initial error. In contrast, if there exists a fixed initial error in the fast dynamics of the coupled Lorenz model, the slow dynamics has an intrinsic finite limit of predictability that cannot be extended by reducing the amplitude of the initial error in the slow dynamics, and vice versa. The findings reported here reveal the possible existence of an intrinsic finite limit of predictability in a coupled system that possesses many scales of time or motion.

关键词： limit of predictability initial error Lorenz model coupled Lorenz model

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The Combined Effect of initial error and Model error on ENSO Prediction Uncertainty Generated by the Zebiak-Cane Model

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Atmospheric and Oceanic Science Letters 2014年第5期7卷 447-452页

作者： ZHAO Peng DUAN Wan-Suo State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) Institute of Atmospheric Physics Chinese Academy of Sciences University of Chinese Academy of Sciences

initial errors and model errors are the source of prediction errors. In this study, the authors compute the conditional nonlinear optimal perturbation （CNOP）-type initial errors and nonlinear forcing singular vector （NFSV）- type tendency errors of the Zebiak-Cane model with respect to El Nifio events and analyze their combined effect on the prediction errors for E1 Nino events. The CNOP- type initial error （NFSV-type tendency error） represents the initial errors （model errors） that have the largest effect on prediction uncertainties for E1 Nifio events under the perfect model （perfect initial conditions） scenario. How- ever, when the CNOP-type initial errors and the NFSV- type tendency errors are simultaneously considered in the model, the prediction errors caused by them are not am- plified as the authors expected. Specifically, the predic- tion errors caused by the combined mode of CNOP-type initial errors and NFSV-type tendency errors are a little larger than those caused by the NFSV-type tendency er- rors. This fact emphasizes a need to investigate the opti- mal combined mode of initial errors and tendency errors that cause the largest prediction error for E1 Nifio events.

关键词： predictability initial error model error optimal perturbation

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The initial errors in the Tropical Indian Ocean that Can Induce a Significant “Spring Predictability Barrier” for La Nina Events and Their Implication for Targeted Observations

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Advances in Atmospheric Sciences 2021年第9期38卷 1566-1579页

作者： Qian ZHOU Wansuo DUAN Xu WANG Xiang LI Ziqing ZU Key Laboratory of Marine Hazards Forecasting National Marine Environmental Forecasting CenterMinistry of Natural ResourcesBeijing 100081China LASG Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China Ministry of Education Key Laboratory for Earth System Modeling Department for Earth System ScienceTsinghua UniversityBeijing 100084China

initial errors in the tropical Indian Ocean(IO-related initial errors) that are most likely to yield the Spring Prediction Barrier(SPB) for La Ni?a forecasts are explored by using the CESM *** initial errors can be classified into two ***-1 initial error consists of positive sea temperature errors in the western Indian Ocean and negative sea temperature errors in the eastern Indian Ocean,while the spatial structure of Type-2 initial error is nearly *** kinds of IO-related initial errors induce positive prediction errors of sea temperature in the Pacific Ocean,leading to underprediction of La Nina ***-1 initial error in the tropical Indian Ocean mainly influences the SSTA in the tropical Pacific Ocean via atmospheric bridge,leading to the development of localized sea temperature errors in the eastern Pacific ***,for Type-2 initial error,its positive sea temperature errors in the eastern Indian Ocean can induce downwelling error and influence La Ni?a predictions through an oceanic channel called Indonesian *** on the location of largest SPB-related initial errors,the sensitive area in the tropical Indian Ocean for La Nina predictions is ***,sensitivity experiments show that applying targeted observations in this sensitive area is very useful in decreasing prediction errors of La ***,adopting a targeted observation strategy in the tropical Indian Ocean is a promising approach toward increasing ENSO prediction skill.

关键词： initial error tropical Indian Ocean La Nina prediction sensitive area targeted observation

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A Case Study of the error Growth and Predictability of a Meiyu Frontal Heavy Precipitation Event

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Acta meteorologica Sinica 2011年第4期25卷 430-440页

作者：罗雨张立凤 Institute of Meteorology PLA University of Science and Technology

The Advanced Regional Eta-coordinate Model （AREM） is used to explore the predictability of a heavy rainfall event along the Meiyu front in China during 3-4 July 2003. Based on the sensitivity of precipitation prediction to initial data sources and initial uncertainties in different variables, the evolution of error growth and the associated mechanism are described and discussed in detail in this paper. The results indicate that the smaller-amplitude initial error presents a faster growth rate and its growth is characterized by a transition from localized growth to widespread expansion error. Such modality of the error growth is closely related to the evolvement of the precipitation episode, and consequently remarkable forecast divergence is found near the rainband, indicating that the rainfall area is a sensitive region for error growth. The initial error in the rainband contributes significantly to the forecast divergence, and its amplification and propagation are largely determined by the initial moisture distribution. The moisture condition also affects the error growth on smaller scales and the subsequent upscale error cascade. In addition, the error growth defined by an energy norm reveals that large error energy collocates well with the strong latent heating, implying that the occurrence of precipitation and error growth share the same energy source-the latent heat. This may impose an intrinsic predictability limit on the prediction of heavy precipitation.

关键词： heavy precipitation predictability initial error model error growth AREM

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error Sensitivity Analysis in 10–30-Day Extended Range Forecasting by Using a Nonlinear Cross-Prediction error Model

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Journal of Meteorological Research 2017年第3期31卷 567-575页

作者： Zhiye XIA Lisheng XU Hongbin CHEN Yongqian WANG Jinbao LIU Wenlan FENGl college of resources and environment chengdu university of information technologyChengdu 610225 plateau atmosphere and environment key laboratory of sichuan province Chengdu 610225 key laboratory of middle atmosphere and global environment observation institute of atmospheric physicschinese academy of sciencesBeijing 100029

Extended range forecasting of 10-30 days, which lies between medium-term and climate prediction in terms of timescale, plays a significant role in decision-making processes for the prevention and mitigation of disastrous met- eorological events. The sensitivity of initial error, model parameter error, and random error in a nonlinear cross- prediction error （NCPE） model, and their stability in the prediction validity period in 1 0-30-day extended range fore- casting, are analyzed quantitatively. The associated sensitivity of precipitable water, temperature, and geopotential height during cases of heavy rain and hurricane is also discussed. The results are summarized as follows. First, the initial error and random error interact. When the ratio of random error to initial error is small （10＂5-10-2）, minor vari- ation in random error cannot significantly change the dynamic features of a chaotic system, and therefore random er- ror has minimal effect on the prediction. When the ratio is in the range of 10-1-2 （i.e., random error dominates）, at- tention should be paid to the random error instead of only the initial error. When the ratio is around 10 2-10-1, both influences must be considered. Their mutual effects may bring considerable uncertainty to extended range forecast- ing, and de-noising is therefore necessary. Second, in terms of model parameter error, the embedding dimension m should be determined by the factual nonlinear time series. The dynamic features of a chaotic system cannot be depic- ted because of the incomplete structure of the attractor when m is small. When m is large, prediction indicators can vanish because of the scarcity of phase points in phase space. A method for overcoming the cut-off effect （m 〉 4） is proposed. Third, for heavy rains, precipitable water is more sensitive to the prediction validity period than temperat- ure or geopotential height; however, for hurricanes, geopotential height is most sensitive, followed by precipitable water.

关键词： extended range forecasting random error initial error model parameter error sensitivity

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Spatial Propagation of Different Scale errors in Meiyu Frontal Rainfall Systems

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Acta meteorologica Sinica 2012年第2期26卷 129-146页

作者：杨舒楠谈哲敏 Key Laboratory for Mesoscale Severe Weather/Ministry of Education and School of Atmospheric SciencesNanjing University

The spatial propagation of meso-and small-scale errors in a Meiyu frontal heavy rainfall event,which occurred in eastern China during 4-6 July 2003,is investigated by using the mesoscale numerical model *** general,the spatial propagation of simulated errors depends on their horizontal ***-scale（L 〈 100 km） initial error may spread rapidly as an isotropic circle through the sound ***,many scattered convection-scale errors are triggered in moist convection zone that will spread abroad through the isotropic,round-shaped sound wave further *** to the evolution of the rainfall system,several new convection-scale errors may be generated continuously by moist convection within the propagated round-shaped *** the above circular process,the small-scale error increases in amplitude and grows in scale ***（100 km 〈 L 〈 1000 km） initial error propagates up-and down-stream wavelike through the gravity wave,meanwhile migrating down-stream slowly along with the rainfall system by the mean *** up-stream propagation of the mesoscale error is very important to the error growth because it can accumulate error energy locally at a place where there is no moist convection and far upstream from the initial perturbation *** moist convection plays an important role in the rapid growth of errors,it has no impact on the propagation of meso-and small-scale *** diabatic heating could trigger,strengthen,and promote upscaling of small-scale errors successively,and provide ＂error source＂ to error growth and *** rapid growth of simulated errors results from both intense moist convection and appropriate spatial propagation of the errors.

关键词： initial error spatial propagation upscale growth moist convection Meiyu frontal rainfall

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On the sensitive areas for targeted observations in ENSO forecasting

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Atmospheric and Oceanic Science Letters 2021年第5期14卷 19-23页

作者： Jingjing Zhang Shujuan Hu Wansuo Duan College of Atmospheric Sciences Lanzhou UniversityLanzhouChina State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG) Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina University of Chinese Academy of Sciences BeijingChina

Using the outputs from CMCC-CM in CMIP5 experiments,the authors identified sensitive areas for targeted observations in ENSO forecasting from the perspective of the initial error growth(IEG)method and the particle filter(PF)*** showed that the PF targets areas over the central-eastern equatorial Pacific,while the sensitive areas determined by the IEG method are slightly to the east of the *** a small part of the areas targeted by the IEG method also lie in the southeast equatorial Pacific,this does not affect the large-scale overlapping of the sensitive areas determined by these two methods in the eastern equatorial ***,sensitive areas determined by the two methods are mutually *** considering the uncertainty of methods for determining sensitive areas in realistic targeted observation,it is more reasonable to choose the above overlapping areas as sensitive areas for ENSO *** result provides scientific guidance for how to better determine sensitive areas for ENSO forecasting.

关键词： Targeted observation ENSO Particle filter initial error

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