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1.
With the Zebiak-Cane (ZC) model, the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation (CNOP). The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model. By analyzing the behavior of CNOPtype errors, we find that for the normal states and the relatively weak E1 Nifio events in the ZC model, the predictions tend to yield false alarms due to the uncertainties caused by CNOP. For the relatively strong E1 Nino events, the ZC model largely underestimates their intensities. Also, our results suggest that the error growth of E1 Nifio in the ZC model depends on the phases of both the annual cycle and ENSO. The condition during northern spring and summer is most favorable for the error growth. The ENSO prediction bestriding these two seasons may be the most difficult. A linear singular vector (LSV) approach is also used to estimate the error growth of ENSO, but it underestimates the prediction uncertainties of ENSO in the ZC model. This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes. CNOP yields the severest prediction uncertainty. That is to say, the prediction skill of ENSO is closely related to the types of initial error. This finding illustrates a theoretical basis of data assimilation. It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill.  相似文献   

2.
With the Zebiak-Cane (ZC) model, the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation (CNOP). The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model. By analyzing the behavior of CNOP- type errors, we find that for the normal states and the relatively weak EI Nino events in the ZC model, the predictions tend to yield false alarms due to the uncertainties caused by CNOP. For the relatively strong EI Nino events, the ZC model largely underestimates their intensities. Also, our results suggest that the error growth of EI Nino in the ZC model depends on the phases of both the annual cycle and ENSO. The condition during northern spring and summer is most favorable for the error growth. The ENSO prediction bestriding these two seasons may be the most difficult. A linear singular vector (LSV) approach is also used to estimate the error growth of ENSO, but it underestimates the prediction uncertainties of ENSO in the ZC model. This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes. CNOP yields the severest prediction uncertainty. That is to say, the prediction skill of ENSO is closely related to the types of initial error. This finding illustrates a theoretical basis of data assimilation. It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill.  相似文献   

3.
穆穆  段晚锁  徐辉  王波 《大气科学进展》2006,23(6):992-1002
Considering the limitation of the linear theory of singular vector (SV), the authors and their collaborators proposed conditional nonlinear optimal perturbation (CNOP) and then applied it in the predictability study and the sensitivity analysis of weather and climate system. To celebrate the 20th anniversary of Chinese National Committee for World Climate Research Programme (WCRP), this paper is devoted to reviewing the main results of these studies. First, CNOP represents the initial perturbation that has largest nonlinear evolution at prediction time, which is different from linear singular vector (LSV) for the large magnitude of initial perturbation or/and the long optimization time interval. Second, CNOP, rather than linear singular vector (LSV), represents the initial anomaly that evolves into ENSO events most probably. It is also the CNOP that induces the most prominent seasonal variation of error growth for ENSO predictability; furthermore, CNOP was applied to investigate the decadal variability of ENSO asymmetry. It is demonstrated that the changing nonlinearity causes the change of ENSO asymmetry. Third, in the studies of the sensitivity and stability of ocean’s thermohaline circulation (THC), the nonlinear asymmetric response of THC to finite amplitude of initial perturbations was revealed by CNOP. Through this approach the passive mechanism of decadal variation of THC was demonstrated; Also the authors studies the instability and sensitivity analysis of grassland ecosystem by using CNOP and show the mechanism of the transitions between the grassland and desert states. Finally, a detailed discussion on the results obtained by CNOP suggests the applicability of CNOP in predictability studies and sensitivity analysis.  相似文献   

4.
穆穆  段晚锁 《大气科学》2013,37(2):281-296
本文总结了近年来条件非线性最优扰动方法的应用研究的主要进展.主要包括四个方面:(1)将条件非线性最优扰动(CNOP)方法拓展到既考虑初始扰动又考虑模式参数扰动,形成了拓展的CNOP方法.拓展的CNOP方法不仅能够应用于研究分别由初始误差和模式参数误差导致的可预报性问题,而且能够用于探讨初始误差和模式参数误差同时存在的情形;(2)将拓展的CNOP方法分别应用于ENSO和黑潮可预报性研究,考察了初始误差和模式参数误差对其可预报性的影响,揭示了初始误差在导致ENSO和黑潮大弯曲路径预报不确定性中的重要作用;(3)考察了阻塞事件发生的最优前期征兆(OPR)以及导致其预报不确定性的最优增长初始误差(OGR),揭示了OPR和OGR空间模态及其演变机制的相似性及其局地性特征;(4)研究了台风预报的目标观测问题,用CNOP方法确定了台风预报的目标观测敏感区,通过观测系统模拟试验(OSSEs)和/或观测系统试验(OSEs),表明了CNOP敏感区在改进台风预报中的有效性.具体地,台风OGR的主要误差分布在某一特定区域,空间分布具有明显的局地性特征,在台风OGR的局地性区域增加观测,有效改进了台风的预报技巧,该区域代表了台风预报的初值敏感区.事实上,上述El Ni(n)o事件、黑潮路径变异以及阻塞事件的OGR的空间分布也具有明显的局地性特征,这些事件的OGR刻画的局地性区域可能也代表了初值敏感区.  相似文献   

5.
The predictability of El Ni?o?Southern Oscillation (ENSO) has been an important area of study for years. Searching for the optimal precursor (OPR) of ENSO occurrence is an effective way to understand its predictability. The CNOP (conditional nonlinear optimal perturbation), one of the most effective ways to depict the predictability of ENSO, is adopted to study the optimal sea surface temperature (SST) precursors (SST-OPRs) of ENSO in the IOCAS ICM (intermediate coupled model developed at the Institute of Oceanology, Chinese Academy of Sciences). To seek the SST-OPRs of ENSO in the ICM, non-ENSO events simulated by the ICM are chosen as the basic state. Then, the gradient-definition-based method (GD method) is employed to solve the CNOP for different initial months of the basic years to obtain the SST-OPRs. The experimental results show that the obtained SST-OPRs present a positive anomaly signal in the western-central equatorial Pacific, and obvious differences exist in the patterns between the different seasonal SST-OPRs along the equatorial western-central Pacific, showing seasonal dependence to some extent. Furthermore, the non-El Ni?o events can eventually evolve into El Ni?o events when the SST-OPRs are superimposed on the corresponding seasons; the peaks of the Ni?o3.4 index occur at the ends of the years, which is consistent with the evolution of the real El Ni?o. These results show that the GD method is an effective way to obtain SST-OPRs for ENSO events in the ICM. Moreover, the OPRs for ENSO depicted using the GD method provide useful information for finding the early signal of ENSO in the ICM.  相似文献   

6.
YU Liang  MU Mu  Yanshan  YU 《大气科学进展》2014,31(3):647-656
ABSTRACT The impact of both initial and parameter errors on the spring predictability barrier (SPB) is investigated using the Zebiak Cane model (ZC model). Previous studies have shown that initial errors contribute more to the SPB than parameter errors in the ZC model. Although parameter errors themselves are less important, there is a possibility that nonlinear interactions can occur between the two types of errors, leading to larger prediction errors compared with those induced by initial errors alone. In this case, the impact of parameter errors cannot be overlooked. In the present paper, the optimal combination of these two types of errors [i.e., conditional nonlinear optimal perturbation (CNOP) errors] is calculated to investigate whether this optimal error combination may cause a more notable SPB phenomenon than that caused by initial errors alone. Using the CNOP approach, the CNOP errors and CNOP-I errors (optimal errors when only initial errors are considered) are calculated and then three aspects of error growth are compared: (1) the tendency of the seasonal error growth; (2) the prediction error of the sea surface temperature anomaly; and (3) the pattern of error growth. All three aspects show that the CNOP errors do not cause a more significant SPB than the CNOP-I errors. Therefore, this result suggests that we could improve the prediction of the E1 Nifio during spring by simply focusing on reducing the initial errors in this model.  相似文献   

7.
Effect of Stochastic MJO Forcing on ENSO Predictability   总被引:2,自引:0,他引:2  
Within the frame of the Zebiak-Cane model,the impact of the uncertainties of the Madden-Julian Oscillation(MJO) on ENSO predictability was studied using a parameterized stochastic representation of intraseasonal forcing.The results show that the uncertainties of MJO have little effect on the maximum prediction error for ENSO events caused by conditional nonlinear optimal perturbation(CNOP);compared to CNOP-type initial error,the model error caused by the uncertainties of MJO led to a smaller prediction uncertainty of ENSO,and its influence over the ENSO predictability was not significant.This result suggests that the initial error might be the main error source that produces uncertainty in ENSO prediction,which could provide a theoretical foundation for the data assimilation of the ENSO forecast.  相似文献   

8.
The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.  相似文献   

9.
用Zebiak-Cane模式和季节内振荡(Madden-Julian Oscillation,MJO)的参数化表述以及条件非线性最优扰动(Conditional Nonlinear Optimal Perturbation,CNOP)方法,分析了以ENSO事件为基态的CNOP型初始误差的空间结构增长规律。结果表明,参数化的MJO对CNOP型初始误差的发展影响较小,其影响主要是使中东太平洋的海表面温度异常增大。CNOP型初始误差比由MJO不确定性产生的模式误差的影响大,前者可能是造成ENSO事件预报不确定性的主要误差来源。由于CNOP型初始误差的局地性,本结论可用来指导ENSO的目标观测和适应性资料同化。  相似文献   

10.
ENSO机理及其预测研究   总被引:19,自引:0,他引:19  
李崇银  穆穆  周广庆 《大气科学》2008,32(4):761-781
资料分析研究表明ENSO(El Ni?o和La Ni?a)实际上是热带太平洋次表层海温距平的循环,而次表层海温距平的循环是赤道西太平洋异常纬向风所驱动的,赤道西太平洋的异常纬向风又主要由异常东亚冬季风所激发。因此可以将ENSO的机理视为主要是由东亚季风异常造成的赤道西太平洋异常纬向风所驱动的热带太平洋次表层海温距平的循环。同时分析还表明,热带西太平洋大气季节内振荡(ISO)的明显年际变化,作为一种外部强迫,对ENSO循环起着十分重要的作用;El Ni?o的发生同大气ISO的明显系统性东传有关。资料分析也表明,El Ni?o持续时间的长短与大气环流异常有密切关系。 用非线性最优化方法研究El Ni?o-南方涛动(ENSO)事件的可预报性问题,揭示了最容易发展成ENSO事件的初始距平模态,即条件非线性最优扰动(CNOP)型初始距平;找出能够导致显著春季可预报性障碍(SPB),且对ENSO预报结果有最大影响的一类初始误差——CNOP型初始误差,进而探讨耦合过程的非线性在SPB研究中的重要作用,提出了关于ENSO事件发生SPB的一种可能机制;用CNOP方法揭示了ENSO强度的不对称现象,探讨ENSO不对称性的年代际变化问题,提出ENSO不对称性年代际变化的一种机制;建立了关于ENSO可预报性的最大可预报时间下界、最大预报误差上界和最大允许初始误差下界的三类可预报性问题,分别从三个方面揭示ENSO事件的春季可预报性障碍现象,比较有效地量化了模式ENSO事件的可预报性。 利用中国科学院大气物理研究所地球流体力学数值模拟国家重点实验室的ENSO预测系统,研究了海洋资料同化在ENSO预测中的应用,该系统可以同时对温、盐剖面资料和卫星高度计资料进行同化。并且在模式中采用次表层上卷海温的非局地参数化方法,可有效地改进ENSO模拟水平。采用集合卡曼滤波(Ensemble Kalman Filter,EnKF)同化方法以及在集合资料同化中“平衡的”多变量模式误差扰动方法为集合预报提供更加精确和协调的初始场,ENSO预报技巧得到提高。  相似文献   

11.
王斌  谭晓伟 《气象学报》2009,67(2):175-188
条件非线性最优扰动(CNOP)是Mu等2003年提出的一个新的理论方法,它是线性奇异向量在非线性情形的推广,克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷,成为非线性系统可预报性和敏感性等研究新的有效工具.然而,由于以往CNOP的求解需要采用伴随技术,计算量相当巨大,限制了该方法的推广应用.为了克服这一困难,本文基于经验正交分解(EOF),提出了一种求解CNOP的快速算法,利用GRAPES区域业务预报模式实现了CNOP快速计算,并在台风"麦莎"的目标观测研究中得到初步检验,通过观测系统模拟实验(OSSE)检验了该方法确定敏感性区域(瞄准区)的有效性和可行性.试验结果表明,用快速算法求解的CNOP,其净能量随时间快速地发展,而且发展呈非线性.在台风"麦莎"个例的目标观测试验中,用快速算法得到的预报时间为24 h的CNOP可以有效地识别瞄准区,并通过瞄准区内初值的改善,可明显减少目标区域(检验区)内24 h累计降水预报误差.尤其,累计降水预报的这种改进效果能够延伸到更长时间(如72 h),尽管检验时间是设在第24小时.进一步分析发现,24 h累计降水预报误差的减少是通过利用瞄准区内改善的初值改进初始时刻台风暖心结构、高空相对涡度以及水汽条件等而得以实现的.  相似文献   

12.
Conditional Nonlinear Optimal Perturbation (CNOP) is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector (LSV) to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function (EOF). The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System (GRAPES), an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity (target) area is evaluated through two observing system simulation experiments (OSSEs). The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors (ARPEs) in the verification region are reduced significantly compared with the "true state," when the initial conditions (ICs) in the sensitivity area are replaced with the "observations." The decrease of the ARPEs can be achieved for even longer prediction times (e.g., 72 h). Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon's initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.  相似文献   

13.
Within a theoretical ENSO model, the authors investigated whether or not the errors superimposed on model parameters could cause a significant ``spring predictability barrier' (SPB) for El Nino events. First, sensitivity experiments were respectively performed to the air--sea coupling parameter, α and the thermocline effect coefficient μ. The results showed that the uncertainties superimposed on each of the two parameters did not exhibit an obvious season-dependent evolution; furthermore, the uncertainties caused a very small prediction error and consequently failed to yield a significant SPB. Subsequently, the conditional nonlinear optimal perturbation (CNOP) approach was used to study the effect of the optimal mode (CNOP-P) of the uncertainties of the two parameters on the SPB and to demonstrate that the CNOP-P errors neither presented a unified season-dependent evolution for different El Nino events nor caused a large prediction error, and therefore did not cause a significant SPB. The parameter errors played only a trivial role in yielding a significant SPB. To further validate this conclusion, the authors investigated the effect of the optimal combined mode (i.e. CNOP error) of initial and model errors on SPB. The results illustrated that the CNOP errors tended to have a significant season-dependent evolution, with the largest error growth rate in the spring, and yielded a large prediction error, inducing a significant SPB. The inference, therefore, is that initial errors, rather than model parameter errors, may be the dominant source of uncertainties that cause a significant SPB for El Nino events. These results indicate that the ability to forecast ENSO could be greatly increased by improving the initialization of the forecast model.  相似文献   

14.
Recent progress in the study of nonlinear atmospheric dynamics and related predictability of weather and climate in China (2007-2011) are briefly introduced in this article. Major achievements in the study of nonlinear atmospheric dynamics have been classified into two types:(1) progress based on the analysis of solutions of simplified control equations, such as the dynamics of NAO, the optimal precursors for blocking onset, and the behavior of nonlinear waves, and (2) progress based on data analyses, such as the nonlinear analyses of fluctuations and recording-breaking temperature events, the long-range correlation of extreme events, and new methods of detecting abrupt dynamical change. Major achievements in the study of predictability include the following:(1) the application of nonlinear local Lyapunov exponents (NLLE) to weather and climate predictability; (2) the application of condition nonlinear optimal perturbation (CNOP) to the studies of El Nin o-Southern Oscillation (ENSO) predictions, ensemble forecasting, targeted observation, and sensitivity analysis of the ecosystem; and (3) new strategies proposed for predictability studies. The results of these studies have provided greater understanding of the dynamics and nonlinear mechanisms of atmospheric motion, and they represent new ideas for developing numerical models and improving the forecast skill of weather and climate events.  相似文献   

15.
The initial errors constitute one of the main limiting factors in the ability to predict the El Nio–Southern Oscillation(ENSO) in ocean–atmosphere coupled models. The conditional nonlinear optimal perturbation(CNOP) approach was employed to study the largest initial error growth in the El Nio predictions of an intermediate coupled model(ICM). The optimal initial errors(as represented by CNOPs) in sea surface temperature anomalies(SSTAs) and sea level anomalies(SLAs) were obtained with seasonal variation. The CNOP-induced perturbations, which tend to evolve into the La Nia mode, were found to have the same dynamics as ENSO itself. This indicates that, if CNOP-type errors are present in the initial conditions used to make a prediction of El Nio, the El Nio event tends to be under-predicted. In particular, compared with other seasonal CNOPs, the CNOPs in winter can induce the largest error growth, which gives rise to an ENSO amplitude that is hardly ever predicted accurately. Additionally, it was found that the CNOP-induced perturbations exhibit a strong spring predictability barrier(SPB) phenomenon for ENSO prediction. These results offer a way to enhance ICM prediction skill and, particularly,weaken the SPB phenomenon by filtering the CNOP-type errors in the initial state. The characteristic distributions of the CNOPs derived from the ICM also provide useful information for targeted observations through data assimilation. Given the fact that the derived CNOPs are season-dependent, it is suggested that seasonally varying targeted observations should be implemented to accurately predict ENSO events.  相似文献   

16.
The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation (CNOP) method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on-off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the ad- joint method. In this study, we attempted to apply a genetic algorithm (GA) to the CNOP method, named GA-CNOP, to solve the predictability problems involving on-off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on-off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.  相似文献   

17.
This paper proposes a hybrid method, called CNOP–4 DVar, for the identification of sensitive areas in targeted observations, which takes the advantages of both the conditional nonlinear optimal perturbation(CNOP) and four-dimensional variational assimilation(4 DVar) methods. The proposed CNOP–4 DVar method is capable of capturing the most sensitive initial perturbation(IP), which causes the greatest perturbation growth at the time of verification; it can also identify sensitive areas by evaluating their assimilation effects for eliminating the most sensitive IP. To alleviate the dependence of the CNOP–4 DVar method on the adjoint model, which is inherited from the adjoint-based approach, we utilized two adjointfree methods, NLS-CNOP and NLS-4 DVar, to solve the CNOP and 4 DVar sub-problems, respectively. A comprehensive performance evaluation for the proposed CNOP–4 DVar method and its comparison with the CNOP and CNOP–ensemble transform Kalman filter(ETKF) methods based on 10 000 observing system simulation experiments on the shallow-water equation model are also provided. The experimental results show that the proposed CNOP–4 DVar method performs better than the CNOP–ETKF method and substantially better than the CNOP method.  相似文献   

18.
奇异向量(singular vectors,SVs)和条件非线性最优扰动(conditional nonlinear optimal perturbation,CNOP)已广泛应用于研究大气—海洋系统的不稳定性以及与其相关的可预报性、集合预报和目标观测问题研究。本文首先回顾了SVs和CNOP的发展历史,并简单描述了它们的基本原理;然后针对二维正压准地转模式,使用不同的范数组合,分析了第一线性奇异向量(first singular vector,FSV)和CNOP之间的异同。结果表明,当优化时间较短时,度量SVs和CNOP大小的范数不同也将导致FSV和CNOP相差很大,而当度量SVs和CNOP大小的范数相同时,FSV和CNOP之间的差别则主要是由非线性物理过程作用的结果。因此,针对不同的物理问题,应该选取合适的度量范数研究FSV和CNOP以及其所引起的大气或海洋动力学的异同,从而揭示非线性物理过程的影响机理。  相似文献   

19.
In this study, the retrospective predictions of ENSO (El Niño and Southern Oscillation) were performed for the period from 1881 to 2000 using a hybrid coupled model, which is an ocean general circulation model coupled to a linear statistical atmospheric model, and using a newly developed initialization scheme of SST assimilation by Ensemble Kalman Filter. With the retrospective predictions of the past 120 years, some important issues of ENSO predictability (measured by correlation and RMSE skills of NINO3 sea surface temperature anomaly index) were studied including decadal/interdecadal variations in ENSO predictability and the mechanisms responsible for these variations. Emphasis was placed on investigating the relationship between ENSO predictability and various characteristics of ENSO system such as the signal strength, the irregularity of periodicity, the noise and the nonlinearity. It is found that there are significant decadal/interdecadal variations in the prediction skills of ENSO during the past 120 years. The ENSO events were more predictable during the late nineteenth and the late twentieth centuries. The decadal/interdecadal variations of prediction skills are strongly related to the strength of sea-surface temperature anomaly (SSTA) signals, especially to the strength of SSTA signals at the frequencies of 2–4 year periods. The SSTA persistence, dominated by SSTA signals at frequencies over 4-year periods, also has a positive relationship to prediction skills. The high-frequency noise, on the other hand, has a strong inverse relationship to prediction skills, suggesting that it also probably plays an important role in ENSO predictability.  相似文献   

20.
Recent Advances in Predictability Studies in China (1999-2002)   总被引:10,自引:2,他引:8  
Since the last International Union of Geodesy and Geophysics (IUGG) General Assembly (1999), the predictability studies in China have made further progress during the period of 1999-2002. Firstly, three predictability sub-problems in numerical weather and climate prediction are classified, which are concerned with the maximum predictability time, the maximum prediction error, and the maximum allowable initial error, and then they are reduced into three nonlinear optimization problems. Secondly, the concepts of the nonlinear singular vector (NSV) and conditional nonlinear optimal perturbation (CNOP) are proposed,which have been utilized to study the predictability of numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be revealedby NSV and CNOP. Thirdly, attention has also been paid to the relations between the predictability and spatial-temporal scale, and between the model predictability and the machine precision, of which the investigations disclose the importance of the spatial-temporal scale and machine precision in the study of predictability. Also the cell-to-cell mapping is adopted to analyze globally the predictability of climate,which could provide a new subject to the research workers. Furthermore, the predictability of the summer rainfall in China is investigated by using the method of correlation coefficients. The results demonstrate that the predictability of summer rainfall is different in different areas of China. Analysis of variance, which is one of the statistical methods applicable to the study of predictability, is also used to study the potential predictability of monthly mean temperature in China, of which the conclusion is that the monthly mean temperature over China is potentially predictable at a statistical significance level of 0.10. In addition,in the analysis of the predictability of the T106 objective analysis/forecasting field, the variance and the correlation coefficient are calculated to explore the distribution characteristics of the mean-square errors.Finally, the predictability of short-term climate prediction is investigated by using statistical methods or numerical simulation methods. It is demonstrated that the predictability of short-term climate in China depends not only on the region of China being investigated, but also on the time scale and the atmospheric internal dynamical process.  相似文献   

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