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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.
The initial errors constitute one of the main limiting factors in the ability to predict the El Nio–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 Nio 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 Nia 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 Nio, the El Nio 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
3.
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
4.
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
5.
Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nio events？ Results from a Theoretical Model 总被引：3，自引：1，他引：2
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
6.
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
7.
ENSO机理及其预测研究 总被引：19，自引：0，他引：19
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
8.
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
9.
Applications of conditional nonlinear optimal perturbation in predictability study and sensitivity analysis of weather and climate 总被引：1，自引：0，他引：1
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
10.
The limits of predictability of El Niño and the Southern Oscillation (ENSO) in coupled models are investigated based on retrospective forecasts of sea surface temperature (SST) made with the National Centers for Environmental Prediction (NCEP) coupled forecast system (CFS). The influence of initial uncertainties and model errors associated with coupled ENSO dynamics on forecast error growth are discussed. The total forecast error has maximum values in the equatorial Pacific and its growth is a strong function of season irrespective of lead time. The largest growth of systematic error of SST occurs mainly over the equatorial central and eastern Pacific and near the southeastern coast of the Americas associated with ENSO events. After subtracting the systematic error, the root-mean-square error of the retrospective forecast SST anomaly also shows a clear seasonal dependency associated with what is called spring barrier. The predictability with respect to ENSO phase shows that the phase locking of ENSO to the mean annual cycle has an influence on the seasonal dependence of skill, since the growth phase of ENSO events is more predictable than the decay phase. The overall characteristics of predictability in the coupled system are assessed by comparing the forecast error growth and the error growth between two model forecasts whose initial conditions are 1 month apart. For the ensemble mean, there is fast growth of error associated with initial uncertainties, becoming saturated within 2 months. The subsequent error growth follows the slow coupled mode related the model’s incorrect ENSO dynamics. As a result, the Lorenz curve of the ensemble mean NINO3 index does not grow, because the systematic error is identical to the same target month. In contrast, the errors of individual members grow as fast as forecast error due to the large instability of the coupled system. Because the model errors are so systematic, their influence on the forecast skill is investigated by analyzing the erroneous features in a long simulation. For the ENSO forecasts in CFS, a constant phase shift with respect to lead month is clear, using monthly forecast composite data. This feature is related to the typical ENSO behavior produced by the model that, unlike the observations, has a long life cycle with a JJA peak. Therefore, the systematic errors in the long run are reflected in the forecast skill as a major factor limiting predictability after the impact of initial uncertainties fades out. 相似文献
11.
With the Zebiak–Cane model, the relationship between the optimal precursors (OPR) for triggering the El Niño/Southern Oscillation (ENSO) events and the optimally growing initial errors (OGE) to the uncertainty in El Niño predictions is investigated using an approach based on the conditional nonlinear optimal perturbation. The computed OPR for El Niño events possesses sea surface temperature anomalies (SSTA) dipole over the equatorial central and eastern Pacific, plus positive thermocline depth anomalies in the entire equatorial Pacific. Based on the El Niño events triggered by the obtained OPRs, the OGE which cause the largest prediction errors are computed. It is found that the OPR and OGE share great similarities in terms of localization and spatial structure of the SSTA dipole pattern over the central and eastern Pacific and the relatively uniform thermocline depth anomalies in the equatorial Pacific. The resemblances are possibly caused by the same mechanism of the Bjerknes positive feedback. It implies that if additional observation instruments are deployed to the targeted observations with limited coverage, they should preferentially be deployed in the equatorial central and eastern Pacific, which has been determined as the sensitive area for ENSO prediction, to better detect the early signals for ENSO events and reduce the initial errors so as to improve the forecast skill. 相似文献
12.
A four-dimensional variational (4D-Var) data assimilation method is implemented in an improved intermediate coupled model (ICM) of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The “observation” of the SST anomaly, which is sampled from a “truth” model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction. 相似文献
13.
Ensemble hindcasts of ENSO events over the past 120 years using a large number of ensembles 总被引：1，自引：0，他引：1
Based on an intermediate coupled model (ICM), a probabilistic ensemble prediction system (EPS) has been developed. The ensemble Kalman filter (EnKF) data assimilation approach is used for generating the initial ensemble conditions, and a linear, first-order Markov-Chain SST anomaly error model is embedded into the EPS to provide model-error perturbations. In this study, we perform ENSO retrospective forecasts over the 120 year period 1886–2005 using the EPS with 100 ensemble members and with initial conditi... 相似文献
14.
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 model. These initial errors can be classified into two types. Type-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 opposite. Both kinds of IO-related initial errors induce positive prediction errors of sea temperature in the Pacific Ocean, leading to under-prediction of La Ni?a events. Type-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 Ocean. However, 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 Throughflow. Based on the location of largest SPB-related initial errors, the sensitive area in the tropical Indian Ocean for La Ni?a predictions is identified. Furthermore, sensitivity experiments show that applying targeted observations in this sensitive area is very useful in decreasing prediction errors of La Ni?a. Therefore, adopting a targeted observation strategy in the tropical Indian Ocean is a promising approach toward increasing ENSO prediction skill. 相似文献
15.
The nonlinear forcing singular vector (NFSV) approach is used to identify the most disturbing tendency error of the Zebiak–Cane model associated with El Niño predictions, which is most potential for yielding aggressively large prediction errors of El Niño events. The results show that only one NFSV exists for each of the predictions for the predetermined model El Niño events. These NFSVs cause the largest prediction error for the corresponding El Niño event in perfect initial condition scenario. It is found that the NFSVs often present large-scale zonal dipolar structures and are insensitive to the intensities of El Niño events, but are dependent on the prediction periods. In particular, the NFSVs associated with the predictions crossing through the growth phase of El Niño tend to exhibit a zonal dipolar pattern with positive anomalies in the equatorial central-western Pacific and negative anomalies in the equatorial eastern Pacific (denoted as “NFSV1”). Meanwhile, those associated with the predictions through the decaying phase of El Niño are inclined to present another zonal dipolar pattern (denoted as “NFSV2”), which is almost opposite to the NFSV1. Similarly, the linear forcing singular vectors (FSVs), which are computed based on the tangent linear model, can also be classified into two types “FSV1” and “FSV2”. We find that both FSV1 and NFSV1 often cause negative prediction errors for Niño-3 SSTA of the El Niño events, while the FSV2 and NFSV2 usually yield positive prediction errors. However, due to the effect of nonlinearities, the NFSVs usually have the western pole of the zonal dipolar pattern much farther west, and covering much broader region. The nonlinearities have a suppression effect on the growth of the prediction errors caused by the FSVs and the particular structure of the NFSVs tends to reduce such suppression effect of nonlinearities, finally making the NFSV-type tendency error yield much large prediction error for Niño-3 SSTA of El Niño events. The NFSVs, compared to the FSVs, are more applicable in describing the most disturbing tendency error of the Zebiak–Cane model since they consider the effect of nonlinearities. The NFSV-type tendency errors may provide information concerning the sensitive areas where the model errors are much more likely to yield large prediction errors for El Niño events. If the simulation skills of the states in the sensitive areas can be improved, the ENSO forecast skill may in turn be greatly increased. 相似文献
16.
Based on the high-resolution Regional Ocean Modeling System(ROMS) and the conditional nonlinear optimal perturbation(CNOP) method, this study explored the effects of optimal initial errors on the prediction of the Kuroshio large meander(LM) path, and the growth mechanism of optimal initial errors was revealed. For each LM event, two types of initial error(denoted as CNOP1 and CNOP2) were obtained. Their large amplitudes were found located mainly in the upper 2500 m in the upstream region of the LM, i.e., southeast of Kyushu. Furthermore, we analyzed the patterns and nonlinear evolution of the two types of CNOP. We found CNOP1 tends to strengthen the LM path through southwestward extension. Conversely,CNOP2 has almost the opposite pattern to CNOP1, and it tends to weaken the LM path through northeastward contraction.The growth mechanism of optimal initial errors was clarified through eddy-energetics analysis. The results indicated that energy from the background field is transferred to the error field because of barotropic and baroclinic instabilities. Thus, it is inferred that both barotropic and baroclinic processes play important roles in the growth of CNOP-type optimal initial errors. 相似文献
17.
Can the uncertainties of Madden-Jullian Oscillation cause a significant “Spring Predictability Barrier” for ENSO events? 
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下载免费PDF全文 With the Zebiak-Cane model and a parameterized stochastic representation of intraseasonal forcing, the impact of the uncertainties of Madden-Jullian Oscillation (MJO) on the ??Spring Predictability Barrier (SPB)?? for El Ni?o-Southern Oscillation (ENSO) prediction is studied. The parameterized form of MJO forcing is added physically to the Zebiak-Cane model to obtain the so-called Zebiak-Cane-MJO model and then the effects of initial error, stochastic model error, and their joint error mode on the SPB associated with El Ni?o prediction are estimated. The results show that the model errors caused by stochastic MJO forcing could hardly lead to a significant SPB while initial errors can do; furthermore, the joint error mode of initial error and model error associated with the stochastic MJO forcing can also lead to a significant SPB. These demonstrate that the initial error is probably the main error source of the SPB, which may provide a theoretical foundation of data assimilation for ENSO forecasts. 相似文献
18.
A hybrid coupled model (HCM) for the tropical Pacific ocean-atmosphere system is employed for ENSO prediction. The HCM consists
of the Geophysical Fluid Dynamics Laboratory ocean general circulation model and an empirical atmospheric model. In hindcast
experiments, a correlation skill competitive to other prediction models is obtained, so we use this system to examine the
effects of several initialization schemes on ENSO prediction. Initialization with wind stress data and initialization with
wind stress reconstructed from SST using the atmospheric model give comparable skill levels. In re-estimating the atmospheric
model in order to prevent hindcast-period wind information from entering through empirical atmospheric model, we note some
sensitivity to the estimation data set, but this is considered to have limited impact for ENSO prediction purposes. Examination
of subsurface heat content anomalies in these cases and a case forced only by the difference between observed and reconstructed
winds suggests that at the current level of prediction skill, the crucial wind components for initialization are those associated
with the slow ENSO mode, rather than with atmospheric internal variability. A “piggyback” suboptimal data assimilation is
tested in which the Climate Prediction Center data assimilation product from a related ocean model is used to correct the
ocean initial thermal field. This yields improved skill, suggesting that not all ENSO prediction systems need to invest in
costly data assimilation efforts, provided the prediction and assimilation models are sufficiently close.
Received: 17 April 1998 / Accepted: 22 July 1999 相似文献
19.
Impact of improved assimilation of temperature and salinity for coupled model seasonal forecasts 总被引：1，自引：0，他引：1
We assess the impact of improved ocean initial conditions for predicting El Niño-Southern Oscillation (ENSO) and Indian Ocean dipole (IOD) using the Bureau of Meteorology’s Predictive Ocean Atmosphere Model for Australia (POAMA) coupled seasonal prediction model for the period 1982–2006. The new ocean initial conditions are provided by an ensemble-based analysis system that assimilates subsurface temperatures and salinity and which is a clear improvement over the previous optimal interpolation system which used static error covariances and was univariate (temperature only). Hindcasts using the new ocean initial conditions have better skill at predicting sea surface temperature (SST) variations associated with ENSO than do the hindcasts initialized with the old ocean analyses. The improvement derives from better prediction of subsurface temperatures and the largest improvements come during ENSO–IOD neutral years. We show that improved prediction of the Niño3.4 SST index derives from improved initial depiction of the thermocline and halocline in the equatorial Pacific but as lead time increases the improved depiction of the initial salinity field in the western Pacific become more important. Improved ocean initial conditions do not translate into improved skill for predicting the IOD but we do see an improvement in the prediction of subsurface temperatures in the Indian Ocean (IO). This result reflects that the coupling between subsurface and surface temperature variations is weaker in the IO than in the Pacific, but coupled model errors may also be limiting predictive skill in the IO. 相似文献
20.
The optimally growing initial errors (OGEs) of El Niño events are found in the Community Earth System Model (CESM) by the conditional nonlinear optimal perturbation (CNOP) method. Based on the characteristics of low-dimensional attractors for ENSO (El Niño Southern Oscillation) systems, we apply singular vector decomposition (SVD) to reduce the dimensions of optimization problems and calculate the CNOP in a truncated phase space by the differential evolution (DE) algorithm. In the CESM, we obtain three types of OGEs of El Niño events with different intensities and diversities and call them type-1, type-2 and type-3 initial errors. Among them, the type-1 initial error is characterized by negative SSTA errors in the equatorial Pacific accompanied by a negative west–east slope of subsurface temperature from the subsurface to the surface in the equatorial central-eastern Pacific. The type-2 initial error is similar to the type-1 initial error but with the opposite sign. The type-3 initial error behaves as a basin-wide dipolar pattern of tropical sea temperature errors from the sea surface to the subsurface, with positive errors in the upper layers of the equatorial eastern Pacific and negative errors in the lower layers of the equatorial western Pacific. For the type-1 (type-2) initial error, the negative (positive) temperature errors in the eastern equatorial Pacific develop locally into a mature La Niña (El Niño)-like mode. For the type-3 initial error, the negative errors in the lower layers of the western equatorial Pacific propagate eastward with Kelvin waves and are intensified in the eastern equatorial Pacific. Although the type-1 and type-3 initial errors have different spatial patterns and dynamic growing mechanisms, both cause El Niño events to be underpredicted as neutral states or La Niña events. However, the type-2 initial error makes a moderate El Niño event to be predicted as an extremely strong event.
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