Impact of observational MJO forcing on ENSO predictability in the Zebiak-Cane model: PartⅠ.Effect on the maximum prediction error

With the observational wind data and the Zebiak-Cane model, the impact of Madden-Iulian Oscillation （MJO） as external forcing on El Nino-Southern Oscillation （ENSO） predictability is studied. The observational data are analyzed with Continuous Wavelet Transform （CWT） and then used to extract MJO signals, which are added into the model to get a new model. After the Conditional Nonlinear Optimal Perturbation （CNOP） method has been used, the initial errors which can evolve into maximum prediction error, model errors and their join errors are gained and then the Nifio 3 indices and spatial structures of three kinds of errors are investigated. The results mainly show that the observational MJO has little impact on the maximum prediction error of ENSO events and the initial error affects much greater than model error caused by MJO forcing. These demonstrate that the initial error might be the main error source that produces uncertainty in ENSO prediction, which could provide a theoretical foundation for the adaptive data assimilation of the ENSO forecast and contribute to the ENSO target observation.

Role of Parameter Errors in the Spring Predictability Barrier for ENSO Events in the Zebiak–Cane Model

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.

The“Spring Predictability Barrier” Phenomenon of ENSO Predictions Generated with the FGOALS-g Model

Using the sea surface temperature （SST） predicted for the equatorial Pacific Ocean by the Flexible Global Ocean-Atmosphere-Land System Model-gamil （FGOALS-g）, an analysis of the prediction errors was performed for the seasonally dependent predictability of SST anomalies both for neutral years and for the growth/decay phase of El Nino/La Nina events. The study results indicated that for the SST predictions relating to the growth phase and the decay phase of El Nino events, the prediction errors have a seasonally dependent evolution. The largest increase in errors occurred in the spring season, which indicates that a prominent spring predictability barrier （SPB） occurs during an El Nino-Southern Oscillation （ENSO） warming episode. Furthermore, the SPB associated with the growth-phase prediction is more prominent than that associated with the decay-phase prediction. However, for the neutral years and for the growth and decay phases of La Nifia events, the SPB phenomenon was less prominent. These results indicate that the SPB phenomenon depends extensively on the ENSO events themselves. In particular, the SPB depends on the phases of the ENSO events. These results may provide useful knowledge for improving ENSO forecasting.

Application of the Conditional Nonlinear Optimal Perturbation Method to the Predictability Study of the Kuroshio Large Meander

A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander （KLM） state using the conditional nonlinear optimal parameter perturbation （CNOP-P） method. Because of their relatively large uncertainties, three model parameters were considered： the interracial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 （SPG2） algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation （CNOP-I） method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.

Applications of Conditional Nonlinear Optimal Perturbation in Predictability Study and Sensitivity Analysis of Weather and Climate

Considering the limitation of the linear theory of singular vector （SV）, the authors and their collabora- tors 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.

Effect of Stochastic MJO Forcing on ENSO Predictability

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.

A new approach to studying ENSO predictability:Conditional nonlinear optimal perturbation

A new approach, the conditional nonlinear optimal perturbation (CNOP) is introduced to study the predictability of El Ni駉-Southern Oscillation (ENSO) using a theoretical coupled ocean-atmosphere model. The differences between CNOP and linear singular vector (LSV) are demonstrated. The results suggest that the nonlinear model and CNOP are superior in determining error growth for studying predictability of the ENSO. In particular, the CNOP approach is used to explore the nature of the 憇pring predictability barrier?in ENSO prediction.

Application of the Analogue-Based Correction of Errors Method in ENSO Prediction

In this study, a method of analogue-based correction of errors(ACE) was introduced to improve El Ni?o-Southern Oscillation(ENSO) prediction produced by climate models. The ACE method is based on the hypothesis that the flow-dependent model prediction errors are to some degree similar under analogous historical climate states, and so the historical errors can be used to effectively reduce such flow-dependent errors. With this method, the unknown errors in current ENSO predictions can be empirically estimated by using the known prediction errors which are diagnosed by the same model based on historical analogue states. The authors first propose the basic idea for applying the ACE method to ENSO prediction and then establish an analogue-dynamical ENSO prediction system based on an operational climate prediction model. The authors present some experimental results which clearly show the possibility of correcting the flow-dependent errors in ENSO prediction, and thus the potential of applying the ACE method to operational ENSO prediction based on climate models.

Diagnosing SST Error Growth during ENSO Developing Phase in the BCC_CSM1.1(m) Prediction System

In this study, the predictability of the El Nino-South Oscillation(ENSO) in an operational prediction model from the perspective of initial errors is diagnosed using the seasonal hindcasts of the Beijing Climate Center System Model,BCC;SM1.1(m). Forecast skills during the different ENSO phases are analyzed and it is shown that the ENSO forecasts appear to be more challenging during the developing phase, compared to the decay phase. During ENSO development, the SST prediction errors are significantly negative and cover a large area in the central and eastern tropical Pacific, thus limiting the model skill in predicting the intensity of El Nino. The large-scale SST errors, at their early stage, are generated gradually in terms of negative anomalies in the subsurface ocean temperature over the central-western equatorial Pacific,featuring an error evolutionary process similar to that of El Nino decay and the transition to the La Nina growth phase.Meanwhile, for short lead-time ENSO predictions, the initial wind errors begin to play an increasing role, particularly in linking with the subsurface heat content errors in the central-western Pacific. By comparing the multiple samples of initial fields in the model, it is clearly found that poor SST predictions of the Nino-3.4 region are largely due to contributions of the initial errors in certain specific locations in the tropical Pacific. This demonstrates that those sensitive areas for initial fields in ENSO prediction are fairly consistent in both previous ideal experiments and our operational predictions,indicating the need for targeted observations to further improve operational forecasts of ENSO.

Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nio events? Results from a Theoretical Model

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 Nio 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 Nio 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 Nio events. These results indicate that the ability to forecast ENSO could be greatly increased by improving the initialization of the forecast model.

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

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.

THE APPLICATION OF CONDITIONAL NONLINEAR OPTIMAL PERTURBATION TO THE BINARY TYPHOONS INTERACTION —FENGSHEN AND FUNG-WONG

The interaction between the typhoons Fengshen and Fung-wong over the Western Pacific in 2002 is studied with the Conditional Nonlinear Optimal Perturbation(CNOP) method.The study discovered that the CNOP method reveals the process of one-way interaction between Fengshen and Fung-wong.Moreover,if the region of Fung-wong was selected for verification,the sensitivity area was mainly located in the region of Fengshen and presented a half-ring structure;if the region of Fengshen was selected for verification,most of the sensitivity areas were located in the region between the Fengshen and the subtropical high,far away from Fung-wong.This indicated that Fung-wong is mainly steered by Fengshen,but Fengshen is mainly affected by the subtropical high.The sensitivity experiment showed that the initial errors in the CNOP-identified sensitive areas have larger impacts on the verification-area prediction than those near the typhoon center and their developments take a large proportion in the whole domain.This suggests that the CNOP-identified sensitive areas do have large influence on the verification-area prediction.

The Role of Nonlinear Forcing Singular Vector Tendency Error in Causing the"Spring Predictability Barrier"for ENSO

With the Zebiak-Cane model, the present study investigates the role of model errors represented by the nonlinear forcing singular vector （NFSV） in the ＂spring predictability barrier＂ （SPB） phenomenon in ENSO prediction. The NFSV-related model errors are found to have the largest negative effect on the uncertainties of El Nino prediction and they can be classified into two types： the first is featured with a zonal dipolar pattern of SST anomalies （SSTA）, with the western poles centered in the equatorial central western Pacific exhibiting positive anomalies and the eastern poles in the equatorial eastern Pacific exhibiting negative anomalies; and the second is characterized by a pattern almost opposite to the first type. The first type of error tends to have the worst effects on El Nifio growth-phase predictions, whereas the latter often yields the largest negative effects on decaying-phase predictions. The evolution of prediction errors caused by NFSV- related errors exhibits prominent seasonality, with the fastest error growth in spring and/or summer; hence, these errors result in a significant SPB related to El Nifio events. The linear counterpart of NFSVs, the （linear） forcing singular vector （FSV）, induces a less significant SPB because it contains smaller prediction errors. Random errors cannot generate an SPB for El Nifio events. These results show that the occurrence of an SPB is related to the spatial patterns of tendency errors. The NFSV tendency errors cause the most significant SPB for El Nifio events. In addition, NFSVs often concentrate these large value errors in a few areas within the equatorial eastern and central-western Pacific, which likely represent those areas sensitive to El Nifio predictions associated with model errors. Meanwhile, these areas are also exactly consistent with the sensitive areas related to initial errors determined by previous studies. This implies that additional observations in the sensitive areas would not only improve the accuracy of the initial field but also promote the reduction of model errors to greatly improve ENSO forecasts.

Analysis Study on Perturbation Energy and Predictability of Heavy Precipitation in South China

The AREMv2.3 mesoscale numerical model is used to explore storm processes in South China during the pre-rainy season in 2006 by imposing perturbations on the initial fields of physical variables （temperature, humidity, and wind fields）. Sensitivity experiments are performed to examine the impacts of initial uncertainties on precipitation, on the error growth, and on the predictability of mesoscale precipitation in South China. The primary conclusion is that inherent initial condition uncertainties can significantly limit the predictability of storm. The 24-h accumulated precipitation is most sensitive to temperature perturbations. Larger-amplitude initial uncertainties generally lead to larger perturbation energies than those with smaller amplitude, but these kinds of differences decrease with time monotonically so the mechanism for the growth of perturbation energy is nonlinear. The power spectra of precipitation differences indicate that predictability increases with accumulated time. This also indicates the difficulties faced for short-term, small-scale precipitation forecasting.

Conditional nonlinear optimal perturbation: Applications to stability, sensitivity, and predictability

Conditional nonlinear optimal perturbation (CNOP) is a nonlinear generalization of linear singular vector (LSV) and features the largest nonlinear evolution at prediction time for the initial perturbations in a given constraint. It was proposed initially for predicting the limitation of predictability of weather or climate. Then CNOP has been applied to the studies of the problems related to predictability for weather and climate. In this paper, we focus on reviewing the recent advances of CNOP's applications, which involves the ones of CNOP in problems of ENSO amplitude asymmetry, block onset, and the sensitivity analysis of ecosystem and ocean's circulations, etc. Especially, CNOP has been primarily used to construct the initial perturbation fields of ensemble forecasting, and to determine the sensitive area of target observation for precipitations. These works extend CNOP's applications to investigating the nonlinear dynamical behaviors of atmospheric or oceanic systems, even a coupled system, and studying the problem of the transition between the equilibrium states. These contributions not only attack the particular physical problems, but also show the superiority of CNOP to LSV in revealing the effect of nonlinear physical processes. Consequently, CNOP represents the optimal precursors for a weather or climate event; in predictability studies, CNOP stands for the initial error that has the largest negative effect on prediction; and in sensitivity analysis, CNOP is the most unstable (sensitive) mode. In multi-equilibrium state regime, CNOP is the initial perturbation that induces the transition between equilibriums most probably. Furthermore, CNOP has been used to construct ensemble perturbation fields in ensemble forecast studies and to identify sensitive area of target observation. CNOP theory has become more and more substantial. It is expected that CNOP also serves to improve the predictability of the realistic predictions for weather and climate events plays an increasingly important role in exploring the nonlinear dynamics of atmospheric, oceanic and coupled atmosphere-ocean system.

Conditional nonlinear optimal perturbation and its applications to the studies of weather and climate predictability

Conditional nonlinear optimal perturbation (CNOP) is the initial perturbation that has the largest nonlinear evolution at prediction time for initial perturba-tions satisfying certain physical constraint condition. It does not only represent the optimal precursor of certain weather or climate event, but also stand for the initial error which has largest effect on the prediction uncertainties at the prediction time. In sensitivity and stability analyses of fluid motion, CNOP also describes the most unstable (or most sensitive) mode. CNOP has been used to estimate the upper bound of the prediction error. These physical characteristics of CNOP are examined by applying respectively them to ENSO pre-dictability studies and ocean’s thermohaline circulation (THC) sensitivity analysis. In ENSO predictability studies, CNOP, rather than linear singular vector (LSV), represents the initial patterns that evolve into ENSO events most poten-tially, i.e. the optimal precursors for ENSO events. When initial perturbation is considered to be the initial error of ENSO, CNOP plays the role of the initial error that has larg-est effect on the prediction of ENSO. CNOP also derives the upper bound of prediction error of ENSO events. In the THC sensitivity and stability studies, by calculating the CNOP (most unstable perturbation) of THC, it is found that there is an asymmetric nonlinear response of ocean’s THC to the finite amplitude perturbations. Finally, attention is paid to the feasibility of CNOP in more complicated model. It is shown that in a model with higher dimensions, CNOP can be computed successfully. The corresponding optimization algo-rithm is also shown to be efficient.

一个ENSO动力相似误差订正模式及其后报初检验

为有效利用历史资料中的相似信息,减小模式误差对ENSO这类跨季节年际尺度预测问题的影响提高动力模式的预测水平。作者利用一种基于统计相似的模式误差订正方法,以国家气候中心简化海气耦合模式为平台建立了相应的动力相似误差订正(DAEC)模式,并着重探讨了系统相似程度(全相似或部分相似)、误差重估周期以及相似样本个数等因素对预报效果的影响。结果表明,利用该方法可以有效地改善原有模式的预报性能,其中“全相似”比“部分相似”更能反映海气耦合系统的相似程度,从而对模式误差做出更为准确的估计,使预报误差明显减小。海洋和大气的误差重估周期对结果也有较大影响,在不同相似程度下分别存在着某种最优配置使得预报效果达到最佳。另外,在对相似样本存在状况及影响的研究中则发现在当前资料长度内整体上只存在着有限个相似样本,在此范围内随着样本取样数目的增加DAEC模式的预报性能逐渐提高。

四个耦合模式ENSO后报试验的“春季预报障碍”

用CliPAS计划中3个气候模式和中国科学院大气物理研究所耦合模式FGOALS-g短期气候异常回报试验结果,将动力和统计方法相结合,考察了1982—2003年厄尔尼诺/拉尼娜事件发展期和衰减期海表温度春季可预报性障碍现象。结果表明,所考察的耦合模式对ENSO事件预报的误差发展存在明显的季节依赖性,最大误差增长通常发生在春季,发生显著的可预报性障碍现象。进一步分析发现厄尔尼诺事件和拉尼娜事件在发展期的季节预报障碍现象比衰减期明显,以厄尔尼诺事件发展期春季可预报性障碍现象最为显著,拉尼娜事件衰减期季节预报障碍现象不显著。研究还发现,预报误差的增长在ENSO事件冷暖位相具有显著的非对称性,发展期暖位相预报误差强于冷位相,而衰减期冷位相的预报误差比暖位相大。通过回归分析,诊断了海-气相互作用的强度,发现耦合系统在春季最不稳定,使预报误差最易在春季发展,从而导致可预报性障碍。

Zebiak-Cane模式中条件非线性最优扰动对ENSO春季预报障碍的影响

使用Zebiak-Cane模式和条件非线性最优扰动(CNOP)方法,研究初始误差和参数误差共同作用对ENSO春季预报障碍现象的影响。选取模式中的8个El Ni?o事件,包括4次强事件和4次弱事件,每个El Ni?o事件又分别从8个不同的起始时间做1 a的预报,这样一共64个预报实验。对每个实验分别计算CNOP误差(初始误差和参数误差同时存在时的最优误差),通过分析误差增长,发现CNOP误差引起的1 a后的预报误差随着初始预报时间的不同有较大差异,并且不同强度的El Ni?o事件也会影响CNOP误差的发展,增长位相中强事件的预报误差要比弱事件的预报误差大一些;而衰减位相中恰恰相反,弱事件的预报误差要比强事件的预报误差要大一些;同时也发现高频El Ni?o事件对误差增长率的影响较大。本结论有助于提高Zebiak-Cane模式预报ENSO的技巧。

ENSO ensemble prediction:Initial error perturbations vs. model error perturbations

Based on our developed ENSO (El Nio-Southern Oscillation) ensemble prediction system (EPS), the impacts of stochastic initial-error and model-error perturbations on ENSO ensemble predictions are examined and discussed by performing four sets of 14-a retrospective forecast experiments in both a deterministic and probabilistic sense. These forecast schemes are differentiated by whether they considered the initial or model stochastic perturbations. The comparison results suggest that the stochastic model-error perturbations, which are added into the modeled physical fields to mainly represent the uncertainties of the physical model, have significant, positive impacts on improving the ensemble prediction skills during the entire 12-month forecast process. However, the stochastic initial-error perturbations have relatively small impacts on the ensemble prediction system, and its impacts are mainly focusing on the first 3-month predictions.