What Kind of Initial Errors Cause the Severest Prediction Uncertainty of El Nino in Zebiak-Cane Model

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.     

Initial Error-induced Optimal Perturbations in ENSO Predictions,as Derived from an Intermediate Coupled Model

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.     

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 Nio 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 Nin?o growth-phase predictions, whereas the latter often yields the largest negative effects on decaying-phase predictions. The evolution of prediction errors caused by NFSVrelated 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 Nin?o 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 Nio 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 Nio 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 Nio 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.     

Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nio 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 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.     

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.     

Can the Uncertainties of Madden–Jullian Oscillation Cause a Significant “Spring Predictability Barrier” for ENSO Events?

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?no–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?no 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.     

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.     

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.     

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.     

Comparison of Constant and Time-variant Optimal Forcing Approaches in El Nio Simulations by Using the Zebiak–Cane Model

Model errors offset by constant and time-variant optimal forcing vector approaches(termed COF and OFV, respectively)are analyzed within the framework of El Nio simulations. Applying the COF and OFV approaches to the well-known Zebiak–Cane model, we re-simulate the 1997 and 2004 El Nio events, both of which were poorly degraded by a certain amount of model error when the initial anomalies were generated by coupling the observed wind forcing to an ocean component. It is found that the Zebiak–Cane model with the COF approach roughly reproduced the 1997 El Nio, but the 2004 El Nio simulated by this approach defied an ENSO classification, i.e., it was hardly distinguishable as CP-El Nio or EP-El Nio. In both El Nio simulations, substituting the COF with the OFV improved the fit between the simulations and observations because the OFV better manages the time-variant errors in the model. Furthermore, the OFV approach effectively corrected the modeled El Nio events even when the observational data(and hence the computational time) were reduced.Such a cost-effective offset of model errors suggests a role for the OFV approach in complicated CGCMs.     

Contrasting the Skills and Biases of Deterministic Predictions for the Two Types of El Nio

The tropical Pacific has begun to experience a new type of El Nio, which has occurred particularly frequently during the last decade, referred to as the central Pacific(CP) El Nio. Various coupled models with different degrees of complexity have been used to make real-time El Nio predictions, but high uncertainty still exists in their forecasts. It remains unknown as to how much of this uncertainty is specifically related to the new CP-type El Nio and how much is common to both this type and the conventional Eastern Pacific(EP)-type El Nio. In this study, the deterministic performance of an El Nio–Southern Oscillation(ENSO) ensemble prediction system is examined for the two types of El Nio. Ensemble hindcasts are run for the nine EP El Nio events and twelve CP El Nio events that have occurred since 1950. The results show that(1) the skill scores for the EP events are significantly better than those for the CP events, at all lead times;(2) the systematic forecast biases come mostly from the prediction of the CP events; and(3) the systematic error is characterized by an overly warm eastern Pacific during the spring season, indicating a stronger spring prediction barrier for the CP El Nio. Further improvements to coupled atmosphere–ocean models in terms of CP El Nio prediction should be recognized as a key and high-priority task for the climate prediction community.     

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 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.     

Impact of Subsurface Entrainment on ENSO Prediction: 1997-98 El Nino

Twenty-one-year hindcasts of sea surface temperature (SST) anomalies in the tropical Pacific were performed to validate the influence of ocean subsurface entrainment on SST prediction.A new hybrid coupled model was used that considered the entrainment of subsurface temperature anomalies into the sea surface.The results showed that predictions were improved significantly in the new coupled model.The predictive correlation skill increased by about 0.2 at a lead time of 9 months,and the root-mean-square (RMS) errors were decreased by nearly 0.2°C in general.A detailed analysis of the 1997-98 El Nio hindcast showed that the new model was able to predict the onset,peak (both time and amplitude),and decay of the 1997-98 strong El Nio event up to a lead time of one year,factors that are not represented well by many other forecast systems.This implies,in terms of prediction,that subsurface anomalies and their impact on the SST are one of the controlling factors in ENSO cycles.Improving the presentation of such effects in models would increase the forecast skill.     

ERROR GROWTH IN NUMERICAL PREDICTION AND ATMOSPHERIC PREDICTABILITY

The article is to report some results of numerical experiments on the error growth and the atmosphericpredictability Experiments with two-level global baroclinic primitive equation spectral model have mainresults as follows.The magnitude of initial errors directly affects the error growth,but its distributionform has little effect on the growth.The loss of predictability resulting from small-scale error is much greaterthan that from large-scale error.The small-scale error rapidly grows and is transferred to the large-scaleerror by interaction between different scale waves,which stimulates the growth of error for the whole systemOrographic forcing restrains planetary-scale error(wavenumbers 0—3)but enhances the small-scale error(wavenumbers 8 or greater).Hence,orographic effects on the error growth closely depend on the characteris-tic scale of initial errors,and there may be a critical wavenumber between 4 and 7.The error growth is great-er in Northern Hemisphere than in Southern Hemisphere if initial errors are the same.In the end we givesome discussions about model,initialization scheme,etc.,to improve model prediction.     

Reducing the Prediction Uncertainties of High-Impact Weather and Climate Events:An Overview of Studies at LASG

This paper summarizes recent progress at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences in studies on targeted observations, data assimilation, and ensemble prediction, which are three effective strategies to reduce the prediction uncertainties and improve the forecast skill of weather and climate events. Considering the limitations of traditional targeted observation approaches, LASG researchers have developed a conditional nonlinear optimal perturbation-based targeted observation strategy to optimize the design of the observing network. This strategy has been employed to identify sensitive areas for targeted observations of the El Ni?o–Southern Oscillation, Indian Ocean dipole, and tropical cyclones, and has been demonstrated to be effective in improving the forecast skill of these events. To assimilate the targeted observations into the initial state of a numerical model, a dimension-reducedprojection-based four-dimensional variational data assimilation(DRP-4DVar) approach has been proposed and is used operationally to supply accurate initial conditions in numerical forecasts. The performance of DRP-4DVar is good, and its computational cost is much lower than the standard 4DVar approach. Besides, ensemble prediction,which is a practical approach to generate probabilistic forecasts of the future state of a particular system, can be used to reduce the prediction uncertainties of single forecasts by taking the ensemble mean of forecast members. In this field, LASG researchers have proposed an ensemble forecast method that uses nonlinear local Lyapunov vectors(NLLVs) to yield ensemble initial perturbations. Its application in simple models has shown that NLLVs are more useful than bred vectors and singular vectors in improving the skill of the ensemble forecast. Therefore, NLLVs represent a candidate for possible development as an ensemble method in operational forecasts. Despite the considerable efforts made towards developing these methods to reduce prediction uncertainties, much challenging but highly important work remains in terms of improving the methods to further increase the skill in forecasting such weather and climate events.     

Assessing the Influence of the ENSO on Tropical Cyclone Prevailing Tracks in the Western North Pacific

Using a statistical model for simulating tropical cyclone (TC) formation and a trajectory model for simulating TC tracks, the influence of the El Nino-Southern Oscillation (ENSO) on the peak-season (July-September) TC prevailing tracks in the western North Pacific basin is assessed based on 14 selected El Nino and 14 selected La Nina years during the period 1950-2007. It is found that the combination of statistical formation model and a trajectory model can simulate well the primary features of TC prevai...     

An Examination of ENSO’s Effect on the Monthly and Seasonal Climate of Hong Kong from a Statistical Perspective

This study aims to examine the effect of El Nino and La Nina on the monthly and seasonal climate of Hong Kong against the ENSO-neutral situation from a statistical perspective. Monthly and seasonal temperature and rainfall of Hong Kong and monthly number of tropical cyclones (TCs) coming within 500 km of the city over the 59-yr (1950-2008) period are examined under three ENSO situations, namely El Nino, La Nina, and ENSO-neutral. It is found that, compared with the ENSO-neutral situation, El Nino tends...     

Idealized Experiments for Optimizing Model Parameters Using a 4D-Variational Method in an Intermediate Coupled Model of ENSO

Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4 D variational(4 D-Var) data assimilation system was developed for an intermediate coupled model(ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer(T_e), which is empirically and explicitly related to sea level(SL) variation.The strength of the thermocline effect on SST(referred to simply as "the thermocline effect") is represented by an introduced parameter, αT_e. A numerical procedure is developed to optimize this model parameter through the 4 D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only,and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling.The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4 D-Var method provides a modeling platform for ENSO studies. Further applications of the 4 D-Var data assimilation system implemented in the ICM are also discussed.     

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.     

A case study of the error growth and predictability of a Meiyu frontal heavy precipitation event

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...