An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction

Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.

Study on Multi-Scale Blending Initial Condition Perturbations for a Regional Ensemble Prediction System

An initial conditions （ICs） perturbation method was developed with the aim to improve an operational regional ensemble prediction system （REPS）. Three issues were identified and investigated： （1） the impacts of perturbation scale on the ensemble spread and forecast skill of the REPS; （2） the scale characteristic of the IC perturbations of the REPS; and （3） whether the REPS＇s skill could be improved by adding large-scale information to the IC perturbations. Numerical experiments were conducted to reveal the impact of perturbation scale on the ensemble spread and forecast skill. The scales of IC perturbations from the REPS and an operational global ensemble prediction system （GEPS） were analyzed. A ＂multi-scale blending＂ （MSB） IC perturbation scheme was developed, and the main findings can be summarized as follows： The growth rates of the ensemble spread of the REPS are sensitive to the scale of the IC perturbations; the ensemble forecast skills can benefit from large-scale perturbations; the global ensemble IC perturbations exhibit more power at larger scales, while the regional ensemble IC perturbations contain more power at smaller scales; the MSB method can generate IC perturbations by combining the small-scale component from the REPS and the large-scale component from the GEPS; the energy norm growth of the MSB-generated perturbations can be appropriate at all forecast lead times; and the MSB-based REPS shows higher skill than the original system, as determined by ensemble forecast verification.

Statistical Downscaling for Multi-Model Ensemble Prediction of Summer Monsoon Rainfall in the Asia-Pacific Region Using Geopotential Height Field

The 21-yr ensemble predictions of model precipitation and circulation in the East Asian and western North Pacific （Asia-Pacific） summer monsoon region （0°-50°N, 100° 150°E） were evaluated in nine different AGCM, used in the Asia-Pacific Economic Cooperation Climate Center （APCC） multi-model ensemble seasonal prediction system. The analysis indicates that the precipitation anomaly patterns of model ensemble predictions are substantially different from the observed counterparts in this region, but the summer monsoon circulations are reasonably predicted. For example, all models can well produce the interannual variability of the western North Pacific monsoon index （WNPMI） defined by 850 hPa winds, but they failed to predict the relationship between WNPMI and precipitation anomalies. The interannual variability of the 500 hPa geopotential height （GPH） can be well predicted by the models in contrast to precipitation anomalies. On the basis of such model performances and the relationship between the interannual variations of 500 hPa GPH and precipitation anomalies, we developed a statistical scheme used to downscale the summer monsoon precipitation anomaly on the basis of EOF and singular value decomposition （SVD）. In this scheme, the three leading EOF modes of 500 hPa GPH anomaly fields predicted by the models are firstly corrected by the linear regression between the principal components in each model and observation, respectively. Then, the corrected model GPH is chosen as the predictor to downscale the precipitation anomaly field, which is assembled by the forecasted expansion coefficients of model 500 hPa GPH and the three leading SVD modes of observed precipitation anomaly corresponding to the prediction of model 500 hPa GPH during a 19-year training period. The cross-validated forecasts suggest that this downscaling scheme may have a potential to improve the forecast skill of the precipitation anomaly in the South China Sea, western North Pacific and the East Asia Pacific regions, where the anomaly correlation coefficient （ACC） has been improved by 0.14, corresponding to the reduced RMSE of 10.4% in the conventional multi-model ensemble （MME） forecast.

A Comparison Study of the Methods of Conditional Nonlinear Optimal Perturbations and Singular Vectors in Ensemble Prediction

The authors apply the technique of conditional nonlinear optimal perturbations （CNOPs） as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-geostrophic （QG） model in a perfect-model scenario. Ensemble forecasts for the medium range （14 days） are made from the initial states perturbed by CNOPs and singular vectors （SVs）. 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear superior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.

MJO ensemble prediction in BCC-CSM1.1(m)using different initialization schemes

The Madden–Julian Oscillation（MJO）is a dominant mode of tropical intraseasonal variability（ISV）and has prominent impacts on the climate of the tropics and extratropics.Predicting the MJO using fully coupled climate system models is an interesting and important topic.This paper reports upon a recent progress in MJO ensemble prediction using the climate system model of the Beijing Climate Center,BCC-CSM1.1（m）;specifically,the development of three different initialization schemes in the BCC ISV/MJO prediction system,IMPRESS.Three sets of 10-yr hindcasts were separately conducted with the three initialization schemes.The results showed that the IMPRESS is able to usefully predict the MJO,but is sensitive to the initialization scheme used and becomes better with the initialization of moisture.In addition,a new ensemble approach was developed by averaging the predictions generated from the different initialization schemes,helping to address the uncertainty in the initial values of the MJO.The ensemble-mean MJO prediction showed significant improvement,with a valid prediction length of about 20 days in terms of the different criteria,i.e.,a correlation score beyond 0.5,a RMSE lower than 1.414,or a mean square skill score beyond 0.This study indicates that utilizing the different initialization schemes of this climate model may be an efficient approach when forming ensemble predictions of the MJO.

ENSEMBLE PREDICTION EXPERIMENTS OF TRACKS OF TROPICAL CYCLONES BY USING MULTIPLE CUMULUS PARAMETERIZATION SCHEMES

Ensemble prediction experiments of the tracks of eight tropical cyclones occurring between 2004-2006 over the western Pacific have been performed by using MM5 with five cumulus parameterization schemes. The results show that the predictions of the tracks of the tropical cyclones are sensitive to the selection of cumulus parameterization schemes. Each scheme has its own advantage and disadvantage, and the predications without cumulus parameterization schemes are not the worst, sometimes even better than the others. And all of the three ensemble methods improve the predictions of the tracks significantly, among which the ensemble method without parameterization schemes, the Grell, Betts-Miller and Kain-Fritsch schemes are the best.

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model,we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics.Four initial perturbation approaches are used in the ensemble forecasting experiments:the random perturbation(RP),the bred vector(BV),the ensemble transform Kalman filter(ETKF),and the nonlinear local Lyapunov vector(NLLV)methods.Results show that,regardless of the method used,the ensemble averages behave indistinguishably from the control forecasts during the first few time steps.Due to different error growth in different time-scale systems,the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem.Due to the coupled dynamic processes,the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables.Regarding the initial perturbation approaches,the NLLVs show higher forecasting skill than the BVs or RPs overall.The NLLVs and ETKFs had nearly equivalent prediction skill,but NLLVs performed best by a narrow margin.In particular,when adding perturbations to slow variables,the independent perturbations(NLLVs and ETKFs)perform much better in ensemble prediction.These results are simply implied in a real coupled air–sea model.For the prediction of oceanic variables,using independent perturbations(NLLVs)and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.

A Nonlinear Representation of Model Uncertainty in a Convective-Scale Ensemble Prediction System

How to accurately address model uncertainties with consideration of the rapid nonlinear error growth characteristics in a convection-allowing system is a crucial issue for performing convection-scale ensemble forecasts.In this study,a new nonlinear model perturbation technique for convective-scale ensemble forecasts is developed to consider a nonlinear representation of model errors in the Global and Regional Assimilation and Prediction Enhanced System(GRAPES)Convection-Allowing Ensemble Prediction System(CAEPS).The nonlinear forcing singular vector(NFSV)approach,that is,conditional nonlinear optimal perturbation-forcing(CNOP-F),is applied in this study,to construct a nonlinear model perturbation method for GRAPES-CAEPS.Three experiments are performed:One of them is the CTL experiment,without adding any model perturbation;the other two are NFSV-perturbed experiments,which are perturbed by NFSV with two different groups of constraint radii to test the sensitivity of the perturbation magnitude constraint.Verification results show that the NFSV-perturbed experiments achieve an overall improvement and produce more skillful forecasts compared to the CTL experiment,which indicates that the nonlinear NFSV-perturbed method can be used as an effective model perturbation method for convection-scale ensemble forecasts.Additionally,the NFSV-L experiment with large perturbation constraints generally performs better than the NFSV-S experiment with small perturbation constraints in the verification for upper-air and surface weather variables.But for precipitation verification,the NFSV-S experiment performs better in forecasts for light precipitation,and the NFSV-L experiment performs better in forecasts for heavier precipitation,indicating that for different precipitation events,the perturbation magnitude constraint must be carefully selected.All the findings above lay a foundation for the design of nonlinear model perturbation methods for future CAEPSs.

Effect of Doubling the Ensemble Size on the Performance of Ensemble Prediction in the Warm Season Using MOGREPS Implemented at the KMA

Using the Met Office Global and Regional Ensemble Prediction System （MOGREPS） implemented at the Korea Meteorological Administration （KMA）, the effect of doubling the ensemble size on the performance of ensemble prediction in the warm season was evaluated. Because a finite ensemble size causes sampling error in the full forecast probability distribution function （PDF）, ensemble size is closely related to the efficiency of the ensemble prediction system. Prediction capability according to doubling the ensemble size was evaluated by increasing the number of ensembles from 24 to 48 in MOGREPS implemented at the KMA. The initial analysis perturbations generated by the Ensemble Transform Kalman Filter （ETKF） were integrated for 10 days from 22 May to 23 June 2009. Several statistical verification scores were used to measure the accuracy, reliability, and resolution of ensemble probabilistic forecasts for 24 and 48 ensemble member forecasts. Even though the results were not significant, the accuracy of ensemble prediction improved slightly as ensemble size increased, especially for longer forecast times in the Northern Hemisphere. While increasing the number of ensemble members resulted in a slight improvement in resolution as forecast time increased, inconsistent results were obtained for the scores assessing the reliability of ensemble prediction. The overall performance of ensemble prediction in terms of accuracy, resolution, and reliability increased slightly with ensemble size, especially for longer forecast times.

Study of perturbing method in regional BGM ensemble prediction system

Based on an Ensemble Prediction System with the BGM method on the regional numerical prediction model AREM, Static State Perturbation （SSP, including Initial Random Perturbation and Perturbation Restriction） and Dynamic State Perturbation （DSP） are designed. The impacts of both perturbations on precipitation prediction are studied by analyzing a slrong precipitation process oc- curring during July 20-21, 2008. The results show that both SSP and DSP play a positive role in prediction of mesoscale precipita- tion, such as lowering the （missing） rate of precipitation prediction. SSP is mainly helpful for the 24-hour prediction, while DSP can improve both 24-hour and 48-hour prediction. DSP is better than the two SSPs in the hit rate of regional precipitation prediction. However, the former also has a little higher false alarm rate than the latter. DSP enlarges in some extent the dispersion of EPS, which is good for EPS.

Verification of Seasonal Prediction by the Upgraded China Multi-Model Ensemble Prediction System (CMMEv2.0)

Based on a combination of six Chinese climate models and three international operational models,the China multimodel ensemble(CMME)prediction system has been upgraded into its version 2(CMMEv2.0)at the National Climate Centre(NCC)of the China Meteorological Administration(CMA)by including new model members and expanding prediction products.A comprehensive assessment of the performance of the upgraded CMME during its hindcast(1993–2016)and real-time prediction(2021–present)periods is conducted in this study.The results demonstrate that CMMEv2.0 outperforms all the individual models by capturing more realistic equatorial sea surface temperature(SST)variability.It exhibits better prediction skills for precipitation and 2-m temperature anomalies,and the improvements in prediction skill of CMMEv2.0 are significant over East Asia.The superiority of CMMEv2.0 can be attributed to its better projection of El Niño–Southern Oscillation(ENSO;with the temporal correlation coefficient score for Niño3.4 index reaching 0.87 at 6-month lead)and ENSO-related teleconnections.As for the real-time prediction in recent three years,CMMEv2.0 has also yielded relatively stable skills;it successfully predicted the primary rainbelt over northern China in summers of 2021–2023 and the warm conditions in winters of 2022/2023.Beyond that,ensemble sampling experiments indicate that the CMMEv2.0 skills become saturated after the ensemble model number increased to 5–6,indicating that selection of only an optimal subgroup of ensemble models could benefit the prediction performance,especially over the extratropics,yet the underlying reasons await future investigation.

Study on ETKF-Based Initial Perturbation Scheme for GRAPES Global Ensemble Prediction

Initial perturbation scheme is one of the important problems for ensemble prediction. In this paper, ensemble initial perturbation scheme for Global/Regional Assimilation and PrEdiction System （GRAPES） global ensemble prediction is developed in terms of the ensemble transform Kalman filter （ETKF） method. A new GRAPES global ensemble prediction system （GEPS） is also constructed. The spherical simplex 14-member ensemble prediction experiments, using the simulated observation network and error characteristics of simulated observations and innovation-based inflation, are carried out for about two months. The structure characters and perturbation amplitudes of the ETKF initial perturbations and the perturbation growth characters are analyzed, and their qualities and abilities for the ensemble initial perturbations are given. The preliminary experimental results indicate that the ETKF-based GRAPES ensemble initial perturbations could identify main normal structures of analysis error variance and reflect the perturbation amplitudes. The initial perturbations and the spread are reasonable. The initial perturbation variance, which is approximately equal to the forecast error variance, is found to respond to changes in the observational spatial variations with simulated observational network density. The perturbations generated through the simplex method are also shown to exhibit a very high degree of consistency between initial analysis and short-range forecast perturbations. The appropriate growth and spread of ensemble perturbations can be maintained up to 96-h lead time. The statistical results for 52-day ensemble forecasts show that the forecast scores of ensemble average for the Northern Hemisphere are higher than that of the control forecast. Provided that using more ensemble members, a real-time observational network and a more appropriate inflation factor, better effects of the ETKF-based initial scheme should be shown.

Heavy Rainfall Ensemble Prediction:Initial Condition Perturbation vs Multi-Physics Perturbation

Mesoscale ensemble is an encouraging technology for improving the accuracy of heavy rainfall predictions. Occurrences of heavy rainfall are closely related to convective instability and topography. In mid-latitudes, perturbed initial fields for medium-range weather forecasts are often configured to focus on the baroclinic instability rather than the convective instability. Thus, alternative approaches to generate initial perturba- tions need to be developed to accommodate the uncertainty of the convective instability. In this paper, an initial condition perturbation approach to mesoscale heavy rainfall ensemble prediction, named as Different Physics Mode Method （DPMM）, is presented in detail. Based on the PSU/NCAR mesoscale model MM5, an ensemble prediction experiment on a typical heavy rainfall event in South China is carried out by using the DPMM, and the structure of the initial condition perturbation is analyzed. Further, the DPMM ensem- ble prediction is compared with a multi-physics ensemble prediction, and the results show that the initial perturbation fields from the DPMM have a reasonable mesoscale circulation structure and could reflect the prediction uncertainty in the sensitive regions of convective instability. An evaluation of the DPMM ini- tial condition perturbation indicates that the DPMM method produces better ensemble members than the multi-physics perturbation method, and can significantly improve the precipitation forecast than the control non-ensemble run.

Progress on the Key Technology Development in Application of Ensemble Prediction Products Associated with TIGGE

This project is supported by the 2007 R ＆ D Special Fund for Public Welfare by Ministry of Science and Technology and Ministry of Finance.Research tasks in this project are proposed based on the implementation plan of the＂THORPEX（The Observing System Research and Predictability Experiment） Interactive Grand Global Ensemble（TIGGE）＂,a sub-project of the THORPEX international program.

Preliminary Comparison of the CMA,ECMWF,NCEP,and JMA Ensemble Prediction Systems

Based on The Observing System Research and Predictability Experiment （THORPEX） Interactive Grand Global Ensemble （TIGGE） dataset, using various verification methods, the performances of four typical ensemble prediction systems （EPSs） from the China Meteorological Administration （CMA）, the European Centre for Medium-Range Weather Forecasts （ECMWF）, the US National Centers for Environmental Pre- diction （NCEP）, and the Japan Meteorological Agency （JMA） are compared preliminarily. The verification focuses on the 500-hPa geopotential height forecast fields in the mid- and higb-latitude Eurasian region during July 2007 and January 2008. The results show that for the forecast of 500-hPa geopotential height, in both summer and winter, the ECMWF EPS exhibits the highest forecast skill, followed by that of NCEP, then by JMA, and the CMA EPS gets in the last. The better system behaviors benefit from the better com- bination of the following： data assimilation system, numerical models, initial perturbations, and stochastic model perturbations. For the medium-range forecast, the ensemble forecasting can effectively filter out the forecast errors associated with the initial uncertainty, and the reliability and resolution （the two basic attri- butions of the forecast system） of these EPSs are better in winter than in summer. Specifically, the CMA EPS has certain advantage on the reliability of ensemble probabilistic forecasts. The forecasts are easy to be underestimated by the JMA EPS. The deficiency of ensemble spread, which is the universal problem of El＇S, also turns up in this study. Although the systems of ECMWF, NCEP, and JMA have more ensemble mem- bers, this problem cannot be ignored. This preliminary comparison helps to further recognize the prediction capability of the four EPSs over the Eurasian region, provides important references for wide applications of the TIGGE dataset, and supplies useful information for improving the CMA EPS.

Evaluation of the NMC Regional Ensemble Prediction System During the Beijing 2008 Olympic Games

Based on the B08RDP（Beijing 2008 Olympic Games Mesoscale Ensemble Prediction Research and Development Project） that was launched by the World Weather Research Programme（WWRP） in 2004,a regional ensemble prediction system（REPS） at a 15-km horizontal resolution was developed at the National Meteorological Center（NMC） of the China Meteorological Administration（CMA）.Supplementing to the forecasters＇ subjective affirmation on the promising performance of the REPS during the 2008 Beijing Olympic Games（BOG）,this paper focuses on the objective verification of the REPS for precipitation forecasts during the BOG period.By use of a set of advanced probabilistic verification scores,the value of the REPS compared to the quasi-operational global ensemble prediction system（GEPS） is assessed for a 36-day period（21 July-24 August 2008）.The evaluation here involves different aspects of the REPS and GEPS,including their general forecast skills,specific attributes（reliability and resolution）,and related economic values.The results indicate that the REPS generally performs significantly better for the short-range precipitation forecasts than the GEPS,and for light to heavy rainfall events,the REPS provides more skillful forecasts for accumulated 6-and 24-h precipitation.By further identifying the performance of the REPS through the attribute-focused measures,it is found that the advantages of the REPS over the GEPS come from better reliability（smaller biases and better dispersion） and increased resolution.Also,evaluation of a decision-making score reveals that a much larger group of users benefits from using the REPS forecasts than using the single model（the control run） forecasts,especially for the heavy rainfall events.

A Recombination Clustering Technique for Forecasting of Tropical Cyclone Tracks Based on the CMA-TRAMS Ensemble Prediction System

Despite marked improvements in tropical cyclone(TC) track ensemble forecasting,forecasters still have difficulty in making quick decisions when facing multiple potential predictions,so it is demanding to develop post-processing techniques reducing the uncertainty in TC track forecasts,and one of such techniques is the cluster-based methods.To improve the effect and efficiency of the previous cluster-based methods,this study adopts recombination clustering(RC) by optimizing the use of limited TC variables and constructing better features that can accurately capture the good TC track forecasts from the ensemble prediction system(EPS) of the China Meteorological Administration Tropical Regional Atmosphere Model for the South China Sea(CMA-TRAMS).The RC technique is further optimized by constraining the number of clusters using the absolute track bias between the ensemble mean(EM) and ensemble spread(ES).Finally,the RC-based deterministic and weighted probabilistic forecasts are compared with the TC track forecasts from traditional methods.It is found that(1) for deterministic TC track forecasts,the RC-based TC track forecasts outperform all other methods at 12–72-h lead times;compared with the skillful EM(118.6 km),the improvements introduced by the use of RC reach up to 10.8%(8.1 km),10.2%(13.7 km),and 8.7%(20.5 km) at forecast times of 24,48,and 72 h,respectively.(2) For probabilistic TC track forecasts,RC yields significantly more accurate and discriminative forecasts than traditional equal-weight track forecasts,by increasing the weight of the best cluster,with a decrease of 4.1% in brier score(BS) and an increase of 1.4% in area under the relative operating characteristic curve(AUC).(3) In particular,for cases with recurved tracks,such as typhoons Saudel(2017) and Bavi(2008),RC significantly reduces track errors relative to EM by 56.0%(125.5 km) and 77.7%(192.2 km),respectively.Our results demonstrate that the RC technique not only improves TC track forecasts but also helps to unravel skillful ensemble members,and is likely useful for feature construction in machine learning.

Verification of tropical cyclones(TC)wind structure forecasts from global NWP models and ensemble prediction systems(EPSs)

Forecasting wind structure of tropical cyclone(TC)is vital in assessment of impact due to high winds using Numerical Weather Prediction(NWP)model.The usual verification technique on TC wind structure forecasts are based on grid-to-grid comparisons between forecast field and the actual field.However,precision of traditional verification measures is easily affected by small scale errors and thus cannot well discriminate the accuracy or effectiveness of NWP model forecast.In this study,the Method for Object-Based Diagnostic Evaluation(MODE),which has been widely adopted in verifying precipitation fields,is utilized in TC’s wind field verification for the first time.The TC wind field forecast of deterministic NWP model and Ensemble Prediction System(EPS)of the European Centre for Medium-Range Weather Forecasts(ECMWF)over the western North Pacific and the South China Sea in 2020 were evaluated.A MODE score of 0.5 is used as a threshold value to represent a skillful(or good)forecast.It is found that the R34(radius of 34 knots)wind field structure forecasts within 72 h are good regardless of DET or EPS.The performance of R50 and R64 is slightly worse but the R50 forecasts within 48 h remain good,with MODE exceeded 0.5.The R64forecast within 48 h are worth for reference as well with MODE of around 0.5.This study states that the TC wind field structure forecast by ECMWF is skillful for TCs over the western North Pacific and the South China Sea.

Ensemble Prediction of Monsoon Index with a Genetic Neural Network Model

After the consideration of the nonlinear nature changes of monsoon index,and the subjective determination of network structure in traditional artificial neural network prediction modeling,monthly and seasonal monsoon intensity index prediction is studied in this paper by using nonlinear genetic neural network ensemble prediction（GNNEP）modeling.It differs from traditional prediction modeling in the following aspects： （1）Input factors of the GNNEP model of monsoon index were selected from a large quantity of preceding period high correlation factors,such as monthly sea temperature fields,monthly 500-hPa air temperature fields,monthly 200-hPa geopotential height fields,etc.,and they were also highly information-condensed and system dimensionality-reduced by using the empirical orthogonal function（EOF）method,which effectively condensed the useful information of predictors and therefore controlled the size of network structure of the GNNEP model.（2）In the input design of the GNNEP model,a mean generating function（MGF）series of predictand（monsoon index）was added as an input factor;the contrast analysis of results of predic- tion experiments by a physical variable predictor-predictand MGF GNNEP model and a physical variable predictor GNNEP model shows that the incorporation of the periodical variation of predictand（monsoon index）is very effective in improving the prediction of monsoon index.（3）Different from the traditional neural network modeling,the GNNEP modeling is able to objectively determine the network structure of the GNNNEP model,and the model constructed has a better generalization capability.In the case of identical predictors,prediction modeling samples,and independent prediction samples,the prediction accuracy of our GNNEP model combined with the system dimensionality reduction technique of predictors is clearly higher than that of the traditional stepwise regression model using the traditional treatment technique of predictors,suggesting that the GNNEP model opens up a vast range of possibilities for operational weather prediction.

Ensemble Hindcasts of ENSO Events over the Past 120 Years Using a Large Number of Ensembles

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 conditions obtained by only assimilating historic SST anomaly observations. By examining the retrospective ensemble forecasts and available observations, the verification results show that the skill of the ensemble mean of the EPS is greater than that of a single deterministic forecast using the same ICM, with a distinct improvement of both the correlation and root mean square （RMS） error between the ensemble-mean hindcast and the deterministic scheme over the 12-month prediction period. The RMS error of the ensemble mean is almost 0.2℃ smaller than that of the deterministic forecast at a lead time of 12 months. The probabilistic skill of the EPS is also high with the predicted ensemble following the SST observations well, and the areas under the relative operating characteristic （ROC） curves for three different ENSO states （warm events, cold events, and neutral events） are all above 0.55 out to 12 months lead time. However, both deterministic and probabilistic prediction skills of the EPS show an interdecadal variation. For the deterministic skill, there is high skill in the late 19th century and in the middle-late 20th century （which includes some artificial skill due to the model training period）, and low skill during the period from 1906 to 1961. For probabilistic skill, for the three different ENSO states, there is still a similar interdecadal variation of ENSO probabilistic predictability during the period 1886~2005. There is high skill in the late 19th century from 1886 to 1905, and a decline to a minimum of skill around 1910-50s, beyond which skill rebounds and increases with time until the 2000s.