The El Niño-Southern Oscillation (ENSO), as the dominant mode of natural climate variability in the tropical Pacific on interannual timescales, has a major impact on the global climate and particularly East Asian climate variability (e.g., Rasmusson and Carpenter, 1982; Zhang et al., 1996, 2012; Wang et al., 2000). In the past three decades, a number of international efforts have been made to find a good method to predict the ENSO phenomenon, and many prediction methods have been proposed, such as statistical models and simplified dynamic air-sea coupled models, as well as fully coupled general circulation models (GCMs) (e.g., Cane et al., 1986; Zebiak and Cane, 1987; Chen et al., 1995, 2004; Luo et al., 2005, 2008; Zheng et al., 2006, 2009; Cheng et al., 2010; Izumo et al., 2010). Following these works, much progress has been made in improving methods for ENSO prediction. There is no doubt that such achievements can be largely attributed to improvements in the understanding of ENSO, climate modelling, and ocean data assimilation ( Moore and Kleeman, 1996; Latif et al., 1998; Kirtman, 2003; Jin et al., 2008; Barnston et al., 2012).

However, there are still many GCMs that are incapable of adequately simulating ENSO and reasonably assimilating ocean initial states. Particularly, when such models are applied to operational ENSO prediction, their prediction performance can be expected to be relatively low. The question is: how do we improve the capability of such models with low performance in predicting ENSO? An efficient way is to develop empirical/statistical correction methods of model prediction errors (e.g., Wang et al., 2000; Chen and Lin, 2006; Zeng, 2009). Generally speaking, the predictions based on coupled GCMs are subject to biases and the raw outputs of the models include systematic errors due to model deficiencies. This kind of systematic bias used to be regarded as a constant and may be largely reduced using model climatology in generating climate anomalies. Nevertheless, the errors in model predictions are flow-dependent with changing climate states, which are correlated to physical predictors and further statistically estimated by them ( Ren, 2008).

Many studies have focused on developing effective methods/schemes to correct such flow-dependent errors in model predictions ( c.f., Ren and Chou, 2007a). In our previous studies, we proposed the method of analogue-based correction of errors (ACE) in model predictions, based on the hypothesis that the flow-dependent errors are to some degree similar under analogous historical states ( Ren and Chou, 2005, 2007b; Ren et al., 2009). With this method, we can empirically estimate the unknown errors of the current prediction using the known prediction errors that can be produced by the same model with historical analogue states. Since 2006, this method has been continually developed with different schemes for applications in seasonal climate prediction. In this paper, we propose a new idea to empirically improve ENSO prediction performance in an operational climate model by applying the ACE method, and report results from an idealized experiment conducted to test the idea.

Here, we briefly introduce the basic idea behind the strategy and methodology of dynamical analogue prediction ( Ren and Chou, 2007b). To effectively use analogous information from historical data in climate prediction based on complicated models, a method of ACE in model prediction has been proposed in previous studies ( Ren and Chou, 2005, 2007b). The main idea of the method can be simply expressed by the equation of analogue correction of errors as follows:

. (1)

The term on the left side of Eq. (1) is the corrected model prediction, and those on the right side are the direct model prediction, historical analogue, and its corresponding prediction with the same model, where M denotes the time integration or time mean prediction, and the wave denotes the analogue. It is clearly seen from Eq. (1) that the question of conducting the model prediction can be transformed into the question of prediction error estimation by extracting information about the model prediction errors from the historical analogue and further correcting the current prediction of the same model.

In fact, the estimated prediction errors can be made much more stationary and acceptable using many historical analogues ( Ren and Chou, 2007b). Therefore, Eq. (1) can be further developed into

, (2)

where m denotes many historical analogues and w_j is the weight function. Based on Eqs. (1) and (2), we can take P_M as the monthly ENSO prediction, such as SST anomalies, and establish an analogue-dynamical ENSO prediction system (ADEPS). Figure 1 shows the schematic diagram for constructing the ADEPS and illustrating its main procedures.

Figure 1

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	Figure 1 Schematic diagram of the analogue-dynamical ENSO predic-tion system.

To validate the idea of applying the ACE method to ENSO prediction, we designed an idealized experiment based on the ADEPS assuming that we could find perfect historical analogues. That is, the best analogues could be determined by directly using the current analysis field that actually emerged after the initial time and needed to be predicted, instead of using the initial analysis field as usual. Through such an experiment, as we will see, we were able to demonstrate the potential of the ACE method to be used in ENSO prediction.

In the experiment, a 30-yr hindcast dataset for the period 1983-2012, produced by the operational air-sea coupled GCM at the Beijing Climate Center (BCC CGCM1) ( Ding et al., 2002) was used; specifically, the March to August ensemble-mean data of 48 members predicted at the end of February. In addition, the initial values of the atmospheric model were generated at 0000 UTC on the last eight days of February from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis dataset (NNRA). The initial values of the oceanic model were generated from the global ocean data assimilation system of the BCC, and were further perturbed and combined into 48 ensemble members of dynamical seasonal prediction. The monthly sea surface temperature (SST) dataset employed in this study was the global sea ice and sea surface temperature analyses from the Hadley Center (HadISST) ( Rayner et al., 2003). The traditional Niño3.4 index can be calculated by taking an average of the SST anomalies in the region of (5°S-5°N, 120-170°W).

The scheme for the experiment applying the ADEPS was designed as: 1) March to August SST anomalies were extracted from the 30-yr hindcast and HadISST analysis datasets for selecting the historical analogues and verifying predictions; 2) the root-mean-square distance between two SST anomaly fields was taken as the metric to measure their analogy and the first four best analogues were used to estimate the prediction errors with equal weighting; 3) an independent validation was conducted for target years from 1993 to 2012, and for each target year all of the data prior to the target year were used to define the climatology and select historical analogues; 4) prediction skill scores were taken as the temporal correction coefficient (TCC) and root-mean-square error (RMSE) between the predicted and observed Niño3.4 SST anomaly indices.

Figure 2 compares the predicted time series of the Niño3.4 indices with the observed indices at different lead months. It is clear that the direct model predictions tend to have a lower amplitude, presumably due to the strong damping effect in the operational BCC CGCM1. This situation becomes more apparent as the lead months increase, and even after three months, the directly predicted indices have become so weak that they are almost not able to provide a useful signal any more. In contrast, the predicted indices generated in the idealized experiment are perfectly consistent with the observed indices. Under the condition of prescribing the historical analogue information, the ADEPS based on the ACE method can extract those prediction errors which are similar in the analogues, and empirically estimate the current prediction error. The correction originated from historical analogues using the same prediction model, not only calibrate well the climate variability signals in the ENSO prediction, but also recover the amplitude of the ENSO variability predicted directly by the model to a large degree.

Figure 2

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	Figure 2 Niño3.4 indices from the observation (square line), direct model prediction (circle line), and corrected model prediction (triangle line) in different forecast months.

To quantitatively present the potential ability of the ACE method to improve the performance of ENSO prediction, Fig. 3 further give the two traditional prediction skill scores—TCC and RMSE—which are widely used in the verification of ENSO prediction. It is quite evident in Fig. 3 that the TCC scores of the direct model prediction appear to be very low, compared with those of the corrected prediction. The former is subject to a quick decrease of values after three lead months, which is probably attributable to the poorly represented air-sea coupling over the tropical ocean in the model. Although, in the last decade, this climate model prediction system has been established and developed on the operational platform of the BCC, the deficiencies in the model coupling processes and ocean data assimilation make this model hard to use to predict ENSO adequately.

Figure 3

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	Figure 3 Prediction skill scores as a function of forecast month: the temporal correlation coefficients TCCs (upper) and RMSE (lower), for direct model prediction (square line) and corrected model prediction (circle line).

In contrast to the direct model prediction, as seen in Fig. 3, the TCC score profile of the corrected prediction based on the ADEPS shows quite a slow decrease as the lead months increase. The TCC at a lead of six months is close to 0.8, although that at a lead of one month is slightly lower than the uncorrected value. Alongside this, the RMSE scores are also much smaller in the corrected prediction than the direct model prediction. Further, the ACE method can be applied to each spatial point in the entire domain. Figure 4 presents the distributions of the TCC scores over the tropical Pacific region. Compared with the low TCC scores in the direct model predictions (not shown), the scores in the analogue-corrected predictions become systematically higher.

Figure 4

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	Figure 4 Spatial distributions of TCCs of the corrected model prediction for March to August, where the skill scores are calculated with data during 1983-2012.

Indeed, the prediction skill scores shown in Figs. 3 and 4 outline an upper limit of predictability using the ACE method for ENSO prediction, in terms of the designed idealized experiment. That is, once the historical analogues have been identified adequately, the unknown current model prediction error can be estimated to some degree by the known prediction errors that the same model made based on the historical analogues. In reality, it is not possible to capture perfect historical analogues using only the information prior to the initial time. Thus, one of the most challenging technical questions in the ACE method is always how to select adequate analogues a priori.

Climate prediction, such as ENSO prediction, based on numerical models is usually subject to model biases. Raw model outputs include systematic errors due to deficiencies in climate models. This kind of systematic bias is usually regarded as a constant and can be reduced by a systematic bias correction using model climatology in defining climatic anomalies. However, model prediction errors are known to be flow-dependent, and difficult to eliminate as a constant. In this paper, we introduced the method of analogue-based correction of errors into an operational climate prediction model which has a poor air-sea coupling, and further exhibited the potential of the ACE method to improve the performance of model ENSO prediction.

The ACE method is based on the hypothesis that the flow-dependent errors are similar to some degree under analogous climate states. Using this method, we were able to empirically estimate the unknown current prediction errors using the known prediction errors that can be produced by the same model with historical analogue states, and thus effectively correct the current model prediction with the estimated prediction error. To apply the ACE method to improving ENSO prediction, we developed an analogue-dynamical ENSO prediction system based on the operational climate prediction model of the BCC, and performed an idealized experiment using the multi-year hindcast data with this model, in order to test whether the system could be applied to the operational model. The experimental results showed an encouraging performance of the ACE method in increasing prediction skill and reducing the prediction errors of ENSO.

This study demonstrated the potential of the ACE method to effectively correct ENSO prediction in low- performing operational climate prediction models. However, we assumed that all the historical analogues are known a priori, and examined the predictability of the ACE method. We are working to develop effective schemes for selecting historical analogues through diagnosing the statistical relationship between initial conditions and model prediction errors. Further results from using this correction method in improving ENSO prediction performance will be presented in another paper. In summary, the current study clearly suggests that the strategy of using the ACE method provides deeper insights into how to improve the performance of ENSO prediction based on the current level of models and data.