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

The model adopted in this work is version 1.1 of the BCC Climate System Model with a moderate atmospheric resolution, BCC_CSM1.1(m) (Wu et al., 2013). The ocean component of the model is Modular Ocean Model version 4 (MOM4)-L40, with a horizontal resolution of 0.3° latitude × 1° longitude by between 30°S and 30°N ranging from 1° latitude at 60°S and 60°N and nominally 1° poleward with tripolar coordinates. The atmospheric component is the BCC Atmospheric General Model with a T106 horizontal resolution and 26 hybrid sigma/pressure layers in the vertical direction. The land and sea-ice components are version 1.0 of the BCC Atmosphere and Vegetation Interaction Model and the Sea Ice Simulator, respectively. The different components are coupled with no flux adjustment. The model is widely used for operational seasonal predictions in Beijing Climate Center (Liu et al., 2015). The hindcast experiments used here are from January of 1991 to December of 2016, with a 13-month forecast integration for each start month. For instance, a prediction made in January 1991 will end with forecast results from January 1991 (lead 0-month) to January 1992 (lead 12-month). The oceanic initial conditions are obtained from the sea temperature of the National Centers for Environmental Prediction (NCEP) Global Oceanic Data Assimilation System, and the atmospheric initial conditions come from the four-times daily air temperature, winds, and surface pressure fields of the NCEP Reanalysis. Each hindcast experiment includes 15 members, through a combination of different atmospheric and oceanic initial conditions at the end of the month preceding the beginning of the hindcast, generally referred to as a lagged average forecasting. Figure 1 shows the spread of 15 members at the target month of predictions with different time leads, and the spread is obtained by subtracting the minimum of the 15 predicted SST anomalies from the maximum. It can be seen that the difference among 15 members in the model generally increases from west to east, and is largest in the eastern tropical Pacific roughly along 120°W. As for the ensemble mean of these initial conditions, it is similarly shown that the prediction uncertainty of this model tends to be more evident in the eastern part of the tropical Pacific, and the maximum prediction errors for varied start months take place during boreal winter (Fig. 2). In general, it is reasonable to use the BCC_CSM1.1(m) to explore the ENSO predictability problem, considering the prediction spread and errors of this model fall in relatively consistent areas.

Figure 1.  The spreads of 15-member tropical SSTA predictions (averaged within 5°S–5°N, units: K) for different forecast lead times (0 months, 3 months, 6 months, and 9 months) in the Pacific, where the y-axis indicates the 12 target times of predictions from January to December. It can be seen that the large spread for the SSTA predictions is mainly in the equatorial eastern Pacific.

Figure 2.  The root mean square (RMS) error of predicted tropical SSTA (averaged within 5°S−5°N) from BCC-CSM1.1(m) ensemble forecasts, with the model starting from January, April, July, and October (vertical coordinates correspond to varying lead times).

The observational data, which are used for analyzing model prediction (hindcast) errors, include the Hadley Center Sea Ice and Sea Surface Temperature data set (HadISST) (Rayner et al., 2003), the NCEP-DOE Reanalysis 2 for surface wind stress (Kanamitsu et al., 2002), and the NOAA Global Ocean Data Assimilation System (GODAS) for subsurface ocean temperature (Behringer et al., 1998). To remain exactly consistent with the output from BCC_CSM1.1(m), all the variable anomalies in observations are calculated for the 1991–2010 period with the 20-year climatology removed. To assess the prediction performance of the model used here, several measures for ENSO-associated SST anomalies are adopted. The Niño-3, Niño-4, and Niño-3.4 indices are defined as the SSTA average over their respective regions. For comparison, the Cold-Tongue and Warm-Pool Niño indices (NiñoCT and NiñoWP) are also considered (Ren and Jin, 2011).

The BCC_CSM1.1(m) model is now running as an operational model at the Beijing Climate Center, and ENSO prediction has come out as an important application of the model’s seasonal outputs. Based on 12-month-lead predictions of this model, traditional ENSO Niño indices, like Niño-3, Niño-4, and Niño-3.4 indices, tend to have higher skills, compared with NiñoWP and NiñoCT indices (Fig. 3). Meanwhile, the Niño-4 index forecast owns the smallest root mean square (rms) errors among these ENSO indices, probably because the SSTAs in the central tropical Pacific have relatively less significant variability, and are also manifested to have the best SSTA persistence there (Ren et al., 2016; Tian et al., 2019). Besides, it is noted that in the earlier studies, contrasting prediction skills may appear under different conditions of ENSO, but the nature of the differences in forecast performance among the different ENSO phases remains unclear (e.g., Jin et al., 2008; Zheng et al., 2016).

Figure 3.  ENSO Niño SST anomaly correlations between the observations (HadISST) and 15-member ensemble mean predictions up to a 12-month lead (left), where the persistence skill of Niño-3.4 prediction is presented for comparison. The RMS error of Niño-3, Niño-4, and Niño-3.4 indices between the observations (HadISST) and 15-member ensemble mean predictions up to a 12-month lead (right).

Here, following Ren et al. (2018), seven El Niño events during the research period are chosen based on observation, these include: 1994−95, 1997−98, 2002−03, 2004−05, 2006−07, 2009−10, and 2015−16. All of the events reach their peak phase during the boreal winter. Therefore, four seasons (based on 3-month-mean values) during their development from the ENSO developing year (marked year 0) of ENSO are defined as MAM (0), JJA (0), SON (0), and DJF (1). For a given target season with a certain lead prediction, the initial time is determined by the first month of the given season. The four seasons are predicted as the target times, and composites of these seven ENSO events are then obtained. The prediction errors of the four seasons during the development of ENSO are then compared directly to those of the four seasons after the ENSO peak time, where the predictions in the ENSO decay year (year 1) are also explored with the four seasons [MAM (1), JJA (1), SON (1) and DJF (2)] as target times of predictions.

Figure 4 shows the Niño-3.4 prediction skills during the ENSO developing year and the following year. In the ENSO developing year, the temporal anomaly correlation score reaches above 0.65 in terms of ensemble mean Niño-3.4 index at the 6-month lead, lower than that in the ENSO decay year which owns a prediction skill of around 0.75. Meanwhile, the ensemble mean has the highest prediction performance compared with any single initial prediction member, and the spread of 15 ensemble members becomes relatively obvious only when the lead time is more than three months.

Figure 4.  ENSO Niño-3.4 SST anomaly correlations between the observations (HadISST) and the 15-member ensemble mean predictions for up to a 12-month lead, for the ENSO developing year (left) and the decay year (right).

For the seven ENSO events, a total of 105 initial conditions could be obtained once the target season of prediction is given in terms of certain lead months. The composites of SSTA prediction errors with different lead months are shown in Fig. 5, where four seasons of the ENSO developing year are shown as target times. For prediction at the 0-month lead (that is the initial time), the prediction errors are inclined to be the lowest, and the distribution characteristics at each target season are time-dependent, in which the errors show a narrow positive "zone" in the equatorial Pacific. Such errors appear more prominent when boreal spring and autumn are the terminal seasons (lead 0). As for the lead times of three months and longer, a more consistent and systematic error pattern appears for each target season. In spring, the negative SSTA errors extend from the central Pacific to the northeast with positive values on the southeast side. During this time, the air-sea coupling is generally weak, and so is the air-sea variability. Thus, it does not mean that the influence of the prediction errors above is small, especially for the errors on the north side of the equator (Vimont et al., 2003; Chang et al., 2007). Meanwhile, the forecast errors, with other seasons rather than spring being the target times, are characterized by the large-scale “cold” SSTA in the equatorial central and eastern Pacific, no matter when the prediction is made. Therefore, the negative SSTA errors in the model tend to have an obvious impact on the occurrence and intensity of ENSO events.

Figure 5.  Composite patterns of SSTA prediction errors for seven ENSO events with the lead months of 0, 3, 6, 9, and 12. The four target seasons from left to right are MAM, JJA, SON, and DJF for the ENSO developing year. Dotted areas indicate the composites of SSTA errors that exceed the 99% confidence level, as determined by a Student t-test.

For the decay year of ENSO, the patterns of predicted SSTA errors are evidently different from those mentioned above (Fig. 6). When the target time is in boreal spring, there are some positive SSTA errors located in the eastern tropical Pacific with weak negative errors to the west. During the other three seasons, the prediction errors of warm SST in the central Pacific could be seen, within which there is an eastward movement of negative SST anomalies. By comparing the prediction errors between the ENSO development year and the second year, it is found that the systematic prediction errors of the ENSO development year are more obvious in the equatorial eastern Pacific (including both intensity and coverage). Therefore, to some extent, it could determine the worse forecast performance for the ENSO development year shown in Fig. 4.

Figure 6.  As in Fig. 5, but for composite patterns of SSTA prediction errors for the ENSO decay year.

As mentioned earlier, the prediction of ENSO in the developing year tends to be more challenging compared with the year following the ENSO peak, yet their prediction performance remains better than those normal years (figure not shown), consistent with previous studies (Jin et al., 2008; Yang and Jiang, 2014). Meanwhile, one may note that the seven ENSO events may be at different stages of their development in the same season, and this point is more likely to become evident in the decay year of ENSO. This determines that the composited prediction errors during the ENSO development year are more representative, particularly for the results of the mature phase of ENSO (the boreal winter). Therefore, we focus on the predictability of the ENSO development and try to demonstrate the source of the prediction errors of those ENSO events in the model.

The evolutionary characteristics of different atmospheric and oceanic initial fields and their effects on the developing phase of ENSO are then investigated. Aside from SSTAs, two key ENSO variables are chosen based on the dynamical processes of the ENSO life cycle and its predictions. One is the westerly wind burst (zonal wind stress), which generally lasts, at most, one month, and could affect short-term ENSO prediction and play an important role during the whole process of ENSO development in the form of air-sea feedbacks (Wu et al., 2009; Lopez and Kirtman, 2014; Chen et al., 2015). The other is the upper-ocean warm water in the equatorial Pacific, and its buildup is believed as a necessary precondition for the development of ENSO (McPhaden, 2003; Ren and Jin, 2013; Zhu et al., 2015; Yang et al., 2020). The extra assimilation of subsurface ocean temperature data is inclined to reduce the so-called ENSO spring prediction barrier (Chen et al., 1995; Yu and Kao, 2007). Specifically, previous studies have pointed out sensitive areas for ENSO predictions and emphasized the role of specific patterns regarding subsurface temperature anomalies (e.g., Duan and Hu, 2016). In their work, the most sensitive subsurface region in the ocean generally is located in the depths of 90–160 m, and this is consistent among varied dynamical models (including the model here), reflecting the thermocline depth in these models (Zhang et al., 2015; Duan and Hu, 2016). Thereafter, SSTA, zonal wind stress anomalies, and subsurface heat content within 90–160 m (termed subsurface heat content) are combined during the evolution of prediction errors. We then analyze the evolution characteristics of the prediction errors in a 12 month period and discuss whether the SSTA prediction error corresponds to the initial error with a particular structure. The seven ENSO events are predicted 12 months in advance, and the starting month of each prediction is December of the year before the ENSO development year. Similarly, if the prediction of the following ENSO year is made 12 months ahead, the December corresponding to the ENSO mature phase is adopted as the initial prediction time.

For the composites of the seven ENSO events, it can be seen in Fig. 7 that the intensity of the SSTAs is weak at the initial time, the strong northeast wind anomaly is helpful for the enhancement of trade wind and evaporation, and negative SSTAs extends into the equatorial central Pacific through the wind-evaporation-SST (WES) feedback mechanism. As a result, the weak positive SSTA errors in the central-eastern Pacific gradually weakened and disappeared, and then transitioned to negative SSTA errors. In early spring, a subsurface signal is evident while SSTA errors are still to be set up in the central-eastern tropical Pacific (Fig. 8). In late spring, the easterly anomaly over the equatorial central-western Pacific increases, accompanied by the SST variation, which contributes to the eastward propagation of cold upwelling from the subsurface and the reduction of heat content in the central-eastern Pacific. Furthermore, the negative errors can then continue and further develop due to the positive Bjerknes feedback and evolve into a mature La Niña-like mode at the prediction time. In particular, corresponding to the changes of wind and the SSTAs, it is noted that the subsurface temperature at the initial time features a dipole structure with negative errors in the west and positive errors in the east. This pattern amplifies as the anomalies propagate eastward, due to the air-sea coupling that is known to play a key role in the development of negative SSTA errors (Figs. 7 and 8). Such subsurface “precursors” also exist in the 9-month lead prediction initiated later in Mar (0) (figure not shown). These results demonstrate that the presence of such initial oceanic errors is essential to the sequential predicted SSTA errors.

Figure 7.  Composite evolutions of initial errors for SSTA (shaded, units: K) and sea surface wind stress anomaly (vectors, units: N m⁻²) in BCC_CSM1.1(m) for seven ENSO events. Here, the prediction of DJF (1) in the developing phase of ENSO (also known as the mature phase) is made with a lead time of 12 months, and corresponding error evolutions are shown in chronological order. The composites of prediction errors only retain those passing the 95% confidence level that each of the variables satisfies, as determined by a Student t-test.

Figure 8.  As in Fig. 7, but for the subsurface heat content anomaly (units: K).

Some studies have also figured out that with different time leads of prediction, ENSO predictability may rely on different, competitive mechanisms and processes, such as potential precursors like the subsurface heat content and stochastic westerly wind burst events (Horii et al., 2012; Chen et al., 2015; Timmermann et al., 2018). In the long-lead predictions of the seven ENSO events, initial errors of the ocean subsurface were detected as the long-term memory for prediction errors. As lead time decreases, zonal wind stress may rapidly affect the likelihood for ENSO events, and the corresponding initial errors need to be checked. Compared with the prediction of the ENSO mature phase with a 12-month lead (Figs. 7 and 8), some different air-sea interactions could be detected if the prediction is made six months in advance (Figs. 9 and 10). Initially, neither the SSTA nor the heat content errors look evidently strong at the starting month Jun (0), implying little of a “precursor” to these prediction errors in the form of negative SSTAs. The wind errors over the central and western Pacific make the warm water transport eastward along and out of the equator, which is conducive to the subsequent thermocline lifting, thus negative heat content anomaly errors strengthen in the subsurface layer of the equatorial central Pacific (see Fig. 10). Negative SSTA errors in the central-eastern Pacific then evolve due to positive feedback. This result reasonably implies that before the subsurface heat content errors are captured, the influence of the initial wind errors are more obvious in the short-term forecast of ENSO development, and errors related to westerly wind anomalies could play a key role in triggering the ENSO prediction errors.

Figure 9.  As in Fig. 7, but the prediction of DJF (1) in the developing phase of ENSO (also known as the mature phase) is made with a lead time of six months.

Figure 10.  As in Fig. 9, but for the subsurface heat content anomaly (units: K).

For the year following the development of ENSO, we have also checked the error evolution of a 12-month lead prediction when the target season is fixed at the boreal winter of that year (figure not shown). It is noted that the error of the subsurface temperature, despite presenting an evolution pattern with lots of noise, mainly accumulated in the equatorial Central Pacific without evident eastward propagation, as did the positive SSTA errors mentioned above (Fig. 6).

Our results show that the BCC operational model presents the large-scale "cold" SSTA errors in the central-eastern Pacific when it comes to predicting the development phase of ENSO. The SSTA prediction biases are closely related to the negative initial errors in the subsurface layer of the central-western Pacific. Besides, these kinds of early “precursors” of errors are prominent when predictions are made with shorter lead times. Therefore, improvement of the initial accuracy of subsurface temperature in this region is thought to help improve the predicted intensity of ENSO events.

Targeted observation has been used for a few decades and focuses on the determination of the sensitive area by investigating what kind of initial error will have a large impact on the forecast within a numerical model (Snyder, 1996; Mu, 2013). Additional observations in the sensitive area, rather than in other regions, are supposed to yield a better forecast. Based on a complicated climate model, Duan and Hu (2016) once conducted perfect model experiments where they assumed that prediction uncertainties are caused only by initial errors. They concluded that ENSO predictions are more sensitive to initial errors in regions like the eastern tropical Pacific (for SSTAs) and the central-western equatorial Pacific (for subsurface temperature anomalies), consistent with those regions representing the sensitive area for targeted observation of ENSO predictions (also see Yu et al., 2012; Zhang et al., 2015). Given the great cost of observation, if we manage to adopt more accurate initial fields by intensifying the observations in the sensitive area rather than in other areas, the ENSO predictions may be greatly improved. Comparatively, the significant errors, as shown in the BCC model, during the ENSO development predictions include negative temperature anomalies in the subsurface of the central-western equatorial Pacific, causing an under-prediction for Niño-3.4 SSTA in tropical Pacific. This implies that some initial errors, of a specific structure relative to other errors in our model, may grow and affect prediction results more easily, as in previous works (Yu et al., 2012; Zhang et al., 2015; Duan and Hu, 2016).

To further explore what kinds of initial errors could lead to worse predictions in this BCC model and compare these errors directly with those in perfect model experiments, a preliminary discussion is carried out, similar to Hua and Su (2020). As for the seven El Niño events, 6-month-lead predictions are considered, each with June (0) being the initial calendar month. The good (bad) predictions can be obtained with the prediction performance being determined by a forecasted Niño-3.4 index over (under) 0.5. The fundamental difference between the two groups depends on whether the occurrence of these warm events in observation is accurately predicted (Fig. 11). Then, two categories of initial fields can be combined with 65 and 40 initial samples from the good and bad groups, respectively. The former sees positive SST anomalies in the central-eastern tropical Pacific dominate initially while warm SSTAs, confined only to the central Pacific, dominate the latter (Figs. 11a1 and b1).

Figure 11.  Composite evolutions of initial SSTA (shaded, units: K) and sea surface wind stress anomaly (vectors, units: N m^-2) (a, b) and for subsurface heat content anomaly (units: K) (c, d) in BCC_CSM1.1(m) for seven ENSO events. Here, the prediction of December (0) in the developing phase of ENSO is made with a lead time of six months. The left (right) row corresponds to good (bad) forecast performance (see text). The composites of initial and prediction conditions only keep those passing the 95% confidence level that each of the variables satisfies, as determined by a Student t-test.

Further, as mentioned earlier, these composite initial errors correspond to negative SSTA errors in the tropical central-eastern Pacific in boreal winter (Figs. 12a2, b2, and 5). For composites of the initial errors corresponding to the good prediction category (Figs. 12a, c), the subsurface signal is evidently accompanied by weak SSTAs and wind errors, which establish themselves in the central-eastern tropical Pacific through positive feedback. Initial wind stress primarily causes negative subsurface heat content to strengthen locally in the eastern tropical Pacific, with subsequent SSTA errors above (Figs. 12a1, c1). Compared to the good prediction category, the predicted SSTA errors of the bad category are much larger. Weakened zonal wind in June is evident and the wind errors over the central and western Pacific causes warm water to be transported along and away from the equator and helps to establish a shallower thermocline there, thus allowing negative subsurface heat content anomalies at the initial time to further develop (Figs. 12b1, d1). It is shown that, at first, the subsurface heat content was located west of 180° in the tropical Pacific, before moving eastward and rapidly enhancing, carrying cold water with it and causing a negative predicted SSTA in the eastern Pacific. The comparison between the two categories illustrates well the role of the combined zonal wind and subsurface heat content in accounting for the larger SSTA errors in the tropical eastern Pacific, emphasizing the negative influence of initial errors in specific areas on ENSO prediction. Previous work related to ENSO predictability, using perfect model experiments, has identified a similar key area where economical, yet efficient observations should be given priority i.e., initial errors of subsurface temperature anomalies in the central-western equatorial Pacific that are consistent with what we find here based on an operational model. This presents a common feature among varied models and suggests the generic sensitive areas for ENSO predictions. As one may notice, other precursors outside of the tropical Pacific were suggested in previous studies (Vimont et al., 2003; Izumo et al., 2010; Ham et al., 2013), and such initial signals may exert an influence on ENSO predictions in models, thus offering an important source of predictability for El Niño. In this sense, regions outside of the tropical Pacific may also contain sensitive areas for targeted observations for El Niño predictions.

Figure 12.  As in Fig. 11, but for the composite evolutions of initial errors.

In the analysis of error evolutions for ENSO predictions, what we have been emphasizing is the influence of the initial errors. However, in the BCC model, both initial and model errors are supposed to coexist, and indeed, some useful methods in terms of model errors have been discussed and introduced to improve ENSO predictions (Ren, 2008b; Liu and Ren, 2017). We further take a look at whether there is an obvious systematic forecast error for each season (target time) in the BCC model. To highlight the credibility of the results, we combine all the years from 1991 to 2016 to analyze the long-term average prediction errors at each season. It becomes evident that no matter how long of a lead time the prediction is made on, the ensemble-mean prediction errors of SSTAs are generally insignificant and less than 0.2 K (figure not shown), which is roughly on the same order of magnitude as the observation error. That is, the multi-year mean does not show obvious systematic prediction errors for different seasons. Although the error evolution of the mature-phase prediction should be the result of the combination of both the initial errors and model errors, more importantly, the multi-year average prediction errors imply and emphasize the key role of the initial errors in the ENSO prediction during its developmental stage. As for the occurrence of ENSO events, some other precursors, as well as their initial errors outside of the tropical Pacific were proposed and may indeed influence ENSO predictions in our model. Diagnoses of error evolution carried out in this manuscript could be applied to other ENSO-related areas beyond the tropical Pacific, and could also be used to investigate other ENSO prediction systems comparatively in the same way as described here. All of this requires further research, with the intent of improving our understanding of dynamical mechanisms related to error evolution in current climate models.

A deeper understanding of the predictability of different ENSO phases helps the research community to better figure out the potential factors that may limit the prediction of ENSO as well as its climatic impact. Based on the seasonal hindcast of BCC_CSM1.1(m), ENSO prediction performance is explored for the period between 1991–2016. A total of seven El Niño events are adopted, where the predictions of both their developing and decay phases are compared. It is demonstrated that the ensemble mean forecasts tend to be more challenging during the developing year of ENSO, compared with those made towards the decay phase. For the development phase, the composites of SST prediction errors are significantly negative and cover a large area in the central and eastern tropical Pacific, thus to some extent limiting the model skill in forecasting the onset and intensity of El Niño. This feature is nonexistent for the predictions of the ENSO decay phase, and large SSTA prediction errors are mainly confined in the equatorial central Pacific.

Considering that the seven ENSO events may be at different stages of their development in the same season, the composites of prediction errors during the ENSO development years are more representative compared with the decay years, and our main attention is given to the predictions of the mature phase of ENSO events. For those predictions with long lead times, the weak positive SSTA errors in the central-eastern Pacific gradually weakened and disappeared, and then turned into negative SSTA errors. Meanwhile, negative subsurface temperature anomalies lift the thermocline of the western equatorial Pacific and generate upwelling Kelvin waves that propagate eastward. Once the negative SSTA errors subsequently develop over the central-eastern Pacific, the cooling errors will be further intensified due to the positive Bjerknes feedback, and evolve into a mature La Niña-like mode at the prediction time. Further, as the lead times for the ENSO predictions decrease, the role of the initial wind errors begins to dominate. The initial wind errors over the central and western Pacific help to lift the thermocline of the central equatorial Pacific and enhance the negative heat content anomaly errors in the subsurface layer there. Our results emphasize the essential accuracy of initial fields and their early evolution in specific areas in terms of ENSO prediction.

The initial errors, which lead to significant SSTA prediction errors during the ENSO developing phase, are found in both subsurface temperature and surface wind stress fields. Why the initial fields of the model forecast show evident errors in these regions are beyond the scope of this work, and further diagnostic research is needed to find out the possible causes of the initial errors above, most especially the initial errors of subsurface temperature anomalies in the central-western equatorial Pacific. These specific errors tend to lead to poorly forecasted SSTAs towards the end of the year and are consistent with previous studies based on perfect model experiments. This represents a common feature among various models, and further indicates those generic sensitive areas for ENSO predictions. It is within these regions where additional observations could be prioritized, with the intent of introducing extra, while at the same time, useful initial data, thus providing support for targeted observation of ENSO operational prediction. As for the occurrence of ENSO events, some precursors as well as their initial errors outside of the tropical Pacific were suggested by previous studies and may exert influence on ENSO predictions in our model, thus offering an important source of predictability for El Niño. In this sense, regions outside the tropical Pacific may also contain sensitive areas for targeted observations for El Niño predictions and needs to be explored in depth.

Though the influence of initial errors is emphasized in this work, we do acknowledge that the ENSO prediction errors in either model are caused both by initial errors and model errors. How the model errors affect prediction performance during different ENSO development stages needs to be explored more in-depth, especially considering that model errors are generally time-dependent and closely associated with physical predictors (D'Andrea and Vautard, 2000; Ren, 2008a). Some other predictability experiments are needed when initial errors and model errors are considered together. Nevertheless, our work is more of a preliminary discussion on the characteristics and evolution of the initial errors in an operational model. Diagnoses of error evolution could be applied to other ENSO-related areas beyond the tropical Pacific, and could also be used to investigate other ENSO prediction systems comparatively in the same way as described here.

Acknowledgements. This work was jointly supported by the National Key Research and Development Program on Monitoring, Early Warning, and Prevention of Major Natural Disaster (Grant No. 2018YFC1506000), and the China National Science Foundation project (Grant Nos. 41606019, 41975094, and 41706016).