Reconciling roles of the South China Sea summer monsoon and ENSO in prediction of the Indian Ocean dipole

The Indian Ocean dipole (IOD) is a remarkable interannual variability in the tropical Indian Ocean. The improved prediction of IOD is of a great value because of its large socioeconomic impacts. Previous studies reported that both El Niño-Southern Oscillation (ENSO) and South China Sea summer monsoon (SM) play a dominant role in the western and eastern pole of the IOD, respectively. They can be used as predictors of the IOD at 3 month lead beyond self-persistence. Here, we develop an empirical model of multi-factors in which the western pole is predicted by ENSO and persistence and the eastern pole is predicted by SM and persistence. This new empirical model outperforms largely the average level of the dynamical models from the North American multi-model ensemble (NMME) project in predicting the peak IOD in boreal autumn, with a correlation coefficient of ∼0.86 and a root mean square error of ∼0.24 °C. Furthermore, the hit rate of positive culminated IOD in this new empirical model is equivalent to that in current NMME models (above 65%), much higher than that for negative culminated IOD. This improvement of skill using the empirical model suggests a perspective for better understanding and predicting the IOD.


Introduction
The Indian Ocean dipole (IOD) is a dominant interannual variability in the tropical Indian Ocean, characterized by a dipole pattern in sea surface temperature (SST) anomalies between the tropical western and eastern Indian Ocean (Saji et al 1999, Webster et al 1999).Numerous extreme weather and climate events with large socioeconomic impacts are attributed to the IOD, such as the extreme hot, droughts, and floods in Indian Ocean rim countries (Ashok et al 2003, 2004, Guan and Yamagata 2003, Cai et al 2009, 2011, Chen et al 2020, Duan et al 2020, Zhou et al 2021).Therefore, improving the prediction skill of the IOD would benefit the affected regions and thereby mitigate local socioeconomic losses.
Continuous effects have been made to improve the prediction of IOD using the state-of-the-art coupled models at seasonal time scales in past decades (Wajsowicz 2005, 2007, Luo et al 2007, 2008, Zhao and Hendon 2009, Shi et al 2012, Zhu et al 2015, Liu et al 2017, Zhao et al 2019, 2020, Song et al 2022).The dynamic forecasting skill of IOD events is typically limited to 3-4 months ahead (approximately one season) due to the strong boreal winterspring 'predictability barrier' (Shi et al 2012, Liu et al 2017) though some individual strong IOD events (i.e. 2006 and 2019) were successfully predicted two seasons in advance (Luo et al 2008, Doi et al 2020).Some studies found that the statistical or dynamic climate models that capture well the IOD-El Niño-Southern Oscillation (ENSO) relationship exhibit a superior predictive skill of the IOD, while the ENSOindependent IOD events seem to have a lower predictability (Song et al 2008, Zhao and Hendon 2009, Shi et al 2012, Yang et al 2015, Zhao et al 2020).
Many empirical models have been implemented to predict the IOD events.For example, multiple linear regression and canonical correlation analysis have been used in previous studies to predict the Indian Ocean SST (Kug et al 2004, Dommenget and Jansen 2009, Chen et al 2022).A simple stochasticdynamical model forced by forecasted ENSO conditions can predict the IOD well up to 6 month ahead (Zhao et al 2019(Zhao et al , 2020)).The above studies demonstrated that the predictability of IOD beyond persistence is largely influenced by ENSO.Recent studies suggest that the South China Sea summer monsoon (SM) is another climate factor affecting the IOD development (Zhang et al 2018(Zhang et al , 2021)).Furthermore, the SM and ENSO have strikingly different effects on the eastern and western pole of the IOD, with the dominant contributions of ENSO to the western pole and SM to the eastern pole, respectively (Zhang et al 2019).This leads us to ask whether the IOD prediction skill could be improved if considering both the preceding SM and ENSO signals, especially at its western and eastern poles.In this study, an empirical model of multi-factors (i.e. the SM, ENSO, and self-persistence) will be established using multiple linear regression, and their predictive skill of the IOD events is further assessed and compared with the North American multi-model ensemble (NMME) forecasting system.

Datasets
The SST observations used here were obtained from the improved Extended Reconstructed SST version 5 on a 2 • × 2 • grid for the period 1948-2022 (Huang et al 2017).The NMME project is generally used to improve prediction skill through the error compensation and greater consistency and reliability between models (Hagedorn et al 2005, DelSole et al 2014).For comparison, the 12 models from the NMME project were utilized during 1982-2018 (Kirtman et al 2014), including the hindcasts  and real-time forecasts (2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018).Each model consists of 4-20 ensemble members, and the forecasts are provided at lead times from 1 month to 4 months.In addition to the ensemble mean forecast characteristics of each individual model, the grand multi-model ensemble (MME) forecasts are employed with equal weight given to each individual model.Table S1 summarized the shortened model names, time period, ensemble size, and lead months for these 12 models.Since the NMME forecast is initialized at the beginning of each month, the lead time is defined as the number of months between the latest available observed data and the center of the 3 month running hindcasting target period.For example, if the latest available observed data is January, the forecast for the January-February-March season has 1 month lead, for February-March-April season 2 month lead, and so on.Monthly anomalies are calculated with respect to climatology from January 1982 to December 2010 in both the observations and each individual NMME model, and the linear trends were removed from the datasets.
The SM index was calculated as the area-averaged summer dynamical normalized seasonality for the 925 hPa wind field within the South China Sea monsoon domain (100 • -125 • E, 0 • -25 • N), which is available at http://lijianping.cn/dct/page/65578 (Li and Zeng 2002, 2003, Li et al 2010).The intensity of the SM index is given by: where || * || is a norm on the monsoon domain of integration, V1 and V represent January climatological wind vector and the mean of January and July climatological wind vectors, respectively, and Vm, n denotes monthly wind vectors in the mth month of the nth year.The significance of correlations between variables X and Y was tested using a two-tailed Student's t-test.The effective number of degrees of freedom (N eff ) is approximately estimated as follows (e.g.Pyper andPeterman 1998, Li et al 2013): where N is the total length of the time series, ρ XX (j) and ρ YY (j) denote autocorrelations of two time series X and Y, respectively.
To compared with the NMME results, the same study period  for the observations is also chosen.The seasonal mean in this study is averaged for boreal JJA (June-July-August), JAS (July-August-September), ASO (August-September-October), SON (September-October-November), and OND (October-November-December).

Methodology
The empirical model used here is established through holdout method (Devroye and Wagner 1979).Holdout (simple) validation depends on a single partitioning of the data.The time series is divided into two parts: the training period is from 1948 to 1981 and the hindcasting period is from 1982 to 2018.As for a single predictor variable, the model is trained during the training period though the linear regression of the predictor variable x three months earlier on the dependent variable z.Though this training model, we can get the regression coefficient a and constant g.Thus, the forecast model can be expressed as: where is f i (x) a function fitted to the predictor variable x.This gives us the relation between the dependent variable z at the ith month and the predictor variable x at (i − 3)th month (x i −3 ) during the hindcasting period.
With two predictor variables, we can also construct a training model by using binary regression of the predictor variables x and y 3 months earlier on the dependent variable z during the training period.Thus, the forecast model is established through the regression coefficients a and b, and the constant g in this training model, which is shown as follows: where f i (x, y) is a function fitted to the predictor variables x and y.This gives us the dependent variable z at the ith month related to predictor variables x and y at the (i − 3)th month (x i −3 and y i −3 ) during the hindcasting period.Similar to the model that includes two predictor variables, the forecast model based on three predictor variables is constructed as follows: where f i (x, y, p) is a function fitted to the predictor variables x, y and p.This gives us the dependent variable z at the ith month related to predictor variables x, y and p at the (i − 3)th month (x i −3 , y i −3 and p i −3 ) during the hindcasting period.
The real predictor variables used here are the standardized SM, ENSO (represented by N34), and self-persistence (PS) of the IOD three months earlier, and the dependent variable is IOD.The SM + N34 + PS forecast models are built as follows: where y i is the IOD at the ith month, SM i −3 , N34 i −3 and PS i −3 is the standardized SM, ENSO, and self-persistence of the IOD at the (i − 3)th month, respectively.a, b, and c are the regression coefficients and g is a constant.According to the previous studies, the SM is more important in the eastern pole of the IOD and ENSO is more important in the western pole of the IOD (Zhang et al 2018(Zhang et al , 2019)).A new empirical model (hereafter as RC-model) is reconstructed as follows: Step 1.The western pole of the IOD is first predicted by N34 + PS three months earlier using binary regression; Step 2. The eastern pole of the IOD is predicted by SM + PS three months earlier using binary regression; Step 3. The predicted IOD is defined as the difference between the western pole predicted by N34 + PS model in Step 1 and eastern pole predicted by SM + PS model in Step 2.
The leaving-one-out cross-validation is applied to estimate the stability of the RC-model according to the previous studies (Grantz et al 2005, Regonda et al 2006, Wang et al 2019), which is briefly introduced as follows: (1) given a time series with length L, one time point is chosen to be a hindcasting point, and the rest of the time series (length: L − 1) is used to build the prediction model using regression analysis.(2) The ensemble hindcast is produced until each time point of the given time series redoes the step (1).
Following Shi et al (2012) and Zhao et al (2020), we evaluate the ability of the models to predict three categories of IOD events: (i) positive IOD events in which the IOD amplitude in SON exceeds 1 standard deviation, (ii) negative IOD events in which the IOD amplitude in SON is less than −1 standard deviation, and (iii) neutral IOD events that fall in between.The contingency table (table S2) is made for the occurrence of observed and predicted IOD events using the SON DMI for each individual model.The hit rate (HR) for correctly forecasting the occurrence of a positive/negative IOD event is defined as: The false alarm rate (FAR), which is a measure of incorrectly forecasting an IOD event when in reality a neutral event occurred, is defined as See table S2 for the definitions of the letters a-i.Based on the threshold, 11 (a + b + c) positive IOD events, 10 (g + h + i) negative IOD events, and 16 (d + e + f ) neutral IOD events occur in SON during 1982-2018.

Connections of the SM and ENSO to the IOD
The relationships of the IOD with SM and ENSO are first investigated (figure 1).The SM and ENSO are significantly correlated with the IOD from JJA to OND during 1948-2018.However, there exist discrepancies in the relation of the SM and ENSO with the eastern and western poles of the IOD (figure 1(a)).The western pole of the IOD has a larger correlation coefficient with JJA ENSO than with the SM (figure 1(b)).In contrast, the correlation coefficient of the western pole of the IOD with SM is significant from JJA to OND, while that with JJA ENSO is insignificant except for ASO (figure 1(c)).After removing the SM (JJA ENSO) signal, the correlation coefficient of IOD with JJA ENSO (SM) is still significant from ASO (JJA) to OND, and the eastern (western) pole of IOD is only significantly correlated with the SM (JJA ENSO) (figures 1(d)-(f)).These results imply that there is a closer relation of eastern and western pole of the IOD to the SM and ENSO, respectively.
From the spatial pattern of the SST anomalies in the tropical Indian Ocean associated with the SM and JJA ENSO, we find that significant cold SST anomalies associated with the SM mainly exist in the tropical eastern Indian Ocean from JJA to SON based on the composite analyses of the ten positive IOD years (table S3), with weak warm SST anomalies in the tropical western Indian Ocean (figures S1(a) and (b)).Compared to the SM, the positive SST anomalies associated with JJA ENSO are clearly observed in the tropical western Indian Ocean, accompanied with weak negative SST anomalies in the tropical southeastern Indian Ocean, especially in SON (figures S1(c) and (d)).The tropical Indian Ocean SST anomalies in JJA and SON associated with both the SM and JJA ENSO are much stronger than those purely associated with either the SM or JJA ENSO (figures S1(e) and (f)), indicative of a synergistic effect of the SM and ENSO (Li et al 2019, Zhang et al 2019).The IOD in JJA intensified by the SM and JJA ENSO tends to contribute to the peak IOD in SON through strong self-persistence (figures S1(g) and (h)).These results support the findings that the SM and ENSO have remarkably different effects in the development and peak period of the IOD and its eastern and western poles (Zhang et al 2019).
Wang et al 2019).The mean percentage of SON IOD explained by the SM (∼33%) is relatively larger than that of JJA ENSO (∼29%), and this is also true for the SM-independent JJA ENSO (17%) and JJA ENSO-independent SM (∼13%) (figures 2(a) and (d)).Further analysis illustrates sharp distinctions in the eastern and western pole of the IOD.For the western pole of the IOD in SON, the contributions explained by the SM are nearly half of JJA ENSO, while for eastern pole of the IOD in SON, the contributions explained by the SM exceed three times of those by JJA ENSO, even reaching twelve times in November (figures 2(b) and (c)).Similar results can be obtained for the independent contributions of the SM and JJA ENSO (figures 2(e) and (f)).
The combined explained percentage of the SM and JJA ENSO are nearly ∼45%, larger than that of either factor alone (∼33% and ∼29%) but weaker than that of self-persistence (∼56%) of IOD in JJA (figure 2(d)).After removing the SM and JJA ENSO signals, the mean explained percentage of the selfpersistence of JJA IOD has been reduced by more than half (figure 2(d)).The independent explained percentage of the self-persistence of JJA IOD (both removing SM and JJA ENSO) is equivalent to that of the JJA ENSO-independent SM (SM-independent JJA ENSO) in the western (eastern) pole of SON IOD (figures 2(e) and (f)).Therefore, the effects of the preceding SM, ENSO, and self-persistence in JJA on SON IOD are not negligible, and these three factors can be used as predictors for the IOD, especially at peak season in SON.

Prediction of the IOD based on empirical and NMME models
Previous studies have revealed the relative roles of the SM and ENSO on the IOD development, especially in its the eastern and western poles (Zhang et al 2018(Zhang et al , 2019(Zhang et al , 2021)).The SM mainly affects the eastern pole of the IOD through the regional Hadley over the Western North Pacific and Maritime Continent, and the Walker circulation serves as the atmospheric bridge linking ENSO and western pole of the IOD (Zhang et al 2019).When the IOD events are purely linked to the SM, the anomalous regional Hadley circulation induced by the SM reinforces the eastern pole of IOD, but with little effect on the western pole of the IOD, which corresponds to the stronger eastern pole of the IOD.On the contrary, when the IOD events are only associated with ENSO, the significant Walker circulation is observed over the tropical Atlantic Ocean, but with casual signals over the tropical Pacific Ocean.This leads to the stronger western pole of the IOD.As the SM and ENSO co-occur, the eastern pole and western pole of the IOD are both intensified, leading to the stronger IOD events (Zhang et al 2019).Overall, the intensity of the eastern pole and western pole of the IOD are mainly affected by the SM and ENSO via atmospheric bridges, respectively.
Based on these possible physical connections with the preceding (3 months earlier) SM, ENSO (represented by N34), as well as the self-persistence (hereafter as PS) of the IOD, new physics-based empirical models (the SM + PS, N34 + PS, and SM + N34 + PS models) for the IOD are established.The predicted skill of the SM + N34 + PS model for the IOD is first assessed by comparison with single-factor model (the PS model) and double-factors models (the SM + PS and N34 + PS models).
These empirical models are constructed using a holdout method (section 2.2).In the development periods (JAS and ASO), the prediction skill of the SM + N34 + PS model is nearly equivalent to that from the single-factor model (PS) and double-factors models (the N34 + PS and SM + PS), and the former model outperforms largely the latter models at the peak (SON) and decay (OND) seasons (figure 3 b)).Moreover, the declining rate of the SM + N34 + PS model is lowest with a value of ∼12% at the target seasons compared to the single-factor model (PS) and double-factors models (the N34 + PS and SM + PS) (figure 3(a)).These results indicate that the SM + N34 + PS model has higher prediction skill for the IOD relative to singleor double-factors models.
For the western pole of the IOD, the N34 + PS and SM + N34 + PS models perform better with high correlation coefficient and low RMSE owing to involving ENSO signals (especially after ASO), whereas the PS and SM + PS models show a sharp drop in terms of correlation coefficient and RMSE due to relatively poor persistence of SST in the tropical western Indian Ocean (figures 3(c) and (d)).On contrary, these four models show equivalent prediction skill in predicting the eastern pole of the IOD due to the strong self-persistence of SST in the tropical eastern Indian Ocean (figures 3(e) and (f)).It is noted that the PS and SM + PS models show relative higher prediction skill than the N34 + PS and SM + N34 + PS models at the decay season in OND, suggesting that the ENSO may be conducive to the decay of the eastern pole of the IOD (figures 3(e) and (f)).
The significance in the improvement between the pair models among the SM + N34 + PS model and PS, N34 + PS, and SM + PS models (section S2 and figure S2).Compared to the PS model, the improvement of the SM + PS, N34 + PS, and SM + N34 + PS models is significant for the IOD and its western pole during SON and OND (figure S2).For the eastern pole of the IOD, the two-and three-factors models are significant relative to the PS model besides the N34 + PS in SON, while the reversed results occur in OND (figure S2).This is because the persistence in the eastern pole of the IOD in SON is partially explained by the SM and ENSO may play a damping role in the IOD decay phase during OND.These results further verify the strikingly distinct roles of the SM and ENSO in predicting the IOD, especially in its eastern and western poles.
The NMME system has been widely used to assess the predictability of the IOD (Zhao et al 2019, 2020, Ling et al 2022, Lu et al 2022).Model predictable skills for the IOD are compared for the SM + N34 + PS model and 12 NMME models.The MME (averaged 12 NMME models) forecast exhibits relatively superior skill in predicting the IOD than most individual model in terms of both correlation coefficient and RMSE (figure 4).The IOD predicted by the SM + N34 + PS model is superior to that predicted by the MME in the development and peak phases of the IOD from JAS to SON (figure 4).
In fact, the SM is more important in the eastern pole of the IOD and ENSO is more important in the western pole of the IOD (Zhang et al 2019).Thus, we reconstruct a new empirical model (hereafter as RCmodel) in which the IOD is obtained as the difference between the western pole predicted by N34 + PS model and eastern pole predicted by SM + PS model (section 2.2).The robust stability of this RC-model in predication performance is demonstrated by using leaving-one-out cross-validation (figure S3).This RC-model has the highest correlation coefficient and lowest RMSE, improving the prediction skill of the IOD at the development and peak seasons from JAS to SON (figure 4).The correlation coefficient (∼0.86) and RMSE (∼0.24 • C) between the RC-model and observations for the culminated IOD at a lead time of 3 months is nearly equivalent to that predicted by the current machine learning methods (Ratnam et al 2020, Liu et al 2021, Ling et al 2022), demonstrating the advantage of the RC-model relative to the SM + N34 + PS model and MME.However, the MME is slightly better than the empirical model in the performance of the decay phase in OND (figure 4).One of the reasons for the low prediction skill in OND for the SM + N34 + PS model is because the early winter is a transitional period for the most IOD events with the lowest signal-to-noise ratio (Zhao et al 2020).
To further document the skills for each individual IOD event, we use one standard deviation threshold to categorize the observations, RC-model, and dynamics model forecasts.The hit rate and the false alarm rate for the RC-model forecasts are shown in figure 5.The RC-model forecast performs better in terms of hit rate for positive culminated IOD in SON, much higher than that in MME and half of dynamical models (figure 5).By contrast, the hit Figure 5. Hit rate for (dashed lines) RC-model, each dynamics models, and MME forecasts of the (orange dots) positive culminated IOD events, (blue dots) negative culminated IOD events, and (green crosses) false alarm rate for both positive and negative culminated IOD events in SON that exceed 1 standard deviation.Dashed orange, blue, and green lines in are the frequency that use RC-model forcing of occurrence of positive, negative, and neutral culminated events, respectively.rate for negative culminated IOD of MME is equivalent to the RC-model though some dynamical models (CanSIPSv2, CMC1-CanCM3, and GFDL-CM2p1-aer04) outperform slightly (figure 5).Moreover, the hit rate for negative culminated IOD is lower than that for positive culminated IOD in both the RCmodel and dynamical models; that is to say, there is asymmetric feature: hit rates for positive culminated IOD events being in the top-ranked group but for negative culminated IOD events hit rates being in the poor performance group.Compared to the hit rate, the false alarm rate of the MME performs best in all individual dynamical models, much better than that in the RC-model forecast (figure 5).Overall, these results suggest the advantage of the RCmodel in predicting the IOD in SON at 3 month lead, which has potential value of operational applications for Climate Prediction Department.

Discussion and conclusions
Some extreme weather and climate events and relevant strong socioeconomic impacts are attributed to the IOD, and the prediction of the IOD is a challenging scientific issue since it was discovered.Previous studies reported that the culminated IOD is significantly correlated with both the SM and ENSO three months earlier, and the joint explained percentage of the preceding (3 months earlier) SM and JJA ENSO is nearly 20% higher than that of either factor alone.Moreover, the SM and ENSO mainly contribute to the eastern and western pole of the IOD, respectively.Therefore, the preceding (3 months earlier) SM and ENSO can be used as the crucial predictors for the culminated IOD beyond persistence.Here, we develop a multi-factor empirical model based on the preceding SM, ENSO as well as the self-persistence to predict the IOD events during the developing and peaking seasons.
The western pole of the IOD is mostly impacted by the ENSO and the eastern pole of the IOD is mainly dominated by SM (Zhang et al 2018(Zhang et al , 2019(Zhang et al , 2021)).Thus, a new RC-model is defined as the western pole predicted by N34 + PS model minus the eastern pole predicted by SM + PS model.This RC-model exhibits a highest skill in predicting the culminated IOD with the high correlation coefficient (∼0.86) and low RMSE (∼0.24 • C) at a 3 month lead time, superior to the single-and multi-factor empirical models (PS, N34 + PS, SM + PS, and SM + N34 + PS).Moreover, this RC-model shows an advantage relative to the average skill level of dynamical NMME models, with a higher hit rate for the positive culminated IOD.
The regression method used in this study may be either simultaneous or at some fixed lag time due to the diversity of ENSO in the amplitudes, temporal evolution, and spatial patterns (Capotondi et al 2015, Zhao et al 2021), and this leads to the influence of preceding ENSO signals on the culminated IOD may be not completely removed.Actually, the spring ENSO signals have the bigger influence on the relationship between the JJA ENSO and SON IOD than the preceding winter ENSO signals (figures S4(a)-(h)).However, there remains a significant dipole structure associated with JJA ENSO after removal of the preceding spring ENSO (figures S4(i)).These results suggest the significant influence of preceding summer ENSO on the following autumn IOD, while it is not neglected the delayed influence of the preceding spring ENSO.Therefore, the contributions of the ENSO isolated with the preceding season signals to the culminated IOD should be investigated deeply, and the linear inverse model method may be a good tool to achieve this goal in the future (Zhao et al 2021).
Additionally, although the RC-model is demonstrated to be an efficient model for improved IOD prediction, the positive IOD events have been reported to be more predictable relative to the negative IOD events.During the prediction period of 1982-2018, the positive IOD events always coexist with El Niño (1982,1985,1994,1997,2006,2015), while the four negative IOD events (1990,1992,1996,2005) occurs without La Niña.The intensity of these pure negative IOD events predicted by the RC-model is closer to the observation than that predicted by NMME models (figure S5), indicating the superior skill of the empirical model in predicting the IOD events without ENSO.The IOD events display asymmetric variations in the positive and negative phases (Hong et al 2008, Cai et al 2009), and the asymmetry of ENSO may have certain contributions since the linear model transfers the asymmetry of the ENSO forcing to the IOD directly (Zhao et al 2020).Therefore, more effects should be made to study the asymmetry of the IOD so as to improve the prediction skill of IOD in both the statistical and dynamical models.

Figure 1 .
Figure 1.Relationships of the South China Sea summer monsoon (SM) and El Niño-Southern Oscillation (N34) during boreal summer (June-July-August, JJA) with the seasonal mean Indian Ocean dipole (IOD) index from JJA to OND (October-November-December).(a) For IOD index, (b) for eastern pole of the IOD, and (c) western pole of the IOD.(d) As (a), but for partial correlations between the SM (N34) and IOD after removing JJA N34 (SM) signals.(e)-(f) As (a), but for western and eastern poles of the IOD.Black dots in (a)-(f) indicates the correlation (partial correlation) coefficients beyond 99% confidence level, respectively.

Figure 3 .
Figure 3. (a) Temporal correlation and (b) root mean square error (RMSE, • C) between predictions and observations during 1982-2018 for the IOD.The PS model (green line with dots), N34 + PS model (blue line with dots), SM + PS model (light blue line with dots), and SM + N34 + PS model (orange thick line with dots).(c)-(f) Same as (a), (b) but for but for western pole and eastern pole of the IOD.
(a)).For the target season, the culminated IOD in SON predicted by the SM + N34 + PS model exhibits a highest correlation (∼0.83) and lowest root mean square error (RMSE, ∼0.27 • C), superior to the double-factors N34 + PS model (correlation coefficient of 0.8, RMSE of 0.29 • C), SM + PS model (correlation coefficient of 0.76, RMSE of 0.32 • C), and PS model (correlation coefficient of 0.7, RMSE of 0.35 • C) (figures 3(a) and (

Figure 4 .
Figure 4. (a) Temporal correlation and (b) RMSE ( • C) between predictions and observations for the peaking IOD in SON from 1982 to 2018.Each line represents one model.12 hindcast models (thin dashed lines with circles), the SM + N34 + PS model (orange thick line with dots), the RC-model (reconstructed by the difference between the western pole predicted by N34 + PS model and eastern pole predicted by SM + PS), and the MME (black thick line with dots) averaged in 12 hindcast models are employed.
Shi et al 2012, Liu et al 2017, Doi et al 2020, Zhao et al 2020) had reported the predictive skill of the IOD based on the IOD mode index, which is defined as the area-averaged SST anomalies in the western Indian Ocean (50 • -70 • E, 10 • S-10 • N) minus those in the eastern Indian Ocean (90 • -110 • E, 10