1. Introduction
The Indian Ocean dipole mode (IOD) is a prominent air–sea coupled phenomenon over the tropical Indian Ocean (TIO), characterized by the opposite sea surface temperature anomaly (SSTA) between the southeastern and western Indian Ocean (Saji et al. 1999). The IOD usually has strong seasonality, which tends to develop in boreal summer, peak in autumn, and decay rapidly in winter. It can significantly modulate atmospheric and oceanic circulation, inducing climate anomalies not only in Indian Ocean rim countries (Ashok et al. 2001; Behera et al. 2005; Cai et al. 2011), but also in remote regions (Saji and Yamagata 2003; Behera et al. 2013).
Seasonal forecasts, including IOD predictions, are typically made by initializing coupled general climate models (CGCMs) with the observed atmospheric and oceanic state (Liu et al. 2016; Wu and Tang 2019). Both model and initialization improvements have enhanced seasonal forecasting skills (Shi et al. 2012; Doi et al. 2017). However, there are still challenges to IOD predictions using CGCMs. For example, remarkable IOD-like sea surface temperature (SST) bias commonly exists in CGCMs during boreal summer and autumn (Li et al. 2015). In the initialization process, the possible initialization shock may arise from the imbalance of the model’s atmosphere and ocean components, degrading the prediction skills. Meanwhile, such an assimilation-initialized forecasting method requires considerable computational resources and can only be conducted by a few large operational forecasting centers. Hindcast experiments, which are used for seasonal prediction studies, are generally available only after 1980 because of resource limitations (Kirtman et al. 2014). This restricts important examinations, such as that of decadal variations in seasonal prediction skills, which require a much longer record of hindcasts from earlier periods.
Analog forecasting (AF) is another method with a long history in weather and climate forecasting (Toth 1989; Gong et al. 2016; Ding et al. 2018; Wang et al. 2020; Shin et al. 2020). It relies on the assumption that adequately similar climate regimes will have similar climate pathways for some duration (Van Den Dool 1989). Thus, the AF method aims to find the best-matched analogs to the observed initial state in a large library dataset. The subsequent evolution of these analogs yields the forecast. For weather forecasting, a library dataset is typically generated from observations, so it can significantly reduce computing costs. However, the observation-based AF method has an apparent disadvantage in that it is only suitable for events with fewer degrees of freedom. For climate forecasting, reliable observations are too short for library datasets. Ding et al. (2018) proposed a model-based analog forecast (MAF) method that utilized a long-term CGCM control run as the library dataset to predict the tropical Indo-Pacific SSTA. Unlike the assimilation-initialized method, MAF’s initialization is within the model’s phase space and the subsequent development of model analogs is the prediction, resulting in no initialization shock. They demonstrated that the MAF method could provide prediction skills comparable to the assimilation-initialized prediction of state-of-the-art dynamical models, but with much more computational effectiveness (Ding et al. 2019).
Although previous works have highlighted the potential of the MAF method in seasonal predictions, most have only focused on El Niño–Southern Oscillation (ENSO; Ding et al. 2018, 2019; Wang et al. 2020; Shin et al. 2020). In this study, we apply the MAF technique for IOD seasonal forecasts, which has not yet been studied. The hypothesis is that the skillful IOD predictions can be expected by MAF through well selected optimal domain and external forcing. The IOD could be influenced by both variabilities over the TIO region and that from the tropical Pacific (Behera et al. 2006; Yang et al. 2015). Thus, we first explore the impact of TIO and tropical Pacific on the IOD prediction, respectively. Then the role of external forcings is further investigated, since it was reported there is a notable warming trend over the TIO region (Ding et al. 2019; Wang et al. 2020). To verify the hypothesis, an ensemble hindcast of TIO SST for 1958–2014 is conducted using 20 CGCMs available through the sixth phase of the Coupled Model Intercomparison Project (CMIP6; Eyring et al. 2016), from which the IOD prediction skill and its features are in details examined.
2. Methods and data
a. MAF method
The analog domain is another important factor for MAF predictions, as denoted by the number N in Eq. (1). In this study, we selected two different regions, the TIO (20°S–20°N, 40°–110°E) and the tropical Indo-Pacific (20°S–20°N, 40°E–90°W), as the basic domains to define the analog criteria. This is because there is still controversy about the physical nature of IOD variations. Some studies argue that the IOD is an intrinsic mode of the TIO region (Saji et al. 1999; Behera et al. 2006), while others emphasize that IOD events can be initiated by ENSO (Yang et al. 2015).
Long-term trends induced by externally forced variability, such as greenhouse gases, aerosols, and other radiative forcings, also affect seasonal prediction skills. It is indicated that including these trends could significantly improve SST predictions over the TIO region and northwestern tropical Pacific (Knutson et al. 2014; Ding et al. 2019). As the preindustrial simulations in CMIP6 retain only the model’s internal climate variability, the derived MAF predictions contain only the internal variability of the climate system.
b. Model and observational dataset
In this study, we used preindustrial control runs from 20 CMIP6 models (Eyring et al. 2016; Table 1). Analyses were based on monthly mean SST and sea surface height (SSH), and for each model, only the last 300 years of the simulations were used. The data were concatenated to a 6000-yr-long multimodel time series, which was used as the library dataset for analog selections. The data of the CMIP6 preindustrial simulations were interpolated on a common 2° × 2° resolution grid. Monthly anomalies were calculated by subtracting the monthly climatology of each model, meaning that the forecasts had their mean biases removed by construction. Surface temperatures from historical simulations of these 20 CMIP6 models were used to estimate externally forced signals between 1958 and 2014 (Table 1).
Preindustrial and historical simulations used in the CMIP6 ensemble.
For comparison, we analyzed SST in an ensemble hindcast product of seven models from the North American Multimodel Ensemble (NMME) phase I (Kirtman et al. 2014; Table 2), which is available at https://www.cpc.ncep.noaa.gov/products/NMME/. The NMME is a multimodel forecasting system that combines state-of-the-art coupled models from North American climate prediction communities. Each model performed assimilated–initialized prediction for each calendar month between 1982 and 2010, with an ensemble size ranging from 6 to 24, as shown in Table 1. For consistency, this study used the ensemble prediction of up to a 6-month lead. The predicted SSTA was formulated with respect to the seasonal cycles of the individual models.
Model used in the NMME, phase I.
The observed monthly mean SST and SSH during 1958–2014 were also used, with SST data from the Met Office Hadley Centre’s Sea Ice and Sea Surface Temperature dataset (HadISST; Rayner et al. 2003) and SSH from the European Centre for Medium-Range Weather Forecasts Ocean Reanalysis System 5 dataset (Balmaseda et al. 2013). These observations were utilized to construct target states in the MAF method and hindcast verification. The IOD index (DMI) was defined by the SSTA difference between the western Indian Ocean (10°S–10°N, 50°–70°E) and the southeastern Indian Ocean (10°S–0°, 90°–110°E).
3. Impacts of domain of analog criteria
Following the MAF method introduced in section 2, we first analyzed the domain selection in the MAF of the IOD. Here, we compared the results based on the TIO region (20°S–20°N, 40°–110°E) and Indo-Pacific region (20°S–20°N, 40°E–90°W) as the domain for the analog selection.
First, we examined the actual prediction skill of the predicted TIO SSTA using these two criteria. Figures 1a–c show the anomaly correlation coefficient (ACC) for the predicted and observed SSTA during 1958–2014 at 1-, 3-, and 6-month leads, using the TIO as the selected domain in the MAF method. Figures 1d–f present the same information as Figs. 1a–c but using the Indo-Pacific region as the initial field. The MAF method could produce skillful predictions (correlation > 0.5) over a large part of the TIO with up to 6-month lead times. The equatorial and southwestern Indian Ocean are characterized by high correlation skills, where ocean dynamics significantly affect changes in SST (Xie et al. 2002; Wyrtki 1973). The SST prediction skill was even higher when the TIO region was used, compared to that using the Indo-Pacific region as the analog criteria, especially at short leads. At a 1-month lead, the ACC over the southwest and equatorial IO regions was above 0.8 in Fig. 1a, but only 0.7 as shown in Fig. 1d. The correlation differences were more pronounced over the southeastern Indian Ocean region, reaching 0.2. Although many studies have reported that tropical Indian Ocean SST could be influenced by the tropical Pacific (Annamalai et al. 2003; Yang et al. 2015), there is a significantly lead–lag correlation between them (Behera et al. 2006). When the whole tropical Indo-Pacific region is selected as the MAF criteria, it will underestimate the role of the TIO region. This result indicates that an extended region could introduce some disturbances in the MAF prediction method to decrease the prediction skill, especially at short leads. As lead time increased, the differences in SSTA skills decreased. At the 3- and 6-month leads, the ACCs were comparable over most TIO regions for both criteria (Figs. 1b,c,e,f). This suggests as lead time increases, the Pacific variability may pose more impact on TIO SSTA predictions, which is consistent with previous studies (Zhao et al. 2020).
We further evaluated the IOD prediction skill using these two regions as analog criteria. Figure 2 shows the ACC between the observed and predicted IOD indices and the SSTA in the eastern and western poles (referred to as the EIO and WIO indices, respectively). In general, the EIO and WIO indices were more predictable than the DMI. When the TIO region was used for analog selection, the correlation skill for DMI dropped rapidly from 0.95 to approximately 0.3 for the 6-month lead, while the prediction of EIO dropped more slowly from 0.95 to 0.55 (Fig. 2a). The skill of WIO was better than that of EIO. At the 0–6-month lead times, the correlation skill of WIO was well above 0.7. Even though the prediction skills of WIO and EIO were relatively high, the IOD itself had much lower prediction skills. This is consistent with previous studies (Song et al. 2008; Liu et al. 2016), most of which attributed this paradox to the strong seasonality in TIO variability. Specifically, IOD events occur during boreal summer and autumn, while basinwide warming following an El Niño event dominates the rest of the year (Saji et al. 1999; Saji and Yamagata 2003). Previous studies have indicated that predictions of the WIO and EIO are also related to the basinwide warming mode (referred to as IOBM), which provides high skills for the two poles other than the IOD seasons (Zhu et al. 2015).
The predictions of the three indices exhibited different changes when using the Indo-Pacific region as the domain for the analog criteria (Fig. 2b). A bootstrap test was conducted to identify the significance of differences between ACC of each index in Figs. 2a and 2b. Compared with the results in Fig. 2a, the skills of the WIO were slightly higher for the long leads, indicating the Pacific variability influences the western IO region. This is consistent with the characteristics of SSTA prediction skills shown in Fig. 1. However, the EIO and DMI skills were significantly lower when the Indo-Pacific was used as the analog domain. Specifically, in Fig. 2a, the ACC of the EIO index reaches 0.95 at the 0-month lead and drops below 0.55 at the 6-month lead. The DMI showed skillful predictions for a 3-month lead. On the other hand, when the entire tropical Indo-Pacific region was used, the ACC of EIO was approximately 0.85 at the initial month, and decreased to 0.5 at about 5–6-month lead. The ACC of DMI was only 0.75 at the 0-month lead and dropped below 0.5 at the 2-month lead (Fig. 2b). As we focus on IOD predictions in this study, hereafter, we use the TIO region as the domain for analog criteria until stated otherwise.
4. Impacts of externally forced trends
Long-term trends induced from externally forced variability, such as greenhouse gases, aerosols, and other radiative forcings, could also impact seasonal prediction skills (Ding et al. 2019). In this section, we analyze how the externally forced trends impact the prediction skills of the IOD from 1958 to 2014.
Figures 3d–f show the hindcast skill of the SSTA at 1-, 3-, and 6-month lead times of internal variability alone, i.e., excluding the projected externally forced component. We observed a lower prediction skill compared with that of the corresponding hindcast with external forcings in Figs. 3a–c. At a 1-month lead, the MAF predictions exhibited correlations ranging between 0.6 and 0.7 (Fig. 3d), with a correlation decrease of approximately 0.2 compared to that including the external component in Fig. 3a. As the lead time increased, prediction skills decreased sharply. At a 3-month lead, the MAF method could only provide skillful SST predictions over the northern and southwestern TIO (Fig. 3e). At a 6-month lead, the correlation differences were more pronounced, reaching 0.4 over most TIO region (Figs. 3c,f). This is consistent with previous studies, which showed that including external forcings could significantly improve SST predictions over the region with a pronounced warming trend (Ding et al. 2019; Wang et al. 2020).
We also evaluated the actual prediction skill of the IOD, EIO, and WIO indices without external forcings. Figure 4b shows the ACC of the three indices as a function of the lead time, indicating that the correlation skills for the EIO and WIO indices dropped dramatically with increasing lead times. For both the EIO and WIO indices, the MAF prediction could provide skillful predictions only 4 months ahead without externally forced trends, which is significantly less predictable than their counterpart with trends in Fig. 4a. However, the prediction skill for DMI remained almost unchanged (Figs. 4a,b), and the ACC differences are insignificant. This suggests that the externally forced component significantly improves the model–analog SST forecast skill over the TIO region, but may only do so for the basin-warming mode and not for the dipole mode.
To explore the impacts of externally forced trends on the seasonality of the prediction skills in the IOD, EIO, and WIO indices, Fig. 5 shows the correlation skill for the MAF forecast as functions of the initial and target months with and without external forced components. For indices with trends, the prediction skills featured strong seasonality (Figs. 5a–c). Specifically, the DMI forecast generally showed high prediction skill when the prediction target was in the boreal autumn but had low skill during other seasons. The skillful predictions with the longest lead times were those initialized in June and July. This is likely because the developmental phase of the IOD usually begins in the boreal summer. The forecast then rapidly degraded in the following winter, which is known as the winter predictability barrier (WPB; Wajsowicz 2004; Ding and Li 2012). For the WIO and EIO indices, the prediction skill had a weak but discernible seasonality (Figs. 5b,c). The EIO featured high skill when targeted at boreal spring and autumn. The WIO showed good skill in all seasons, with the highest skill when targeted in August and September. Compared with the DMI prediction, the relatively high prediction skill in the WIO and EIO can be mostly attributed to the IOBM, which provides high skills other than the IOD peak season of the boreal autumn.
The external forcings had very different impacts on the prediction skills for these three indices (Figs. 5d–f). In particular, it only had a limited influence on IOD prediction, as shown in Figs. 5a and 5d. The differences between IOD predictions with and without trends were statistically insignificant (not shown). However, for the WIO and EIO indices, the external forcings largely improved the prediction skills, especially for long leads. Without external forcings, the EIO only exhibited high prediction skills in the boreal spring and autumn seasons and suffered low skills in the following winter (Fig. 5e). For the WIO, the prediction without trends presented skillful predictions only for 2–3-month leads for all seasons except the boreal spring (Fig. 5f). We also examined the trend component for all three indices. The estimated externally forced trends accounted for approximately 0.6°C for both EIO and WIO indices from 1958 to 2014, with the WIO slightly larger than the EIO index. The external forcings explain about 18% and 30% of the variance in EIO and WIO, respectively. This suggests a large potential for external trends in seasonal predictability in these regions. Moreover, the trend component could pose a more significant role in the WIO than the EIO index. However, the trend for the DMI was very low, at approximately 0.05°C for the period, as the SST trend was strongly in phase between the EIO and WIO regions. This is consistent with previous studies indicating that the warming trend in the WIO is generally comparable to that in the EIO region after the 1950s (Ihara et al. 2008). Notably, as the region with the largest warming trend during the study period, the external forcings had limited impacts on the prediction skills of the IOD itself. This suggests the importance of delineating the relationship between SSTA in the western and eastern poles over the long term considering the warming trend.
External forcings may impact the climatological ocean condition and then change the IOD characteristics. It has been reported that stronger positive events appeared after 1950 (Ihara et al. 2008). As global warming continues, the frequency of extreme positive IOD events may further increase in the future (Cai et al. 2018; An et al. 2022). Thus, external forcings may influence the IOD prediction in an indirect way. However, this is beyond the scope of this study and requires further investigation.
5. Decadal variations of IOD prediction skills
To explore the decadal variation of IOD prediction skills, the ACC for each calendar month at a 3-month lead is shown in Fig. 6, with an 11-yr running window. Additionally, we tried 15- and 21-yr running windows, but all the results exhibited significant decadal-to-decadal variations (not shown). The early 2000s period of reduced skill was evident but not unique, as skill was also low before 1985. Conversely, high skill was evident in the late 1980s and the 1990s, in which significant prediction skill was observed even in boreal winter. Decadal variations in prediction skill have also been noted in previous studies using climate models (Lim et al. 2017; Song et al. 2018). Additionally, no significant trend in skills was observed over the entire study period.
There are some works to explore the source of IOD prediction skills. Among them are the two most important hypotheses. First, it is dominated by the amplitude of IOD itself. It is indicated that some strong IOD events could be predicted at longer leads (Song et al. 2008; Liu et al. 2016). Second, the IOD prediction skills could be influenced by the ENSO. IOD events are reportedly more predictable when they cooccur with ENSO events (Yang et al. 2015; Tanizaki et al. 2017). Zhao et al. (2020) improved IOD prediction by seasonally modulating ENSO forcing together with a more realistic ENSO–IOD link. Hence, we further investigated the connection of the decadal transition of the IOD prediction skill to the IOD amplitude and the ENSO–IOD link.
We first calculated the IOD strength by the standard deviation of DMI at each calendar month (Fig. 6b). It shows that the decadal variations of the IOD strength have good relationships with that of the IOD predictions skills, with high values during late 1980 and 1990s and low values during early 2000s and before 1985. This consists with previous studies, indicating that stronger IOD signals lead to more predictable information (Song et al. 2022). The decadal variation in the ENSO–IOD relationship is shown in Fig. 6c, using a simultaneous correlation of the observed Niño-3.4 index and DMI with an 11-yr running window. ENSO and IOD displayed the strongest link in the late 1980s and the 1990s, while showing relatively weak coupling before 1970 and after the early 2000s (Yuan and Li 2008; Ham et al. 2017; Lim et al. 2017). A marked correspondence was observed between the modulation of IOD prediction skill and the ENSO–IOD link after the late 1980s, such that higher and lower skill was coincident with stronger and weaker ENSO–IOD coupling, respectively. But before 1985, the IOD prediction skills are not significantly related to the ENSO–IOD link. Overall, the IOD strength, rather than the ENSO–IOD relation, is the main factor influencing the decadal variation of IOD prediction skills. This may be because the IOD generally showed skillful predictions when the prediction was initialized in the boreal summer and targeted in autumn (Fig. 6a). The IOD events usually onset in May and start to develop with established Bjerknes feedback in summer. The stronger signals of the strong IOD events in summer will provide enhanced predictability and vice versa (Song et al. 2022). On the other hand, the ENSO may pose limited influences in determining IOD prediction skills, owing to the dominant role of the local Bjerknes feedback in the TIO region (Luo et al. 2010; Song et al. 2022). Yet, it could not exclude that a few strong ENSO events favor the IOD evolution during summer (Luo et al. 2010) and may also result in enhanced IOD predictions.
6. Comparison with the assimilated–initialized hindcast
Figure 7 shows the IOD prediction skill from the MAF hindcast and the state-of-the-art model dataset of NMME. As most NMME models only provide the hindcast from 1982 to 2010 due to computational limitations, we also selected the MAF hindcast in the same period, as shown in Fig. 7. In general, the prediction skill with MAF showed a significant improvement relative to that in the single NMME model. As defined by a correlation skill of 0.5, all NMME models could provide skillful IOD prediction at only 2–3 months, while the MAF hindcast showed similar skillful predictions up to a 4-month lead. According to the bootstrap results, the MAF hindcast was significantly superior to the multimodel ensemble (MME) of the NMME hindcast, with an ACC improvement of approximately 0.1 at all leads.
7. Summary and discussion
The IOD is one of the most prominent interannual variabilities over the tropical region and plays a vital role in modulating the global climate. In this study, we explored the seasonal prediction skills of the IOD during 1958–2014 using 20 CMIP6 models. The MAF method, a statistical approach, was applied. The MAF method can forecast the observed target states based on long climate simulations, in which analogs are defined from model states that minimize the distance to the target states. The subsequent evolution of these model analogs provides a forecast ensemble. The MAF method shows significant potential for seasonal predictions of the ENSO; however, this has not been previously implied in IOD prediction studies (Ding et al. 2018, 2019, 2020; Wang et al. 2020). Here, we evaluated the impacts of domain selection and externally forced trends on IOD predictions and explored decadal variations in IOD prediction skills.
The optimal field of analog criteria should be determined by the prediction target in the MAF method. Previous studies have indicated that for ENSO predictions, it is reasonable to choose the tropical Indo-Pacific region as the analog domain of the MAF method (Ding et al. 2018, 2019, 2020; Wang et al. 2020). As the IOD variability could be influenced by the tropical Pacific climate (Annamalai et al. 2003; Yang et al. 2015), we checked the prediction skill of the IOD using the tropical Indo-Pacific as the domain of the analog criteria. We also explored IOD skills using only the TIO as the analog domain. The results suggest that the TIO region is more suitable for IOD predictions than the entire tropical Indo-Pacific region. The IOD prediction skill is much lower if the entire tropical Indo-Pacific region is selected, especially for short-term leads. This implies that a large range of the analog domain cannot only provide more information but also introduce noise in the MAF method. Also, previous studies reveal that ENSO lags the IOD by about 3 months (Behera et al. 2006); thus, when the whole tropical Indo-Pacific region is selected at the same time, it will underestimate the role of the TIO region, leading to a weak and rapid decline in IOD skills. In conclusion, as the IOD precursor signals are primarily located in the TIO, this area is suitable as the analog domain for IOD prediction in the MAF method.
Previous studies have shown that, with the inclusion of projected external forcings, the MAF hindcast could significantly improve the prediction skills of the TIO SST (Ding et al. 2019; Wang et al. 2020). Given the large trends in the boundary condition, such as greenhouse gas and aerosols, these likely also provide a significant source of predictability. Our results indicate that including the external forcing component enhances the prediction skills of the east and west poles of the IOD. The MAF hindcast could provide skillful predictions corresponding to longer than 6- and 4-month leads with and without external forcing components for these two indices, respectively. This may be because the externally forced trends represent a substantial component of the SST variability, which accounts for 18% and 30% of SST variance over the EIO and WIO regions, respectively. The trends hence can provide a significant amount of skill. However, because the externally forced trends are mainly in phase in both poles after 1950 (Ihara et al. 2008), they could only pose a limited influence on the DMI prediction during this period.
Our results support the hypothesis that skillful IOD predictions can be achieved by the MAF method. When the TIO region is selected, the MAF method can provide significantly improved predictions for the IOD forecast relative to state-of-the-art dynamical models. Specifically, the assimilated–initialized dynamic models could provide skillful DMI prediction at only 2–3 months, while the MAF hindcast showed skillful predictions up to a 4-month lead. In addition, the DMI prediction skill would not change with or without external forcings. This suggests that we can determine the IOD skill of the openly accessible CMIP6 model data without running them as traditional assimilation-initialized forecast models.
IOD prediction skills exhibited significant decadal variations, with low prediction skills after the early 2000s and before 1985. Conversely, high skill levels were evident during the late 1980s and 1990s. Further analyses indicate that the decadal variations in the IOD prediction skill are primarily due to the decadal transition of the IOD strength. It occurs because the stronger signals associated with the strong IOD events will provide more predictable information, leading to enhanced predictability. There are also some works that emphasize the decadal transition of IOD predictability is dominated by the ENSO–IOD link rather than IOD strength (Lim et al. 2017; Song et al. 2018). However, Lim et al. (2017) only investigate the IOD predictability during 1985–2014, when it shares similar features with the ENSO–IOD link. In Song et al. (2018), the IOD hindcast is performed by a tropical intermediate coupled model, in which some important processes may be missing.
The MAF method can make seasonal IOD forecasts by taking advantage of freely available, large model simulation databases. This suggests that the MAF technique is a good alternative for IOD prediction studies, but requires significantly less computational resources. Our findings support our hypothesis and we are able to confidently conclude that the MAF technique is effective in predicting the IOD and can provide valuable insights for seasonal prediction researchers.
Acknowledgments.
This work is jointly supported by the National Natural Science Foundation of China (42176028), the Fundamental Research Funds for the Central Universities, Hohai University (B210201021), and the National Natural Science Foundation of China (41530961).
Data availability statement.
The CMIP6 data, the NMME hindcasts, and the reanalysis data used in this study are all openly available at locations cited in the reference section.
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