Introduction

The Indian Ocean Dipole (IOD) is a primary interannual climate variability mode in the tropical Indian Ocean, which has a peak phase during the fall season (for convenience, the seasons in this study follow those in the Northern Hemisphere)1,2,3,4. During the positive phase, the southeastern tropical Indian Ocean sea surface temperature (SST) becomes colder, whereas the western tropical Indian Ocean SST becomes warmer than normal. The opposite pattern is observed during the negative phase5,6,7,8,9,10,11. Due to substantial climate impact of the IOD not only in neighboring countries but also in remote regions5,6,7,8,9, an in-depth understanding of IOD dynamics is crucial for precise long-term climate prediction and the effective mitigation of climate risks associated with IOD events.

Despite its complexity, the development mechanism of the IOD can be largely understood by categorizing its contributors into three parts: the internal feedback process, external forcing, and stochastic forcing. Internal feedback processes include Bjerknes feedback (involving winds, thermocline tilt, and SST)1,12, wind–evaporation–SST feedback

Results

Decadal modulation of observed IOD variability

To examine decadal variation in the IOD, the 30-year moving variance of the 3-month to 8-year bandpass-filtered Dipole Mode Index (DMI) was computed (Fig. 1a; see Methods). Abrupt intensification of the IOD variability was first observed after the mid-1940s and then again after the late-1970s. The maximum IOD variance during the 2000s was more than double the minimum IOD variance around the 1940s, indicating substantial decadal modulation of IOD variance. Although the absolute value of the IOD variance of each reanalysis dataset was somewhat different, the overall tendency of the interdecadal variation of the IOD variance was similar among the eight reanalysis datasets (Supplementary Fig. 1). Therefore, the results of this study are not dependent on the selected dataset.

Fig. 1: Decadal changes in IOD variability and parameters of the IOD model.
figure 1

a Timeseries of the centered 30-year moving variance [°C2] of the reanalysis DMI (black line) and the reconstructed DMI variance by using the IOD model (blue line) during 1900–2022. b The 30-year moving variance of the band-pass filtered and normalized DMI for each calendar month (shading). The peak month has a 30-year moving DMI variance and each year is indicated by the black curve. 30-year monthly moving timeseries of (c) dam** rate λm [month−1], (d) ENSO-forcing parameter βm [month−1], and (e) noise standard deviation σm [°C month−1] for the IOD model. The black contour lines are the zero contours.

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To analyze decadal modulation in the temporal evolution of the IOD, the 30-year moving variance of the DMI for each calendar month was computed, and the month with the maximum DMI variance was identified (Fig. 1b). Month with the strongest IOD variance is mostly observed in September, indicating a seasonal phase locking. Moreover, there are decadal fluctuations in a phase locking feature. The month with the strongest IOD variance was observed in August in the 1940s and in October in 1980s to 2000. Besides the peak phase change, the IOD variance in spring and summer has increased since the late-1970s (Supplementary Fig. 2a). This means that the variability of the IOD has been strengthened not only during fall season when IOD variability is strongest but also during spring to summer when IOD develops in recent decades, probably reflecting recent increased frequency of early developed IOD events32.

Decadal changes in parameters of the IOD model

To reveal the origins of the decadal modulation of IOD properties, we adopted a low-order IOD model, including parameters such as growth rate (λm; a dam** rate with an opposite sign), ENSO forcing (βm), and noise residual (σm) (please refer to the Method). Subsequently, we computed the parameters of the IOD model with a 30-year moving window, where the window was moved by one-year. To validating the performance of the model, we reconstructed the DMI using the IOD model in each window, where integration was performed with the real initial condition and repeated 1000 times by inputting another random noise. By doing so, we reproduced a 30-year moving variance time series by concatenating the averages of the variances calculated for each of the 1000 noise ensembles.

The correlation coefficient between the observed and reproduced 30-year moving DMI variance was 0.95, which was statistically significant at a 99% confidence level by Student’s t-test with an effective degree of freedom (DOF) of 5.9, wherein the root mean squared error (RMSE) was 0.09 (Fig. 1a). Moreover, the 30-year moving variance of the reconstructed DMI for each calendar month was similar to that of the original data with statistical significance (Supplementary Fig. 3). Therefore, we conclude that the IOD model is suitable for investigating the decadal variations of the IOD variance on monthly timescales, despite some biases which arise from unconsidered factors in the IOD model, such as the influence of the Atlantic Ocean or subtropical oceans, as well as nonlinear processes22.

Strong decadal changes in each parameter are shown in Fig. 1c–e. For ease of interpretation, the original value was subtracted from climatology to assess the extent of the increase or decrease (Supplementary Fig. 2). The growth rate λm during summer reached a minimum around the 1940s and a maximum around the 1960s, increasing by approximately 110% compared to the 1940s. Meanwhile, λm in January-February-March (JFM), when the IOD damps, shows a pronounced increase since the late-1970s by about 113% and even positive values for some decades (Fig. 1c). Comprehensively, the minimum λm in JJA in the 1940s and the pronounced increase of the λm in JFM after the late-1970s correspond to the weak IOD amplitude in the 1940s and the strong increasing trend of the IOD amplitude since the late-1970s, respectively (Fig. 1a).

The ENSO parameter (βm) showed an annual cycle with a peak in April before the 1940s, and then its overall amplitude tends to decrease until 1960s. Afterwards, the amplitude of βm is recovered. Interestingly, its peak moved from May to July between 1960s and 1980s as widening (Fig. 1d). That is, duration in which ENSO influences the IOD has been increased in the late twentieth century. However, unlike the significant relationship between growth rate λm and DMI variance (correlation coefficient of 0.77 with DOF = 10.4, 99% confidence level), the relationship between ENSO parameter (βm) and the DMI variance is insignificant (correlation coefficient of 0.38 with DOF = 5.7) on a yearly timescale.

On the other hand, the noise residual (σm), reflecting weather noise or other missing physics, also shows an annual cycle with a peak in June, especially between the 1950s and 1960s, probably related to the abrupt increase in DMI variability during that period (Fig. 1e).

Decadal changes in IOD variability

To quantify the factors responsible for the decadal changes in IOD variability, we performed sensitivity experiment using the IOD model. In this experiment, one of the three parameters (λm, βm, and σm) was held constant at its climatological mean value (1900–2022), while the other two parameters were varied. When the growth rate (λm) is maintained at its climatological mean, the correlation coefficient between the resulting 30-year moving DMI variance and the control experiment (i.e., all three parameters are time-varying) is 0.72 (DOF = 15.5, p-value = 0.002, RMS = 0.09). Likewise, when the ENSO parameter (βm) is held constant or when the noise forcing (σm) does, the corresponding correlation coefficients are 0.80 (DOF = 7.6, p-value = 0.02, RMS = 0.09) and 0.81 (DOF = 6.6, p-value = 0.04, RMS = 0.08), respectively. Hence, the primary factor responsible for the decadal modulations in IOD variability is identified as changes in the growth rate (λm), with changes in the ENSO (βm) and noise (σm) playing secondary roles (Fig. 2a).

Fig. 2: Each role of IOD model parameters in decadal changes of IOD variability.
figure 2

a The timeseries of centered 30-year moving variance of the reconstructed DMI obtained from the IOD model for the control experiment (black line; [°C2]), and one parameter experiment (colored lines; [°C2]). In control experiment, all parameters are time varying. In one parameter experiment, one of the three parameters (λm(red line), βm (blue line), and σm (purple line)) is kept a constant of its climatological-mean value. The correlation and RMSE between the 30-year moving DMI variance for the different reconstructions are shown as inserts. b Correlation coefficient for each calendar month in 30-year moving DMI variances between the control experiment and each constant parameter experiment. The dots in Fig. 2b indicate insignificant correlations at the 95% confidence level using a Student’s t test, and otherwise statistically significant. The effective degrees of freedom are calculated by each calendar month. c–e Shows the differences in 30-year moving monthly variances [°C2] between the control experiment and each constant parameter experiment for (c) λm, (d) βm, and (e) λJFM.

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To assess when and to what extent changes in each parameter influenced IOD variance, we examined the difference in DMI variances and the correlation between the control and sensitivity experiments by fixing a parameter (constant-parameter) (Fig. 2b–e). The correlation analysis between the control experiment and the constant-parameter experiment shows a statistically significant reduction from April to July when growth rate (λm) kept constant, whereas when ENSO parameter (βm) is fixed, the reduction of correlation is evident in October and November (Fig. 2b). This implies that temporal changes in the ENSO impact are a dominant factor influencing IOD variance in fall season. On the other hand, the time-varying growth rate (λm) acts to enhance IOD variance from spring to summer after the late-1970s (Fig. 2c). This effect becomes even stronger after the 2000s. The time-varying ENSO parameter (βm) causes the increased variance since the late-1960s, especially fall season (Fig. 2d). In comparison, the impact of noise (σm) is not as remarkable as that of growth rate (λm) and ENSO (βm) (Fig. 2b).

To quantify the relative role of each factor leading to the abrupt increase in DMI variance since the late-1970s, we compare DMI variance difference between before and after 1980 (1953–1978 (P1) versus 1980–2005 (P2)) of two experiments (constant either λm or βm). Note that noise (σm) is not associated with the abrupt increase after 1980. In the control experiment, the DMI variance increased by approximately 16% in P2 compared to P1 (Table 1). However, the constant λmexperiment captured only 7% of the abrupt increase in IOD variance. While in the constant βm experiment, DMI variance increased by 10%, capturing more than half the increase in the control experiment. Therefore, the observed abrupt increase in IOD variance since the late-1970s was due to both an increased growth rate (λm) and a strengthened ENSO effect (βm).

Table 1 Contribution of λm and βm to the increase in IOD variance after 1980
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IOD seasonal synchronization

In the previous section, we demonstrated that both the growth rate (λm) and the ENSO forcing (βm) have a dominate annual cycle. Consequently, our objective is to comprehend the temporal evolution of IOD and its decadal change, in association with their annual cycles. Here, we quantified the respective roles of the IOD growth rate and ENSO effect on decadal changes in IOD seasonal synchronization using the IOD model. As a first step, the growth rate (λm) is approximated using a sinusoid19:

$${\lambda }_{m}\, \approx \, {\lambda }_{0}+{\lambda }_{a}\,\cos ({\omega }_{a}t+{\varphi }_{l})$$
(1)

where φl is the phase of the annual cycle and \({\omega }_{a}=\frac{2\pi }{12}[mont{h}^{-1}]\) is the angular frequency of the annual cycle. Thus, growth rate (λm) is linearly separated into annual mean (λ0) and annual cycle parts (\({\lambda }_{a}\,\cos ({\omega }_{a}t+{\varphi }_{l})\)). We note that the decadal changes in the peak phase of DMI variance with modulated growth rate above were almost identical to those observed (Supplementary Fig. 4). Subsequently, two additional sensitivity experiments are conducted. In the first experiment, we removed the ENSO forcing term (βmE(t)) to explore its role, in which all other parameters remained time-varying, as in the control experiment. In the second experiment, meanwhile the phase of growth rate (λm(φl)) was fixed as its climatological value (1900–2022) to explore its role. This is because the IOD model does not properly reproduce the DMI without the growth rate term.

When ENSO forcing (βmE(t)) is set to zero in the IOD model, the peak phase of DMI variance in calendar months is shifted forward by 0.9 months since the late-1970s (Fig. 3). In contrast, when φl is fixed as a climatology for whole period, the peak timing of the reconstructed DMI variance remains unchanged until 1980s, and it is slightly delayed thereafter (Fig. 3). In other words, IOD events influenced by the ENSO reached their peak phases at a later time, whereas those independent of the ENSO attained their peak phases earlier. Therefore, our results suggest that an enhanced growth rate in winter resulted in earlier IOD growth, whereas the ENSO led to a delay in IOD growth after 1980s.

Fig. 3: Each role of IOD model parameters in decadal changes of IOD seasonal synchronization.
figure 3

Timeseries of DMI peak month obtained from the control experiment (black line), the constant φl experiment (red line), and the non-ENSO-forcing experiment (βmE(t); blue line). DMI peak month is determined over 30-year moving band by computing DMI variance for each calendar month for each band.

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Rapid growth of IOD starting from winter season

In the previous section, we showed that an enhanced growth rate (λm) is the main cause for the abrupt increase in IOD variance since the late-1970s, particularly in JFM (Figs. 1c, 2c). To further verify this finding, we divided the calendar year into four seasons, ranging from JFM to October–November–December (OND), and conducted additional sensitivity experiments. In these experiments, we maintained the growth rate (λm) for one specific season at its climatological-mean value (from 1900 to 2022), while allowing the growth rate for all other seasons to vary over time. All other parameters except λm were varying over time as in the control experiment. When the growth rate in JFM (λJFM) was kept constant at its climatological value, the IOD variance exhibited an increase during P1 period (1953–1978) and a decrease during P2 period (1980–2005) in all calendar months (Fig. 2e). It indicates that the decadal changes in λJFM are significant modulating IOD variance. On the other hands, when the growth rate was allowed to vary in each of the other seasons, only minor or opposite decadal changes in DMI variance were observed (Supplementary Fig. 5). A exception to this trend is noted in the growth rate in April-May-June season (AMJ), which has significantly contributed to an increase in IOD variance, but only since the 2000s (Supplementary Fig. 5). In summary, we confirm that the early IOD growth during the winter season plays a crucial role in the notable increase in IOD variance observed between P1 and P2 periods.

To get a better dynamical insight on the rapid growth of IOD events, especially in relation to the enhanced local feedback (i.e., λm) since the late-1970s, we analyzed the regression patterns of various physical variables associated with the IOD. We focused on comparing two distinct periods: 1953–1978 (P1) and 1980–2005 (P2) (Supplementary Fig. 6), in terms of the growing tendency of IOD during JFM, which was estimated by computing the difference in the regression pattern against the September–October–November (SON) DMI between April and January, using the forward Euler discretization method. The growing tendencies of tropical Indian Ocean SST, sea-level pressure (SLP), wind stress, and subsurface temperature anomalies with respect to the following autumn (SON) normalized DMI were calculated for each P1 and P2 periods, and their differences (P2–P1) (Fig. 4). In P1 period, the growing tendency pattern in SST resembled a negative IOD – like pattern, suggesting the limited IOD development (Fig. 4a). Conversely, in P2 period, a positive IOD – like pattern, inferring early development of IOD, was observed, characterized by warming in western IO and cooling in eastern IO, along with high SLP anomalies (gray contours) extending further westward and anomalous southeasterly winds (Fig. 4b). The emergence of anomalous SLP high associated with these anomalous southeasterly winds seems to linked to the subtropical IOD during the winter season (Fig. 4b), aligning with previous studies that have noted an increased connection between the IOD and the subtropical Indian Ocean since the late-twentieth century16,33. The difference in the growing tendency between P1 and P2 clearly demonstrates the enhanced IOD growth during the winter season (Fig. 4c).

Fig. 4: Winter mean changes associated with IOD variability for two decadal periods.
figure 4

a Difference between April and January regression map of SST (shading, [°C]), wind stress (vector, [N m−2]), sea level pressure anomalies (gray contours, 0.3 [hPa]), and subsurface temperature (5°S to 5°N) anomaly (shading, [°C]) against the September–October–November mean normalized DMI during P1 (1953–1978). (b) same as in (a) but for P2 (1980–2005). (c) difference between (b) and (a). Boxes in figure indicate the western and eastern pole of IOD.

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The IOD-related oceanic subsurface change also supports stronger IOD growing tendency in JFM. In P1 period, there was a weak subsurface cooling tendency observed in both the eastern and western IO (Fig. 4a). However, during P2 period, the strong subsurface warming in western IO and cooling in southeastern IO, along with easterly anomalies in surface winds were observed. This pattern resembles the anomalous subsurface temperature pattern observed during the positive IOD events, suggesting a significant increase in the growing tendency of IOD (Fig. 4b). Moreover, the zonal contrasting pattern in the growing tendency of sea surface height anomalies during P2 period is more pronounced compared to P1 period, consistently indicating the enhanced early growth of IOD during P2 period (Supplementary Fig. 7). Consequently, the increase in growing tendency of IOD during winter is evident not only at the surface but also in the subsurface ocean.

Mean state changes contributing to the rapid growth of IOD during winter

In previous section, we demonstrated that the increased growth rate in the late winter was a key factor in the recent decadal changes in IOD variability. Here, we investigate how the changes in the climatological mean state intensify the air-sea coupled feedback, which is linked to the early emergence of IOD during the winter season. In the following, we qualitatively assess the influence of the climate state changes, specifically between P1 and P2 periods, on air-sea coupled feedback, considering both thermodynamic and dynamic aspects.

The climatological mean SST in the tropical IO during the boreal winter season typically exceeds 28 °C (Fig. 5a), a threshold sufficient to induce convective instability. During the P2 period, the SST is observed to be higher in most areas of the tropical IO compared to the P1 period. As a result, the response of atmospheric convection, along with its corresponding variability to SST changes, is expected to be more pronounced, leading to an enhancement in air-sea coupling during P2 period. Additionally, there is a noticeable weakening of the westerly winter monsoon flow over the southeastern IO during P2 period, particularly off the coast of Sumatra (Fig. 5a, b). Typically, from a wind-evaporation-SST (WES) feedback perspective, when easterly (westerly) anomalies occur, the decrease (increase) in mean wind speed leads to reduced (increased) evaporation, resulting in anomalous warming (cooling) of SST. This implies that the feedback acts as a hindering factor in the development of the IOD. However, as the mean westerly weakens and occasionally shifts to easterlies (P2), it becomes an ineffective suppressing mechanism and may instead contribute to the growth of IOD during the winter season (Supplementary Fig. 8).

Fig. 5: Observed winter climatological mean changes over 1948–2022.
figure 5

a Climatological January-February-March (JFM) mean SST (contours) and surface winds (vectors) for whole available data periods (1948–2022), and differences in JFM-mean SST (color shading) between P1 and P2 periods (Unit: °C). b As in (a) except for climatological JFM-mean surface zonal winds (color shading) and differences in surface winds (vectors) (unit: ms−1). c As in (a) except for the longitude-depth section of the climatological JFM mean ocean subsurface temperature averaged over 10°S–5°N (contour) and differences in ocean subsurface temperature (color shading). d As in (c) expect for the zonal ocean current averaged over 10°S–5°N (unit; ms−1). In case of SST, area-averaged difference of SST over Indian Ocean domain (20°S–20°N, 40°E –100°E) has been removed. Stippling area by black dots indicate statistically significant values at the 95% confidence level, determined by a Student’s t-test with n−2 degrees of freedom.

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The weakening of the northwesterly winter monsoon flow over the southeastern IO (Fig. 5b) leads to the shoaling of thermocline near off the coast of Sumatra (between 100° and 120°E; Fig. 5c). Moreover, changes in sea surface height (SSH) are consistent with thermocline shoaling during P2 period such that SSH in the IOD-eastern region significantly decreased (Supplementary Fig. 9), with a 99% confidence level, from 47.5 cm to 45.8 cm (p-value < 0.001). The shallower mean thermocline observed during P2 period leads to the enhancement in coupling feedback between the atmosphere and ocean34,35. by increasing the sensitivity of the mixed layer temperature to change in anomalous thermocline depth in southeastern IO during P2 period compared to P1 period. Such enhanced sensitivity contributes to a stronger interaction and feedback mechanism between the ocean and atmosphere in the IOD region.

The climatological westward surface current on the equatorial region (5°S–5°N and 40–80°E) during the late winter season is a significantly strengthened from −0.06 ms−1 in P1 to −0.08 ms−1 in P2 with a 99% confidence (Fig. 5d). This change is presumably driven by the strengthened easterly wind in the central equatorial Indian Ocean region (3°S–3°N and 70–85°E) (from −0.0005 Nm−2 to −0.003 Nm−2, p-value < 0.1). This strengthened easterly wind and the westward mean current in the equatorial IO is dynamically linked to the significant decrease in mean upwelling in the IOD-western region (from 0.1 m month−1 to −0.5 m month−1, p-value = 0.0002).

In summary, from a thermodynamical perspective, the rise in mean SST in the tropical IO coupled with the weakening of the westerly winter monsoon flow over the southeastern IO contributes to an intensification of air-sea coupling strength. On the dynamical front, the reduction in mean upwelling in the western IO and the shallowing of the mean thermocline in the southeastern IO enhance the air-sea coupling feedback through the intensification of the thermocline feedback mechanism. Consequently, these changes in the climatological mean state during the P2 Period result in a strengthened growth rate of the IOD during the boreal winter season. These combined thermodynamic and dynamic changes effectively contribute to the observed increase in the IOD’s intensity and variability during this period.

Discussion

Over the last 123 years, the variability of IOD has undergone two abrupt and stepwise increases: the first in the mid-1940s and the second in the late-1970s. This study aimed to unveil the physical mechanisms behind the decadal modulation of the IOD variance, utilizing reanalysis data and a low-order IOD model. The low-order IOD model well reproduced the observed decadal changes in the IOD variance, including its peak timing within the seasonal cycle and its changes.

Firstly, we found that the decadal change in the IOD growth rate (or the local feedback strength of the IOD) is the primary factor for the decadal variation in IOD variance, and ENSO plays a secondary role. Since the late-1970s, there has been a notable strengthening of the IOD growth rate, especially from the late winter to early spring, which significantly affects IOD development from spring to summer. The influence of ENSO on the IOD, which intensified since the 1960s, extended the IOD growth period from the 1980s onward (Fig. 3). This altered ENSO effect corresponds with both an increase in ENSO variance (by about 10% in P2 period compared to P1 period) and the ENSO-IOD connection (Supplementary Fig. 10a, b, respectively). The increased ENSO variance during P2 period is responsible for the overall increase in the DMI variance (Supplementary Fig. 10a). Moreover, the correlations between monthly DMI and Niño3.4 on September through December during P2 period are significantly stronger than those during P1 period, indicating a significant contribution to increase DMI variance, especially during the fall to early winter season (Supplementary Fig. 10b).

Secondly, we found that while the IOD growth rate remains the dominant factor in determining IOD seasonal synchronization, the influence of the ENSO forcing has become more dominant in recent decades. These two factors had opposite effects on IOD seasonal synchronization in the late 20th century such that the seasonal phase of the IOD dam** rate advanced by ~0.9 month, while the ENSO effect was delayed by ~0.4 month. This result explains the more frequent occurrence of early IOD events, apart from ENSO, in recent decades.

Lastly, our study demonstrates that the rapid increase in the growth rate of IOD during JFM season is the primary contributor to the increase in IOD variance since the late 1970s. This marked rise in the IOD’s growth rate during the JFM season can be ascribed to several key factors occurring in the recent decades: the overall surface warming across the tropical Indian Ocean (IO), the weakening of the westerly winter monsoon flow in the southeastern IO, the shallowing of the mean thermocline in the southeastern IO, and the decrease in mean upwelling in the western IO. These decadal changes have served to amplify the air-sea coupling process in each of these specific areas during the recent decadal periods. This enhanced coupling has, in turn, played a significant role in driving the observed changes in the behavior and intensity of the IOD, particularly in its growth rate during the JFM season.

The low-order IOD model utilized in this study is based on a linear system, which tends to underestimate the amplitude of extreme IOD events, such as those that occurred in 1997, 2016, and 2019. Additionally, the IOD model did not account for the spatial diversity of ENSO, as it solely relied on Niño3.4 index to represent ENSO forcing. For example, there has been an increased frequency of central Pacific El Niño events since the early 1990s36,37,38,39, which may influence the IOD differently compared to the conventional ENSO events40. Despite these limitations, the IOD model well reproduced an increase in the IOD variance observed in recent decades. Furthermore, the linear framework allowed us to delineate the relative role of each process in contributing to the IOD variance changes over time. The current state-of-the-art climate models exhibit considerable uncertainty in their future projections of IOD variability in warmer climates28,29. While some models projected increased IOD variability, others do not. Therefore, there is an urgent need to better understand how changes in the mean climate state and other climate phenomena influence the IOD. In this study, by analyzing IOD variability over the last century, we quantified the processes driving these variations in IOD variance over the historical period. Applying our framework to longer observational records and future projections will help reduce some of these uncertainties.

Methods

Datasets

The primary dataset used in this study was the Extended Reconstructed Sea Surface Temperature version 5 (ERSST v5)41 from 1900 to 2022 with a horizontal resolution of 2° × 2°. We also examined IOD decadal variability modulation using different observational and reanalysis products for their respective available time periods. These datasets include the Hadley Center Global Sea Ice and Sea Surface Temperature version 1.1 (HadISST)42, Centennial in Situ Observation Based Estimates of SST (COBE)43, NOAA Optimum Interpolation SST version 244, European Center for Medium-Range Weather Forecasts Ocean Reanalysis System 545, Simple Ocean Data Assimilation version 2.2.4 (SODA2.2.4)46, and National Centers for Environmental Prediction Global Ocean Data Assimilation System (GODAS)47 and the German contribution to the Estimating the Circulation and Climate of the Ocean project, version 3 (GECCO3)48. For SODA2.2.4, GODAS, and GECCO3, a potential temperature of 5 m was used to represent the SST. To further investigate the reasons behind decadal changes in IOD growth, we analyzed SLP, u, and v data for 1948–2018 obtained from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR)49 reanalysis. We also analyzed HadISST and slp data from the Met Office Hadley Centre (HadSLP2)50, which yielded similar results. wherein the analysis period was from 1948 to 2018.

Indices

To investigate the interannual variability of the IOD, a bandpass filter (3-month to 8-year) was applied to the quadratic detrended SST. The results of this study are not sensitive to the detrending method. The IOD is defined as the difference in SST anomalies between the western TIO (50°E to 70°E and 10°S to 10°N) and southeastern TIO (90°E to 110°E and 10°S to the equator) and is known as the Dipole Mode Index (DMI)1. To describe ENSO, the Niño3.4 index was adopted, which indicates the average SSTA over the tropical Pacific Ocean (170°W to 120°W and 5°S to 5°N). All indices were normalized prior to the analysis.

A low-order IOD model

To investigate the decadal change in the IOD, we used a low-order stochastic-deterministic model (hereafter IOD model19,21,22,51,52) as follows:

$$\frac{\partial T}{\partial t}={\lambda }_{m}T(t)+{\beta }_{m}E(t)+{\sigma }_{m}{\xi }_{t}$$
(2)

where T is the DMI, E(t) is the Niño3.4 index, and ξt is Gaussian white noise with zero mean and unit standard deviation. The subscript ‘m’ indicates the calendar month (m = 1, 2, …,12). The parameters λm, βm and σm are measures of the dam** rate determined by local IO feedback processes, the sensitivity parameter of DMI to the external ENSO forcing, and the amplitude of the stochastic forcing, respectively. A least-square fitting with the forward Euler method was applied to the band-pass filtered and normalized DMI and Niño3.4 indices to compute λm and βm for each calendar month. Then, σm is calculated as the standard deviation of the residual for each calendar month. The autocorrelation of the residuals was close to that of white noise, indicating that the stochastic forcing term in the IOD model refers to a random process. Using the estimated parameters, a reconstructed DMI was calculated at one-month time steps by integrating the model forward.

First, we calculated each parameter using all 123 years of the three datasets (ERSSTv5, HadISST, and COBE) to examine the general characteristics of the parameters. All three parameters showed an annual cycle (Supplementary Fig. 11)22 The dam** rate λm shows a maximum in the summer and strong decrease after fall. The remote impact of ENSO βm is positive throughout most of the year except during winter. This positive impact reflects the characteristic of the IOD growing simultaneously with ENSO from spring to fall. The noise residual σm is always positive and reaches its maximum in June, coinciding with the timing of the active stochastic forcing responsibility for initiating IOD events. In summary, the seasonal evolution of these three parameters provides an understanding of various seasonally varying IOD processes.