3.a. Distinct modern dynamics associated with ISM wind and rainfall

Based on historical observations from the year 1871 to 2010 AD, we first compare the ISMR and the detrended DNS time series (Fig. 1a). Since the DNS is highly correlated with the South Asian (5º N-22.5º N, 35º E-97.5º E) averaged zonal wind at 850 hPa (R = +0.86, lag=0, p = 1.18*10^-42), it is a reliable ISM wind intensity index. The correlation between DNS and ISMR is only +0.26 (lag = 0, p = 0.002), largely due to their similarity on multidecadal time scales. By comparing regression coefficients against the DNS index and the ISMR index, we found that they are associated with distinct changes of surface pressure, 850 hPa winds and rainfall anomalies (Figs. 2a-d).

For higher DNS, JJAS westerlies of ISM are enhanced from the Arabian Sea to the South China Sea (SCS) and can be explained by a stronger surface pressure gradient between the southwestern IO and Asian continent (Fig. 2a). Meanwhile, JJAS rainfall is increased over most regions of India, BOB, Indo-China Peninsula, and SCS, but is decreased over Bangladesh and the TIO (Fig. 2b). However, for higher ISMR, JJAS surface pressure anomalies are dominated by negative values over the WIO in contrast to those positive values over the Indo-China Peninsula and SCS (Fig. 2c), which induce larger magnitudes of anomalous easterlies from SCS to BOB (turning to south wind anomalies over India), and only left moderate magnitudes of anomalous westerlies over the southwestern Arabian Sea. Associated rainfall is decreased in the Indo-China Peninsula and SCS, but increased in the SWIO, equatorial Indonesia, and the South Asian region (5º N-30º N, 60º E-95º E) (Fig. 2d).

These results suggest that, although the stronger ISM westerlies due to land–sea pressure gradients can indeed result in higher ISMR at multi-decadal scales, the interannually increased ISM rainfall should be more related to anomalous easterlies due to surface high pressure and anticyclonic circulation from SCS to BOB. The latter linkage can be explained in the context of ENSO and IOD.

3.b. Interannual modulation of ENSO on ISMR relies on IOD

Consistent with previous studies (Annamalai et al. Reference Annamalai, Hamilton and Sperber2007; Wu RG et al. Reference Wu, Chen and Chen2012; Chakraborty, Reference Chakraborty2018), the SOI_JJA and SOI_DJF time series share much similarity (Fig. 1b) and their correlation with ISMR show clear seasonal inverse feature (Fig.1f). Before the spring of Year (Yr) 1, both SOI_JJA (Yr 0) and SOI_DJF (Yr 1) are weakly related to the increased ISMR in Yr 1 (R = −0.23 and −0.14, p = 0.01 and 0.11), but after spring, SOI_JJA (Yr 1) and SOI_DJF (Yr 2) are significantly correlated to ISMR in Yr 1 (R = +0.42 and +0.50, p = 3.13*10^-7 and 5.54*10^-10).

Regression coefficients against the minimum of SOI_JJA (Yr 0, El Niño) and the maximum of SOI_JJA (Yr 1, La Niña) (Fig. 2e–f and Fig. 2g–h) are both featured by increased ISMR during the summer of Yr 1, accompanying with anomalous surface high pressure, anticyclonic circulation from SCS to BOB. These SOI_JJA associated anomalies are similar to those higher ISRM-associated changes (in Fig. 2c-d), and stand for two types of ENSO impact on ISMR (Wu RG et al. Reference Wu, Chen and Chen2012; Chowdary et al. Reference Chowdary, Chaudhari, Gnanaseelan, Parekh, Rao, Sreenivas, Pokhrel and Singh2014, Reference Chowdary, Parekh, Kakatkar, Gnanaseelan, Srinivas, Singh and Roxy2016; Chakraborty, Reference Chakraborty2018). One type is the lagged impact of decayed El Niño (from Yr0 JJA to Yr1 DJF) through the IPOC mechanism, the other is the simultaneous impact of developing La Niña through atmospheric circulation during the summer of Yr 1.

We noted that these two ENSO impacts show distinct responses in TIO that may be related to different phases of IOD. Since the SOI_JJA and DMI time series have a significant correlation of −0.55 (p = 2.09*10^-12), it means that a summer El Niño always appear with positive IOD event (or La Niña with negative IOD). This explains those differences in zonal surface pressure gradient in TIO: The west low-east high pressure pattern (Fig. 2e) reflects the persistent effect of positive IOD during the decayed El Niño phase, and the reversed gradient (Fig. 2g) may be influenced by negative IOD during the developing La Niña phase. How will these different phases of IOD impact on ISMR?

3.c. Positive IOD can greatly suppress ISMR in the same summer

Also consistent with previous studies (Saji et al. Reference Saji, Goswami, Vinayachandran and Yamagata1999; Gadgil et al. Reference Gadgil, Vinaychandran, Francis and Gadgil2004; Ihara et al. Reference Ihara, Kushnir, Cane and De la Peña2007), the correlation is +0.07 (lag = 1, p = 0.43) when ISMR lags DMI by 1 year (Fig. 1f), suggesting a poor lagged linkage from the DMI of Yr 0 to the ISMR of Yr 1. But this correlation becomes −0.29 (p = 0.0006) for lag = 0, indicating that ISMR will be significantly damped by positive IOD in the simultaneous summer. Similar to Li et al. (Reference Li, Lin and Cai2017), our regression coefficients against the maximum of DMI (Yr 0) are featured by anomalous surface westerlies from BOB to SCS, and reduced rainfall in most parts of India (Fig. 3d and 3g). This negative DMI–ISMR coherence in regression and correlation analysis seems to contradict with modern AGCM simulations, in which higher ISMR will be forced by positive IOD-like SST anomalies (Ashok et al. Reference Ashok, Guan, Saji and Yamagata2004, Reference Ashok, Behera, Rao, Weng and Yamagata2007). But recently it has been explained by the dominant influence of ENSO on ISMR overwhelming that of IOD (Li et al. Reference Li, Cai and Lin2016; Hrudya et al. Reference Hrudya, Varikoden and Vishnu2021). For example, during those time intervals of strong ENSO–IOD coherence, the ENSO–ISMR correlation is high, and the IOD–ISMR correlation is low (Ashok et al. Reference Ashok, Guan and Yamagata2001). So the decreased ISMR by El Niño may have much larger magnitude than the increased ISMR by positive IOD.

Our moving correlation shows that strong ENSO–IOD coherence mainly appears in two intervals of Yr 1883–1928 and of Yr 1969–1998 (red line in Fig. 1e). But these multidecadal (30-50 years) evolutions of ENSO–IOD coherence impact little on those of DMI–ISMR and SOI_JJA–ISMR coherences, which only exhibit interdecadal (20 years) fluctuations. From Yr 1871–2010 AD, the negative correlation of DMI–ISMR (lag = 0) becomes stronger (close to or lower than −0.4) during those time intervals of larger SOI_JJA–ISMR coherences (lag = 0) (brown and orange lines in Fig. 1d). It means that the ENSO–IOD coherence changes are hardly to explain the simultaneous negative relationship between ISMR and DMI.

Our modern sensitivity experiments of CAM4 suggest that, if forced by positive IOD-like SST anomalies during JAS, there will be only slightly increased summer rainfall over the northeastern BOB (Fig. 4b). More drastically is the decreased rainfall with anomalous surface high pressure and easterlies extending from the southwestern BOB to the Arabian Sea (Figs. 4a-4b). This anomalous meridional rainfall seesaw pattern is mainly contributed by the warmer WIO (Figs. 4c-4d), but only moderately cancelled by the cooler EIO (Figs. 4e-4f). Totally, ISMR is reduced by −0.15 mm/day over land, in which the warmer WIO and cooler EIO contribute to −0.27 mm/day and +0.12 mm/day, respectively.

Compared to previous studies that mainly emphasize the role of EIO cooling (Ashok et al. Reference Ashok, Guan and Yamagata2001, Reference Ashok, Guan, Saji and Yamagata2004; Krishnan et al. Reference Krishnan, Ramesh, Samala, Meyers, Slingo and Fennessy2006, Reference Krishnan, Sundaram, Sundaram, Swapna, Kumar, Kumar, Ayantika and Mujumdar2011), our CAM4 simulations illustrate the importance of WIO warming and provide another reasonable explanation for the damped ISMR by positive IOD in the simultaneous summer. Of course, the relative contributions of WIO and EIO to ISMR may be varied temporally and depend on particular IOD-like thermal gradient or the phase combination of IOD and ENSO, or the recent global warming background. For example, our summer WIO warming induces anomalous anticlockwise circulation over WIO of 10º S–20º N (Figs. 4a and 4c), which may weaken the climatological cross-equatorial low level jet stream and associated moisture transport into ISM regions. But this positive IOD induced feature mainly appears during those intervals of stronger ENSO–IOD coherence, and disappears in recent several decades with weaker ENSO–IOD coherence under global warming (Li et al. Reference Li, Cai and Lin2016; Hrudya et al. Reference Hrudya, Varikoden and Vishnu2021; Chakraborty and Singhai, Reference Chakraborty and Singhai2021).

3.d. Decayed IOD can also modulate upper OHC and ISMR

Moreover, the winter WIO warming during the decayed positive IOD or El Niño may also impact ISMR. Although the correlation between ISMR and JFM WIO OHC26 index (OHC26_{_WIO}) from Yr 1871 to 2010 AD is only +0.25 (lag = 0, p = 0.0029), it is comparable to the simultaneous impact of DMI on ISMR (R = −0.29). For the JFM OHC26__WIO index, the largest correlation is 0.43 (p = 1.84*10^-7) with DMI (+) of Yr 0, and is −0.42 (p = 2.17*10^-7) with the SOI_DJF of Yr 1 (Fig. 1f). Moving correlation further shows that, except for the time interval of Yr 1944-1968, its moving correlation with DMI (+) of Yr 0 is generally positive and comparable with its correlation with SOI_DJF of Yr 1 (black and gray lines in Fig. 1e). And at multidecadal scales, both the DMI and SOI_DJF show stronger coherence with OHC26_{_WIO} during time intervals of strong ENSO–IOD coherence and vice versa. This probably indicates a significant role of WIO OHC on ISMR that depends on the interplay of ENSO and IOD.

But the OHC26_{_WIO} only exhibits higher correlation (larger than +0.4) with ISMR during the interval of Yr 1944–1968 (cyan line and shaded in Fig. 1e), corresponding to a weakened ENSO-IOD coherence (red line in Fig. 1e). This interval is also accompanied with a sharply reduced correlation (from positive mean value of +0.5 to negative mean value of −0.13) between OHC26_{_WIO} and DMI (+) of Yr 0 (black line in Fig. 1e). Although not significant, the correlation between DMI (+) of Yr 0 and ISMR also falls from positive to negative (brown line in Fig. 1e). This may suggest for a dominant role of IOD on the winter WIO OHC and associated ISMR, because there seems to be no similar sharp changes in the coherence between SOI_DJF and OHC26_{_WIO} (gray line in Fig. 1e).

Note that the simultaneous relation between DMI (or SOI_JJA) and ISMR is still significant during this time interval (brown and orange lines in Fig. 1d), one possibility is that the concurrences of La Niña and negative IOD (both favoring increased ISMR) are relatively rare, as indicated by weakened SOI_JJA–DMI coherence. More extremely, the damping effect of positive IOD on ISMR may largely cancel the increased ISMR during the summer of La Niña. In other words, the simultaneous effects of ENSO and IOD on ISMR will be greatly reduced during time interval of weakened SOI_JJA–DMI coherence. This may result in a relative larger contribution of winter WIO OHC on ISMR and explain the significant coherence between them during Yr 1944-1968. But considering that most correlations among DMI, SOI, OHC, and ISMR during this interval are not significant, it is hard to resolve their true causal relationships. Here, we can only focus on the overall role of winter WIO OHC in bridging IOD and ISMR across the 20th century.

By regressing OHC26 onto the normalized timeseries of DMI (Figs. 3a-3b), we can see that positive IOD is accompanied by a zonal seesaw pattern of JAS OHC26 anomalies in the TIO, and those positive OHC26 anomalies in the WIO are still significant during JFM of next year. Interestingly, the higher ISMR-associated JFM OHC26 anomalies (Fig. 3c), JJAS surface pressure, 850hPa wind, and rainfall (Figs. 2c and 2d), all share many similarities with those of IOD-induced lagged air–sea anomalies (Figs. 3b, 3e and 3h). Note that similar features can also be found in those summer anomalies regressed onto OHC26__WIO (Figs. 3f and 3i), it, is reasonable to say that at interannual scales of the 20th century, historical positive IOD events can also greatly modulate the upper OHC in the TIO, and result in the increased OHC26__WIO during JFM of next year, then associated IPOC effect triggers anomalous high pressure and AAC over the SCS and BOB (Xie et al. Reference Xie, Kosaka, Du, Hu, Chowdary and Huang2016; Du et al. Reference Du, Chen, Xie, Zhang, Zhang and Cai2022), finally induce following JJAS ISM anomalies (surface easterlies and higher ISMR).

Using another modern sensitivity experiment of CAM4 (experiment CAM__control__{WIOsst_jfmP}), we can preliminarily illustrate the summer atmospheric response to the JFM SST warming anomalies in WIO. The rainfall increased over BOB and India south of 20º N but decreased over land regions north of 20º N (Fig. 4h), resulting a slightly reduced ISMR by −0.01 mm/day over land. Associated surface pressure and wind anomalies (Fig. 4g) also have smaller magnitudes and opposite signs relative to those summer SST induced changes (Figs. 4a and 4c). One reason is that the winter SST forcing (+0.1K to +0.2K in Figs. 4h) is smaller than the summer SST forcing of positive IOD (+0.4K to +0.6K in Figs. 4b). Another reason may be that those air–sea feedbacks following the winter WIO warming is also essential for the IPOC mechanism induced by positive IOD.

So far, we still cannot separate the delayed impacts of ENSO, IOD, and winter WIO warming on increased ISMR by regression analysis and CAM4 simulations. Although many studies highlighted the lagged impact of decayed El Niño on ISMR through IPOC (Mishra et al. Reference Mishra, Smoliak, Lettenmaier and Wallace2012; Darshana et al. Reference Darshana, Chowdary, Gnanaseelan, Parekh and Srinivas2020), here, we argue that when the coherence of El Niño and positive IOD (in Yr 0) is higher, the decayed IOD can also result in higher JFM WIO OHC in Yr 1, and may favor the following increased ISMR. In future studies, this IOD-induced lagged impact on ISMR should be not only further separated from the simultaneous impact of IOD, but also from those simultaneous and lagged anomalies induced by ENSO.

3.e. Precession forced paleo-IOD also dominates OHC and ISMR

Previous studies have shown that precessional insolation changes can induce significant tropical air–sea coupled responses assembling modern IOD mode (Abram et al. Reference Abram, Gagan, Liu, Hantoro, McCulloch and Suwargadi2007, Reference Abram, Hargreaves, Wright, Thirumalai, Ummenhofer and England2020; Brown et al. Reference Brown, Lynch and Marshall2009; Kwiatkowski et al. Reference Kwiatkowski, Prange, Varma, Steinke, Hebbeln and Mohtadi2015; Wang et al. Reference Wang, Jian, Zhao, Chen and Xiao2015; Mohtadi et al. Reference Mohtadi, Prange, Schefuß and Jennerjahn2017; Iwakiri & Watanabe, Reference Iwakiri and Watanabe2019; Windler et al. Reference Windler, Tierney and deMenocal2023). Associated zonal or meridional temperature/pressure gradients across the Indian Ocean may have greatly modulated hydroclimate changes in the African–Asian–Australian monsoon regions (Tierney et al. Reference Tierney, Oppo, LeGrande, Huang, Rosenthal and Linsley2012; Bolton et al. Reference Bolton, Chang, Clemens, Kodama, Ikehara, Medina-Elizalde, Paterson, Roberts, Rohling, Yamamoto and Zhao2013; deBoer et al. Reference de Boer, Tjallingii, Vélez, Rijsdijk, Vlug, Reichart, Prendergast, de Louw, Vincent Florens, Baider and Hooghiemstra2014; Weldeab et al. Reference Weldeab, Rühlemann, Ding, Khon, Schneider and Graya2022). But the role of upper OHC in bridging IOD and ISMR at orbital scales is still unclear.

Figure 5 illustrates those air–sea coupled paleoclimate changes associated with higher ISMR (mainly at the precession band) from experiment CESM_ghg. During JFM, negative OHC26 anomalies dominate large areas of the Indian Ocean (especially the northeastern and southwestern parts), largely as a result of decreased boreal winter insolation (Fig. 5a) (Wang et al. Reference Wang, Jian, Zhao, Chen and Xiao2015). While during JAS, OHC26 anomalies in Figure 5b are featured by a positive IOD-like zonal seesaw pattern (similar to modern observation, Fig. 3a), mainly induced by increased boreal summer insolation (Wang et al. Reference Wang, Jian, Zhao, Chen and Xiao2015). Annual mean OHC26 anomalies are generally dominated by those JAS OHC26 anomalies but also greatly reflect the contribution of JFM OHC26 anomalies (especially in the Indian Ocean south of 10º S) (Fig. 5c). The latter is also supported by the concurrence of precession parameter minima and the Mg/Ca-SST minimum of core WIND28K, reflecting decreased JFM insolation and mixed layer temperature (Fig. 6a).

In short, increased ISM rainfall at the precession band mainly corresponds to higher OHC26 in the equatorial WIO during boreal summer–autumn and also corresponds to lower OHC26 in the equatorial EIO during the whole year. Thus, the positive linkage between JFM OHC26_{_WIO} and JJAS ISMR from modern interannual climate changes cannot be directly analoged to long-term paleoclimate changes, especially at the precession band with seasonal reversed insolation anomalies. It also means that the modern observed 1-year lagged response of ISMR to IOD through the bridging effect of JFM OHC26_{_WIO} may be interrupted by external forcing (winter precessional insolation).

As shown in Figure 5e, higher ISMR is also accompanied by increased JJAS rainfall from the tropical Indian Ocean to equatorial Indonesia, but with reduced rainfall over the southeastern Indian Ocean, southern parts of the SCS and BOB. Note that these TIO rainfall anomalies between 15º S and 15º N are similar to modern IOD-related JJAS rainfall changes in CAM4 (Fig. 4b). Dose it means that the JJAS ISMR under precessional forcing may be also reduced by IOD-associated summer OHC anomalies in the tropical Indian Ocean?

Modern observation and simulation (Krishnan et al. Reference Krishnan, Ramesh, Samala, Meyers, Slingo and Fennessy2006, Reference Krishnan, Sundaram, Sundaram, Swapna, Kumar, Kumar, Ayantika and Mujumdar2011) suggest that due to intensified equatorial easterlies (during positive IOD), decreased upper OHC prevails with shallower mixed layer and local atmospheric subsidences in the equatorial EIO from June to August, which further induces remote upward motions over India through meridional vertical atmospheric circulation anomalies, and induce increased ISMR through stronger cross-equatorial monsoon flow and moisture export from the southeast Indian Ocean (Behera et al. Reference Behera, Krishnan and Yamagata1999; Ashok et al. Reference Ashok, Guan, Saji and Yamagata2004). Paleoclimate proxies and simulation also show that upper ocean thermal structure changes in the EIO (and associated zonal/meridional thermal gradients) during boreal summer–autumn can significantly modulate ISM, generally with cooler EIO corresponding to stronger ISM westerlies or increased monsoon rainfall (Bolton et al. Reference Bolton, Chang, Clemens, Kodama, Ikehara, Medina-Elizalde, Paterson, Roberts, Rohling, Yamamoto and Zhao2013; Weldeab et al. Reference Weldeab, Rühlemann, Ding, Khon, Schneider and Graya2022). This represents a direct atmospheric linkage from the EIO to ISM during boreal summer.

Considering that the ice sheet was fixed as modern values and the ice-albedo feedback was muted in our transient simulation, the modeled glacial–interglacial climatic changes may be underestimated and hinder the direct comparison with proxy data. In Figures 6a–6c, we choose to remove the long-term trend (dashed lines) from SST proxies using 3-order polynomial fitting method and ignore those proxy-model discrepancies in magnitudes of short term changes. After detrending, those U^K’ ₃₇-SST residuals in WIO and EIO (orange lines) show many similarities with our simulated SST (black lines) and only just lack some precessional cycles (Figs. 6b-6c). Consistent with our simulated DMI, U^K’ ₃₇-SST based DMI is also dominated by precessional cycles except for the time interval of 120∼200 ka (Fig. 6d). Moreover, these precessional cycles of two DMI indexes seem to be more contributed by EIO changes that are out of phase with ISMR (Figs. 6c–6e). Thus, it seems that our transient simulations and paleo-proxies all support the notion of EIO-dominated IOD modulation on ISMR at the precession band.

3.f. Relative role of IOD, ENSO, and land–sea thermal contrast on ISMR at the precession band

Our simulated paleo-IOD also prevails with anomalous equatorial easterlies from the central Pacific Ocean to the WIO (Figs. 5e-5f), indicating that the climatological summer Walker circulation is enhanced over the western to central Pacific but weakened over TIO (Wang et al. Reference Wang, Jian, Zhao, Chen and Xiao2015, Reference Wang, Jian, Zhao, Xu, Dang, Liu, Xiao and Chen2019; Wang et al. Reference Wang, Jian, Lückge, Wang, Dang and Mohtadi2018). This is in contrast to the modern observed positive IOD and El Niño combination and reflects the independent TIO response under external forcing. To explain the coupling between the two anomalous zonal-vertical circulations, we identified a meridional wave-like pattern of those rainfall anomalies (negative-positive-negative-positive) from the southeast TIO to ISM region (Fig. 5e). This meridional pattern represents three local anomalous meridional vertical atmospheric circulations (with descent-ascent-descent-ascent from south to north) (Fig. 5d), probably excited by the colder SST and atmospheric subsidence in the EIO, or by the summer oceanic warming and atmospheric upward motions in the WIO.

Although we highlight the modulation of IOD on ISMR, the precession-forced La Niña-like conditions in the western-central Pacific Ocean may also contribute to the higher ISMR. More importantly, orbital changes of ISMR (Figs. 5e and 6e) have been largely attributed to land–sea thermal difference at the precession band (Wang et al. Reference Wang, Jian, Zhao, Xiao and Chen2016). Here, we further assess the relative contribution of land–sea contrast, ENSO and IOD on ISMR based on sensitivity experiments of CAM4. As a start, the influence of land–sea thermal gradient under precessional forcing can be illustrated by those JJAS differences between experiments CAM_P_min and CAM_control (Figs. 7a-7b), which are featured by anomalous surface high pressure and AAC over the North Indian Ocean, and by reduced rainfall in regions of 5º S–20º S and of 5º N–20º N, but with increased rainfall in regions of 5º S–5º N and north of 20º N. Then composite differences between experiments CAM_P_{min_nptpsst} and CAM_P_min show that the Pacific SST anomalies can induce anomalous surface low pressure and westerlies over South Asia and increased rainfall over India, BOB, and SCS regions (Figs. 7c-7d). It means that the precessional forced summer “central Pacific type” La Niña-like pattern (Wang et al. Reference Wang, Jian, Zhao, Xu, Dang, Liu, Xiao and Chen2019) can produce stronger ISM westerlies and higher ISMR.

Figure 7. Composite differences of JJAS atmospheric variables between experiments CAM_P_min and CAM_{_control} (a–b), between experiments CAM_P_{min_nptpsst} and CAM_P_min (c–d), and between experiments CAM_P_min__TIOsst and CAM_P_min (e–f). The left panels are surface pressure (shaded) and 850 hPa horizontal winds (vectors, small winds (magnitude < 0.5 m/s) are not shown). The right panels are the same as the left panels but with surface pressure replaced by rainfall (shaded). Characters in parentheses show the forcing factor for composite differences in each panel.

As shown by composite differences between experiments CAM_P_min__TIOsst and CAM_P_min, TIO SST anomalies during all seasons induce anomalous surface high pressure and more drastically reduced rainfall in the northern Arabian Sea and India (15º N-25º N), and in BOB and SCS regions (10º N-25º N) (Figs. 7e–7f). Meanwhile, significant anomalous low pressure and increased rainfall occupy the WIO and the EIO of 0º N–10º N. Additional CAM4 experiments (CAM_P_min__{TIOsst_JJA}, CAM_P_min__{TIOsst_JJAP}, and CAM_P_min__{TIOsst_JJAN}) prove that, the meridional wave-like pattern of summer rainfall from the southeast TIO to ISM region is mainly contributed by summer WIO SST anomalies (as shown by Figs. 8b and 8d). And they are accompanied by anomalous surface easterlies extending from the southwestern BOB to the Arabian peninsula, and by anomalous cross-equatorial northerlies over WIO of 10º S–20º N (Figs. 8a and 8c). Although these precessional forced anomalies are similar to those induced by modern positive IOD (Figs. 4a–4b), the EIO wave-like rainfall pattern seems have larger meridional extension (Fig. 8b relative to Fig. 4b). This may indicate larger contributions from those SST warming anomalies in WIO and the EIO of 0º N–10º N, but can also be attributed to the smaller magnitudes of SST cooling in the southeast TIO (−0.1 K–−0.2 K, cyan contours in Fig. 8b) relative to modern situations (−0.2 K–−0.6 K in Fig. 4b).

Figure 8. Similar to Figure 7, but for composite differences between experiments CAM_P_min__{TIOsst_JJA} and CAM_P_min (a–b), between experiments CAM_P_min__TIOsst_ _JJAP and CAM_P_min (c–d), and between experiments CAM_P_min__{TIOsst_ JJAN} and CAM_P_min (e–f). Cyan contours in (b), (d), (f), and (h) show the spatial distributions of SST anomalies prescribed in each experiment.

Note that the Pacific SST tends to increase the ISM rainfall everywhere, but the effect of TIO SST and land–sea contrast are spatially inhomogeneous over the Indian subcontinent (wetter north and drier south). Totally, the ISMR is increased by +0.69 mm/day for the land–sea contrast effect and by +0.52 mm/day for the Pacific SST, but is decreased by −0.48 mm/day for the TIO SST effect. For this damping effect of TIO SST, the summer IOD-like SST anomalies only contribute −0.16 mm/day because of the mutually offsetting by WIO warming (−0.44 mm/day) and EIO cooling (+0.28 mm/day). Thus, large parts (−0.32 mm/day) of the TIO damping effect actually should be attributed to SST anomalies of autumn, winter, and spring. Moreover, if TIO SST anomalies were added to experiment CAM_P_{min_nptpsst} (rather than experiment CAM_P_min), although associated anomalous rainfall pattern is similar, the TIO damping effect will become −0.79 mm/day and the ISMR will be only increased by +0.42 mm/day relative to experiment CAM__control. It means there exist significant nonlinear interactions in atmosphere when combined SST forcing from different regions.

Finally, in our equilibrium CESM simulations (experiments CESM_P_min and CESM_{_control}), the ISMR is increased by +1.58 mm/day, close to the difference of +1.71 mm/day between 10ka and 0ka in the experiment CESM_ghg (Fig. 6e). This includes not only those positive contributions from land–sea contrast and paleo-ENSO (+1.2mm/day), but also the damping effect of TIO SST in different seasons (−0.48 or −0.79 mm/day, including but not limited to paleo-IOD). Clearly, there is a large gap in the magnitude of ISMR changes between CESM and CAM4. In other words, the real contribution of positive paleo-IOD to higher ISMR requires further studies by considering the role of air–sea feedbacks.