Different role of spring season Atlantic SST anomalies in indian summer monsoon rainfall (ISMR) variability before and after early 2000

The present study shows that the weak (out-of-phase) correlation between the boreal spring Atlantic Meridional Mode (AMM) index and Indian summer monsoon rainfall (ISMR) during the 1990–2001 periods turned into a significant positive relationship after that. During the first period, boreal spring (MAM) season Atlantic SST variability is dominated by stronger cooling in the southeastern region. After 2002, the spring season SST pattern has north Atlantic warming extending to the equatorial region and continuing to summer (JJAS). The primary mode of the Atlantic SST co-occurred with a pre-existing El Nino during period 1 and the formation of La Nina by summer during period 2. During period 1, ENSO-induced anomalies dominated with weak divergence over India and the Atlantic region, while during period 2, the warm SST anomalies of north Atlantic-induced off-equatorial convection and associated circulation extended to the Indian Ocean and Indian land region resulting in increased monsoon rainfall during JJAS. The study further showed that during period 2, the increased correlation of ENSO and ISMR is also contributed by the Atlantic SST anomalies with additional off-equatorial wind anomalies and circulation from the north Atlantic extending to the Indian Ocean and monsoon region. Thus, MAM season Atlantic SST anomalies play a significant role in ENSO phase reversal and ISMR during the recent period. Many of the seasonal prediction models that participated in the NMME project capture the phase reversal of AMM-ISMR correlation when initialized during February. But models have more robust equatorial SST patterns during the summer season, and the north Atlantic SST anomalies are vital in the absence of ENSO. The study indicates that the spring season AMM index can provide a predictive signal for ISMR in seasonal prediction models. Still, they need to improve the simulation of the Atlantic basic state and its teleconnection with the tropical east Pacific.


Introduction
Indian summer monsoon rainfall (ISMR) is the lifeline of millions of people in India as a source of water for life and agriculture and controlling its economy. Thus, the prediction of its interannual variability, even though it is less than (Walker 1924). Shifting of the warm pool and associated convection towards the east Pacific during the developing phase of El Nino in the Pacific suppresses the rainfall over the south Asian region (Walker 1924, Rasmusson and Carpenter 1983, Webster and Yang 1992 Annamalai 2012 among many others). The opposite phase of El Nino (La Nina) is associated with increased convection over the Asian region. Kripalani and Kulkarni (1996) suggested that about 50% of droughts in India are associated with ENSO. The remaining may be influenced by other climate factors like variations of snow cover over Eurasia (Kripalani and Kulkarni 1999;Bamzai and Shukla 1999), SST anomalies in the Indian Ocean (Rajeevan et al., 2002), and Atlantic Ocean (Kucharski et al. 2007(Kucharski et al. , 2009. The ENSO-ISMR relationship started weakening after the late 1970s ( Kumar et al. 1999), as evidenced by the strongest El Nino of the 20th century, 1997/98 was associated with slightly above normal ISMR. The drop in the ENSO-ISMR relationship is attributed to many features by different studies. They range from changes in atmospheric variability due to global warming (Kumar et al. 1999), natural low-frequency atmospheric variability (Krishnamurthy and Goswami 2000), and Pacific decadal variability (Krishnan and Sugi 2003).
Meanwhile, during the phase of reduced ENSO-ISMR teleconnection, another oceanic variability in the Indian Ocean known as Indian Ocean Dipole (IOD, Saji, et al. 1999) has an increased role in ISMR (Saji and Yamagata 2003;Ashok et al. 2004). The IOD influences ISMR through the modification of local Hadley circulation. Ashok and Saji (2007) showed that positive IOD co-occurring with El Nino is critical in reducing the ENSO effect on monsoon. At the same time, many of the IOD events occur independently of ENSO and influence Indian summer monsoon variability (Ashok et al. 2004;Mohankumar 2010, Chakravarty et al. 2016). Studies such as Goswami et al. (2006), Li et al. (2008), Rajeevan and Sridhar (2008), etc., showed the influence of North Atlantic SST on ISMR variability. They showed that the positive SST anomalies over the North Atlantic Ocean shift the North Atlantic Jet northwards. The associated circulation changes in the upper troposphere influence the Indian monsoon through the circumglobal teleconnection across central Asia. Another study by Sabeerali et al. (2019) observed an inverse relationship between Atlantic zonal mode, which is the area-averaged SST anomalies averaged over the eastern equatorial Atlantic Ocean (5 o S to 3 o N, 20 o W to 10 o E), and ISMR during the summer period. In this study, the influence of ENSO is removed from the tropical Atlantic SST and so they argued that the Atlantic SST influence is deprived of ENSO influence. At the same time, a recent study by Borah et al. (2020) showed that the negative SST anomalies over the North Atlantic region are associated with drought conditions over India. Altogether these studies show the influence of south, north, and equatorial SST anomalies over the Atlantic Ocean influences ISMR.
Other studies such as Kucharski et al. (2007Kucharski et al. ( , 2009 found that tropical Atlantic SST anomalies can modulate the ENSO-Monsoon relationship. Their numerical experiments with Atlantic SST anomalies also produced the observed trend of ISMR. The studies of Chang et al. (2006); Hu and Huang (2007) etc., along with Kucharaski et al. (2007 showed that local air-sea processes, including slow Rossby wave propagation, Ekman pumping, and Bjerknes feedback, intensify the south Atlantic Ocean SST. The response of warm (cold) SST anomalies in the tropical Atlantic is associated with upward (downward) motion and upper-level divergence (convergence) in the equatorial Atlantic and African regions. Opposite anomalies over the central-western Pacific areas can influence ENSO and Indian Ocean processes. Ham et al. (2013) showed that spring warming in the north tropical Atlantic can induce a low-level cyclonic atmospheric flow over the eastern Pacific Ocean that produces a low-level anticyclonic flow over the western Pacific during the following months. This flow generates easterly winds over the western equatorial Pacific that cool the tropical Pacific and may trigger a La Niña event the next winter. Rodwell and Hoskins (2001) and Ren et al. (2021) indicate that the boreal summer south and north Atlantic warming is accompanied by a pair of anomalous low-level anticyclones over the western tropical Pacific. Still, the NTA-related anticyclone is more prominent and influences the ENSO evolution.
Altogether the above studies show the influence of south, north, and equatorial SST anomalies in the Atlantic Ocean on Indian rainfall and ENSO. But a concise relationship of the importance of Atlantic SST or its predictive value on ISMR independent of ENSO is not explained fully. A recent study by Vittal et al. (2020) showed that the Atlantic meridional mode (AMM) has a predictive contribution to Indian monsoon rainfall. They showed that the AMM index (Chiang and Vimont 2004) of the spring season has a significant contribution towards the summer ISMR and thus is helpful for the ISMR prediction initialized during the spring season. Yang and Huang (2021) also showed that Atlantic SST anomalies in the spring season are instrumental in restoring the ENSO-monsoon relationship. Another study by  also showed that after 2000, the ISMR had a good correlation with north Atlantic Ocean SST despite increased ISMR-ENSO correlation. Pillai et al. (2022) showed that models initiated during the boreal spring could not capture the Atlantic SST pattern, and its teleconnection decreased ISMR skill after 2000. Thus, the role of Atlantic SST in the ISMR needs to be understood in detail, especially as AMM is reported to have a predictive signal for ISMR a season 1 3 ahead (Vittal et al. 2020). We also estimate how AMM is associated with ENSO during the study period and their interaction to make a stronger relationship with ISMR during the recent period. The same relationship is analyzed in some of the present-generation seasonal prediction models from the U.S National multi-model ensemble project (NMME, Kirtman et al. 2014), which has hindcast data for long periods from 1981 to 2020.

Observation data
The Indian summer monsoon rainfall (ISMR) is the Indian land point average rainfall from the high resolution (0.25 o x0.25 o ) gridded observations from India Meteorological Department (IMD, Pai et al. 2014) averaged for June to September season. Global Precipitation climatology precipitation (GPCP v2.1, Hufmann et al. 2009) of the horizontal resolution of 2.5 o x 2.5 o for the same period is also used to represent tropical rainfall. SST for the same period is taken from Met Office Hadley Centre sea ice and sea surface temperature (HadISSTv1.1, Rayner et al. 2003) at 1 o x1 o horizontal resolution. The zonal and meridional wind at 850 hPa and 200 hPa are taken from fifth generation European Centre for Medium-Range Weather Forecast reanalysis (ERA5, 0.5 o x 0.5 o horizontal resolution, Hersbach et al. 2020). All the above data sets share a common period of 1981-2020.

Model setup
AMM-ISMR relationship is analyzed from different seasonal prediction models that participated in National Multi-Model Comparison Project (NMME, Kirtman et al. 2014) for the period 1981-2020. The NMME is a multi-model predicting system consisting of a series of coupled climate models from U.S. modeling centers, including NCEP, GFDL, NASA, NCAR, and the Canadian Meteorological Centre. The models used for the study are given in the first column of Table 1. Here the models have 10 ensembles and a hindcast of a minimum of nine months. All the models except CFSv2 are initialized every first day of the month with 00 UTC ocean-atmosphere initial conditions, and the perturbation method is used for producing ensembles. CFSv2 uses lagged ensemble method and initial conditions of every five-day interval for ensembles for the specific month. SST and rainfall data for all these model hindcasts are available on the IRI data server: http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/. We have taken 10 ensembles from all these models, except CCSM3, which has only 6 ensembles. Model hindcasts initialized using February month boundary conditions (Feb IC) are used for JJAS target months as we calculate the AMM index for boreal spring.

Methodology
The Atlantic meridional mode (AMM) index time series (Chiang and Vimont 2004) is taken from the national oceanographic and atmospheric administration (NOAA) website of the AMM index https://psl.noaa.gov/data/timeseries/ monthly/AMM/ammsst.data. The corresponding index is also calculated as the SST anomalies difference between that of the equatorial northern tropical Atlantic ( The following method is adopted from Kucharski et al. (2009) to differentiate between the Atlantic SST and ENSOinduced anomalies. For a variable X (SST, rainfall, etc.), the residual, which is not influenced by remote ENSO from ENSO (Xres(t)) is calculated as.
Here XENSO(t), the component forced by remote ENSO is calculated as.
Here b is the constant calculated from the X(t) and Nino3.4(t) linear regression. It is to be noted that the above method  -Nino3.4 1990-Nino3.4 -2002-Nino3.4 2003-Nino3.4 -2020-Nino3.4 1990-Nino3.4 -2002-Nino3.4 20032020 weak correlation (correlation coefficient, cc = 0.2) for AMM and ISMR for the entire 40-year period may result from the opposite phase relationship between the decades. At the same time, after 2000 the correlation increases to 0.52 (Table 1), which is well above the 90% significance level. It also needs to be noted that as the significant correlation is for the spring season AMM index for the recent period, it is an added advantage for the summer monsoon rainfall prediction perspective, as suggested by Vittal et al. (2020). Meanwhile, the negative correlation during the first period and then its reversal poses a scientific problem in understanding the cause of the reverse relationship between the two periods. To understand the influence of spring season AMM on summer rainfall, the cases with the same phase and opposite phase relationship need to be studied separately and are performed below. Figure 2 shows the boreal summer season (JJAS) composite anomalies of SST, rainfall, 850 hPa wind, and 200 hPa velocity potential for positive minus negative AMM years that co-occurred with the opposite phase (in the left panels) and same phase (right panels) of ISMR. Here the years during which both the spring season AMM index and summer season ISMR index anomalies are above +/-0.5 standard deviations are only considered for composites. As most of the years falling in the in-phase category occurred after 2000, the composite also shows the recent reverse of the relationship between AMM and rainfall. The SST pattern of the same phase relationship composite in Fig. 2a shows a strong positive SST anomaly on the northern side of the Atlantic basin and a weak negative SST anomaly on the southeastern side with cool SST anomalies in the tropical eastern Pacific. Associated convection (Fig. 2b) has increased rainfall over the north Atlantic, Indian land only removes the linear effect of ENSO (Nino3.4 SST) from the SST anomalies of other regions.
To analyze the decadal variability of the AMM-ISMR relationship an 11-yr running correlation and that of two different periods such as 1990-2002 and 2003-2020 is also carried out based on the 11 years running correlation from Fig. 1. Figure 1 shows the 11-year running correlation between the spring (MAM) season AMM index and boreal summer (June to September, JJAS) average Indian land rainfall for the 1981-2020 period. The AMM index calculated using the Empirical Orthogonal Function (EOF) method (Chiang and Vimont 2004) is downloaded from the NOAA website (https://psl.noaa.gov/data/timeseries/monthly/AMM/ ammsst.data). AMM index is also calculated using the SST anomaly difference method of Doi et al. (2019). Both the time series have a correlation of 0.92 for the spring season. The AMM index is again calculated after removing the ENSO influence, as shown in Eq. 1 to avoid any possible impact of ongoing ENSO on the Atlantic index. The correlation of the AMM index from the above three calculations with summer season Indian land rainfall in Fig. 1 indicates the same relationship for AMM and ISMR irrespective of AMM calculation method. The figure suggests an out-ofphase relationship between these two variables from 1990 to 2002, while it is strongly positive after that. The overall with reduced convection over the ISMR region (Fig. 2e). There is increased easterly flow at lower levels over India and with converges over the eastern Indian Ocean (Fig. 2f). The upper-level velocity potential also shows increased convergence over the south Atlantic extending up to the western IO with divergence over the eastern IO and west Pacific (Fig. 2f). The next question is whether these deviations in the tropical SST and circulations are induced by the change in the Atlantic Ocean itself or if the reversal of the ENSO pattern in the Pacific is responsible for AMM-ISMR phase change.

Changes in Atlantic Ocean SST during two periods
Empirical Orthogonal Function (EOF) analysis of both boreal spring (MAM) and summer (JJAS) season SST anomalies in the tropical Atlantic Ocean are conducted to understand any possible change of Atlantic SST variability between the periods. EOF1 for the pre and post-2002 periods MAM and JJAS seasons are shown in Fig. 3. Before 2002, EOF1 of the MAM season explains 44% of the variability with weak positive loading over the tropical north Atlantic and significant negative loading in the south tropical region, while it has a more robust positive loading in the north extending southward explaining 50% of the variability after 2002. The summer pattern has cooling concentrated just south of the equator and extending northward during period 1, and it is changed to a similar pattern as MAM during period 2. The boreal summer season EOF pattern by Ren et al. (2021) showed east south equatorial Atlantic concentrated SST pattern as EOF1 and that with stronger loading in the north as EOF2 for the entire period from 1979 to 2018. But here, these two patterns appear as EOF1 for period 1 and period 2, respectively. The previous composite figure (Fig. 2), with SST cooling in the south Atlantic before 2002 and warming in the north after that confirms the EOF analysis. MAM season PC1 has a correlation of above 0. Spring season has warm SST anomalies in the north and region, maritime continent, eastern equatorial Indian Ocean, and western part of the American continent with reduced convection over the central and west Pacific. There is robust cross-equatorial flow and easterly wind anomalies to the Bay of Bengal from the western Pacific at the 850 hPa level (Fig. 2c). Upper-level velocity potential (Fig. 2c) indicates stronger divergence over North Atlantic and extending to the Indian Ocean (IO) and Indian land regions.
The positive AMM years associated with weak ISMR have decreased warming in the north Atlantic by summer and increased negative anomalies at the southern region (Fig. 2d). This pattern is related to weak dipole anomalies in IO and more substantial ENSO-like warming in the tropical east Pacific. Thus, different from same phase years (Fig. 2a), opposite phase years have more cooling in the southern Atlantic associated with El Nino in the Pacific. The associated rainfall has strong negative anomalies in the equatorial Atlantic and negative dipole convection in the IO, The summer pattern in Fig. 5 indicates that the cool SST anomalies in the south Atlantic strengthen along with a more robust El Nino pattern in the Pacific during period 1 (Fig. 5a). This is associated with more vigorous convection and upper-level divergence over the east-central Pacific and upper-level convergence and reduced rainfall in the Indian Ocean extending to Indian land masses. During period 2, the summer SST pattern is associated with stronger warming in the north Atlantic and a La Nina -like cooling in the eastern Pacific (Fig. 5b). There is decreased convection in the central Pacific and increased convection over eastern IO extending to India and the warmer areas of the north Atlantic. There is upper-level divergence over the north Atlantic and Indian land mass centered at the east IO. Thus the spring season is associated with an ongoing El Nino with warm SST anomalies in the north Atlantic during period 1, while the ENSO decay co-occurred during period 2, and its phase changed by summer. The rainfall and SST pattern of period 1(period 2) in Fig. 5 closely resembles the negative (positive) AMM-ISMR correlation years composite in Fig. 2.
Atlantic SST anomalies have pattern change in both epochs and ENSO reversal during summer. It may be cooling in the southeastern part during period 1, along with an El Nino-like warming in the eastern equatorial Pacific Ocean (Fig. 4a). Decreased convection over the south equatorial Atlantic and maritime continent and increased convection over the central Pacific are induced by EOF1 mode. There is upper-level (200 hPa) convergence over the equatorial Indian Ocean and divergence over the eastern Pacific. During period 2, the MAM season SST anomalies are warmer over the north Atlantic extending to the south equatorial region. There is weak warming in the Pacific, indicating a decaying El Nino with basin-wide warming in the north Indian Ocean (Fig. 4b). There is increased convection over the north Atlantic and the equatorial Indian Ocean, with an upper-level divergence center over the north Atlantic extending to the Indian Ocean and an off-equatorial convergence center in the north Pacific. This leads to the conclusion that along with the change in the Atlantic SST pattern and associated circulation, the persisting El Nino pattern in the Pacific during the spring season of period 1 changed to a decay pattern after 2002. co-occurring ENSO has played an essential role in the dominant pattern of STA anomalies during period 1 and negative AMM-ISMR correlation. During period 2, the north Atlantic warming is confined to the northern part indicating that the extended pattern of NTA warming to the STA region is contributed by the co-occurring summer season La Nina. Meanwhile, AMM-induced rainfall persists in the absence of ENSO. Still, it is slightly weaker compared to Fig. 5d and there is increased rainfall over the Indian land mass and east Indian Ocean region (Fig. 6d). Thus, even though the ENSO-induced pattern is absent during summer, the Atlantic SST can induce increased rainfall over the monsoon region during period 2.

Role of Atlantic SST in ENSO and ENSO-ISMR relationship
The present section analyses the possible role of Atlantic SST in the ENSO phase reversal and its relationship with ISMR. Figure 7 shows the boreal spring and summer season interesting to investigate how these different patterns in both these oceans contribute to the summer rainfall over India. i.e., whether the ISMR change is induced by the Atlantic SST alone or is the result of phase change of co-occurring ENSO. Earlier studies also indicated that after 2000, Atlantic SST anomalies have a more substantial role in ENSO phase reversal during the early summer, and the ENSO-ISMR relationship is more potent after 2000 (Devika and Pillai 2020; Yang and Huang 2021; Pillai et al. 2022). Is the Atlantic SST change alone the reason for the changes in AMM-ISMR relationship, or the recent ENSO modification influencing it is subject to understanding the mechanism behind the AMM-ISMR phase reversal?
To study the above two questions, we performed the AMM regression analysis with the SST, rainfall and velocity potential at 200 hPa (vp200) anomalies after removing the linear influence of ENSO from the variables, as explained in Sect. 2 and shown in Fig. 6. The summer pattern indicates that in the absence of ENSO-induced anomalies, the cooling in the eastern Atlantic during period 1 is weaker and there is a weak positive (above normal) rainfall anomaly over the monsoon region (Fig. 6c). This confirms that the 1 3 summer are stronger during period 1 compared to period 2 ( Fig. 7c and d). Figure 7 supports the results from Figs. 4 and 5, indicating the change in SST anomaly pattern in the Atlantic for both periods and the commencement of equatorial east Pacific SST anomalies by summer during period 2. This gives the impression that the NTA SST pattern is instrumental in the ENSO phase reversal during period 2 as suggested by Yang and Huang (2021). They stressed that ENSO is in the decay phase of the spring season of the post-2000 period and that NAT SST can influence ENSO more than the continuing ENSO pattern of period 1. Our analysis of MAM SST anomalies induced by ENSO after removing Atlantic SST influence (Fig. 8a) indicates that the east Pacific warming and southeast Atlantic cooling observed during period 1 (Fig. 7a) persists after removing Atlantic SST influence. But after 20,002, there is weak warming in the equatorial region in the absence of Atlantic SST influence, which was absent in Fig. 7b. Tropical Atlantic cooling is also inadequate in Fig. 8b. The pattern has not had much difference, at least in the Pacific Ocean sector, for the two periods if the Atlantic SST-related anomalies are removed. This also confirms that more than the basic pattern changes of ENSO, Atlantic mode change, as evidenced by the EOF1 induced the SST pattern variability between the two periods in the Atlantic and Pacific Oceans.
Meanwhile, studies such as Devika and Pillai (2020), Yang and Huang (2021), and Pillai et al. (2021Pillai et al. ( , 2022 indicated an increase in ENSO-ISMR correlation after 2002. The present study also shows that the ENSO-ISMR correlation, which was about − 0.28 during period 1 increased to -0.65 after that. Previous analysis showed the importance of boreal spring season NAT SST anomalies in setting up the boreal summer ENSO pattern during period 2. The following section analyses whether the increased ENSO-monsoon teleconnection is due to the changes originating with the Atlantic pattern change in spring or whether the ENSO impact on ISMR is independent of the Atlantic SST variability. Figure 9 shows the boreal summer pattern of SST, rainfall, and circulation anomalies associated with ENSO in the Pacific, both in the presence and absence of NTA SST anomalies during the 2002-2020 period. Here in the presence of tropical north Atlantic SST anomalies, we have cooling in the tropical Atlantic, concentrating north of the equator with a dipole pattern in the Indian Ocean along with ENSO-related warming in the eastern Pacific. Meanwhile, in the absence of that, Atlantic cooling is confined to the southeast region and basin-wide warming is in the Indian Ocean. Strong easterly anomalies in the Arabian Sea (AS) and off-equatorial westerly anomalies over the Bay of Bengal (BoB) and northwest Pacific are induced in the presence of NTA SST anomalies. This leads to stronger rainfall anomalies over the Indian land region in the presence of pattern of El Nino minus La Nina year SST composite for both periods. During period 1, there is El Nino-related warming in the eastern Pacific along with cooling in the southeastern Atlantic from boreal spring onwards (Fig. 7a) and is strengthened during summer. The Atlantic cooling extends to the northern hemisphere also. Meanwhile, during period 2, Pacific warming is off equatorial in the northeastern part, the tropical Atlantic has stronger cooling in the NTA region, and the El Nino-related warming in the eastern Pacific begins by summer. The ENSO anomalies in the The presence of north Atlantic cooling associated with El Nino induces Dipole anomalies in the Indian Ocean with intensified wind anomalies in the northern Indian Ocean. At the same time, the independent ENSO has weak SST and circulation anomalies in the Indian Ocean resulting in a weaker relationship between ENSO and ISMR.
The above analysis confirms that during period 1 the SST anomalies in the southeast Atlantic were cooler during MAM with weak warming in the north. It is intensified by the summer season in the presence of co-existing El Nino resulting in a weak negative relationship between AMM and ISMR. But after 2002, the ENSO phase reversal is induced by the warm SST anomalies in North Atlantic and the pattern also strengthened by summer. The AMM influenced ISMR through the off-equatorial circulation and the La Nina-induced equatorial easterly wind anomalies during period 2. Thus we have a positive AMM-ISMR relationship and an increased ENSO-ISMR relationship during period 2. Atlantic for out-of-phase years ( Fig. 11a and c). ISMR also follows the same anomalies as observations. Meanwhile, the negative SST anomaly during the same phase is stronger than observed and extends the equatorial belt and the warm anomalies are more northward. Thus, a belt of equatorial cooling appears in the equatorial Atlantic during period 2 inducing reduced convection over the equatorial Atlantic region (Fig. 11b). The negative anomaly during the outof-phase years is also extending northward. Thus there is a difference in the observed position of SST and rainfall anomalies for CCSM4, even though the model captures the AMM-ISMR relationship as observed. CFSv2 also has a similar AMM-ISMR relationship, with the cool SST anomalies in the south Atlantic in the equatorial region during period 2. Figure 12 shows the spatial pattern of the first leading mode of tropical Atlantic SST anomalies for MAM and JJAS seasons for both periods for CCSM4. During period 1, MAM EOF1 has strong negative loading in the southern Atlantic and extends to the northern region during summer. During the second period, there is strong positive loading north of the equator with cooling in the south equatorial region between the equator and 5 0 S. The cooling becomes stronger and covers the equatorial belt during summer. The equatorial cooling during period 2 is the significant difference between the observed (Fig. 3d) and model simulated pattern. The northern Atlantic warming is weak during both periods. The correlation of MAM PC1 with North Atlantic, south Atlantic and Atlantic Nino SST indices shows that both period PC1 has a weak correlation (0.27) with north Atlantic SST, while the correlation with south Atlantic is

AMM -ISMR relationship in NMME models
The present section compares the ability of recent general circulation models from the NMME project (Kirtman et al. 2014) for the AMM-ISMR relationship. The mean picture (SST bias, not shown) of tropical Atlantic SST shows that during the spring season, three GFDL models have warm SST bias in the entire tropical Atlantic. CanCM4i, Can-SIPSv2, and CCSM3 have a warm bias in the northern part and cold bias in the southern part and CCSM4 and CFSv2 have a cold bias in the entire region. The bias is east-west oriented for all models during the summer season, with a stronger bias in the south Atlantic. The biases do not differ much between the two periods before and after 2002. Figure 10 shows the time series of 11 years running correlation of the model hindcasts like Fig. 1. CCSM4, CFSv2, and NEMO models have a negative correlation between 1992 and 2000 and are positive afterward, like observations (Fig. 1). The negative correlation extends to 2008-09 for CanSIPSv2, CanCM4i, and GFDL models, while the in-phase AMM-ISMR correlation starts much before 2000 for CCSM3. AMM-ISMR correlation is weak and negative for all the models before 2000. During the second period, CanCM4, CanSIPSv2, CCSM3, and CCSM4 have inphase relationship and is close to observed for CCSM3 and CCSM4 (Table 1). AMM-ENSO relationship is also close to observation for CCSM4 during the second period.
Similar to observations, strong minus weak AMM index years composite is made for AMM-ISMR same phase and opposite phase years for models. Figure 11 shows the composite of SST and rainfall for the above two cases for CCSM4 (best model as per the Table 1). CCSM4 captures the observed pattern of stronger warming over the northern Atlantic for in-phase years and cooling in the southern Tropical SST anomalies induced by the AMM and Nino3.4, after removing the influence of each other are shown in Fig. 13. The AMM influence in absence of ENSO ( Fig. 13a and b) has stronger north Atlantic warming during both periods. Meanwhile, period 2 has stronger equatorial cooing as seen from the EOF pattern in Fig. 11d. Thus the equatorial cooling during period 2 is the internal variability of Atlantic Ocean SST in the models. Still, the absence of ENSO increases the off-equatorial warming in the north Atlantic. The Nino3.4 influence in absence of AMM ( Fig. 13c and d) have different anomalies in the Atlantic with weak cooling in the southeastern region during period 1 changed to strong warming during period 2. This change in ENSO-induced SST anomalies is not there in observations, where the ENSO pattern remained the same for both epochs. Thus the Atlantic PC1 relationship with ENSO and change in the ENSO-induced anomalies in the Pacific are significant (cc = 0.57) during period (1) ATL3 has a correlation of -0.42 during period 1 and it increased to -0.47 during period (2) This is also different from the observed  different in models as compared to observations. These interactions need to be studied further.

Summary and conclusion
In recent periods Atlantic Ocean SST anomalies are found to significantly contribute to the tropical climate (see the review article by Cai et al. 2019), including the Indian summer monsoon (Vittal et al. 2020;Yang and Huang 2021). The present analysis of boreal spring (MAM) season Atlantic Meridional Mode (AMM) index and Indian summer monsoon rainfall (ISMR) indicates that the relationship has undergone substantial decadal variability with a weak negative correlation from 1990 to 2002 which reverses to a significant positive correlation after that. During the in-phase relationship (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020), there is strong warming in the North Atlantic region. The upper-level circulation induced by the warming extends to the Indian land region and the Indian Ocean with additional divergence over the northeast Pacific. But the opposite phase relationship has strong cooling in the southern part of the equatorial Atlantic Ocean. This divergent circulation extends to the western Indian Ocean and India with a contrasting pattern in eastern IO and has reduced convection over India. The possible role of any change for Atlantic SST between the two periods centered around early 2000 and its relationship with ENSO and ISMR is discussed in the study.
During the first period, the tropical Atlantic SST anomaly of the MAM season has weak warming in the northern region and stronger cooling in the southern Atlantic. The south Atlantic cooling is strengthened by the co-existing El Nino and extends to the north equatorial Atlantic by JJAS. But during the second period, the SST pattern of the MAM has more substantial warming in the north Atlantic and continues to the summer season extending to the south Atlantic with weak opposite loading south of that. This pattern has a stronger relationship with NAT SST only. ENSO is in the decay stage during spring and changes its phase by summer. Earlier studies (Ren et al. 2021) considered both periods together and reported an STA-related pattern as EOF1 and an NTA-related pattern as EOF2 for the summer season.
Here when the analysis is performed for two periods centered in 2002, STA-related variability appears as EOF1 for periods before 2000 and NTA-related pattern as EOF1 for post-2000 periods.
Further analysis indicated that Atlantic SST anomalies during the MAM season play a significant role in the summer ENSO phase reversal during period 2. In a similar line, a study by Yang and Hang (2021, Fig. 6a-e) has a similar pattern for ENSO anomalies as in our Fig. 5a and b for period 1 and 2 and they concluded that during period 1, the ENSO phase is continuous from the previous year winter, while after 2000, it is developing phase. In the developing stage, the ENSO is influenced by Atlantic SST. The present study also shows that Atlantic SST affects the ISMR through off-equatorial circulation patterns in the tropical Pacific and over Africa and the north Arain Sea during period 2. The La Nina formed during summer also induces equatorial circulation anomalies from the central pacific to the monsoon region. Both these mechanisms act together to intensify the ISMR during period 2. The study also showed that the increased strength of the ENSO-ISMR relationship after 2002 resulted from stronger Atlantic variability and associated circulation during the period. At the same time, before 2002, El Nino intensified the STA cooling during summer as evidenced by the EOF analysis and composite analysis. Ren et al. (2021) argued that the STA region might not induce local convection and associated circulation as NTA due to the presence of cold SST in the southeast Atlantic. Thus the Atlantic influence on tropical circulation and monsoon dominates during period 2 only when the ENSO onset is late and is influenced by Atlantic SST.
The ability of recent seasonal prediction models from the NMME project is analyzed to understand the model's ability to capture the AMM role in ISMR. Models such as CCSM3, CCSM4, CFSv2, CanCM4i, etc. have captured the reversal of AMM-ISMR correlation from negative to positive, but some other models have more negative periods than positive. But the best models also differ in significant mode of Atlantic variability after 2000 with more muscular equatorial SST anomalies, which are swapped with opposite polarities south and north of it than the observed SST pattern. There is a more equatorial-oriented response for the models compared to observations, and the north Atlantic variability is more robust in the absence of ENSO only. The Atlantic variability has a stronger relationship with ENSO during both periods. Thus even though many models capture the AMM-ISMR and ENSO-ISMR correlation reverses correctly, the SST pattern in the Atlantic needs to be simulated better.