Local Ocean-Atmosphere Interaction in Indian Summer Monsoon Multi-Decadal Variability

The signicant multi-decadal mode (MDM) of the Indian summer monsoon rainfall (ISMR) during the past two millennia provides a basis for decadal predictability of the ISMR and has a strong association with the North-Atlantic variability with the Atlantic Multi-decadal Oscillation (AMO) as a potential external driver. It is also known that the annual cycles and interannual variability of ISMR and sea surface temperatures (SST) over the tropical Indian Ocean (IO) are strongly coupled. However, the role of local air-sea interactions in maintaining or modifying the ISMR MDM remains unknown. A related puzzle we identify is that the IO SST has an increasing trend during two opposite phases of the ISMR MDM, namely during an increasing phase of ISMR (1901 to 1957) as well as a decreasing phase of ISMR (1958-2007). Here, using a twentieth-century reanalysis (20CR), we examine the role of air-sea interactions in maintaining two opposite phases of the ISMR MDM and unravel that the Bjerknes feedback is at the heart of maintaining the ISMR MDM but cannot explain the increasing trend of SST in the tropical IO during the opposite phases. Large-scale low-level vorticity inuence on SST and net heat ux changes through circulation and cloudiness changes associated with the two phases of the ISMR MDM together contribute to the SST trends. The decreasing trend of low-level wind convergence during the period between 1958 and 2007 is a determining factor for the decreasing trend of ISMR in the backdrop of an increasing trend of atmospheric moisture content. Consistent with the lead of the AMO with respect to ISMR by about a decade, the AMO drives the transition from one phase of ISMR MDM to another by changing its phase rst and setting up low-level equatorial zonal winds conducive for the transition.


Introduction
The share of agriculture in the gross domestic product (GDP) of India hovered between 17 and 19 percent during 2003 and 2020 and reached almost 20 percent making it a bright spot in the GDP performance of the country during 2020-21, according to the Economic Survey 2020-2021 (Kapil 2021). Dependence of the country's economy on agriculture makes the socio-economic welfare of the large population of the region vulnerable to the vagaries of the ISMR with both the total food production as well as the GDP strongly correlating with the ISMR (Webster et al. 1998;Parthasarathy et al. 1988; Gadgil and Gadgil 2006; Amat et al. 2018Amat et al. , 2021. The seasonal rainfall anomalies during extremes of ISMR year-to-year variability manifesting in the large scale ' oods' and 'droughts' tend to be homogeneous over the country (Shukla 1987) as also evident from the dominant pattern of the year-to-year variability of the ISMR (Mishra et al. 2012;Choudhury et al. 2021). Therefore, a forewarning of even the quantum of seasonal rainfall over the country (ISMR) one season in advance is useful for the policymakers and farmers and has a long history in India starting with Blanford (1884) and Walker (1924). For the same reason, longer lead forecasts of ISMR such as at 6-month or 12-month leads would be highly useful for farmers and policymakers to plan for water resources and for alternative crop strategies to minimize loss. However, even the one season forecast of ISMR has remained a grand challenge problem ( Potentially the ISMR, as a measure of the Indian summer monsoon, is a highly predictable system (Charney andShukla 1981, Saha et al. 2019) and the predictability comes from association of the ISMR with some predictable slowly varying drivers such as the El Niño and Southern Oscillation (ENSO) and the Atlantic Multi-decadal Oscillation (AMO). One of the challenges in seasonal prediction of ISMR has been that the interannual correlation between ISMR and the predictors undergo signi cant epochal variations (Kripalani and Kulkarni 1997;Krishnamurthy and Goswami 2000; Kumar et al. 1999;Xavier et al. 2007).
This epochal variability is partly due to the inherent signi cant multi-decadal variability of ISMR (Kriplani and Kulkarni 1997; Goswami et al. 2006a; Goswami et al. 2015) and the predictors like the ENSO (Zhang et al. 1997), the AMO, and the Paci c Decadal Oscillations (PDO, Mantua and Hare 2002). A model decomposition of long time series of instrumental records of ISMR (1813-2006, Sontakke et al. 2008) indicates that apart from a quasi-biennial mode (2.7-year period), the MDM with period around 65-years is the only other statistically signi cant mode of ISMR variability (Rajesh and Goswami 2020). That the MDM of ISMR with a period of around 65-years is a robust mode of ISMR variability is evident in rainfall reconstruction from tree ring records for more than 500 years in south India (Goswami et al. 2015) and in oxygen isotope records (correlated with rainfall amount) in cave deposits from central India/north India over the past two millennia (Sinha et al. 2011(Sinha et al. , 2015. The MDM of ISMR in uences or modulates the seasonal predictability through modulation of its interannual variability. From the instrumental record of ISMR, it has been observed that the frequency of occurrence of oods (droughts) increases (decreases) by a factor of 2 during the positive (negative) phases of ISMR MDM (Rajesh and Goswami 2020). The inability to simulate the AMO and ISMR MDM with delity by climate models has one roadblock to improving skill of seasonal predictions systems of today. The CMIP6 models are showing notable improvement in simulating the AMO as well as ISMR MDM (Choudhury et. al., 2021) with optimism for improving ISMR prediction in coming years. A better understanding of the drivers of the MDM of ISMR and associated teleconnection mechanisms is, therefore, critical for simulating the same by climate models and making advances in seasonal prediction of ISMR.
Its robust existence during the past two millennia indicates that the MDM of ISMR with an approximate period of around 65 years is a natural mode of the South Asian monsoon system. What drives the MDM of ISMR has been the subject of intense investigation in recent years. On centennial and millennial time scales, paleo-evidences indicate strong linkages between mega-droughts of Indian monsoon and cooling of North Atlantic water (Burns et al. 2003;Gupta et al. 2003). Analysis of instrumental records of ISMR and SST over the North Atlantic reveal a signi cant association between the two on multi-decadal time scales as well (Goswami et al. 2006a) and the teleconnection is supported by coupled model simulations (Zhang and Delworth 2006;Wang et al. 2009;Luo et al. 2011Luo et al. , 2018. In a recent study, Borah et al. (2020) show that all the non-El Niño droughts of ISMR are associated with cooling of the North Atlantic associated with the negative phases of the AMO. The potential for the AMO to enhance the predictability of ISMR led to explore the teleconnection mechanisms between the AMO and the seasonal mean ISMR in several recent studies. Goswami et al. (2006a) proposed that the North Atlantic SST associated with the AMO sets up a stationary wave and in uences the ISMR through modulating the tropospheric temperature gradient (TTG) over the Indian monsoon region, a mechanism that was supported by a number of modeling studies (Lu et al. 2006;Li et al. 2008). The nature of the stationary wave has been elucidated in the form of a Rossby wave train in some recent studies (Syed et al. 2012 Borah et al. (2020) showed that the modulation of the large scale circulation by the Rossby wave train clusters the monsoon 'breaks' in one phase of the seasonal cycle leading to a 'long break' and resulting in weakening of the ISMR. Generalizing the Borah et al. (2020) study, Rajesh and Goswami (2020) show that during the positive (negative) phase of the AMO, similar Rossby wave trains cluster 'active' ('break') phases in one segment of the seasonal cycle leading to 'long active' ('long break') spells and resulting in strengthening (weakening) of the seasonal mean ISMR. While the teleconnection is largely through an atmospheric bridge, the possibility of an oceanic bridge involving the Atlantic Meridional Overturning Circulation (AMOC) is also indicated (Rajesh and Goswami 2020) while a detailed pathway remains unknown. The Rossby wave train appears to be set up by episodic barotropic vorticity forcing over the SST anomalies in the North-Atlantic (Borah et al. 2020).
Unlike in the tropics, the extra-tropical SST being largely a response of atmospheric forcing, the driving of the episodic barotropic vorticity remained unclear. While on high frequency synoptic time scale, indeed the atmospheric uxes determine the SST, on time scales longer than 10-days, large scale SST anomalies could in uence meridional surface pressure gradients, displace the storm tracks and create stationary barotropic vorticity (Rajesh and Goswami 2020; Goswami et al. 2021). Thus, compelling evidence has emerged for AMO as a major driver of the ISMR MDM. An alternative pathway to the modulation of the sub-seasonal oscillations by the Rossby wave train has been indicated in some recent studies (Sun et al. 2017(Sun et al. , 2018 where it is shown that the AMO could in uence ISMR on decadal to multi-decadal time scale through modulation of western Paci c SST, which in turn in uence the Arabian Sea SST through a regional atmospheric bridge thereby in uencing the moisture ux to the Indian monsoon region. The Indian summer monsoon system, on the other hand, is a coupled ocean atmosphere system where local ocean-atmosphere interactions not only maintain the annual cycle of SST in the region, the Inter-Tropical Convergence Zone (ITCZ) and monsoon rainfall (Webster et al. 1998 and has been the subject matter of several studies lately. Through a modeling study, Bollasina et al. (2011) indicate that the cooling due to anthropogenic aerosols is responsible for the decreasing trend of ISMR during the period. The revival of the ISMR after 2002, however, is not consistent with aerosol as primary forcing (Jin et al. 2017). In another interesting study, Swapna et al. (2014) show that the increasing trend of SST over the IO is responsible for the decreasing trend of ISMR during this period  while the weakening trend of ISMR support the increasing trend of SST, through circulation and ux changes, indicating positive feedback. Again, the revival of the ISMR after 2002 (Jin et al. 2017) while the SST is still increasing is also inconsistent solely with positive feedback. Here, we explore a hypothesis that the ISMR MDM is largely driven by teleconnection with the AMO through modulation of the regional circulation but the observed periodicity and amplitude of the ISMR MDM is a result of modi cation through local air-sea interactions and aerosol forcing.
Our hypothesis is rooted in the following observations. A longer time series of ISMR ( that the simulated NCEPv3 ISMR multi-decadal variability replicates variability of observed ISMR (Fig. 1a) reasonably well. However, the phases of simulated multi-decadal variability of ERA-20CM ISMR during 1901-1957 and 1958-2007 are opposite to that of observed ISMR. Therefore, we use the NCEPv3 winds in this study instead of ERA-20CM winds. The seasonal mean net heat uxes (Q net ) are extracted from the two reanalyses (NCEPv3, ERA-20CM), calculated from net downward shortwave radiation ux, net upward longwave radiation ux, sensible heat ux, and latent. TropFlux is a hybrid product (Kumar et al. 2012) where shortwave radiation uxes are used from International Satellite Cloud Climatology Project (ISCCP) and uses bias and amplitude corrected ERA-I (10-m winds, 2-m air, and sea temperature, 2-m air relative humidity, and downward radiative uxes. In order to get an idea of the biases in the Q net from reanalysis, we compare the climatology of the Q net from reanalyses with that extracted from the TropFlux data set. To see integrated moisture convergence and water vapour, we use speci c humidity data from NCEPv3. The Bjerknes feedback originally proposed by Bjerknes (1969) for explaining the El Nino and Southern Oscillation (ENSO) in the Paci c is applicable for the tropical Indian Ocean as well. The equatorial surface winds driven by east-west surface pressure gradients lead to thermocline adjustment via equatorial Ekman divergence (convergence) and modify the original equatorial SST gradients. Associated modi cation of surface pressure gradients modi es the original equatorial winds. Over the Indian Ocean during northern summer, the Bjerknes feedback is closely linked with the Indian monsoon as the monsoon heat source in uences the equatorial winds in the region. As the zonal wind forcing at the equator plays a critical role in the Bjerknes feedback an empirical orthogonal function (EOF) analysis of zonal mean surface zonal winds averaged between 70°E to 90°E is carried out between 35°S and 35°N for the period 1901-1957 (P1 The southeasterly cross-equatorial ow and southwesterly ow to the north of the equator as a result of the Indian monsoon heat source creates a large-scale anticyclonic vorticity around the equator. Year-toyear variation in the intensity and location of the monsoon heat source would give rise to anomalous cyclonic or anti-cyclonic large-scale vorticity around the equator. Anomalous upwelling and down welling forced by the vorticity could in uence the SST over the tropical belt. Change in SST over the tropical belt leads to change in moisture ux transported and converged over the monsoon region and affect the monsoon that caused the vorticity anomaly over the equator. In order to examine this aspect of ocean atmosphere interaction, an EOF analysis carried out on the meridional shear of zonally averaged (u wind from NCEPv3) surface wind and -d

Regression analysis:
Regression is a useful statistical tool used to determine relationships between two or more dependent and independent variables. Among all the different regression models we used linear regression in our study. A linear regression analysis has been done to nd how the SST and ISMR is varying with the zonally averaged (u wind from NCEPv3) surface wind and -d[u]/dy for both the periods P1 and P2.

Bjerknes Feedback
Bjerknes feedback where surface wind forcing leads to east-west SST gradient in the equatorial Paci c basin, which in turn feeds back to strengthen the original surface winds is at the heart of the ENSO (Bjerknes 1969)  variance. The leading EOF (henceforth, referred to as EOF1) of surface winds zonally averaged over 70°E to 90°E during the two periods P1and P2 (Fig. 2a and Fig. 2b) show some interesting differences in large scale circulation during the two periods. While the deep equatorial belt was dominated by higher frequency of occurrence of easterly forcing during the early period (1901-1957), the later period is dominated by higher frequency of occurrence of westerly wind forcing (Fig. S1b,c). The corresponding PCs (Fig. 2c,d), while having large interannual variation, do not indicate any signi cant trend. The propensity of zonal mean easterly wind forcing at the equator during the period P1, and westerly forcing in the period P2 contribute to the easterly trends of surface winds at the equator in the period P1 between 70 E and 100 E (Fig. 3a) as against westerly trends of surface winds at the equator during the period P2 ( Fig. 3b) between 60 o E and 90 o E. The trends in the zonal winds are also consistent with trends of SST during both periods (Fig. 3a,b). Much stronger and wide-spread increasing trends of SST during P2 compared to that during P1 are consistent with a weaker increasing trend of area averaged SST in Fig. 1b compared to a relatively stronger increasing trend of area averaged SST during the period (P2) . Also, maximum SST trend during P2 is over the west-central equatorial IO, as noted in earlier studies (Swapna et al. 2014;Koll et al. 2014).
A regression of PC1 of zonally averaged zonal winds on seasonal mean rainfall anomaly over India during the periods P1 and P2 (Fig. 4a,b) show that the zonal wind variations during P1 are associated with the increasing tendency of rainfall over the core monsoon region and west of the Western Ghat consistent with Fig. 1a, while that during period P2 are associated with a decreasing tendency of rainfall over core monsoon and west of Western Ghat, consistent with Fig. 1a. The SST anomaly patterns associated with the zonal wind variations (regression with PC1) during the period P1 (P2) (Fig. 4c,d) are closely similar to a positive (negative) IOD pattern (Saji et al., 1999). They are consistent with easterly (westerly) driving as evident from Fig. S1a (Fig. S1a). During an easterly driving regime, shoaling of thermocline to the east gives rise to cold anomaly while depression of thermocline to the west gives rise to warm anomaly. The situation reverses during the westerly driving regime. During P1 the SST dipole has a cold anomaly over a smaller region in the east and a much larger region of warm anomaly to the west. In contrast, during the period P2, the SST dipole has a warm anomaly over a smaller region in the east, with a much larger region of cold anomaly to the west (Fig. 4c,d). The overall easterly (westerly) driving during P1 (P2) is due to the fact that the equatorial zonal winds averaged over (70 E to 90 E, 5 S to 5 N) have higher propensity of easterly zonal wind during P1, while the propensity of westerly zonal wind is higher during P2 ( Fig. S1d,e). The easterly (westerly) winds at the equator during P1 (P2) is a result of the stronger (weaker) than normal ISMR while the warmer (colder) SST to the western part of IO as a result of equatorial dynamics leads to higher (lower) moisture ux to the continent and tends to strengthen (weaken) the monsoon further. This is how the Bjerknes feedback at the equator and ISMR, an offequatorial heat source are linked. The decadal variability of the IOD has also been documented (e.g., Ashok et al. 2001Ashok et al. , 2004. We nd westward surface currents around the equatorial belt, forced by predominantly easterly surface winds during the period P1 (Fig. 5a). Associated equatorial upwelling and coastal upwelling depletes the HC in the eastern IO anked by a horseshoe pattern build-up of HC in the western IO (Fig. 5a). The offequatorial heat depletion in the eastern IO seems to be due to episodes of equatorial upwelling Kelvin waves that were driven by the easterly winds, and subsequently travelled as a coastal Kelvin wave towards north after hitting the eastern boundary and radiated westwards as Rossby waves. The signature of a coastal Kelvin wave in the Bay of Bengal is rather apparent (Fig. 5a). Similarly, the buildup of HC in the eastern IO during the period P2 seems to be due to episodes of down welling equatorial Kelvin waves driven by the westerly zonal winds, which subsequently have travelled north and south as coastal Kelvin waves and radiated as down welling as Rossby waves (Fig. 5b). Even in this case, coastal Kelvin waves in the Bay of Bengal could be seen clearly. The surface currents during the period P2 are also consistent with surface wind forcing. However, the westward surface currents in this case are limited to the central and eastern equatorial IO east of 70 O E (Fig. 5b). This explanation is supported by the sea surface height (SSH) anomaly patterns associated with zonal mean zonal winds (regression with PC1) over the two periods (Fig. 5c,d).

Large-scale vorticity of surface zonal winds and SST
While there is considerable evidence that a Bjerknes feedback operates in maintaining the MDM of ISMR, the large increasing trend of SST during the later period (P2) cannot be explained by this feedback. In fact, purely due to this feedback SST should have a decreasing trend. As ISMR is a result of low-level moisture convergence, a higher SST over the IO would be associated with higher moisture availability and should be associated with stronger ISMR. Therefore, the association of a decreasing trend of ISMR and an increasing trend of SST over the IO during this period is counterintuitive. Hence, instead of the increasing trend of SST over the IO during this period driving the decreasing trend of ISMR, it is more likely that the large-scale wind changes associated with the decreasing trend of ISMR is driving the increasing trend of SST. We propose that the change in large-scale vorticity due to the weakening of monsoon circulation during that period played a role in the warming trend. There are two other manifestations of low-level atmospheric circulation, which might have potentially contributed to SST changes over the IO during the P2. Firstly, apart from the equatorial zonal wind, the large-scale low-level monsoon winds over IO, are associated with off-equatorial vorticity, which leads to deepening or shoaling of the thermocline. This mechanism is particularly effective in in uencing SST in regions where the mean thermocline is shallow, such as the eastern equatorial IO and the central Indian Ocean thermocline dome, south of the equator. The other factor that could also contribute to the SST changes is the net heat ux (Q net ) at the surface as a result of surface wind changes and changes in the cloudiness. In this section, we explore the contributions of large-scale vorticity.
The leading EOFs of vorticity of zonal mean surface zonal winds during the monsoon season for the periods P1 and P2 are shown in Fig. 6a,b while the corresponding PCs for the two periods are shown in Fig. 6c,d. From Fig. 6c and 6d, we see a decreasing trend during P1 and an increasing trend during P2, both statistically signi cant at 0.05 level from a Mann-Kendall test. The leading EOFs (Fig. 6a,b) indicate important changes in the large-scale monsoon winds over the IO from P1 to P2. While during P1, a cyclonic vortex centered on the equator dominated the wind pattern, during P2, a pair of cyclonic vortices on either side of the equator seems to dominate the low-level wind pattern. This is clearly evident in the vector wind pattern associated with the PC1 of vorticity arising from meridional shear of the zonal mean surface zonal winds (Fig. 7a,b). A regression of the PC1 of vorticity of zonal mean surface zonal winds on seasonal mean rainfall over India (Fig. 6e,f) indicates that the signi cantly increasing trend of the PC1 contributes to a strong negative trend of ISMR during the period P2. On the other hand, during the period P1, the decreasing trend of the PC1 is associated with a positive trend of rainfall anomaly pattern over most of India strengthening ISMR more in the early part of the period and less during the latter part of the period resulting in a relatively weak increasing trend of ISMR consistent with Fig. 1a.
Furthermore, a regression of JJAS SST on to the PC1 indicates a positive SST anomaly in the central IO ( Fig. 7c) induced by the trend in low level meridional shear of zonal wind (-d[u]/dy) in P1. Similar regression analysis for the P2 indicates a positive SST anomaly in the equatorial eastern IO anked by colder SST anomaly in the western equatorial IO (Fig. 7d). The larger positive SST anomaly over the central south-equatorial IO is consistent with the cyclonic low-level wind vortex sitting over the thermocline dome in that region. In period P2, large-scale vorticity forcing increases the positive SST anomaly over a much larger region (Fig. 7d) compared to that due to direct zonal wind forcing at the equator (Fig. 4d). The positive SST anomaly over the Bay of Bengal is consistent with the northern component of the twin cyclonic vortices (Fig. 7b). The fact that PC1 during the P2 has a signi cant increasing trend indicates that the large-scale vorticity of the monsoon ow over the region does contribute to the increasing trend of SST over IO during P2.  (Fig. S2a) while the ISMR has an increasing trend during P1 and a decreasing trend during P2. As the ISMR is driven largely by moisture convergence rather than local moisture availability, an increasing trend of vertically integrated moisture convergence during P1 and decreasing trend of the same during P2 are consistent with trends of ISMR during the two periods (Fig. S2b). What makes the moisture convergence decrease during P2 in the backdrop of the moisture content of the atmosphere that has been increasing? The answer lies in the changes of the large-scale winds. The wind changes have led to a decreasing trend of wind convergence (Fig. S2c) that forced the moisture convergence to decrease even when the moisture content was increasing.

Net heat ux (Q net ) driving of SST trend
However, the increasing trend of SST during P2 is much stronger than that during P1 (Fig. 1b) the changes in SST forced by Bjerknes feedback or by the large-scale vorticity of zonal winds appear inadequate to explain the differences in the trends. As we noted, the two different phases of the ISMR MDM P1 and P2 are associated with signi cant changes in the large-scale circulation, particularly surface winds. These changes in circulation are bound to be associated with changes in cloudiness distribution. As a result, it may be natural to expect that the net heat ux (Q net ) would have similar changes during the two periods. The climatological mean Q net during JJAS over the tropical IO between 20 S and 20 N is positive (~10Wm -2 , see Fig. 8) leading to seasonal warming of SST over the region during the summer season. Here we explore if the changes in Q net over the period could also contribute to an increasing trend of the seasonal warming leading to an overall weaker increasing trend of SST during P1 and a stronger increasing trend during P2.
The net heat ux into the ocean is a sum of different heat exchange processes at ocean surface, which includes heating due to net shortwave radiation (NSWR), net outgoing longwave radiation (NLWR), sensible heat ux (SHF), and latent heat ux (LHF). Climatologically, the rst one is the contributor to the heat gain of the ocean, and all the other processes lead to heat loss, except for SHF, which depends on air-sea temperature difference. From all the four variables net heat ux can be calculated using the formula: (1) Where, NSWR = DSWR − USWR and NLWR = ULWR -DLWR, together with, Downward shortwave radiation (DSWR), Upward shortwave radiation (USWR), Upward longwave radiation (ULWR), Downward longwave radiation (DLWR) (e.g., Pokhrel et al. 2020) A simple thermodynamic understanding about the upper ocean is that the rate of change of SST is proportional to net heat ux. Such a balance can be expressed as hCρ (δ/δt SST) = Q net , (2) where, h is the depth of the mixed layer, C is the speci c heat of seawater; ρ is the density of seawater and Q net is net heat ux (e.g., Sengupta et al. 2001). Here mixed layer depth is calculated using the density criteria (Kazunori et al. 2004), i.e., starting from the upper-most available observation to the depth at which the density is equal or greater than a speci c value (e.g., 0.125 g/cm 3 ) than that at the surface is considered as the mixed layer depth (MLD).
To be consistent with SST and precipitation (ISMR), here we use the mean JJAS Q net between 1901 to 2007 to estimate its contribution to the SST trends during the two periods, P1 and P2. However, we recognize that all heat ux products, whether from reanalysis or 'observations' have their own biases (Pokhrel et al. 2020). To have an idea of biases in Q net climatology from NCEPv3, we compare the climatology of JJAS Q net from NECPv3 for the two periods (Fig. 8a,b) with those from two other ux products namely from ERA-20CM (Fig. 8c,d) and TROPFlux (Fig. 8e). The TROPFlux data is available only for the period 1979-2018 and hence its climatology may be compared only with P2.
It is interesting to note that the Q net averaged over the tropical IO region, de ned as bound by 50 E-100 E, 20 S-20 N, during P1 has a statistically signi cant decreasing trend (p = 0.001) from about +13 Wm -2 to about +5 Wm -2 while that during P2 has a weakly signi cant increasing trend from about +24 Wm -2 to about +29 Wm -2 (Fig. 9a,b). The net heat ux leads to a statistically signi cant (p = 0.003) decreasing trend of mixed layer temperature (Fig. 9c) resulting in approximately 0.5 O C decrease during P1. It is interesting to note that the Q net during the P2 drive a statistically signi cant increasing trend (p = 0.02) of mixed layer depth temperature resulting in an increase of 0.75 O C during P2 (Fig. 9d).

Discussion
A rather strikingly-decreasing trend of ISMR during the period 1951 to 2000 encouraged several studies to investigate potential drivers for this trend. Ocean-atmosphere interaction involving increasing trend of SST over the IO during that period (Swapna et  increasing phase during 1901 and 1957, approximately represent two opposite phases of ISMR multidecadal variability, and provide us an opportunity to examine local ocean-atmosphere interaction during two opposite phases of ISMR. For this purpose, surface winds that are internally consistent with the data sets of monsoon rainfall (ISMR) and SST are essential. The observed ISMR is not necessarily consistent with various independent analyses of surface winds and SST, as observed precipitation is not used to constrain these analyses. Therefore, we need to use a 20 th Century reanalysis for our study of air-sea interaction, where the analysis system generated precipitation over the Indian region during the summer monsoon season is consistent with surface winds and the winds are consistent with SST. For our analysis of the air-sea interaction to be meaningful to observed multi-decadal variability of ISMR, however, the analyzed ISMR, from the 20 th century reanalysis should have multi-decadal variability similar to that from the observed during the period between 1901 and 2007. We nd that the reanalyzed-ISMR in NCEPv3 (Fig. 1c) follows the multi-decadal variability in the observed ISMR (Fig. 1a) during the period, while the multi-decadal variability from the ERA-20CM (Fig. S3) during the same period has phases that are opposite to those of ISMR. For this reason, winds from NCEPv3 and SST from HadISST, where the SST is consistent with the winds have been used in this study to examine air-sea interaction during two opposing phases of ISMR.
Our results indicate that the basic multi-decadal oscillation of ISMR may be driven by teleconnection with North-Atlantic SST, but a local Bjerknes feedback and a large-scale vorticity help to maintain and modify it. During the increasing phase of ISMR (P1), a higher propensity of occurrence of a positive IOD pattern of SST anomaly with cold water in the eastern Indian IO while warm waters in the western IO reinforce easterly equatorial surface winds that drive them. During a decreasing phase of ISMR (P2), just the opposite happens, with a higher propensity of negative IOD events reinforcing the westerly equatorial surface winds that drive them. The Bjerknes feedback, however, does not contribute signi cantly to the trend of SST over the IO on multi-decadal time scale. We also note that the SST in uences the ISMR and ISMR in uences the winds and cloudiness distribution and thereby in uences the Q net . Therefore, the JJAS mean Qnet contains some of the other two contributions through ISMR in uence. It is also noted that over most part of the IO, SST is driven by the Q net except small regions over the coasts of Somalia and Sumatra where upwelling is important. Thus, the Qnet largely drives the SST over 20 O S and 20 O N and 70 O E and 100 O E. While we could comment on their contributions to the SST (or mixed layer trends), therefore, it is not fair to combine them to estimate a combined contribution to the SST trend. With this caveat, we examined the contributions of vorticity feedback and Q net to the stronger increasing trend of SST over IO during P2 and nd that it is consistent with additive contributions to increasing trends of SST due to the large-scale vorticity forcing and SST forced by Q net during the period. However, a similar comparison during the period P1 indicates that the small increasing trend of SST in the backdrop of a decreasing trend of Q net could not be explained by the weak increasing trend of contributions from vorticity feedback. The result indicates that some of the missing physics such as advection and entrainment may be important in maintaining the weak increasing trend of SST during P1. The overall weak increasing SST trend during P1 is consistent with the weaker increasing SST trends over most regions and a weak negative trend south of 10 O S between 60 E to 80 E (Fig. 3a). It may be noted that the rst order in uence on the SST trend comes from the climatological JJAS mean Q net (Fig. 8e) with cooling tendency south of 10 O S and warming tendency north of it. The negative or weak positive SST trend south of 10 O S and positive SST trend north of it during both periods (Fig. 3) are consistent with the spatial structure of climatological Q net. The actual trend of SST at any location will also depend on the mean mixed layer depth with the deepest mixed layer being south of 10 O S and shallower mixed layers over the equatorial belt and North Bay of Bengal (Fig. S4b). The largest SST trends (Fig. 3) around the equatorial belt are again consistent with this. The trends of Q net and mixed layer depth (MLD) during the period P1 (Fig. S4 a,c) add second-order trends on the SST. The negative SST south of trend 10 O S during P1 is a result of the combined in uence of the two forces.
The anomalous changes in the climatological low-level winds during the two periods, P1 and P2 (Fig.  7a,b) are the key to explain the differences in air-sea interaction during the two opposite phases of the ISMR multi-decadal oscillation. Once the background winds for a phase are established (like that during P1), the air-sea interaction sets up SST distribution conducive for strong monsoon and perpetuates the easterlies at the equator until the wind climatology is changed to westerlies to reverse this process. We envisage the transition to take place in the following way. Let us start with the positive AMO phase and increasing trend of ISMR like the period P1. When the NA SST MDM changes to a negative phase, it starts introducing westerly zonal wind forcing over the equator. However, the ISMR is still in the positive MDM phase supporting easterly zonal winds at the equator. Therefore, it takes a few years for the westerly to weaken the ISMR so that it start supporting the westerly forcing at the equator and to establish the opposite feedback. A negative phase of ISMR MDM gets established. As shown by Rajesh and Goswami (2020) there is a phase lag between the ISMR multi-decadal mode (MDM) and the North-Atlantic SST MDM with the latter leading by 8 years. This lag is consistent with the proposed mechanism of transition. And hence, two speci c periods of ISMR like P1 and P2 could not be exactly matched with two phases of the AMO.

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