We use the high-resolution model ECCO2 (Estimating the Circulation and Climate of the Ocean Phase II, cube92 version), based on the Massachusetts Institute of Technology general circulation model (MITGCM, Marshall et al., 1997), with a spatial resolution of 0.25° longitude× 0.25° latitude and temporal resolution of 3 days. There are 50 levels covering 5-5906 m in the vertical. The model includes variables such as temperature, salinity, three-dimensional currents, etc. The current climatology is calculated based on 13 years from 2005 to 2017.

The surface current velocity data used in this study are from drifter-derived climatology of Global Near-surface Currents developed by Laurindo et al. (2017), which is updated to July 2020. This dataset builds on the climatology of Lumpkin and Johnson (2013), derived from satellite-tracked surface drifter data. The data provide monthly near-surface (15-m) currents climatology. Uncertainties in the dataset are related to the number of observations and the variance, but, the Indian Ocean is reasonably well sampled. Following the study of L’Hegaret et al. (2018), the daily currents are derived from the monthly current data, with a spatial resolution of 0.25° longitude× 0.25° latitude.

The surface drifter data used are obtained from the Global Drifter Program (GDP), which is a plan of the Atlantic Oceanographic and Meteorological Laboratory (AOML). The drifters provide 15-m currents, location, velocity, and sea surface temperature (Lumpkin and Pazos, 2007). The data are screened through the quality control procedures by the Drifter Data Assembly Center (DAC) of the AOML and interpolated into 6-hour intervals using the Kriging method (Hansen and Poulain, 1996; Lumpkin and Centurioni, 2019). Previous studies have shown that the drifter trajectories represent the characteristics of the Indian Ocean current field well (e.g. Wu et al., 2020).

The monthly salinity and temperature from the Argo dataset obtained from the International Pacific Research Center (IPRC) are used to validate the model output. The gridded Argo data cover the period of 2005 to 2017 with 27 vertical layers from 0 m to 2000 m, and a horizontal resolution of 1° longitude ×1° latitude. The monthly wind data used to calculate the Ekman transport are from the European Centre for Medium-Range Weather Forecasts Interim Reanalysis (ERA-Interim). We use the data from 2005-2017, with a spatial resolution of 1° longitude×1° latitude.

The Lagrangian analysis is an effective way of identifying the origin and destination of water particles. Herein, we used a diagnostic Lagrangian tool, a. k. a. the CMS (Connectivity Modelling System, Paris et al., 2013), which is an open-source Fortran toolbox, created by the University of Miami, for the multiscale tracking of biotic and abiotic particles in the ocean. The CMS uses a 4^th-order Runge-Kutta integration method to calculate particle advection and position. The CMS has been used in many topics in a variety of studies (e.g. Peña-Izquierdo et al., 2015; Cheng et al., 2016; Tamsitt et al., 2017; Kourafalou et al., 2018). The CMS has been used on velocity fields from many high-resolution models such as OFES, HYCOM, ECCO2, and many other ocean models. To analyze the pathways of cross-equatorial currents in the EIO, the trajectories of water masses are described using the Lagrangian analysis method.

The thermocline of the Indian Ocean is strong and stable. The heat and salt transports of the upper ocean can be estimated using ECCO2, Argo temperature, and salinity data. The MHT and MST are estimated as shown in Equation (1) and Equation (2), respectively:

where x_E is the east boundary; H =50 m; ρ, s, v, c_p , θ denote the density, salinity, meridional current, specific heat, and potential temperature, respectively.

The seasonal distributions of observed and simulated currents, SSS, and SST are cross-validated in Figures 1 , 2 . The results suggest that the ECCO2 model can reproduce the seasonal and spatial structure of the observed data fairly well in the EIO. In boreal winter, driven by the northeast monsoon, a strong westward NMC appears in southern Sri Lanka. The NMC extends from the southeast of the BOB to the southern Arabian Sea, which transports the low salinity water from the BOB into the Arabian Sea. As the surface circulation is adjusted with the monsoonal forcing in spring, the NMC disappears gradually. Under the influence of the westerly wind, strong eastward WJs appear between 2°S and 2°N, which force the formation of the SJC (Clarke and Liu, 1993; Clarke and Liu, 1994; Qu and Meyers, 2005) entering the southeastern Indian Ocean along the Sumatra-Java coasts before joining the westward SEC. In boreal summer, influenced by the strong southwest monsoon, the SMC appears on the southeast side of Sri Lanka with a maximum of 0.5 m·s^-1, which transports high salinity waters from the Arabian Sea eastward into the BOB. The southwest monsoon weakens gradually in fall, forcing stronger WJs north of the equator than in the south. The eastward SMC (WJs) in summer (fall), the southward current along the western coasts of Sumatra, and the westward SEC form a cyclonic circulation system.

Low salinity waters are located in the BOB and the eastern boundary, with a minimum of 32.0 psu ( Figures 1E–H , 2E–H ). In contrast, the salinity of the Arabian Sea is much higher, with a maximum exceeding 36.0 psu; Associated with the salinity distributions in the Arabian Sea and the BOB, the SSS near the equator has a large zonal gradient, which is generally high in the west and low in the east. During the monsoon transition seasons, the WJs carry high salinity waters from the western Indian Ocean to the east, forming a high salinity tongue along the equator. In addition, salt exchange between the BOB and the Arabian Sea occurs through the SMC (NMC) during the summer (winter), forming a high (low) salinity tongue south of Sri Lanka. South of the equator, there is a westward extending low salinity tongue, which is due to the transport of low salinity waters by the ITF and SEC.

The SST in the EIO is higher year-round in climatology, with the SST in most sea areas higher than 28 °C ( Figures 1I–L , 2I–L ). Generally, the SST is higher near the equator than that off the equator, and north of the equator than in the south. In spring, the Pacific-Indian Ocean warm pool SST is the highest. In boreal summer and fall, the spatial temperature difference is the smallest. In winter, the SST in the north decreases due to the change in sea surface thermal conditions.

Surface particles are tracked using the Lagrangian analysis method. Here we select two background fields: ECCO2 and drift-derived currents. The seasonal variation in the drift-derived current is consistent with the ECCO2 simulation, suggesting the reality of the model simulation.

The particles are released in the EIO on the first day of each month and tracked for a year following the vertically averaged currents in the upper 15 m. The 501 particles in total are released along 5°N from 85°E to 95°E, with an interval of 0.02° in the zonal direction. For the sake of clarity, only 10% of the particle trajectories are shown in the plot. Seasonal variations of the trajectories in Figures 3 , 4 suggest that the BOB waters move southward across the equator along the eastern boundary of the Indian Ocean during spring through summer, whereas they are transported into the Arabian Sea all through winter before crossing the equator in the central basin. Almost all the particles released at the mouth of the BOB move southward in summer, consistent with the southward surface Ekman transport of the southwest monsoon. In fall through winter, nearly no particles move southward, except near the western boundary, suggesting the north advective by the surface Ekman transport of the northeastern monsoon.

According to the spatial distribution of particles, we divide the study region into three parts ( Figure 3 ): the northern part of the EIO (NEIO, east of 80°E and north of the equator), the southern part of the EIO (SEIO, east of 80°E and south of the equator), and the western Indian Ocean (WIO, west of 80°E). There are significant seasonal variations of particles ( Figures 3 , 4 ). During the monsoon transition period (March-May, Figures 3C–E , 4C–E ), the equatorial region was controlled by strong westerly winds as the northeast monsoon subsided gradually and the southwest monsoon began to strengthen. The surface circulation of EIO is adjusted in two states: the mouth of the BOB is dominated by eastward currents and southward surface Ekman transport, which prevented the particles from entering the BOB; The strong eastward WJs near the equator between 2°S and 2°N force the particles to concentrate near the eastern boundary region. In summer (June-August, Figures 3F–H , 4F–H ), the WJs disappear and the particles are to spread westward. However, most of the particles are still concentrated on the east boundary due to the strengthening of the southwest monsoon, which forces the eastward SMC to reverse directions. At this time, a southward surface Ekman transport across the equator dominates the eastern mouth of the BOB and the western Sumatra coastal areas. This surface branch of the CEC forms a cyclonic circulation system with the eastward SMC, the SJC, and the westward SEC in the Southern Hemisphere, which forces most of the particles to travel across the equator into the Southern Hemisphere and eventually join the SEC.

In boreal fall, the surface circulation changes with the wind field. Advected by the WJs, most particles are concentrated near the eastern boundary. With the strengthening of the northeast monsoon, the Ekman transport is northward and particles are transported northward to join the NMC. In addition, the north branch of the WJs contributes to the northward movement of particles along the eastern boundary (Wang, 2017). Under the influence of both, the particles enter the BOB ( Figures 3I–K , 4I–K ).

In boreal winter (December-February, Figures 3B, L , 4A, B, 4L ), the northeast monsoon forces the NMC south of Sri Lanka to intensify. The NMC extends from southeast of the BOB to the region west of 65°E, resulting in some particles entering the western Indian Ocean. The intensity of NMC peaks in January, with a maximum velocity of 0.5 m·s^-1, introducing the largest number of particles into the western Indian Ocean. Moreover, due to the northward surface Ekman transport and the anticyclonic circulation in the BOB, particles move to the north and enter the bay off the east coasts of India. During the northeast monsoon season, the cyclonic circulation of the EIO is similar to that in the southwest monsoon season, except that the northern boundary is occupied by the SMC and WJs. The southern boundary is still the SEC as in the southwest monsoon season. However, the northward surface Ekman transports prevents the particles from moving southward across the equator. The number of cross-equatorial trajectories is much less than that in spring and summer.

To further quantify the seasonal variations of the trajectory, the percentage distribution of particles released from the different months in the NEIO, the SEIO, and the WIO is calculated ( Figure 5 ). The largest number of particles is seen in the NEIO where particles are released. The concentrations of particles also exhibit apparent seasonal variability. In May, the numbers of particles in the NEIO and SEIO reached the minimum and maximum, respectively. At the time, Ekman transport was southward since the southwest monsoon recently began, and the particles have enough time to cross the equator. Many particles are transported northward in the fall before reaching the equator since southward Ekman transport reverses directions. When the northeast monsoon strengthens and the NMC intensity reaches its maximum, the largest number of particles concentrate in the WIO in winter. The statistical analysis using drifter-derived currents shows similar and consistent seasonal distributions of the particles.

Three representative paths of the particle trajectories are identified according to the distribution of particles, and the three-dimensional trajectories of particles under three typical paths selected from the Figure 3 are shown in Figure 6 . In path I, particles move northward into the BOB and are trapped in the bay; In path II, the particles move swiftly westward into the western Indian Ocean with the NMC, and then across the equator in the central and western basin; In path III, the particles move southward across the equator along the west coasts of Sumatra-Java and join the SEC. Compared with the vertical movement, path I and path III are dominated by the horizontal movement ( Figures 6A, B, E ). The cross-equatorial trajectories in the EIO show significant differences from those crossing the equator in the central and western basin in Path II. Particles crossing the equator along Paths I and III are mainly concentrated in the upper layer (<50 m), whereas, the particles following path II show significant vertical movement down to as deep as 80 m depths after crossing the equator. The particles in path II first move westward, then cross the equator southward and descend to 60-80 m, due to the subduction of the off-equatorial waters ( Figures 6C ). At the peak of the summer monsoon, northward surface currents and southward subsurface currents in the Indian Ocean (a. k.a. the equatorial roll) appear in the western and central Indian Ocean (Wacongne and Pacanowski, 1996; Schott et al., 2002; Miyama et al., 2003). Under the influence of the equatorial roll, the cross-equatorial particles in path II move to the deeper waters. In contrast, the movement of the particles across the equator is mainly confined in the surface layer in the EIO due to the surface Ekman transports.

The trajectories and velocity of the surface drifters in the EIO are analyzed based on the GDP data. We selected 151 drifters in total passing through the study area (5°N, 85°E-95°E) for each season, and their trajectories are analyzed throughout their lifetime ( Figure 7 ). The trajectories of the surface drifters show three main paths, which are consistent with the model results. The drifters released in winter are difficult to move southward due to the northward surface Ekman transports. Some drifters entered the BOB while others drifted with the NMC into the western Indian Ocean ( Figure 7 ). Similar to in winter, the drifters are influenced by the eastward WJs in fall, most of which cannot move westward ( Figure 7 ). Due to the southward surface Ekman currents, some of the drifters released in summer are transported to the south, also consistent with the model results. In the ensuing months, as the direction of the monsoon reverses, the drifters that do not reach the Southern Hemisphere turn back to the north, and finally end in the BOB ( Figure 7 ). In comparison, the drifters released in spring have enough time to move southward, with only a few of them ending in the BOB ( Figure 7 ).

The cross-equatorial exchange of the particles directly affects the balance of the salt and heat budgets of the North and South Indian Ocean. The Lagrangian trajectories of the particles have shown that most particles cross the equator near the eastern boundary. Therefore, we select the eastern boundary region (east of 90°E) to estimate the MST and MHT of the upper layer. The annual mean transport ( Figure 8 ) is calculated as the zonally accumulated MST and MHT integrated from the eastern boundary, showing an alternating zonal distribution, with southward transport south of 5°N, northward transport between 5°N and 15°N, and southward transport north of 15°N. The MHT and MST on the equator are southward, indicating cross-equatorial southward transport of salinity and heat, with the transport intensity increasing with latitude in the South Indian Ocean. The annual mean cross-equatorial MST and MHT estimated by the model (observational) data are -0.06 ×10⁹ (-0.11 ×10⁹) kg·s^-1 and -0.20 (-0.38) PW, respectively ( Table 1 ).

The MHT and MST show sizable seasonal variations in the EIO ( Figures 9 , 10 ), especially in the region north of the equator where the southward currents dominate from May to September, and northward currents from October to April. The change of the transport direction is associated with the monsoon climate of the Indian Ocean. The southwest and northeast monsoons prevail in the northern Indian Ocean in summer and in winter, respectively, with the surface Ekman transports changing directions under the influence of the monsoon, hence the strong seasonal variability. The seasonal variations inside the BOB are significantly different from those on the equator, which may be due to the complicated circulation in the bay.

The meridional transport on the equator is governed by the equatorial Sverdrup transport [i. e., V E k m a n = − ( ∂ τ x ∂ y ) / β ρ where τ^x is the zonal wind stress, β=∂f/∂y f is the Coriolis parameter, y is the latitude, and ρ is the water density], since the Coriolis parameter vanishes on the equator (Horii et al., 2013). North of the equator, the zonally integrated MST and MHT are southward from May to September, and northward from October to April. On and south of the equator, the zonally integrated MST and MHT are southward throughout the year except in winter, when the northeast monsoon peaks, and there is weak northward transport on and south of the equator ( Figures 11B ). The seasonal variations in zonally integrated MST and MHT are dominated by the surface Ekman transports ( Figure 11 ). The Ekman transports at different latitudes exhibit different seasonal variations, with significant correlations with the MHT and MST above the 95% confidence level in ECCO2 (observation) data. The correlation coefficients are 0.94 (0.98) at 5°N, 0.93 (0.86) at the equator, and 0.65 (0.51) at 5°S, suggesting the strong influence of the monsoon in the North Indian Ocean than in the south.