Seasonal variation of eddy activity and associated heat/salt transport in the Bay of Bengal based on satellite, Argo and 3D reprocessed data

. Based on satellite altimetry data spanning over 26 years in combination with Argo profile data or three‐ dimensional (3D) reprocessed thermohaline fields, the eddy synthesis method was used to construct vertical temperature and salinity structures of eddies in the Bay of Bengal, and the seasonal thermohaline properties of eddies and the heat and salt transport by eddies were analyzed. Analysis revealed that mesoscale eddy activities and the vertical thermohaline structures 10 in the Bay of Bengal have evident seasonal variation. Temperature anomalies caused by eddies are usually between ±1°C and ±3°C, positive for anticyclonic eddies (AEs) and negative for cyclonic eddies (CEs), and the magnitude varies seasonally. Salinity anomalies caused by eddies are small and disturbance signals in the southern bay due to the small vertical gradient of salinity there; salinity anomalies in the northern bay are generally between ±0.2 psu and ±0.3 psu, negative for AEs and positive for CEs. Owing to seasonal changes of both the eddy activity and the vertical thermohaline structure in the Bay of 15 Bengal, the eddy-induced heat and salt transport in different seasons also changes substantially. Generally, high heat and salt transport is concentrated in eddy-rich regions, e.g., the western, northwestern and eastern parts of the bay, the seas to the east of Sri Lanka, and the region to the southeast outside of the bay. The southern part of the bay shows weak salt transport owing to the inconsistent salinity signal within eddies. The result of the divergence of eddy heat transport illustrates that the 10−20 W·m -2 value of the eddy-induced heat flux is comparable in magnitude with the annual mean Air−Sea net heat flux in the 20 Bay of Bengal. Compared with the large-scale net heat flux and freshwater flux at surface, the eddy-induced heat/freshwater transport can contribute substantially to regional and basin-scale heat/freshwater variability. This work provides data that could support further research on the heat and salt balance of the entire Bay of Bengal


Introduction
Oceanic mesoscale eddies are rotating coherent structures of ocean currents, which generally refer to ocean features 25 with spatial scales from tens to hundreds of kilometers and time scales from days to months (Robinson, 2010). Following recent advances in remote sensing satellites and the abundance of in situ observational data, it has been established that mesoscale eddies can be found nearly everywhere in the world's oceans (Chelton et al., 2011a;Xu et al., 2011;Fu, 2009;Chaigneau et al., 2009), and they transport water, heat, salt, and other tracer materials as they propagate in the ocean, impacting water column properties and biological activities (Chelton et al., 2011b;Xu et al.,2011;Dong et al., 2014). seasonal changes are not completely synchronized with the monsoon transition (Vinayachandran et al., 1999;Qiu et al., 2007;Sreenivas et al., 2012). Figure 1: Climatological monthly sea surface temperature fields (color), mean surface currents (arrows), and surface salinity (contours) in the Bay of Bengal. The climatological sea surface temperature fields are from monthly averaged OISST dataset with 0.25° regular grid at global scale from Jan. 1982to Dec. 2011(Banzon et al., 2014; ftp://eclipse.ncdc.noaa.gov/pub/OI-daily-v2/). The climatological surface currents are from monthly averaged global total velocity field (MULTIOBS_GLO_PHY_REP_015_004) at 0 m and 15 m with 0.25° grid from Jan. 1993 to Dec. 2018(Etienne, 2018. The climatological surface salinity fields are from the global SSS/SSD L4 Reprocessed 75 dataset (MULTIOBS_GLO_PHY_REP_015_002) with 0.25° grid from Jan. 1993 to Dec. 2018(Mertz et al., 2018. The latter two datasets are available on http://marine.copernicus.eu. The surface characteristics of oceanic eddies can be inferred from remote sensing data, and the vertical thermohaline profile of subsurface waters can be provided by Argo buoys. In recent years, by combining satellite altimetry and Argo 80 profiling float data, analysis of the vertical structure of eddies has become an important part of the study of oceanic eddies (Chaigneau et al., 2011;Yang et al., 2013;Amores et al., 2017). Knowledge of the vertical structure of the ocean is vital both for comprehensive understanding of ocean dynamic processes and for analysis of the ocean circulation and energy transport.
Based on satellite altimetry and Argo floats, Lin et al. (2019) and Gulakaram et al. (2020) showed that eddy-induced ocean anomalies in the Bay of Bengal are mainly confined to the upper 300 m and eddy thermohaline structure has a seasonal 85 character. Cui et al. (2021) found that the thermohaline properties of mesoscale eddies in the Bay of Bengal are different in the north-south direction. Combining estimated eddy diffusivity from 25 years of altimetry data with corresponding tracer gradients from the World Ocean Atlas 2013, Gonaduwage et al. (2019) investigated the meridional and zonal eddy-induced heat and salt transport in the Bay of Bengal, and they found that the baroclinic instability, local wind-stress curl and remote forcing from the equator contribute to the seasonal modulation of eddy-induced heat transport. circulation and regional monsoons, the eddy activity in the Bay of Bengal has obvious seasonal differences. Specifically, the seasonal variation of surface eddies, 3D thermohaline structure of eddies and its regional variation, seasonal heat/salt transport and their spatial distribution characteristics have not been analyzed comprehensively.
In this study, based on merged satellite altimetry data spanning over 26 years, the automatic identification method was used to extract information on the position and shape of mesoscale eddies in the Bay of Bengal, and the seasonal variation of 100 the eddies was analyzed in detail. Then, by combining the satellite altimetry data with either Argo profile data or 3D thermohaline fields, the eddy synthesis method was used to construct the 3D thermohaline structures of eddies in the study area, their seasonal thermohaline properties and regional thermohaline variations were analyzed. Finally, based on eddy movement and thermohaline properties, the heat and salt transports by eddies were estimated, and their seasonal variation and spatial distribution characteristics were analyzed. The remainder of this paper is organized as follows. Section 2 105 describes the data and methods adopted in the study. Section 3 presents the seasonal variations and seasonal 3D thermohaline properties of the eddies. Section 4 analyzes the seasonal heat and salt transports by eddies in the Bay of Bengal. Finally, summary and discussion are presented in Section 5.

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The daily and monthly 0.25°×0.25° gridded sea level anomaly (SLA) product (SEALEVEL_GLO_PHY_L4_REP_ OBSERVATION_008_47) from January 1993 to February 2019 are used to determine the presence and positions of mesoscale eddies in the Bay of Bengal. The SLA product is processed by the Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) and distributed by the European Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu).

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The Argo float profiles provided by the Coriolis Global Data Acquisition Center of France (http://www.coriolis.eu.org) are used to analyze the vertical temperature and salinity structures of eddies. In the analysis, we have taken pressure, temperature, and salinity profiles with quality flag 1, and have followed Chaigneau et al. (2011) for the selection of the profiles from the year 2001 to 2019. The final dataset includes of total 29,219 available profiles in our study region. Potential temperature θ and salinity S data in each profile were linearly interpolated onto 101 vertical levels from the surface to 1000 120 dbar with an interval of 10 dbar using the Akima spline method. To get the thermohaline structures of mesoscale eddies, potential temperature anomaly θ′, and salinity anomaly S′ of Argo profiles were computed by removing Argo seasonal-mean climatologic profiles.
The ocean reprocessed data can provide the 3D thermohaline information of the surface eddies captured by the satellite altimetry. The Global ARMOR3D L4 Reprocessed dataset (MULTIOBS_GLO_PHY_REP_015_002, distributed by 0.25° regular grid and on 33 depth levels from the surface down to the bottom (Guinehut et al., 2012). The ARMOR3D dataset is obtained by combining satellite (SLA, geostrophic surface currents, SST) and in-situ (temperature and salinity profiles) observations through statistical methods. The dataset is available as weekly means for the period 1993-2019.
Similar to Argo profiles, the 3D temperature and salinity anomaly fields were computed by removing ARMOR3D 130 seasonal-mean climatologic fields.

SLA-based eddy identification and tracking
In SLA fields, mesoscale eddies can generally be identified as regions enclosed by SLA contours. A geometric algorithm for eddy identification based on the outermost closed contour of an SLA has been proposed by Chelton et al. 135 (2011a). Following the algorithm, an eddy is defined as a simply connected set of pixel grids that satisfying some criteria.
For the Bay of Bengal, the minimum amplitude of an eddy is increased from the original 1 cm used by Chelton et al. (2011a) to 3 cm in this study. The reason for this change is that the accuracy of measuring heights using Jason series altimeters (including TOPEX/Poseidon and Jason-1/2/3), which currently have optimal performance for observing ocean dynamics, is only about 2 cm in the open sea (Dufauet al., 2016). Furthermore, the distance between the two furthest-apart internal points 140 in an eddy is less than 600 km for avoiding enclose elongated regions.
Based on daily SLA fields, the mesoscale eddies in the Bay of Bengal are identified, and the eddy amplitude, eddy scale/radius, and eddy propagation velocity are quantified over the study area. The eddy amplitude is defined here to be the magnitude of the SLA difference between the eddy boundary and the eddy center (local extremum). The eddy scale/radius is defined as the equivalent radius of a circle with the same area which is delimited by the eddy boundary. Based on the eddy identification results in the continuous time series, the evolution process of eddies (eddy trajectories) in the ocean can be tracked by comparing the eddy positions and dynamic properties (Chaigneau et al., 2008;Henson and Thomas, 2008;Nencioli et al., 2010;Souza et al., 2011). For an eddy at day n, its trajectory is tracked by searching the most similar eddy at the subsequent day n+1 in terms of the type and eddy characteristics within a circle of eddy radius (Chaigneau et al., 2008;Cui et al., 2021). To avoid the false tracking of the eddies, the same eddy is searched continuously for 10 days with circles of growing radius (max double eddy radius in the 10 th day) when no match eddy is detected in subsequent time step n+1. The lifetime of an eddy represents the duration of an eddy from its generation to its termination. The eddy propagation velocity is defined as the change of the eddy center position as a function of time.
In addition, in order to study the seasonal spatial distribution of eddies, monthly eddies are identified from the monthly SLA fields without trajectory tracking. For such monthly eddies, the tracking processing is not performed, and the monthly result identified from monthly SLA fields are processed as individual eddies.

3D eddy reconstruction 165
Combined with the satellite altimetry data and the Argo profiles, composite 3D structures of a single CE and a single AE were created based on eddy synthesis method in the study, respectively. The 3D structures of eddies were constructed by surfacing the Argo float profiles into SLA-based eddy areas, as shown in Figure 2. We considered the detection results (from daily SLA fields) of the long-lived eddy (eddy trajectories with lifetime ≥30 days) to match the Argo profiles on the same day, and selected Argo profiles with a distance of <1.5 radii from eddy center for vertical eddy structure analysis. By matching identified eddies with Argo profiles in a long time (from the year 2001 to 2019), a large number of Argo profiles within eddies can be obtained. Consequently, 3882 and 4097 Argo profiles were selected for cyclonic and anticyclonic eddy reconstruction, respectively. These Argo profiles were interpolated to create an average CE and an average AE 3D profile.
Due to Argo profiles captured by eddies are scattered (spatially nonuniform), it is necessary to transform these Argo profiles into a unified eddy-center coordinate, so as to combine the vertical temperature and salt information provided by all profiles to obtain the 3D thermohaline structures of the composite eddy. Specifically, for each Argo profile matched by an eddy, we calculated the relative zonal and meridional distances to the eddy center. The relative distances were normalized relative to the eddy radius (nondimensionalization). Then, all the Argo profiles were transformed into the normalized eddy coordinate space, and θ, S and θ′, S′ data of Argo profiles were mapped onto 0.1×0.1 grid using inverse distance weighting interpolation at each vertical level from the surface to 1000 dbar. Finally, composites of 3D thermohaline structures were reconstructed in each normalized grid location. Considering the hydrological differences from north of the bay to the south, here the Bay of Bengal is divided into north and south subregions with 12°N as the boundary to study the eddy 3D structure of each subregion. The Argo profiles acquired within eddies were classified according to season, so the 3D structures of eddies were reconstructed in different seasons.
Since the Argo float only provide one-dimensional information on the profile, and Argo profiles are scattered, we can 185 only reconstruct one 3D thermohaline structure of eddies in a region by the above method. The ocean reprocessed data provide the 3D temperature and salinity field data covering the entire space. This allows us to obtain the 3D thermohaline structure of the surface eddies captured by the satellite altimetry by matching the eddy results with the reprocessed 3D field data. Here, the weekly ARMOR3D reprocessed dataset were used to provide vertical structure information on the surface eddies. We matched the eddy results identified from daily SLA fields with the weekly 3D field data at the closest time such 190 that we could obtain the 3D temperature and salt structure of each eddy ( Figure 2a). Similar to the handling of Argo profiles, all eddies were classified by season, and the 3D structures of all vortices in a season were averaged and used for comparison with the reconstruction results of Argo profiles.

Eddy-induced heat and salt transport estimation
A nonlinear eddy can maintain its own water body characteristics and have minimal exchange with the surrounding 195 water mass as it propagates in an ocean. By combining the spatial-scale information of the eddies provided by the SLA fields with the vertical temperature and salt anomaly information provided by the ARMOR3D temperature and salinity fields, the heat anomaly He and salt anomaly Se could be obtained for each eddy (the subscript e means eddy): Here, the mean upper ocean density and heat capacity are 0 = 1025 kg·m -3 , 0 = 4200 J·kg -1 ·°C -1 . R is the eddy region, D0 is the integration depth (500 dbar for He and 300 dbar for Se; Lin et al. (2019); Gulakaram et al. (2020); also, Section 3.2), x and y represent horizontal position, z represents the vertical depth. The unit of eddy heat anomaly He is J, and that of salt anomaly Se is kg.
Instead of using eddy propagation velocity to calculate eddies' heat transport (Dong et al., 2014), eddy trajectories are 205 used to calculate transport by eddy movements (Dong et al., 2017). Here we use 0.25° grid cells to calculate the eddy-induced heat and salt transport through following the eddy trajectory and check whether it crosses grid cell boundaries.
If an eddy crosses the west or east boundary, it results in zonal transport, whereas eddy crossing of the north or south boundary results in meridional transport. In addition, the east and the north transport are defined as positive, while the west and the south are negative. For a grid cell, the zonal heat and salt transport Qhz and Qsz (the subscript z means zonal) are

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Here the unit of heat transport Qhz is W·m -1 , and that of salt transport Qsz is·kg·m -1 ·s -1 . The time length T is 26 years corresponding to the time-series length of SLA products used for the eddy identification from Jan. 1993 to Feb. 2019. The denominator factor of 2 is because we separately considered the east and west boundaries of the eddy moving through the grid. Similarly, the eddy-induced meridional heat and salt transport Qhm and Qsm are calculated by Here, Dz is the zonal length of the grid. In the actual calculation, a moving average filter with 1°×1° box size is applied to reduce noise.

Seasonal spatial distribution of eddies 225
The Bay of Bengal is affected by the Southwest Monsoon and Northeast Monsoon, and its entire circulation system is  Figure S1) show that eddy activities have obvious seasonal variation, but messy trajectories obscure the distribution characteristics.
In order to understand the seasonal distribution characteristics of eddies in the Bay of Bengal more intuitively, we used monthly averaged SLA fields to identify eddies that occur frequently in certain regions (here we call them "the monthly eddies"). For such monthly eddies, the tracking processing is not performed, and these monthly results identified from monthly SLA fields are processed as individual eddies. Each individual monthly eddy is counted as one eddy. As a result, a  Figure S1). In the Spring premonsoon season, a basin-scale anticyclonic gyre appears and dominates the bay. Within the anticyclonic gyre, AEs are clustered in western and northwestern parts, while some small but high-strength CEs are clustered in northernmost and western parts of the bay (Figure 4 b and f). Owing to river runoff and coastal current baroclinic instability, cyclonic structures are prone to appear in the northernmost part of the bay (Patnaik et al., 2014;Babu et al., 2003;Kumar and Chakraborty, 2011). In the 260 Summer monsoon season, the EICC becomes variable. In western parts of the bay, some persistent CEs often appear on the northern side of the EICC, while AEs are often shed on its southern side ( Figure 4 c and g). In addition, many CEs and AEs are clustered in the eastern and northeastern parts of the bay, which are mainly driven by equatorial zonal winds, with both nonlinearity and coastline topography (Cheng et al., 2018). It is noteworthy that a large number of high-amplitude CEs (refers to the Sri Lanka Dome, Vinayachandran and Yamagata, 1998)

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The heat and salt transport efficiencies of mesoscale eddies are related closely to eddy propagation speed (Dong et al., 2014;Gonaduwage et al., 2019;Stammer, 1998). In order to study the propagation direction and speed of mesoscale eddies

Seasonal variation of vertical thermohaline structure of eddies
To reveal the seasonal variation of the vertical thermohaline structure of eddies in the Bay of Bengal, the 3D thermohaline structures of the eddies were constructed by surfacing the Argo float profiles into SLA-based eddy areas. In this study, all eddy trajectories with lifetime ≥30 days from daily SLA fields and Argo profiles chosen following Chaigneau approximately 80 dbar (100 dbar), which is shallower than that in the northern bay due to the shallower thermocline in the southern bay (Cui et al., 2021). The θ′ of CEs is the largest in summer, reaching −3°C, the smallest in winter, less than −2°C; the θ′ of AEs is larger in summer and autumn, around +2°C, and smaller in winter and spring, around +1.5°C.  control of the low-salinity Bay of Bengal Water at the surface and the Indian Equatorial Water in the deep ocean (Stramma et al., 1996), the northern bay presents the salinity structures of positive S′ inside CEs and negative S′ inside AEs in the thermocline (upper panels in Figure 7). The maximum S′ of CEs in spring can exceed +0.3 psu, whereas it is around +0.25 psu in autumn, and weakest in winter is only +0.2 psu. The extremum of negative S′ in AEs in autumn can reach −0.35 psu, values are around −0.25 psu in spring and summer, and −0.2 psu in winter. In addition, the S′ of CEs and AEs in the 30 dbar 325 shallow surface water in summer and autumn exhibit some perturbation (positive/negative signals in CEs/AEs). For S′ in the southern bay (lower panels in Figure 7), the magnitude of S′ signal is significantly small. Just in summer, the S′ of CEs and AEs are exceeding ±0.2 psu; while in other seasons, the S′ of CEs and AEs are less than 0.1 psu.
In addition, to verify the vertical thermohaline structure obtained from Argo profiles, the weekly ARMOR3D temperature and salinity field data were also used to analyze the seasonal variation of the vertical thermohaline structure of

Seasonal eddy-induced heat and salt transports in the Bay of Bengal
Eddy heat transport is traditionally estimated within a Eulerian framework (Qiu and Chen, 2005;Roemmich and Gilson, areas of the Bay of Bengal. The detailed method, as described in Section 2.2, considers not only the direction and speed of eddy propagation, but also the variation of the properties of the intrinsic heat and salt during eddy movement.

Eddy-induced heat transport and its seasonal variation
The seasonal heat transport attributable to mesoscale eddies in the Bay of Bengal is illustrated in Figure 9. It can be seen that CEs/AEs present eastward/westward heat transport in most regions due to CEs/AEs generally carry 370 negative/positive heat anomalies westward across the bay (upper and middle panels). The heat transport associated with CEs and AEs jointly determines the heat transport of all the eddies (lower panels). The eddy-induced heat transport is generally higher in regions where eddies are clustered. In the area to the south of 8°N, the southeast outside of the bay, the high eastward heat transport in winter and spring is related to the large-scale CEs that often appear there and move westward at a high speed (e.g., >10 cm·s -1 , Figure 5). The seas to the east of Sri Lanka are dominated alternately by CEs and AEs in 375 different seasons. Thus, in this region, the directions of heat transport are different in different seasons (e.g., in autumn and winter, westward-moving AEs lead to westward heat transport; in summer, northward-moving CEs lead to southward heat transport), and the magnitude of this transport is generally >15×10 6 W·m -1 . The western bay is dominated by CEs and presents eastward heat transport in autumn and winter; conversely, it is dominated by AEs in spring and summer and presents westward heat transport. The eastern bay generally corresponds to westward heat transport in autumn and winter, due to the 380 prevalence of AEs moving westward in the seasons (Cheng et al., 2018).
We integrated the zonal heat transport Qhz by mesoscale eddies at each 0.25° grid from north to south, and obtained the integrated zonal heat transport = ∫ ℎ in the entire meridional direction, where dy is the meridional unit distance (unit: m) such that the unit of ZHT is Watts (abbr. W). Similarly, the zonally integrated meridional heat transport MHT can be expressed as = ∫ ℎ , where Qhm is the meridional heat transport and dx is the zonal unit distance. The seasonal  Here, Qh = (Qhm, Qhz) is a vector whose components are the meridional and zonal heat transports, the arrows indicate the transport direction, and the color indicates the transport magnitude.

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To estimate the impact of heat transports by eddy movements in the Bay of Bengal, we calculated the divergence of eddy heat transports ℎ and smoothed it using a moving average filter with half width of 5° longitude and 3° latitude. The divergence of the heat transports ℎ is calcualted as ℎ = ∇ • ℎ , here ℎ = ( ℎ , ℎ ) is the horizontal heat transport vector, ∇ • is the horizontal divergence operator. ℎ represents the heat flux by eddy movements in the horizontal direction, the unit is W·m -2 . Figure 11 a-e shows the − ℎ .in different seasons in the Bay o f Bengal, positive 410 values of − ℎ represent oceanic heat gains from eddies, negative values represent oceanic heat losses, which means heat is transported away by eddies.
In terms of the annual mean result (Figure 11e), the ocean loses heat due to eddy movements in the eastern, southeastern and western coastal regions of the bay, while the ocean gains heat from eddies in the northern and central regions. The magnitude of the ocean heat loss/gain caused by eddy movements is about 10−20 W·m -2 , of which the heat loss can reach 20 415 W·m -2 in the southern and western coastal areas of the bay. As a comparison, the annual mean Air−Sea net heat flux at surface in the Bay of Bengal is on the order of 20−50 W·m -2 (Sanchez-Franks et al., 2018;Pokhrel et al., 2020; also see Supplementary Material Figure S4). The eddy-induced heat flux is comparable in magnitude with the Air−Sea net heat flux, implying that the mesoscale eddies can exert a strong impact on the oceanic heat transport and redistribution in the Bay of Bengal. In addition, the − ℎ caused by eddies varies substantially in different seasons. In autumn and winter, the geographical distribution of − ℎ is similar to the annual mean result, showing a sandwich structure of ocean heat loss−gain−loss from west to east. In spring, ocean heat loss is seen overall, with ocean heat gain only in limited areas in the western and northeastern parts. In summer, due to the strong eddy activities, the heat gain and heat loss alternately appear in the western part of the bay from north to south, and the magnitude can exceed 50 W·m -2 . Despite Air−Sea net heat flux into the ocean in the eastern seas of Sri Lanka, a cold pool is still formed there in summer due to the intrusion of cold water 425 carried by the Southwest Monsoon Current (SMC, Vinayachandran et al., 2020;Das et al., 2016). The high eddy-induced ocean heat gain here suggests that eddy activities (mainly the northward input of AEs carrying warm waters and the northward outflow of CEs carrying cold waters) would somewhat balance the heat loss due to the SMC intrusion. Without the heat input from eddy movements, the temperature of summer cold pool caused by SMC intrusion would be lower, and the lower summer cold pool might change the direction of the Air−Sea heat flux. Compared with the large-scale Air−Sea 430 heat flux, the eddy-induced heat transport can contribute substantially to regional and basin-scale heat variability.

Eddy-induced salt transport and its seasonal variation
The spatial distribution of eddy-induced salt transport Qs in the Bay of Bengal is shown in Figure 12. In the part of the bay to the north of 12°N, the salinity anomalies caused by eddies are relatively uniform with little interference by surface disturbances, and the salt transport Qs is basically westward/eastward for CEs/AEs (CEs/AEs carry positive/negative salinity anomalies moving westward-westward/eastward salt transport). The high salt transport of all eddies is also concentrated in 440 the northern part. In winter, AEs dominate the salt transport eastward and northeastward; in spring, summer, and autumn, CEs dominate southwestward salt transport, which causes the salinity to decrease in the northern bay. The Qs in the part of the bay to the south of 12°N is notably smaller than that in the northern part. The reason for the low salt transport in the southern part is related not only to the small number of eddies and their weak strength, but also to the complex structure of salinity anomalies caused by the eddies. In Section 3.2, the spatial characteristics of the vertical salinity anomalies of eddies 445 ( Figure 8) shows that the salinity signals in the southern bay become turbulent, which may be caused by the invasion of the low-latitude equatorial circulation (Cui et al., 2021). Disturbance of salinity anomaly signals in the surface or subsurface waters reduces the salt transport capacity of CEs and AEs over the entire vertical structure.  Qsz) is a vector whose components are the meridional and zonal salt transports, the arrows indicate the transport direction, and the color indicates the transport magnitude. Figure 13 shows the meridionally integrated zonal salt transport = ∫ and the zonally integrated meridional salt transport = ∫ caused by eddies, which represent the salt flux (unit: kg·s -1 ) in the entire meridional and zonal directions, respectively. The ZST direction of all eddies is largely consistent with that of CEs. The maximum ZST of CEs in autumn is greater than 400×10 3 kg·s -1 in the longitude of about 86°N. The ZST of AEs is relatively low, except in winter, the magnitude in other seasons is less than 100×10 3 kg·s -1 . In terms of MST, the magnitude of the mean transport is <50×10 3 kg·s -1 for both CEs and AEs, which is substantially smaller than that of ZST (black lines in Figure 13). The MST direction of CEs is southward in the northern bay and northward in the southern bay. Northward salt transport of AEs is 16°N, and northward MST in the central and southern parts (Figure 13f). Compared with the north-south variation of the annual mean net freshwater flux at surface (Supplementary Material Figure   S4), the spatial distribution of − shows an east-west variation, which indicates that mesoscale eddies plays an important role in maintaining the east-west freshwater or salt balance in the Bay of Bengal. Owing to the seasonal variation of eddy activities in the Bay of Bengal, the − caused by eddies varies substantially. The northernmost part of the bay exhibits freshwater losses only in winter and freshwater gains in the rest of the seasons, and the maximum freshwater gain in autumn can exceed 20×10 -6 kg·m -2 ·s -1 . The EICC area in the western bay shows eddy-induced freshwater losses in spring, summer and autumn, and the extreme value in autumn can reach 50×10 -6 kg·m -2 ·s -1 . The eastern part of the bay presents freshwater gains of greater than 20×10 -6 kg·m -2 ·s -1 in winter. The magnitude of freshwater gains and losses in the southern part of the bay is small in all seasons, which is mainly related to the weaker salt transport caused by the inconsistency of 485 salinity signal within eddies (Figure 8).

Summary and Discussion
The Bay of Bengal, occupying the eastern part of the tropical Indian Ocean, is characterized by the seasonal circulation and intense eddy activity throughout the year. The mesoscale eddies in the Bay of Bengal were determined from satellite altimetry data spanning over 26 years from January 1993 to February 2019. The eddy result revealed that mesoscale eddy 490 activity in the Bay of Bengal has evident seasonal variation.
Generally, there are three main areas of distribution of mesoscale eddies in the Bay of Bengal. One is the EICC region in the west and northwest of the bay, indicating that variation or reversal of the western boundary current EICC will often shed rich eddy structures, especially in spring and summer. Another region is the northeastern part and the eastern boundary, where eddies generated in spring and summer move southwestward into the central bay in autumn (some even reach the 495 western bay). The eddies are mainly driven by equatorial zonal winds, with both nonlinearity and coastline geometry essential for eddy generation (Cheng et al., 2018).  (Thadathil et al., 2007), which attenuates temperature 510 changes through vertical movement of the water body. The maximum θ′ of CEs in the southern bay in summer is associated with the persistent and strong Sri Lanka Dome which often appears in May and disappears in September. CEs (AEs) produce notable positive (negative) S′ signals at the subsurface in the northern bay, but small magnitude in the southern bay. The spatial distribution of eddy-induced salinity anomalies illustrates that the salinity signal becomes turbulent owing to the invasion of the low-latitude equatorial circulation. For example, AEs present disordered positive salinity anomalies in the 515 southern bay. Owing to differences in the salinity anomaly signal between the northern and southern parts of the bay, the perturbation of the salinity anomaly will appear in the surface during analysis of the 3D structure of one eddy in the entire Bay of Bengal (Figure 7; Lin et al., 2019;Gulakaram et al., 2020). Some studies suggested that this reflects a salinity dipole structure in the near surface layer due to the horizontal advection, eddy rotation and background temperature/salinity meridional gradient Amores et al., 2017). If the average thermohaline structure of the entire region were used to estimate the eddy-induced heat/salt transport, the marked regional characteristics would be smoothed.
By combining the temperature and salinity anomalies of eddies, provided by the weekly ARMOR3D thermohaline field data, with the details of eddy movement (propagation trajectory), provided by gridded multimission altimeter products, we estimated the eddy-induced heat and salt transport in different areas of the Bay of Bengal. Generally, high heat and salt transport is concentrated in eddy-rich regions, e.g., the western, northwestern and eastern parts of the bay, the seas to the east 525 of Sri Lanka, and the region to the southeast outside of the bay. The southern part of the bay shows weak salt transport owing to the inconsistent salinity signal within eddies. Owing to obvious seasonal variation of eddy activities, the heat and salt transport in different seasons also changes substantially. The magnitude of the seasonal ZHT of CEs and AEs in the whole bay is in the order of 10×10 12 W, with higher values in autumn and winter and smaller values in spring and summer. The result is basically same with theoretical calculation by Gonaduwage et al. (2019) in the distribution of high eddy transport, To estimate the impact of heat/salt transports by eddy movements in the Bay of Bengal, the divergence of eddy heat/freshwater transports were calcualted. The 10−20 W·m -2 value of the eddy-induced heat flux is comparable in magnitude with the annual mean Air−Sea net heat flux, implying that the mesoscale eddies can exert a strong impact on the oceanic heat transport and redistribution in the Bay of Bengal. Notable, the high eddy-induced ocean heat gain in the eastern 540 seas of Sri Lanka in summer suggests that eddy activities would somewhat balance the heat loss due to the intrusion of cold water carried by the Southwest Monsoon Current. Without the heat input from eddy movements, the temperature of summer cold pool caused by SMC intrusion would be lower, and the lower summer cold pool might change the direction of the Air−Sea heat flux. Compared with the north-south variation of the annual mean net freshwater flux at surface, the spatial distribution of eddy-induced freshwater flux (the magnitude is generally 0−20×10 -6 kg·m -2 ·s -1 , seasonal variation is higher, 545 up to 50×10 -6 kg·m -2 ·s -1 regionally) shows an east-west variation, which indicates that mesoscale eddies plays an important role in maintaining the east-west freshwater or salt balance in the Bay of Bengal. Compared with the large-scale Air−Sea heat flux and net freshwater flux at surface, the eddy-induced heat/freshwater transport can contribute substantially to regional and basin-scale heat/freshwater variability. This work provides data that could support further research on the heat and salt balance of the entire Bay of Bengal.

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acknowledge all the data providers for the data utilized in this study.

Code/Data availability
The altimeter products (SEALEVEL_GLO_PHY_L4_REP_OBSERVATION_008_47) and the Global ARMOR3D L4 Reprocessed dataset (MULTIOBS_GLO_PHY_REP_015_002) used here are distributed by the European Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu). The Argo profiles are provided by Coriolis