The data analyzed here were collected during eight oceanographic cruises in seven different regions: the EUREC4A-OA campaign along the northern coast of Brazil, which studied mesoscale eddies and the ocean–atmosphere coupling; the Maria S. Merian MSM60 expedition, which was the first basin-wide section across the South Atlantic following the SAMBA/SAMOC line at 34° 30^′ S; the Physindien 2011 experiment along the Omani coast (western Arabian Sea), which studied the eddy field in this area; the FS Meteor M124 expedition, which was the first of the two SACross2016 expeditions; the MSM74 cruise, which was dedicated to determining the intensity of southward water mass transport and transformation in the boundary current systems off the sea; the M160 measurements, which contributed to the understanding of the ocean eddies generated in the Canary Current system; and three cruises – KB 2017606, KB 2017618, HM 2016611 – whose main objective was to study eddy dynamics in the Lofoten Basin. The goal was to collect a relatively large number of eddies sampled in different regions at different times of their life cycle. To be able to derive our diagnostics from the data, the campaigns must not only have carried out hydrological measurements, but also velocity measurements over the same depth range. This requirement significantly reduces the number of potentially available cruises. Table  summarizes the basic information about the cruises. The instruments used are conductivity, temperature, and depth (CTD) sensors, underway CTDs (uCTDs), and (lowered and ship-mounted) acoustic Doppler current profilers (lADCP or sADCP).

Here, we recall the measurement uncertainties for each instrument used. They will be important for estimating errors in the calculated diagnostics. For the CTD instrument, temperature and salinity are measured with uncertainties of ±0.002 °C and ±0.005 psu, respectively. For the uCTD instrument, the uncertainties are ±0.01 °C and ±0.02 psu for temperature and salinity measurements, respectively. And for the ADCP instrument, the horizontal velocity is typically measured with an uncertainty of ±3 cms-1.

Oceanographic research cruises often collect data along vertical sections that include vertical profiles. Therefore, we define the resolution of a vertical section as the average of all distances between successive profiles along the same section. Since hydrological and velocity instruments do not sample the ocean with the same resolution, the two types of measurements are distinguished (see Table ). For example, the hydrological properties of the surface anticyclonic eddy from EUREC4A-OA (denoted no. 1 in Table ) were sampled using CTD and uCTD instruments with a resolution of 3.5 km horizontally and 1 m vertically, while its dynamical properties were measured using sADCP (75 kHz) instruments with a resolution greater than 1 km horizontally and 8 m vertically.

The raw data were calibrated and then interpolated. To limit noise, linear interpolations were performed in the x (horizontal) and z (vertical) directions. We chose first-order polynomial functions to avoid creating artificial fields. The typical grid size of the interpolated data is 1 km horizontally and 1 m vertically. The data were then smoothed with a numerical low-pass filter of order 4 (scipy.signal.filt in Python). The choice of cut-offs is subjective and depends on the scales considered. Here we are considering mesoscale eddies, so we chose Lx≥10 km and Lz≥10 m for the horizontal and vertical length scales where possible to remove submesoscale processes that can blur eddy boundaries. In fact, the cut-off period must be longer than the sampling resolution of the calibrated data. The smoothing parameters are summarized in Table .

Since on density vertical sections the rotating flow mainly satisfies the geostrophic equilibrium with often a small cyclostrophic correction , eddies can be identified by observing vertical deviations of isopycnals; they are usually accompanied by changes in the sign of the velocity field orthogonal to the section. To analyze the true thermohaline anomalies in eddy cores, the ship must have passed close enough to the eddy center. In the following, we separate such sampled eddies from others. We call Rmax⁡ the radius of maximum velocity if the eddy is axisymmetric and e the distance between the eddy center and its orthogonal projection on the ship's track (see Fig. ). An eddy is considered well-sampled if e≤Rmax⁡/2. Obviously, eddies are not completely axisymmetric and we adjust the criterion for this case using L as defined in Fig. . Using the Pythagorean theorem, an eddy is well-sampled if the following condition is satisfied: e≤L/3. Table  summarizes the basic properties of eddies and describes which eddies are well-sampled. In fact, this table underscores the difficulty of obtaining complete (all boundaries visible) well-sampled structures with in situ data. For a mesoscale eddy marked “B” in the table, the eddy radius cannot be calculated and dashes are used. Note that the radius L has also been estimated for non-well-sampled eddies.

The position of the eddy center is estimated using the routine from at the depth of the observed maximum velocity, assuming that the position of the center does not vary too much with depth. The routine constructs a rectangular area around the ship track with a given grid size. Then, for each grid point, the distance-weighted average of the tangential velocity is computed using each velocity vector measured along the transect. The center of the eddy is defined as the point where the mean tangential velocity is maximum. This routine is implemented at each geopotential level on a 2D grid plane.

Finally, we are able to locate every well-sampled eddy during the eight cruises. In practice, however, some non-well-sampled eddies have sufficient characteristics to assess their thermohaline coherence. In total, 25 eddies with 17 anticyclonic eddies (hereafter AEs) and 8 cyclonic eddies (hereafter CEs) were sampled, including 19 well-sampled eddies (12 AEs and 7 CEs).

Here we specify the determination of the eddy type. On the one hand, the cyclonic or anticyclonic aspect is derived from the deviation of the isopycnals. On the other hand, the surface or subsurface intensification of the vortex depends on the variable used to characterize its vertical structure. Thus, two variables can be used: the location of the maximum velocity and the location of the maximum thermohaline anomalies (defined later by Eqs. 1 and 2). A kinematic subsurface eddy (KSub) is defined as an eddy for which the maximum velocity is below -70 m depth. Conversely, a kinematic surface eddy (KSurf) has its maximum velocity in the upper -70 m depth. A thermohaline subsurface eddy (TSub) is an eddy for which the maximum of the thermohaline anomalies on isopycnals (see separate section) is below -70 m depth. In contrast, thermohaline surface eddies (TSurf) have their maximum anomalies defined within this upper layer. In fact, ADCP data are only accurate after two or three bins of depth. Some cruises do not even provide data in the first -50 m. In addition, isopycnal levels must match between the section and the climatological mean, which is rarely satisfied near the surface due to near-surface variability. As a result, it is often impossible to calculate anomalies above -70 m. Therefore, the -70 m depth threshold has been chosen to have a unique value regardless of the variable being considered. In some cases, eddies are not thermohaline coherent and no maximum of anomalies can be found at the center of the eddy (see Sect. 5.1). Therefore, only the velocity is used to evaluate the vertical structure. One can note that an eddy labeled KSurf is not necessarily TSurf.

To compare the surface and subsurface signature of sampled eddies, we present satellite altimetry data and a detection algorithm based on absolute dynamical topography (ADT) derived from these data.

Sampled eddies are identified and tracked in time by the TOEddies automatic detection algorithm . This detection is applied to ad hoc near-real-time (NRT) ADT maps during the field experiments. These products are provided by Collecte Localisation Satellites (CLSs) and have been generated using a mean dynamic topography (MDT) with a higher resolution (1/8° instead of 1/4°) than the standard MDT product .

The TOEddies method is based on the algorithm proposed and developed by and has already been used in studies analyzing different aspects of Atlantic Ocean dynamics, such as the origin and evolution of the Agulhas Current rings , the role of mesoscale eddies in meridional transport over the zonal South Atlantic GO-SHIP section of the MSM60 cruise , the EUREC4A-OA region , and the effect of mesoscale eddies on the formation and transport of South Atlantic subtropical mode water .

Assuming that eddies are in geostrophic equilibrium, TOEddies identifies eddies as closed contours of the ADT that contain only a local extremum. As a result, at any given time, eddy streamlines should coincide with the closed isolines of the daily ADT maps. Thus, the ADT, and not the sea level anomaly (SLA), represents the geostrophic stream function. In fact, the SLA is very sensitive to large sea surface height (SSH) gradients associated with intense currents and quasi-stationary meanders or eddies that characterize the MDT (see an example in ). TOEddies thus identifies the local ADT extrema (maxima and minima) and searches for the outermost closed ADT contour around each extremum. In addition to the outermost closed ADT contour, TOEddies also identifies the contour where the mean azimuthal velocity is maximum using geostrophic velocities derived from ADT maps.

The ability of eddies to trap and transport water masses is the basis of the MC definition. Here, we evaluate this definition by computing temperature and salinity anomalies on isopycnals in eddy cores relative to a climatological average following the method of . The climatological average of temperature and salinity on geopotential levels is calculated using Argo float profiles over 20 years in a small area around the sampled eddy. It is worth noting that the average is computed using profiles measured during the corresponding month in which the considered eddy was sampled. The Coriolis database at https://dataselection.euro-argo.eu (last access: 21 January 2025) is used. A square with 0.5° sides is built around the eddy center estimate so that the center is at the intersection of the diagonals. Taking T* and S* as two reference profiles in temperature and salinity (outside the eddies) and T and S as in situ profiles (inside the eddies), thermohaline anomalies on isopycnals are computed as follows: 1∀σ,ΔT(σ)=T(σ)-T*(σ),2∀σ,ΔS(σ)=S(σ)-S*(σ), where σ is the potential density at atmospheric pressure. These anomalies are computed on isopycnal surfaces but interpolated to the geopotential levels to facilitate comparison with other criteria. As introduced earlier, we define a thermohaline subsurface eddy (TSub) as an eddy with an anomaly maximum location deeper than -70 m. Conversely, a thermohaline surface eddy (TSurf) exhibits an anomaly maximum above -70 m depth. These anomalies can separate two water masses that have the same potential density but differ in their thermohaline compositions. As a result, they are highly effective in delineating the TC core of an eddy. Taking into account the resolution of the instruments, the uncertainty in the thermal (or salinity) anomalies is approximately ±0.01 °C (±0.02 psu) when uCTD data are considered and ±0.002 °C (±0.005 psu) when only CTD measurements are used.

These anomalies are highly dependent on the temperature or salinity gradient along the isopycnals. Therefore, we compare the maximum values of our anomalies with the standard deviation of the temperature and salinity fields in each region in the period 1991–2020 provided by the World Ocean Atlas 2023 . The standard deviation of salinity and temperature for the month of each cruise is selected in a square with 1∘ sides where the center of the eddy is located. Since these climatological standard deviations are based on Argo float profiles, eddy anomalies are often included in the construction of the climatological mean. Therefore, we consider our anomalies to be significant if their values are above the temperature and salinity standard deviations. Therefore, we define an eddy as TC if at least one of the two anomalies (temperature, salinity) is significant.

Let (x,z) be the vertical plane of the section, and using smoothed data, the derivatives of a quantity a are approximated by a second-order Taylor expansion as follows: ∂xa(x,z)≈(a(x+Δx,z)-a(x-Δx,z))/(2Δx) (same for the variable z). For a given quantity a(x,z), the norm of a gradient in a 2D slice is defined as follows: 3|∇a|=(∂xa)2+(∂za)2. Since an eddy locally modifies isothermal or isohaline conditions with respect to the rest state, we expect this quantity to be useful for detecting eddy boundaries.

We also define the anomaly of the Brunt–Väisälä frequency as 4N2=-gσ0∂σ′∂z, where σ0 is a reference value averaged over each profile of the section, g is the acceleration due to gravity, and σ′(x,z)=σ(x,z)-σ‾(z) is the anomaly of the potential density computed on geopotential levels with respect to the climatological mean σ‾. Since the eddy properties deviate from those of the background environment along the isopycnal surfaces, they are actually stratification anomalies. As such, the core appears as a region of low (or high) gradients for AEs (or CEs).

To calculate the relative vorticity, derivatives in two different horizontal directions are needed. For a single section from a research cruise this is not possible without further assumptions. An approximation of the relative vorticity is the “poor man's vorticity” (PMV) introduced by . It decomposes the measured velocities into a cross-track component v⟂ and an along-track component v∥. The relative vorticity is then approximated as ζz≈2∂v⟂∂x. The factor 2 is added so that the PMV is equal to the actual ζ in an eddy core with solid-body rotation. However, and used the along-track derivative of the cross-track velocities without the factor 2. The two approximations differ only in the way they estimate the cross-track derivative of the along-track velocities. This method can be criticized, and other approximations can be found in the literature. In this article we arbitrarily choose the 2D approximation of : 5ζz≈∂v⟂∂x. Unless otherwise stated, the velocity field is always perpendicular to the section plane. Relative vorticity has been used extensively in studies based on analyses of satellite altimetry data or high-resolution numerical models to locate eddies . Some Lagrangian criteria are also based on this quantity and are therefore of interest .

For these gradients, we refer the reader to Appendix B for details on uncertainties.

Here the 3D formula of EPV is simplified and applied to in situ data. Under the Boussinesq approximation and hydrostatic equilibrium, the vertical momentum equation can be replaced by the hydrostatic approximation ∂zp=-ρg, where p is the pressure, ρ the total density, and g the acceleration due to gravity. We also approximate 1/σ by 1/σ0. Therefore, following the method of , the EPV for a 2D vertical section has the following form: 6EPV=EPVx+EPVz=-∂Vo∂z∂b∂x+ζz+f0∂b∂z, where b(x,z)=-gσ(x,z)/σ0 is the buoyancy, Vo(x,z) is the velocity component orthogonal to the section plane, f0 the Coriolis parameter, and ζz(x,z) is as defined above. Note that this expression only gives a 2D approximation of the real EPV with a baroclinic term EPV_x and a term including the relative vorticity and stretching EPV_z. Therefore, the climatological EPV average of the considered ocean region (hereafter EPV‾) is 7EPV‾=f0db‾dz, where b‾(z) is the climatological reference profile of buoyancy in the area of the eddy. The Ertel potential vorticity anomaly is then calculated on density surfaces (i.e., using density as the vertical coordinate) as follows: 8ΔEPV(x,z)=EPVx(x,z)+ΔEPVz(x,z),9ΔEPVz(σ)=EPVz(σ)-EPV‾(σ), where (x,z) are the coordinates on a ship section. As with thermohaline anomalies, this quantity is calculated on isopycnic surfaces and then represented on geopotential levels. This quantity has been widely used to define the materially coherent core of eddies and is therefore of interest .

Following the approach of , we also define the ratio between the anomaly of the vertical component ΔEPVz and the horizontal one EPV_x: ΔEPVz/EPVx. In fact, it was shown that the eddy boundary is not locally defined and behaves like a frontal region subject to symmetric instabilities. These instabilities occur when the baroclinic term is not negligible compared to the vertical term . Consequently, a criterion of the type 10ΔEPVzEPVx>β, with β≫1, will detect the core water that is not in the turbulent frontal region. Symmetric instabilities can erode the core by changing the properties of the water parcels at the boundaries or by generating small-scale turbulence . This detected water is more stable and is subject to drift with the eddy without being altered by the environment.

The goal here is to determine which of the criteria defined in the preceding section (thermohaline anomalies, gradients, EPV) is most effective in detecting the coherent core. Some criteria have already been studied by . They showed that the eddy core is surrounded by a turbulent region subject to instabilities characterized by a value of EPVx/EPVz close to 1. Consequently, the largest values of the ratio ΔEPVz/EPVx define the eddy core, which is less subject to instabilities and where the trapped water is less likely to be mixed and modified by the environment. By superimposing the thermal anomaly and the ΔEPVz/EPVx contours, we determine the materially coherent core, which should undergo little change in properties during the eddy drift. However, this criterion must be applied to the eddy core where the distinct water is retained.

To capture the true materially coherent core of an eddy, two criteria must be used. First, thermohaline anomalies on isopycnal surfaces must be computed to detect the region where the trapped water is located. The outermost closed contour is used to bound an approximate core. However, the boundary provided by thermohaline anomalies is only a line. But some water in its vicinity may cross it and escape the core due to instabilities. Therefore, the ΔEPVz/EPVx criterion is used within the first region to remove the boundary region subject to instabilities. The last region is much more restrictive but represents the stable confined water inside the core.

Ertel potential vorticity combines the stratification anomaly, the rotating flow, and the influence of the Earth's rotation. As a result, the boundaries determined by the thermohaline anomalies on isopycnals, the relative vorticity, and the buoyancy frequency drive those determined by Ertel potential vorticity.

In practice, it is difficult to apply the ΔEPVz/EPVx criterion to in situ data because it requires high-resolution data due to multiple spatial derivatives and is quite sensitive to noise. We now show that this criterion can be theoretically approximated by the buoyancy frequency.

In the region where EPVz/EPVx≫1, we have 11EPV=(ζz+f0)∂b∂z. We then decompose the buoyancy field such that b(x,z)=b‾(z)+b′(x,z), where b‾ is the climatological average and b′ the anomaly resulting from the eddy dynamics. Because EPVz/EPVx≫1, ΔEPV≈ΔEPVz. Following Eq. (9), on isopycnal surfaces, the anomaly of EPV is thus decomposed into three terms: 12ΔEPVz=f0∂b′∂z+ζz∂b′∂z+ζzdb‾dz. Now, to analyze orders of magnitude, we have to keep in mind that the vertical scale for b′ will not be the same as b‾. For b′, we take H previously defined as b′, which is related to the isopycnal deviation. From Table , H=200 m. For db‾/dz, a typical order of magnitude in the ocean is N02=10-3 s-1. Then, we use Δb′=1 kg m⁻³ for a typical scale of b′ , V for Vo(x,z), and R for the eddy radius. Dimensionless quantities are marked with a hat. By nondimensionalizing ΔEPVz with f0Δb′/H, we obtain 13EPV^=∂b^∂z^+Roζz^∂b^∂z^+RoN02HΔb′ζz^db‾^dz^, where Ro=V/(f0R) is the Rossby number for an axisymmetric vortex. For mesoscale eddies, Ro<1 and even Ro=O(0.1). By construction, ζz^ is of order 1. So the second term is always smaller than the first one. Then N02H/Δb′=0.2, which is smaller than 1, and finally, the third term is also dominated by the first one. Therefore, the buoyancy frequency anomaly defined in Eq. (4) is a good proxy for our criterion. We confirm what was found using in situ data from . Note that f0∂zb′ has already been considered a PV anomaly in previous studies .

Consider an eddy whose boundaries are defined by a criterion (a given isoline of temperature or salinity anomaly, EPV, or gradients; see ). This eddy was sampled by a ship transect that does not necessarily cross the real eddy center, defined as the location of the zero velocity. Therefore, the difference between the exact eddy center and the center on the resulting 2D section will affect the reconstruction of the 3D structure and thus the volume.

To illustrate this fact, consider a perfect cylindrical vortex core with radius R and height H. We assume that it is located at the ocean surface and that it has been sampled by a ship track as shown in Fig.  so that L appears as the eddy radius on the 2D vertical section. An estimate by a simple calculation of the eddy volume using this 2D vertical section gives a volume of πL2H, which has to be compared with the real volume of πR2H. Using the Pythagorean theorem, it can be shown that the relative error, expressed as a fraction of the exact volume, is e2/(2R2), assuming e≪R. The relative error is less than 5 % if e≤R/10≈0.316R. In this case, e must be less than 31.6 % of R for this condition to be true. This condition is not really restrictive, and the reconstruction can be quite faithful.

If we now assume that the eddy is cone-shaped with a base of radius R and height H, the relative error is different. Assuming that the eddy was sampled by a ship's cruise, as in Fig. , the boundary of the eddy will appear as a hyperbola of maximum height He on the 2D vertical section. Now the eddy will appear to be less deep than it is in reality. The relative error between the exact and reconstructed volumes will be 3e/R. This result follows only from basic geometric considerations (see Fig. ). In this case, for the relative error to be less than 5 %, e must be less than 1.7 % of the eddy radius, which is very restrictive. Given the horizontal resolution of the data, and thus the uncertainty in the radius, the reconstruction method will be highly inaccurate.

Therefore, depending on the shape of the eddy, the distance between the ship track and the eddy center e is a critical parameter and strongly influences the uncertainty of the volume approximations. To ensure an accurate estimation of volume, we have computed the values only for eddies with a very small value of e. This approach helps us minimize the potential uncertainty in the computed volumes. Our database includes only four eddies (nos. 1, 2, 7, and 24) that have been sampled by a ship track crossing the eddy within a very small distance from its center (i.e., with e<3 km). These eddies are suitable for computing volumes due to their proximity to the center.

Different idealized volumes can be calculated analytically, and the same approach can be followed for subsurface eddies. As shown in previous studies, surface eddies appear to have shapes close to cylindrical or conical volumes (not necessarily with a circular basis), but some approximations exist for subsurface eddies. Some of them have described eddy EPV anomalies as pancakes because the horizontal scale is much larger than the vertical one . In reality, however, an eddy has a more complex shape, depending on the criterion used to define its boundaries. It is not perfectly axisymmetric and its rotation axis is not perfectly vertical. More precisely, the shape is determined by the rotating flow and depends on the deformation that the vortex undergoes. It can be stretched and sheared by the mean background flow. It has been shown that the flow function of the rotating flow can be decomposed into azimuthal normal modes . Depending on the order of the modes, the flow pattern is modified. If the eddies are strongly disturbed, the decomposition of the flow function into normal modes may include high-order terms. In most cases, however, three modes dominate: order 0, which corresponds to a purely circular eddy; order 1 which is the dipolar mode typical of self-propagating eddies; and order 2, which corresponds to an elliptical eddy . In this context, we propose two approaches to approximate the volume (associated with a criterion) of an eddy sampled by a ship section, assuming first that mode 0 and then mode 2 is dominant. Both approaches use the f-plane approximation. Both reconstructions are thus performed in a Cartesian space, neglecting the local curvature of the sea surface.

The methodology is illustrated in Fig. . We now reconstruct the 3D structure of an eddy using the same approach as in Fig. , but we take into account its vertical tilt. The eddy remains perfectly circular at each geopotential level, its center being the one given by the ship's section. The total volume is the sum of the volumes of the elementary cylinders.

This method preserves the variation of the eddy radius with depth and the variation of the eddy rotation axis on the vertical. This reconstruction is also relatively straightforward. However, it assumes that the eddy is perfectly circular at each geopotential level, which is a strict hypothesis. Also, the center is that of the 2D ship section, and the calculation of the volume does not depend on e, although we have shown that it has an influence. In summary, the approach consists of three steps. First, a criterion (the outermost closed contour of a given size) is chosen to delimit the materially coherent eddy core from its surroundings on the 2D vertical slice. Then, the position of the apparent eddy center is computed as the location where the orthogonal velocity Vo is zero and the eddy radius L(z) is associated with the selected criterion. Finally, the approximate volume is calculated as a sum of elementary cylinders.

This method defines the uncertainty due to resolution: 14δΩΩ=∫-H-Δz0π(L(z)+Δx)2dz∫-H0πL2(z)dz-1, where Ω is the approximated volume, Δx is the horizontal resolution, and Δz is the vertical resolution (depending on the type of device). This formula is valid for a surface eddy. In the subsurface case, the integral must be replaced by ∫-H+Δz2H+Δz2.

By employing a comparable methodology and making use of certain geometrical considerations, we are able to extrapolate the eddy volume using elliptically based tubes. Please refer to Appendix B for a detailed description of the methodology. This methodology enables the construction of two possible elliptically based tubes from a single ship section. On a ship section, the eddy center separates the core into two parts, which are then used to determine the volumes through the application of two ellipses, designated (E1) and (E2). The resulting volumes are determined by the left or right sides of the ship section, respectively. As the vertical shape of eddies is not well-understood, especially the shape of their thermohaline coherent core, in the literature, we present the two ellipses as examples of what an eddy core can look like in 3D.

For each mesoscale eddy, thermohaline anomalies on the isopycnals have been computed using the methodology described in Sect. 3.1. Examples of anomalies computed for some eddies are shown in Figs.  and . We inform the reader that all other vertical sections can be found in the Supplement (Figs. S1 to S16). Both salinity and temperature anomalies are calculated for each eddy.

For the subsurface AEs sampled in the Lofoten Basin (no. 24 in Table 2), a significant thermohaline anomaly is visible in the middle of the temperature and salinity panels between -700 and -1150 m depth. The location of this anomaly coincides with the maximum isopycnal anomaly, indicating that it corresponds to the eddy core. The trapped water is warmer and fresher than the climatological average. Compared to the surrounding water, the trapped water appears warmer and saltier.

A distinct negative anomaly can be observed in the vertical sections of the subsurface AEs sampled during EUREC4A-OA (no. 2). This eddy transports water that is fresher and colder than the surrounding water. In the case of the surface AEs sampled during Physindien 2011, the warmer and saltier core is located at x≈470 km and is surrounded by colder and less salty water that forms a rim around it. The subsurface cyclone sampled during M124 also shows anomalies in the region where the isopycnals show the greatest anomaly. Water that is hotter and saltier than its surroundings is trapped in the eddy core. However, the core is less well-localized than in other examples, suggesting either that the eddy is losing water through instability and filamentation or that it is not well-resolved in terms of the horizontal resolution of vertical thermohaline properties.

In Fig.  the thermohaline anomalies on isopycnals are collected for each eddy. The anomalies are computed with respect to climatological averages, but especially for Fig.  the maximum value between the eddy core and the surrounding water is computed using as a boundary the outermost closed contour of ΔT and ΔS (see Fig.  for examples). The maximum values of the anomalies represent the difference between the properties of the potential trapped water and the surrounding water. An eddy is considered to be TC when the maximum anomaly is reached at the eddy center (region where the velocity tends to zero) and there is a marked difference in values between the trapped and surrounding waters.

According to the data, 18 out of 25 eddies have a significant thermohaline anomaly on isopycnals in their core, which means higher than the climatological standard deviation in the considered region. Thus, 72 % are found with a significant anomaly in their core and are observed to transport distinct water in their core. Even eddies sampled far from their origin show an anomaly in their core (see Agulhas ring nos. 15, 16). Others have no significant difference in values between the enclosed and surrounding waters. Note that AEs are not automatically associated with positive temperature anomalies, and, conversely, CEs are not always associated with negative temperature anomalies.

A key point here is that eddies contain water characteristic of their region of formation. For example, showed that subsurface AE no. 24 (Fig. ) was generated by baroclinic instability of the Norwegian Atlantic Slope Current, which flows along the Norwegian Atlantic coast. Due to the β effect, its westward propagation results in heat and salt transport to the central part of the Lofoten Basin. The trapped water coming from the Norwegian coast appeared warmer and saltier than the fresh and cold water of the Lofoten Basin, resulting in positive anomalies in the eddy core. showed that the AE sampled in the Arabian Sea (no. 7, Fig. ) transports Persian Gulf Water. In this region, this high-salinity water spreads into the Sea of Oman via the Strait of Hormuz under the influence of energetic mesoscale eddies. Eddy no. 7 is one of them. showed that the water transported by subsurface AE no. 2 (Fig. ) comes from the North Brazil Current retroflection region, which appears colder and fresher than the surrounding waters. Finally, showed that Algulhas rings transport water from the Mozambique Channel to the South Atlantic Ocean. The water trapped by CE no. 9 is thus hotter and saltier than the surrounding water.

Figures  and present a comparison of sampled eddies with eddies identified by the TOEddies algorithm using satellite altimetry. Our comparison is qualitative, as we are primarily interested in the surface or subsurface character of eddies. We will leave the quantitative aspects to a future study. These figures focus on 17 well-sampled eddies that provide important information. Please note that eddies 3 and 8 are not included in the analysis as they are subsurface-intensified eddies that lie below the main thermocline. For more detailed information on these eddies, please refer to the Supplement.

Let us first examine panel (a) in Fig. . This panel shows subsurface eddy no. 2, which is also shown in Fig. . TOEddies detects this eddy as an anticyclone. The TC core of the vortex (location of the anomaly) is below -150 m and the velocity field tends to zero at this geopotential level. It is important to note that while the TOEddies algorithm successfully detects an AE, it does not correspond to a surface-intensified eddy. This aligns with findings in analogous cases discussed in and . Therefore, knowledge of an eddy's vertical structure is crucial for assessing its characteristics and classification.

Panel (b) in Fig.  presents another example of an eddy, eddy no. 24, which is also shown in Fig. . As in the previous example, the ADT signature of the eddy corresponds to the actual sampled eddy. In this case, the ADCP velocity field at the surface is not zero. However, the TC core is located at approximately -1000 m depth. In fact, it is not possible to determine from satellite altimetry alone whether a given feature is a surface- or subsurface-intensified eddy. This is similarly the case for panels (c), (d), (e), and (f) in Fig.  and panels (a) and (b) in Fig. . Some eddies give rise to a surface dynamic topography signal discernible in ADT maps. However, the distinct water that is trapped within them is situated at a considerably deeper level. For further details, please refer to the Supplement, which illustrates thermohaline anomalies on isopycnals for each eddy discussed in this article.

Our dataset indicates that the maximum thermohaline anomaly is often found at depth rather than at the surface. This is also true for eddies that have been identified by satellite altimetry. By limiting the analysis to geostrophic velocity fields derived from satellite altimetry or other surface properties, the resulting eddy assessments lack the vertical properties of eddies. This is also the case for eddies that have been identified through satellite altimetry. Lagrangian studies suggest that the ability of eddies to trap a water mass is a consequence of closed flow trajectories . It should be noted, however, that such trajectories cannot be calculated from surface velocity fields alone. As has been previously discussed, a considerable number of eddies are found to be intensified in the subsurface. Moreover, satellite altimetry has a limited horizontal resolution in comparison to the dimensions and varying velocities of eddies. Consequently, integrating the geostrophic velocities derived from satellite altimetry introduces a bias in the diagnostic of eddy material coherence provided by Lagrangian estimates of water parcel trajectories. Indeed, numerous eddies that were previously classified as incoherent have been found to exhibit coherence when their full vertical extent is taken into account. Therefore, our study underscores the inherent limitations of relying on satellite altimetry or any surface field to ascertain eddy characteristics.

Consequently, the accuracy of tracer transport estimates is contingent upon the manner in which eddies are observed and characterized. It should be noted that the proportion of thermohaline subsurface-intensified eddies indicated by our in situ dataset is 60.7 %. Even if the number of surface-intensified eddies is underestimated due to the fact that in situ velocity measurements often sample only the ocean below -50 m depth, this ratio serves to highlight the ubiquity of subsurface eddies. Furthermore, it highlights the inherent bias of studies based solely on satellite altimetry. This indicates a significant discrepancy between the surface geostrophic velocity derived from satellite altimetry and the velocity of the eddy core. This is exemplified by eddy nos. 1, 4, 7, 23, and 24 in Fig. . Furthermore, in cases where the overlying water is well-stratified, the subsurface eddies may be entirely undetectable in altimetry fields. This is illustrated by AE no. 2 in Fig. .

In conclusion, a typical correlation can be observed between eddy velocity and thermohaline anomalies on isopycnals. However, a notable proportion of eddies identified by satellite altimetry are subsurface-intensified, exhibiting a deep maximum of velocity and thermohaline anomalies. The presence of these eddies introduces a significant degree of uncertainty into the estimation of tracer transport based on satellite altimetry data alone.