Is There the Equatorial Water Mass in the Atlantic Ocean?

Using temperature and salinity profiles from the Argo data repository, a detailed volumetric temperature‐salinity diagram is compiled for the upper 2,000 m layer of the Atlantic Ocean. It is generally accepted that, unlike the Pacific and Indian Oceans where the Equatorial Water is present, there is no Equatorial Water in the Atlantic Ocean and its place is occupied by the South Atlantic Central Water (SACW). However, the detailed volumetric T‐S diagram shows that the main thermocline in the latitude range of 10°S–10°N is characterized by its own tight T‐S relationship which is relatively close to but clearly distinguishable from the tight T–S relationship of SACW in the latitude range of 10°S–40°S. We argue that the Atlantic Equatorial Water can be considered as a separate water mass which is probably formed by isopycnal mixing of SACW and the North Atlantic Central Water (NACW) in proportion approx. 3.5:1.

mixed layer into the geostrophic flow below.According to Stommel (1979), vertical velocity generated in STC by the Ekman pumping is smaller than vertical velocity of the seasonal cycle fluctuations of the mixed layer depth.As a result, a water parcel that is pumped down from the mixed layer in summer, when the mixed layer is shallow, is again trapped into the mixed layer in autumn/early winter when the mixed layer depth increases due to convective mixing.The Stommel's (1979) selective mechanism contributes to the tightening of the T-S relationship in CWs.Schmitt (1999) argued that the salt fingering also contributes to the tightening of the T-S relationship in Central and Equatorial waters.It acts to remove spice anomalies (i.e., thermohaline anomalies which are compensated in density), causing warm salty anomalies to rise across density surfaces (because they lose more salt than heat), and cold fresh anomalies to sink across density surfaces (because they gain more salt than heat) (Stern, 1967).Schmitt (1981) reported that T-S diagrams in CWs are much better described by a curve of constant density ratio in Equation 1 than by a straight line.
where  = −0 −1 ∕ ,   = 0 −1 ∕ , ∆T and ∆S are the differences in T and S over some vertical interval, ρ 0 is the reference density, S is salinity, T is the potential temperature and ρ is the potential density.According to Schmitt (1981), the constancy of R ρ is explained by salt-finger convection that intensifies at small R ρ ≤ 2, transfers more salt than heat, and acts to remove perturbations in R ρ .
Unlike CWs, which originate from the ocean surface, the Equatorial Water masses in the Pacific and Indian Oceans (PEW and IEW, respectively) are formed by subsurface processes of mixing (Sverdrup et al., 1942).Two CWs in the equatorial Atlantic Ocean, SACW and NACW, are separated by a region of transition with intermediate T-S relation, while in the Pacific, they are separated by a well-defined PEW (Sverdrup et al., 1942).The origin and geographical distribution of CWs and their relation to the circulation pattern in the Atlantic Ocean were studied in detail based on the analysis of numerous hydrographic data (Garzoli & Gordon, 1996;Kirchner et al., 2009;Mémery et al., 2020;Sprintall & Tomczak, 1993;Stramma & England, 1999;Stramma & Schott, 1999) and using the optimal multi-parameter (OMP) method (Azar et al., 2021;Liu & Tanhua, 2021;Poole & Tomczak, 1999;Tomczak & Large, 1989), but none of these works addressed the issue of the absence of the Equatorial Water mass.Azar et al. (2021) identified six source water types (SWTs) that contribute to CWs in the Atlantic Ocean.They are two varieties of the Subtropical Mode Water (STMW) from the North Atlantic (the Eighteen Degree Water (EDW) and Madeira Mode Water (MMW)), three varieties from the South Atlantic (formed in the eastern South Atlantic (STMW18), the Brazil-Malvinas confluence (STMW14), and along the edge of the subtropical front (STMW12)), and one variety from the Indian Ocean (STIMW) advected into the South Atlantic Ocean through the Agulhas leakage.The OMP method was applied to estimate the SWTs contributions to the Atlantic CWs.The contribution of EDW to NACW was found at the upper thermocline of the North Atlantic subtropical gyre until the 26.6 kg/m 3 isopycnal, while MMW contributes to the denser layer between 26.8 and 27.0 kg/m 3 .The contributions of EDW and MMW to the thermocline layer in the equatorial Atlantic were limited to a mixing fraction of approx.20%-25% (see Figure 3 of Azar et al. (2021)); similar estimation was previously reported by Poole and Tomczak (1999).In the Southern Hemisphere, the contribution of STMW14 was restricted to the southwestern side of the South Atlantic subtropical gyre, while STIMW influenced SACW between 20°S and 30°S with a mixing fraction of 34% ± 20% mainly at isopycnals of 26.2-26.4kg/m 3 .The STIMW weakly influenced the thermocline layer in the equatorial Atlantic with a mixing fraction dropping from approx.15% in the west to 5% in the east (see Figure 5 of Azar et al. (2021)).The main contribution to SACW between 20°S and 30°S and to the thermocline layer in the equatorial Atlantic with a mixing fraction above 50% was provided by STMW18 and STMW12.In earlier studies (Poole & Tomczak, 1999;Stramma & England, 1999), the contribution of STIMW to the Atlantic CWs was assessed differently with Azar et al. (2021).Namely, it was stated that SACW is of South Atlantic origin in the subtropical gyre, while SACW in the tropical region partly originates from the South Indian Ocean.
It seems astonishing that the Equatorial Water mass presents in the Pacific and Indian oceans but is missing in the Atlantic Ocean because the equatorial circulation and mixing in all three oceans have common features such 10.1029/2023GL104866 3 of 8 as the equatorial undercurrent and the equatorial waves.The issue is worthy to re-examine using modern data of high quality and large volume collected within the framework of Argo program.
Since 1998, when the Argo program was launched, more than 2 million high-quality vertical temperature and salinity profiles have been sampled in the upper 1,000-2,000 m layer (Wong et al., 2020), and the task was to ensure that these profiles are more or less evenly distributed over the whole World Ocean.The Argo data set is extremely suitable to build a detailed distribution of the water volume versus temperature and salinity or so-called volumetric T-S diagram (Cochrane, 1958;Montgomery, 1958;Pollak, 1958;Worthington, 1981) in order to re-examine the features of Central and Equatorial Water masses.

Approach
We suppose that the 3D fields of temperature T(x,y,z) and salinity S(x,y,z) are known with sufficient accuracy and spatial resolution for a given time in a water body (e.g., in the Atlantic Ocean).The next steps are followed: 1. We break the water body into elementary portions (bins) of the same volume δv = δx • δy • δz and estimate the spatially mean temperature ̃ and salinity ̃ of each bin, where k = 1,2,…,N, N = V/δv, and V is the volume of the water body; 2. Then we break the full ranges of temperature and salinity of the water body, [T min , T max ] and [S min , S max ], respectively, into n T = (T max − T min )/δT and n S = (S max − S min )/δS intervals of a small size δT and δS, and calculate the number of ( ̃ , ̃ ) pairs, n ij , in each (δT,δS) bin defined by condition ̃ [ min + ( − 1) 3. Finally, we divide the number of pairs n ij in the bin by the bin's "square" δT • δS and the full number of ̃ , ̃ pairs, N: where Obviously, distribution 2 satisfies the condition approximation of the distribution of the water volume on the (T,S) plane, p(T,S),  ∫

Application of the Approach to Argo Data
In order to apply the suggested approach, we have to find a way to extract (T,S) pairs from the Argo data (Argo, 2021), such as each of the pairs corresponds to approximately the same elementary volume of water δv = δx • δy • δz.To achieve this goal, the following steps have been consistently taken.
1. Vertical profiles of temperature and salinity with the Argo quality control flag 1 (good data), a high resolution (no worse than one record per 10 m depth) and a wide depth range (5-1,990 m), were interpolated to the δz = 5 m step.The potential temperature relative to the sea surface has been calculated from the in situ temperature, and henceforth letter T is reserved for potential temperature instead of in situ temperature.The total number of the vertical profiles chosen in the Atlantic Ocean was 265,354.2.An additional quality control of the T-S profiles was undertaken.All profiles with at least one inversion of potential density of more than 0.01 kg m −3 were discarded.Approximately 1.3% of the total number of profiles did not pass the quality control.3.If the distance between two successive profiles of the same Argo buoy did not exceed 20 km, then one of the two profiles was discarded.As a result, a sequence of profiles of the same Argo buoy remained with the distance between successive profiles exceeding 20 km.Such thinning of the profiles was undertaken in order to make the horizontal distribution of Argo profiles more uniform resulting in 16.5% decrease of the total number of profiles.4.This step aimed to select an equal number of profiles randomly distributed within each of the one-degree bins of the same area.The sequence of profiles that fell into each of the one-degree bins in latitude and longitude was randomly shuffled.Taking into account that more than 80% of the one-degree bins in the Atlantic Ocean in the latitude range of 60°S-60°N contained at least int(20 • cosφ) Argo profiles, where φ is the latitude and function int(X) rounds real number X down to the nearest integer, the first int(20 • cosφ) profiles of the randomized sequence were selected from each one-degree bin if the length of the sequence exceeded int(20 • cosφ) profiles.
Otherwise, all profiles from the one-degree bin were selected if the sequence of the profiles was shorter than int(20 • cosφ).The remaining profiles were discarded resulting in 39.5% decrease of the total number of profiles.
As a result, a series of ( ] and the number of (T,S) pairs that fell into each bin, n(T,S), was counted.Since n(T,S) varied over a wide range from 0 to 80,000, for the sake of better visualization of the temperature-salinity-volume relationship in the full range of n, it was decided to plot ln(n),n ≥ 1, instead of n versus S and T. Note that when calculating n(T,S), only those T-S pairs were taken from each vertical profile, where the temperature was smaller than the surface temperature by more than 0.5°C.Thus, the upper mixed layer was excluded from consideration.

Results
In the n(T,S) plot for the Atlantic Ocean (Figure 1), one can see several highly elongated areas of elevated n values in the shape of a steep-sided ridge-the red strips that correspond to the most voluminous water masses.By constructing similar to Figure 1 plots for various parts of the Atlantic Ocean, such as the equatorial zone, the Southern and Northern Atlantic outside the equatorial zone, etc., one can identify geographical affiliation of these water masses and recognize SACW, NACW, as well as their eastern and western parts, ESACW, ENACW, WSACW, and WNACW, respectively (see Figures 1 and 2).In Figures 1 and 2, there is an intriguing detail that requires special attention.It is generally accepted that, unlike the Pacific and Indian oceans, there is no Equatorial water mass in the Atlantic Ocean and its place is occupied by SACW (Emery, 2001;Sverdrup et al., 1942).According to the volumetric T-S plots in Figure 2, in the latitude range of 10°S-10°N there is a tight T-S relationship (a red strip denoted as "AEW") which is relatively close to but clearly distinguishable from the tight T-S relationship of SACW in the latitude range of 10°S-40°S.This red strip may be interpreted due to its geographical affiliation as the Atlantic Equatorial Water (AEW) which is missing in the classical list of main water masses of the oceans (Emery, 2001;Sverdrup et al., 1942).The volumetric T-S diagrams shown in Figures 1 and 2 suggest that the newly introduced AEW can be considered as a separate water mass.
The SACW, AEW, and NACW strips in Figure 1 are almost parallel and the AEW strip located in between is at a distance of approx.3.5 times closer to the SACW strip than to the NACW strip (the distance is measured along the isopycnals).Given this mutual arrangement of the SACW, NACW, and AEW strips, we hypothesize that AEW can be formed by isopycnal mixing of SACW and NACW in proportion of approx.3.5:1.This proportion is in agreement with the mixing fractions of the South Atlantic/Indian and North Atlantic STMWs in the thermocline layer of the equatorial Atlantic as estimated from the OMP approach (Azar et al., 2021).
Following Schmitt (1981) who argued that the T-S diagrams in the CWs are much better described by a curve of constant density ratio than by a straight line, we calculated R ρ = constant curves that provide the best fit to the SACW, AEW, and WNACW strips in Figure 1.To do that, a differential equation was numerically solved for different values of R ρ = constant and for the boundary condition S = S 0 at T = T 0 , where (T 0 ,S 0 ) is a T-S pair located at the Central or Equatorial Water strip.The R ρ = constant curves that provide the best fit to the CW strips and the Equatorial Water strip on the volumetric T-S plot are shown in Figure 1 by black thin curves.The SACW, AEW, and WNACW strips are satisfactory described by curves of R ρ = 1.83, 1.96, and 1.81 in temperature ranges of 6-12°C, 7-13°C, and 9-18°C, respectively.
To identify detailed geographic affiliation and depth range of the high volume strips on the volumetric T-S diagram (Figure 1) and relate them to the ocean dynamics, maps of potential temperature and depth on different isopycnals were addressed (Figures 3 and 4).Keeping in mind that CWs originate in the surface in late winter, the maps were compiled using Argo profiles sampled in January-April in the Northern Hemisphere and July-October in the Southern Hemisphere.
According to Figure 1, on isopycnal surface σ 0 = 26.8kg/m 3 the SACW, AEW, and NACW strips are characterized by potential temperature values of approx.10, 11, and 14.5°C, respectively.Accordingly, the map of potential temperature on σ 0 = 26.8kg/m 3 (Figure 3a) displays three wide zones of low thermoclinicity marked as SACW, AEW, and NACW, separated by thermohaline fronts with temperature jumps of approx.1°C in the Southern Hemisphere and 3.5°C in the Northern Hemisphere.The circulation pattern in the depth range of 200-500 m is illustrated by a topography map of the σ 0 = 26.8kg/m 3 isopycnal (Figure 3b) which identifies the location of anticyclonic subtropical gyres (a profound bowl-shaped depression of the isopycnal surface in the latitude range of 15-40° in both hemispheres) and multiple alternative zonal flows near the equator.Comparing maps of Figure 3 with the detailed maps of geostrophic currents in the Atlantic Ocean (Azar et al., 2021;Stramma & England, 1999) one can conclude that the thermohaline fronts between SACW and AEW and between AEW and NACW basically follow the southern branch of the South Equatorial Current (SSEC) and the North Equatorial Current (NEC), respectively.10.1029/2023GL104866 7 of 8 According to Figures 3 and 4, the low thermoclinicity pool in the equatorial Atlantic marked as AEW, which is laterally separated from CWs at higher latitudes by thermohaline fronts, can be clearly identified within the isopycnal range of σ 0 = 26.5-27.1 kg/m 3 .This isopycnal range corresponds to the depth range of approx.150-500 m (the bathymetry of corresponding σ 0 surfaces is not shown for brevity).The shape of temperature contours in Figures 4a-4c, confirms the conclusion by Azar et al. (2021) that the influence of the Brazil-Malvinas STMW is restricted to the southwestern side of the South Atlantic subtropical gyre (a warm water pool centered at approx.35-45°W, 35°S), while the Indian STMW influences SACW between 20°S and 30°S (a cold water tongue elongated from Cape Town toward northwest).

Discussion and Conclusions
CTD data of high quality and large volume sampled in the framework of Argo program are used to compile detailed volumetric T-S plots in order to re-examine properties of water masses in the main thermocline of the Atlantic Ocean.A new result is obtained to our current knowledge.Namely, the main thermocline in the equatorial zone of the Atlantic Ocean is characterized by a tight, unique T-S relationship marked as AEW in Figure 1 which is observed neither to the south of 18°S nor to the north of 18°N (cf.Figures 1-4).In spatial coordinates, the AEW strip corresponds to a low thermoclinicity pool between the 26.5 and 27.1 kg/m 3 isopycnals (∼150-500 m depth) laterally separated from NACW and SACW by thermohaline fronts that basically follow the SSEC (see Stramma and England (1999)) in the Southern Hemisphere and the NEC in the Northern Hemisphere (Azar et al., 2021).Such a low thermoclinicity water body with a tight, unique T-S relationship and thermohaline fronts at the lateral boundaries can be considered as a separate water mass and referred to as the Atlantic Equatorial Water (AEW) in this particular case.The tight T-S relationship of AEW is relatively close to but clearly distinguishable from the tight T-S relationship of SACW in the latitude range of 10°S-40°S.The T-S curves of SACW, AEW, and NACW are almost parallel and the AEW curve being in between is at an along-isopycnal distance approx.3.5 times closer to the SACW curve than to the NACW curve.This is consistent with a hypothesis of AEW formation by isopycnal mixing of SACW and NACW in proportion of approx.3.5:1.This proportion corresponds to the ratio of the mixing fractions of the South Atlantic/Indian STMWs and the North Atlantic STMWs in the thermocline layer of the equatorial Atlantic previously obtained from the OMP approach (Azar et al., 2021).
Historically, the concept of a water mass was introduced as being defined by a segment of T-S curve clearly distinguishable from that of other water masses (Helland-Hansen, 1916;Sverdrup et al., 1942;Worthington, 1981).
The only reason to consider AEW, which actually is a mixture of SACW and NACW, as a separate water mass is that it has its own tight T-S relationship clearly distinguishable from the T-S relationships of the water masses subjected to mixing.In this sense, the situation in the Pacific, Indian and Atlantic oceans is similar: the main thermocline of the equatorial zone is characterized by a unique T-S curve which is believed to be a result of subsurface mixing.The difference is that PEW and IEW were introduced decades ago (Sverdrup et al., 1942), while only dense Argo profiles made it possible to separate T-S curves of AEW and SACW.
Based on the results presented above and the results of previous studies, the process of formation of the AEW can be represented as follows.According to a schematic map of geostrophic currents in the CW layer (∼100-500 m) of the tropical Atlantic (Stramma & Schott, 1999; see also Tuchen et al., 2022), SACW and, to a lesser extent, NACW enter the equatorial zone along the western coast of Atlantic with the North Brazil Undercurrent (NBUC) flowing to the north and the Guiana Undercurrent (GUC) flowing to the south, respectively.The NBUC and GUC feed the equatorial under/counter currents.The equatorial zone is characterized by a variety of alternative zonal jet currents, such as the central, equatorial, and northern branches of the South Equatorial Current flowing to the west, and the South Equatorial Countercurrent, South Equatorial Undercurrent, Equatorial Undercurrent, and North Equatorial Undercurrent flowing to the east (Stramma & Schott, 1999).The alternative zonal jets cause enhanced dissemination of liquid particles on isopycnals that can be parameterized by the increase of the apparent isopycnal diffusivity.As a result, the incoming SACW and NACW mix up isopycnally, forming a low thermoclinicity pool in the equatorial zone's thermocline and the thermohaline fronts at the lateral boundaries as shown in Figures 3 and 4.
Our analysis made it possible to refine and supplement the volumetric TS-diagram of various water masses in the main thermocline of the Atlantic Ocean.The identified new water mass, AEW, allowed to complete (or at least to more accurately describe) the phenomenological pattern of basic water masses of the World Ocean.The disadvantage of our analysis is that we used only TS-characteristics to identify the new water mass.A promising continuation of the study is an analysis using other characteristics of water masses, for example, isotopic ratios, oxygen, silicate, nitrate and phosphate.We hope that such future studies will confirm our assumption about the genesis of AEW.

Figure 1 .
Figure 1.Natural logarithm of the number of T-S pairs in a cell of the size dT = 0.02℃, dS = 0.02 • PSU versus temperature and salinity in the upper 2,000 m layer of the Atlantic Ocean (excluding the surface mixed layer).Black thin curves are the R ρ = constant curves fitted to the SACW, AEW, and WNACW strips.