Surface Water Mass Transformation in North Atlantic Based on NCEP CSFR Reanalysis

Abstract

This paper focuses on the analysis of variability of density fluxes and water mass transformation in the North Atlantic, the quantities reflecting the intensity of intermediate and deep water formation. The authors assess the influence of atmospheric processes on the intensity of formation of subpolar modal waters, subtropical modal waters and Labrador Sea waters using the density fluxes and water mass transformation. This analysis is carried out on a seasonal and climatic time scale. The main result of the study is the seasonal and climatic dynamics of water mass transformation in the Labrador Sea, subtropical and subpolar modal waters based on CFSR reanalysis data. The results obtained help to understand the main factors influencing vertical circulation in the region, which can be used in further model experiments.

1. Introduction

The formation of surface water masses in the World Ocean occurs under the influence of atmospheric processes. The ocean responds to changes in the atmosphere by changing its density. Water masses formed in areas of active interaction between the ocean and the atmosphere transfer the signal of climate change to the intermediate and deep layers. Changes in the conditions for the formation of vertical mass flows affect the intermediate and deep layers of the ocean and thus affect the entire climate system [1]. The interaction between the ocean and the atmosphere is carried out through heat and moisture exchange and impulse transfer from the atmosphere to the ocean [2]. The intensity of these processes is subject to seasonal and annual variability. Variability in atmospheric characteristics such as precipitation, evaporation, and heat fluxes influences the variability of the mixed layer depth and mixing intensity in the World Ocean [3].

Speaking of past research on the topic of energy exchange between the ocean and the atmosphere, much of the one-dimensional theory concerning the ocean surface turbulent boundary layer, or mixed layer, relies on the validity of two fundamental assumptions. The first assumption is that vertical mixing within the turbulent boundary layer, as well as entrainment mixing at its base, is primarily driven by local atmospheric forcing—specifically, the surface wind stress and the net heat transfer (whether radiated or conducted) across the ocean–atmosphere interface [4]. The second key hypothesis is that the mechanical energy budget plays a central role in understanding and predicting the dynamics of the mixed layer. The turbulent motions within this layer adjust according to local atmospheric conditions, with their behavior being influenced by factors such as the depth of the mixed layer and the intensity of turbulence [5].

In any case, both mean and turbulent kinetic energies in the mixed layer are expected to reflect the local boundary conditions for wind stress and surface buoyancy flux [6].

The Monin–Obukhov similarity theory length is the depth at which the wind-generated turbulence is balanced by the buoyancy due to surface warming and freshening (salting) by precipitation (evaporation) [7].

In those areas of the World Ocean where the intensity of atmospheric processes is at a maximum, their influence extends not only to the mixed layer but also to deep convection processes. Thus, the interaction of the ocean and the atmosphere influences the formation of intermediate waters of the World Ocean, which circulate in the subpolar gyres and form deep links of global interoceanic circulation [8,9].

Ventilated thermocline is forced by air–sea interaction processes to deepen and cool polewards. Where there is flow from the mixed layer into the interior, the mixed layer depth (MLD) and density fields help to set the potential vorticity of subducted fluid. It is possibly due to the ventilation model which is forced by Ekman pumping and surface heating [10].

The global buoyancy balance constrains two key parameters: the subtropical gyre’s mid-ocean outcrop latitudes for surfacing layers and the eastern-boundary interface depths for non-outcropping layers. These variables regulate the mean layer thicknesses and—combined with diapycnal diffusivity—set the mean diffusive buoyancy flux per active layer. Thus, wind-driven circulation and surface buoyancy fluxes collectively govern the area–mean stratification [11].

Atmospheric variability appears to be the primary driver of large-scale sea surface temperature (SST) anomalies in the South Atlantic Ocean. These anomalies are generated by wind variations linked to atmospheric pressure disturbances, which alter latent heat flux and deepen the mixed layer. Other factors, such as additional heat flux components and Ekman transport, have a minimal influence. Variations in latent heat flux result from both wind speed fluctuations and anomalous atmospheric heat advection. Once formed, SST anomalies are gradually dampened by latent heat flux. Notably, there is no observable feedback from SST anomalies affecting atmospheric circulation [12].

The depth of the mixed layer can be influenced by short-term events. For example, the passage of a cyclone in the Gulf Stream region can increase heat flows from the ocean to the atmosphere, which can reach 1000 W/m². This is due to the arrival of cold continental air and an increase in the values of latent and sensible heat flows. This led to a deepening of the mixed layer by 35 m and a decrease in temperature of 0.65 degrees [13].

During cold-air outbreak (CAO) events, cooling was most strongly influenced by cold-water entrainment from the thermocline, largely due to mixed-layer deepening, while latent and sensible heat fluxes contributed to a lesser extent. In this study, cooling in the mixed layer due to entrainment primarily depends on the specified temperature just below the thermocline. This temperature was derived from observed typical values of mixed layer depth (MLD), sea surface temperature (SST), and temperatures at 150 m depth, as established by the experiments. Despite this, the resulting SST changes—driven by atmospheric forcing and linked to CAO events—align well with the actual observations from both buoys, located in the western and eastern regions of the Gulf of Mexico [14].

The MLD also depends on the subarctic front and western boundary flow, for example, the Kuroshio extension front in North Pacific. The winter mixed layer (ML) exhibits substantially greater depth on the southern flank of the Subantarctic Front (SAF) compared to its northern side. The maximum ML depth typically occurs about 50–100 km poleward of the SAF, coinciding with the location of peak air–sea flux values. This spatial correlation indicates that the mesoscale variability of air–sea fluxes associated with the SAF plays an important role in shaping the structure of the upper ocean layers in this region [15].

When studying water masses, various data sources are usually used (ship observation data from ICOADS [16], ocean–atmosphere flux database, ARGO buoy data). Over the past decades, the number of measurements of flows at the ocean–atmosphere boundary has increased [17,18]; in addition, these data have begun to be assimilated in atmospheric reanalyses [19,20], which has made it possible to study the transformation of water masses at the ocean surface using numerical circulation modeling [21,22,23].

Surface water transformation depends on large-scale atmospheric fluctuations; surface water transformation for the North Atlantic has been found to be associated with the North Atlantic Oscillation (NAO) and Arctic Oscillation index [24,25]. Although at first the modeling of transformation processes in circulation models was carried out on grids with a coarse resolution of the order of 1° [26], later it became possible to model the processes of transformation of water masses on grids of the order of 1/15° [27]. This study employs a coupled modeling system combining an R30-resolution atmospheric general circulation model with an ocean mixed layer model to investigate upper ocean variability in the Northern Hemisphere. The model demonstrates notable skill in reproducing winter-to-winter SST anomaly correlations exceeding 0.6 in regions with deep winter mixed layers, particularly in the subpolar North Atlantic. This successful simulation implies that mixed layer dynamics alone can sustain thermal anomalies over seasonal timescales, without requiring contributions from ocean current advection or thermohaline circulation processes [28].

Atlantic meridional overturning circulation (AMOC) volume and heat transport sensitivities were found to suggest that a persistent slowdown in overturning could lead to a cooling of the North Atlantic Ocean over a decade to a century; however, over millennia this cooling will diminish and could potentially give way to surface warming [29].

Loss of surface heat from the Subpolar Gyre in winter increases the AMOC with a lag of approximately 6 months. However, the same surface heat flow anomaly in summer leads to a weakening of the AMOC, occurring with a lag of 8 months. However, it should be taken into account that heat flow anomalies will lead to changes in freshwater flows (cooling—less evaporation, heating—more) [30].

This article examines the inter-seasonal and inter-annual variability of density fluxes in the North Atlantic based on CFSR/CFSv2 reanalysis data. The main objective of the study is to identify periods with high density fluxes for each water mass and to conduct inter-annual variability of winter transformation processes.

2. Materials and Methods

2.1. Density Flux

To assess the intensity of the surface water formation process, this study uses the density flux value, first proposed in [26]. This value reflects the change in the density of waters in the surface layer of the ocean depending on the flows of heat and fresh water at the ocean–atmosphere boundary and is the inverse value of the buoyancy flux. The use of density fluxes in the study of convective processes in the North Atlantic has a number of key advantages that allow us to better understand the mechanisms of water mass formation, the meridional circulation (AMOC), and the climatic role of the region. Firstly, there is a direct connection with convection and vertical mixing. Convection in the ocean occurs due to the loss of buoyancy by surface waters, which leads to their sinking. Secondly, buoyancy fluxes combine various thermal and freshwater effects, which are critical for the North Atlantic, where in winter there can be strong cooling from the ocean surface, melting processes of Greenland ice, and salinization processes during ice formation. This method gives a general answer to questions about the dynamics of convection as a result of the interaction of the ocean and the atmosphere. It is quite simple compared to similar modeling. Transformation of ocean water in general is the loss of water’s original properties. In this study, water mass transformation is the mass transfer of seawater across a surface with a constant density value. The transformation rate value is the integral of the density flux along the isopycnal (Formula (4)). In the classical oceanological literature, the criterion for the allocation of surface water masses is depths up to 150–200 m. In this study, an analysis of surface waters is carried out, which means waters at depths up to 5 m, since this layer is most susceptible to transformation due to heat and moisture exchange with the atmosphere. In this study, the limitation of the considered depths to 5 m is due to several key factors. This is the area of formation of turbulent mixing, where vertical gradients of temperature and salinity are most pronounced. At depths of up to 5 m, the influence of atmospheric flows (latent and sensible heat, evaporation, precipitation) significantly exceeds the influence of deep processes (advection, upwelling, internal waves). Deeper than 5–10 m, seasonal dynamics begin to dominate. In addition, practical measurements, such as buoy and satellite measurements, which are assimilated by reanalyses, also cover depths of up to 5 m. The salinity of the ocean surface layer contained in the NCEP CFSv2 reanalysis data corresponds to a depth of 5 m.

Positive values of the density flux characterize an increase in the density of surface waters, and, accordingly, negative values are an indicator of a decrease in density on the ocean surface. This value is determined by the following ratio [26]:

f = (−α)/C_P Q_net + ρ₀β(E − P)S/((1 − s)),

(1)

where Q_net is the resulting heat flux between the ocean and the atmosphere, C_p is the specific heat capacity of water at constant pressure, ρ₀ is the density of water, E is evaporation, P is precipitation, S is salinity in units of practical salinity (PSU), (1 − s) is the salinity anomaly, where s is salinity in fractions of one, and α and β are partial derivatives with respect to the temperature and salinity of the equation of state, widely known as the thermal expansion and salinity compression coefficients, respectively, which are equal [31].

A = ∂ρ/ρ∂T, β = ∂ρ/ρ∂S,

(2)

where ρ is density, S is salinity, and T is temperature.

As noted before, the reanalysis provides temperature and salinity values for the ocean surface layer at a depth of 5 m. The resulting heat flow between the ocean and the atmosphere (Qnet) is determined by the following relation [32]:

Q_net = (DS − US) + (DL − UL) − LH − SH,

(3)

where DS is the short-wave flux density directed from the atmosphere to the ocean, US is the short-wave flux density directed from the ocean to the atmosphere, DL is the long-wave flux density directed from the atmosphere to the ocean, UL is the long-wave flux density directed from the ocean surface to the atmosphere, LH is the latent heat flux density, and SH is the sensible heat flux density.

Buoyancy fluxes (reciprocal of density flux) (B) at the ocean surface represent a combination of the haline and thermal forcing, and therefore a joint interpretation of the haline (BS) and thermal (BT) buoyancy flux components is desirable when analyzing B variability. In the past, a simple ratio of BT/BS has been used as a diagnostic tool [33].

The transformation rate characterizes how much water of a given density was transformed in a given area per unit of time. To move from density flux to the surface water transformation rate, it is necessary to additionally take into account the surface area and density of sea water. The transformation rate is determined by the following relationship:

$$F\left(\rho \right)=\underset{∆\rho \to 0}{\lim }{\displaystyle \frac{1}{∆\rho }}\left({\displaystyle \frac{1}{T}}\int dt{\iint }_{xy}fdxdy\right),$$

(4)

where T is the time period (months), f is the density flux, xy is the surface area of water with potential density values in a certain range, and $\Delta \rho$ is a certain range of density.

The dimension of the transformation rate is defined as [m³s⁻¹]. Therefore, this value can also be represented in Sverdrup (1 Sv = 10⁶ m³s⁻¹)—this unit of measurement is traditionally used in oceanology when analyzing the transport of ocean currents.

Ice cover in the subpolar and polar regions of the World Ocean is an important component of climate and weather formation. The presence of ice cover significantly reduces the amount of heat exchange between the ocean and the atmosphere. For this reason, calculations of density fluxes and transformation rates were carried out only for those areas where the ice cover is less than 15%.

Previously, the authors tested the sensitivity of the density flux to salinity changes. Sea surface salinity is considered to be the least accurately determined of the variables used. Using salinity from the CFSR does not give significant differences compared to salinity from Glorys or Aquarius [34]. The authors tested the sensitivity of the density flux to the temporal resolution of the salinity: 6 h versus the monthly average. The studies also showed an insignificant effect.

The transformation rate of a water mass can be determined from the surface buoyancy flux if horizontal mixing is ignored and if vertical mixing is strong in the surface layer with isopycnals very close to vertical, and zero in the deep ocean below the surface layer.

2.2. Reanalysis NCEP CFSv2

Calculation of surface water density fluxes for regional analysis of seasonal mean characteristics and intra-annual variability was based on the NCEP CFSv2 reanalysis [35] provided by the US National Center for Environmental Prediction (NCEP). This reanalysis covers the time period from 2011 to the present and is a new generation of the NCEP CFSR reanalysis [36], which contains information for 1979–2011. Unlike the first generation of reanalysis, NCEP CFSv2 has global coverage (previously the calculation area was from 75° S to 65° N), uses the MOM4 ocean circulation model (previously the MOM3 model was used [37]), and the spatial resolution ocean data is 0.5° (previously it was 1°). The ocean circulation model takes into account the thermodynamics of ice and the equation of the state of sea water described in [38] (instead of EOS-80 in the first reanalysis). The time resolution of the provided data is 6 h. The NCEP CFSv2 reanalysis implements cyclic assimilation of field observation data [39] and uses a joint NCEP GFS atmospheric model [40] with the NOAH land surface model [41] and the GFDL MOM4 ocean model [37], which, along with high spatial resolution and time discreteness, is an advantage of using NCEP CFSv2 for the purposes of this study. The spatial resolution of the atmospheric model is 0.205°. To obtain salinity values on the ocean surface in NCEP CFSv2, direct observation data from the TAO, PIRATA, and TRITON [42,43] buoys are assimilated, while at great depths salinity in the reanalysis is a synthetic characteristic calculated based on ARGO profiles [44] and local climatological relationships between potential temperature and salinity contained in the World Ocean Database [45].

3. Results

The transformation of surface water masses is a necessary condition for the occurrence of convective movements in the water column. The transformation characteristics are calculated based on the data of the NCEP CFSR reanalysis and its second version, NCEP CFSv2. This paper analyzes the inter-seasonal variability of surface water transformation characteristics.

The North Atlantic region is one of the key regions in the global oceanological conveyor. Both surface and intermediate and deep waters of the World Ocean are formed here. The formation of these waters occurs due to the active energy exchange between the ocean and the atmosphere in this region. In this study, the year 1979, the first year of the CFSR series, is used as an example of a specific year to illustrate the spatial features of the density flux value distribution. Using the averaged full series of years would give a smoother picture of the general appearance. Using a specific year gives a more detailed picture. In 1979, the NAO index was near zero, which preceded the positive phase of the NAO in the 1980s, which allows us to consider an average year in atmospheric activity as an example.

The North Atlantic exhibits the highest oceanic density fluxes globally during January, with peak values reaching 4.5 × 10⁻⁵ kg m⁻² s⁻¹ in the Gulf Stream region (Figure 1a). Such magnitudes are characteristic of warm western boundary currents during winter.

Positive density fluxes dominate nearly the entire North Atlantic in January, driven by winter cooling that increases surface water density. The sole exception occurs at low latitudes, where negative fluxes (up to −1.3 × 10⁻⁵ kg m⁻² s⁻¹) arise from precipitation exceeding evaporation.

March (Figure 1b) is a transitional period for this region. The highest values of density fluxes are still in the Gulf Stream area up to 3·× 10⁻⁵ kg m⁻²·s⁻¹. The area of water areas with negative density fluxes is increasing. This is because radiation cooling is replaced by radiation heating during this month (Figure 1b). The largest negative values of the density flux up to −1.3·× 10⁻⁵ kg·m⁻²·s⁻¹ also belong to equatorial waters.

In July (Figure 1c), negative density flux values dominate nearly the entire North Atlantic, including regions of western boundary currents. The most pronounced negative fluxes occur near the Newfoundland Bank (reaching −1.3 × 10⁻⁵ kg m⁻² s⁻¹) and in equatorial waters (up to −1.2 × 10⁻⁵ kg m⁻² s⁻¹). The only exception appears in equatorial waters west of Africa, where small positive density fluxes (up to 8 × 10⁻⁶ kg m⁻² s⁻¹) occur. These localized positive values result from reduced heat flux due to persistent cloud cover associated with the Intertropical Convergence Zone (ITCZ).

Based on the calculated density fluxes, an analysis of the transformation of surface waters was carried out. This value includes the density flux and area and characterizes the transformation of waters of a particular density in a given area. Separately, an analysis of the transformation due to thermal and salinity components, as well as for the total density flux, was carried out. The positive values of the transformation indicate that waters of a given density tend to increase in density over the period under consideration. Negative transformation values correspond to a decrease in water density. Moreover, the transformation due to the thermal component (Figure 1c) makes a greater contribution to the overall transformation of surface waters of all densities.

Seasonality is observed for the waters of the North Atlantic and two periods can be distinguished (Figure 2). For most waters, the period from October to March exhibits a positive transformation, that is, a positive density flux, which is a consequence of winter water cooling. The period from April to September is characterized by a negative transformation of all waters, which is a consequence of the heating of waters under the influence of heat exchange with the atmosphere. Thus, heating and cooling periods are identified. The least susceptible to seasonal variability are waters with densities of 1022–1023 kg/m³—these are waters of equatorial regions with a strong influence of atmospheric precipitation. Thus, for this region, less dense waters tend to have a negative transformation, while denser waters tend to have a positive transformation.

Following the quantitative analysis of the transformation of waters of different densities, the next logical step is the analysis of the qualitative characteristics of the transformed waters. For this purpose, temperature–salinity (TS) analysis is used, which is widely used in oceanology in the study of water masses.

In Figure 3, all the characteristics of the transformed waters in the North Atlantic are represented on the TS plane; the color shows the value of the transformation of the waters.

On the TS chart for January (Figure 3a), two transformation maxima can be distinguished. Waters with temperatures from 16 to 23 ° C and salinity from 36.5 to 37.5% belong to the first, so it can be reliably stated that this maximum transformation corresponds to subtropical water masses. The second maximum of transformation belongs to waters with temperatures from 7 to 13 °C and salinity from 34.6 to 35.4, which corresponds to the subpolar waters of the North Atlantic. In addition, waters with temperatures of 5 °C and below and salinity from 34.9 to 35.4 have a positive transformation; this corresponds to the waters of the Labrador Sea. Negative transformation in winter is characteristic of the warmest waters of the region, with temperatures above 26 °C; these are the waters of the equatorial region. In March (Figure 3b), the heating period begins, and the values of positive transformation decrease and become negative for subtropical waters. However, despite this, there is a maximum of positive transformation for subtropical and subpolar waters. In the summer (Figure 3c), most of the waters are subject to heating, so you can observe a positive transformation of the waters.

A similar calculation of the annual course of transformations of waters of different densities was made on the basis of CFSR/CFSv2 data for 1979–2018. The average climatic transformation and the monthly transformation anomaly were calculated.

In Figure 4, positive values mean that the transformation exceeds the average climatic one, while negative values are associated with low values of transformation. Waters with a density of 1021.5–1023 kg/m³ from 1979 to 2003 exceeded the average climatic value for transformation, while after 2003 the transformation became lower than the average climatic value. Since these waters are characterized by a negative transformation throughout the year (Figure 2), we can talk about higher density fluxes for these waters. Such changes occur due to an increase in the heat flow for these waters, since the density flux depends on its thermal component. For waters of 1023–1026 kg/m³ in the period from 1979 to 2005, the transformation was below the average climatic values; since 2005, the transformation has increased above the average climatic values.

Waters with a density of 1026 kg/m³ are of greater interest, since waters with such a surface density form subtropical modal waters, subpolar modal waters, and waters of the Labrador Sea, which require separate consideration. First, let us consider the temporal changes in the transformation of subtropical modal waters (Figure 5), waters associated with the Gulf Stream.

Subtropical modal waters water (STMW) is formed from surface waters with densities of 26.4 < σ0 < 27.2 kg/m³. Thus, there is a density field for each month from 1979 to 2018 from CFSR/CFSv2. The annual average transformation from October to March is estimated, which is considered positive. The minimum transformation value for subtropical modal waters was 232 Sv in 1989. The maximum was 388 Sv in 2005. For the period from 1980 to 2005, there was an increase in the value of the transformation of the STMW to maximum values. Then, after 2005, there was a decrease in the values of the transformation of the STMW from values of 380 Sv to 300 Sv. The increase in the positive winter transformation over the observed period indicates an increase in heat fluxes; the water area was cooling more each year. Several factors may influence this, as this is a region of action of warm western boundary currents. Above these currents, there are high values of latent and sensible heat fluxes. The increase in winter transformations may be a consequence of the increase in contrast between the ocean temperature and the water temperature in winter.

Subpolar modal waters (SPMW), 27.2 < σ0 < 27.7 kg/m³, have lower transformation values (Figure 6). They exhibit cyclical dynamics of transformation. The minimum transformation of the SPMW was observed in 1987 and was 111 Sv. The maximum transformation of the SPMW was observed in 2014 and was 168 Sv. In the period from 1979 to 2005, there was a general decrease in the average transformation values from values of about 150 Sv to 125 Sv. After 2005, there was an increase in the transformation values up to the maximum values. In the first two decades (1979–2000), relative stability with moderate oscillations is observed. After ~2000, an increase in the amplitude of oscillations is noticeable, as well as a possible weak trend towards an increase in transformation (especially in the 2010s). In some years (e.g., in the early 1990s and mid-2010s), sharp jumps occur, which may indicate extreme events related to anomalous heating or cooling, since the transformation mainly depends on heat flows.

The transformation of the Labrador Sea waters (Figure 7) is an order of magnitude lower than previously considered, but it is very indicative of the climatic dynamics of the hydrological structure of the region. The dynamics of transformation depend on the atmospheric effect. The transformation corresponds to variability in the NAO index [43].

Thus, three periods can be distinguished according to the dynamics of transformation of the waters of the Labrador Sea. The first period is from 1979 to 1995 with high transformation values; this was due to the high values of the NAO index (Figure 8) and led to high mixing values during this period. Further, from 1995 to 2012, there were no long-term high NAO values; therefore, low transformation values and low values of the mixed layer were observed during this period [46]. Further, since 2012, the growth of transformation values began, which is consistent with the growth of the values of the mixed layer, although the NAO index did not have a pronounced positive anomaly, as in the period 1979–2005. However, in calculating the transformation based on reanalysis, there has been a clear increase in values since 2012. Thus, the values of density and transformation fluxes are more reliable indicators of the mixing intensity.

4. Discussion and Conclusions

In this paper, we analyze the seasonal and inter-annual variability of surface water transformation in the North Atlantic based on the NCEP CFSR CFSv2 reanalysis data. The transformation dynamics based on changes in the density flux value manifest in the form of clear seasonality. Seasonality is mainly associated with periods of heating and cooling of surface waters and to a lesser extent with the dynamics of precipitation and evaporation. The highest values of density fluxes are associated with the waters of western boundary currents, such as the Gulf Stream, which in this region is associated with the formation of subtropical water masses. In summer months, the transformation dynamics are reversed, and negative values of the density flux are associated with the widespread heating of water areas. Thus, the seasonality of the transformation value is largely associated with periods of heating and cooling and to a lesser extent with the difference in precipitation and evaporation.

Water masses of different densities respond differently to seasonal and inter-annual atmospheric forcing, with subtropical and subpolar modal waters showing different transformation patterns, while the Labrador Sea waters are significantly affected by atmospheric variability; in particular, the NAO is most strongly manifested and coincides with the dynamics of the transformation of the waters of the Labrador Sea, which coincides with the depths of the mixed layer [46]. Inter-annual trends show significant variability in the transformation of key water masses such as the subtropical modal water (STMW), subpolar modal water (SPMW), and Labrador Sea waters.

The long-term dynamics of the subtropical and subpolar modal waters show an increase in values by 2005, followed by a decrease. These changes are related to large-scale, long-term atmospheric dynamics in the region, associated with such values as the NAO index. The Labrador Sea waters show the greatest relationship with this index. For a more accurate determination of water masses and their transformations, visualization on the TS plane is used. In particular, the study identifies TS classes of subtropical and subpolar waters and the Labrador Sea by characteristic maxima and minima of transformation, which also allow us to analyze their seasonal variability.

Calculation of transformation based on CFSR data for 12 months showed that the values of LSW transformations are about 12–14 Sv, which correspond to estimates in the foreign literature [26,47,48]. The transformation of the SPMW shows the same inter-annual dynamics as in [22] without any trend towards an increase or decrease in transformation. In the first half of the 1990s, the peak of the transformation of the LSW is also clearly reproduced [49]. The STMW in [49] does not have a trend towards an increase in transformation over the years, unlike our study.

This study provides a new perspective on the inter-annual analysis of water mass transformations. Based on the seasonal variation of the density flux value for all waters in the region, a period of positive and negative transformation was identified. For the inter-annual assessment of winter transformation processes, the months from October to March were used, which allows us to assess the variability of exclusively winter processes.

It is worth noting that this study is based on the NCEP CFSR reanalysis alone, which will have some limitations. Uncertainties in wind speed (especially under extreme conditions such as storms) affect the calculations of mechanical mixing and evaporation. Systematic biases in precipitation, especially in the tropics and high latitudes, can upset the freshwater balance. Errors in evaporation due to humidity and wind lead to incorrect calculations of ocean salinity and stratification. The coarse resolution (~0.2–0.5°) can smooth out mesoscale processes (e.g., ocean fronts, eddies) that are critical for local heat and moisture fluxes. The time discretization (6-hourly output) does not always capture the rapid variability associated with convective events or short-lived storms. Although CFSv2 uses assimilation of satellite and ship observations, data density over the ocean remains poor, especially in the Southern Hemisphere and remote areas. The quality of the assimilated SST and atmospheric data can vary, introducing additional uncertainties.

Overall, this study tells about the influence of density flux and transformation values on the intermediate waters of the North Atlantic. These are waters that are subject to deep convective processes, which are located in regions with deep mixed layer depths. This work justifies the need to work with global data, where there is a coupled ocean–atmosphere model, since this reveals the mechanisms of ocean–atmosphere interactions on individual spatial and temporal scales. Combining detailed quantitative transformations with qualitative TS analysis, the presented results provide a comprehensive basis for studying the future variability of water masses in terms of their vertical circulations and influences on the global ocean conveyor.