Geothermal Convection and Double Diffusion Based on Profiling Floats in the Black Sea

Here, we revisit the existing concepts of the vertical structure of deep layers in the Black Sea using data from sensors deployed on profiling floats. The deep transition layer (DTL) between 700 and 1,700 m acts as an interface between the baroclinic layer and the largest bottom convective layer (BCL) of the world oceans. On top of DTL are the warm intermediate layer and deep cold intermediate layer. They both showed strong trends in the last 15 years due to warmer climate and intensification of warmer intrusions from Bosporus. A “salinity wave” was detected in 2005–2009 below ∼1,700 m, which evidenced for the first time the penetration of gravity flow from Bosporus down to the bottom. The layering of water masses was explained as resulting from the different distribution of sources of heat and salt, double diffusion, and balances between the geothermal and salinity flows in the BCL.

In stable stratified fluids, a double-diffusive regime could form because the molecular diffusivity of temperature k T = 1.4 · 10 −7 m 2 s −1 is 2 orders of magnitude larger than that for salt ks = 1.1 · 10 −9 m 2 s −1 (Radko, 2013;Stern, 1960). In the Black Sea, as in the Arctic, double diffusion is a result of the competition between a destabilizing temperature gradient and a stable salinity gradient; hence, thermal stratification provides the energy source for diffusive convection. This situation occurs in laboratory experiments when a salinity-stratified tank is heated from below (Turner, 1965(Turner, , 1968. In most of the water column of the Black Sea, the density ratio, which is defined as R , ranges from ∼0.5 to infinity. Here  and S are the potential temperature and salinity, respectively, and α and ß are the coefficients of thermal expansion and salinity contraction. Double diffusion, which is known to occur in this range, is most likely the main vertical transport mechanism for heat and salt in the Black Sea pycnocline and below it (J. W. Murray et al., 1991;Ozsoy et al., 1991). Because it is still not possible to clearly identify the depth ranges where double diffusion occurs, we will refer to the layer between 700 and 1,700 m as the deep transition layer (DTL, more justification of this name will be given later). As explained in these works and by Ruddick and Richards (2003), a number of mechanisms, such as gravity current dynamics and associated entrainment, trigger interleaving and set the depth reached by the Bosporus plume. The mixing between coastal and open ocean waters is evidenced by thermohaline intrusions in strong fronts, thus interleaving bridges mesoscale stirring and molecular dissipation.
Over the past 15 years, profiling floats have provided a considerable amount of data and proved to be a powerful instrument to detect the intrusive properties of Black Sea water masses (A. Falina et al., 2007;Stanev et al., 2017Stanev et al., , 2018. However, those data were analyzed mainly in the upper layers of the sea. In the present study, we revisit the composition and evolution of thermohaline properties in the deep part of the Black Sea based on data from profiling floats. The major objective of this study is to further clarify the existing concepts and provide new interpretations of the structure of water masses and processes below the main pycnocline. We focus on the formation mechanisms of deep-water masses, which are still not very clear, as well as on the corresponding temporal and spatial evolution patterns, including recent trends. Of fundamental interest are the dynamics of DTL playing the role of a thick interface between the pycnocline and BCL. New findings about deep-ocean ventilation are also presented.

A Description of Observations
Profiling floats deployed after 2005 (Akpinar et al., 2017;Grayek et al., 2015;Korotaev et al., 2006;Stanev et al., 2013Stanev et al., , 2019 provide almost uniform coverage of the Black Sea area ( Figure 1a). Here, we use data from 31 floats, or 5,927 profiles in total. Most data are from the upper 900 m of the water column; however, their amount down to 1,500 m is large (see the inset in Figure 1a) compared to those from earlier studies. Three of the floats collect data down to 2,000 m, which is approximately the maximum basin depth. Notably, 52 profiles in the BCL were available for the analysis (the black symbols in Figure 1a). Technical information and methodological details such as parking depths, locations, vertical sampling depths, float types, and sensor characteristics are given in the supporting information and in the above-cited publications.
Two floats collected data every 1 m from 200 to 1,000 dbar. Figure 1b demonstrates how the extremely small vertical temperature gradient of ∼0.02°C/100 m in the DTL is resolved with a sampling rate of 1 db and sensor accuracy of 0.001°C. The regularly distributed "stairs" reveal a discrete linear increase in temperature, as seen by the observational setup. Five recorded values with equal temperatures are followed by a jump to a temperature that is 0.001°C higher. Obviously, the accuracy of the temperature sensor is the limiting factor, and depth oversampling can occur. The observed temperature stairs thicker than 10 m demonstrate that profiling floats can detect traces of double diffusion below the pycnocline. The capabilities of individual floats to detect the "stairs" as dependent on the vertical sampling rate is shown in Figure S1.
One example of how a deep float observes the variability in temperature and salinity below 400 m is shown in Figures 1c and 1d. While salinity is a monotonously increasing function of depth,  displays several STANEV ET AL.

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warm intrusions at ∼500 m due to a mixture of warm Marmara Sea water and ambient water (A. Falina et al., 2007;Ozsoy, et al., 1993). Below these intrusive depths is a layer at ∼700 m with low temperatures (herein called the deep cold intermediate layer, DCIL). Below DCIL,  increases with increasing depth. In a number of locations, the temperature shows higher or lower temperatures below 1,200 m, illustrating that the properties at these depths are far from horizontally uniform. These changes are recorded down to ∼1,600 m, which is close to the upper boundary of the BCL.

Vertical Structure of Water Masses
The enlarged presentation of the vertical structure of water masses in Figure 2 is used to show the specific variability ranges in the entire water column (left panels), lower part of the main pycnocline and DTL (panels in the middle), and BCL (panels on the left). With the large number of available profiles, credible statistics can be obtained; therefore, the data are presented as probability distributions of the respective properties, illustrating the corresponding spreads in individual layers (bins). Because the number of profiles in the BCL is relatively low for obtaining results with statistical credibility, the individual profiles are shown in the panels on the right-hand side. is similar to the CIL in the sense that the vertical gradients of  are near zero in both cases. J. W. Murray et al. (1991) were the first to discover a DCIL; however, it has not been well addressed in the literature, nor have its dynamics and persistence.
Figure 2b reveals a warm intermediate layer (WIL) with a core at ∼541 ± 60 m. Positive temperature anomalies at these depths have also been documented by J. W. Murray et al. (1991) and A. S. Falina and Volkov (2004); however, they have not received much consideration. The "pair" WIL-DCIL in Figure 2b shows a fundamental transition of Black Sea physics at the bottom of the pycnocline. The positive temperature anomalies above the dominant mixing curves in the main pycnocline (Figures 2b and 2k) illustrate the intrusions of warm waters from the Bosporus down to σ θ = 17.1. While the WIL is clearly related to deep intrusions (warm waters of Bosporus origin "pull" the temperature profiles toward higher values), the origin of the DCIL is not so clear because no cold intrusions are seen in Figure 2k. What has not been documented before is the spread of data below 750 m seen as positive temperature anomalies (to the right of the blue line in Figure 2b). Their positions marked by the red triangular symbols in Figure 1a suggest enhanced deep water mixing on the continental slope.
The accuracy of sampling does not allow us to sufficiently resolve the double-diffusive instability, which operates on centimeter scales. Therefore, the focus is placed on the macroscale features associated with double diffusion. Rρ gives a robust estimate of the possibility of double diffusion. At ∼550 m (WIL), Rρ > 60 ( Figure 2g) and becomes very small below 1,500 m. Because of the very small values, 1/Rρ profiles are also presented in Figures 2h and 2i. Obviously, the diffusive regime of instability 1 < Rρ < 10 (Radko, 2013) is characteristic for most depths below 800 m (see staircases in Figure 1b). Staircases at shallower depths ( Figure S1) suggest that either double diffusion could occur for larger Rρ values (this would confirm a similar statement of Radko, 2013), or those are traces of intrusions in the WIL. There are also many individual profiles up to the DCIL for which Rρ < 10, that is, double diffusion could also occur there.
Below the core of the DCIL and down to the upper boundary of the BCL at ∼1,750 m, θ increases almost linearly ( Figure 2b, see individual profiles in Figure S1). However, the increase in S over the same depth interval is clearly nonlinear (Figure 2e). Therefore, 1/Rρ increases nonlinearly (Figure 2h). The deep-ocean θ-S curves reverse curvature at depths between the WIL and DCIL (Figure 2k). The almost linear θ-S relationships in the pycnocline ( Figure S2) transform into curved profiles (a similar individual profile was shown by J. W. Murray et al., 1991), demonstrating the dominant role of diapycnal mixing in the DTL (see also Schmitt, 1981).
At the base of the DTL, θ-S curves asymptotically approach density lines, which means that at these depths, the contributions of temperature, and salinity to the density are approximately equal. The DTL can be considered a thick (∼1,000 m) water body in which θ-S lines change direction from almost normal to isopycnal (in the halocline) to tangential (in the BCL). Vertical profiles of θ show a vertically uniform distribution in the BCL (panels on the right, see also Figure S1). The kink at ∼1,700 m identifies the top of the BCL; its depth ranges ∼150 m ( Figure S1)  (Figures 2c and S1). Furthermore, the warming from the shallower bottom tends to penetrate higher in the DTL (Figure 1c). Obviously, the BCL is not stationary, nor is it spatially uniform. Its upper boundary is not horizontal, which can be due to spatial changes in geothermal flow (Starostenko et al., 2014).
STANEV ET AL.
10.1029/2020GL091788 5 of 10  Figure S3). The CTD profiles at 800 m are ∼0.005°C colder than the coldest profiles from the floats, illustrating a recent warming below the baroclinic layer (compare also the observations in Figure 2b and Figure S2b with respect to the position of blue line). The WIL-DCIL pair was less pronounced at the beginning of 2000s. Notably, there are two CTD profiles down to 2,000 m where BCL does not occur, similar to the case with the profiling floats described above.

Temporal and Spatial Variability
The time versus depth diagrams in Figure 3 show all the profiles below 400 m, each of which appears chronologically. This presentation is meaningful because the spatial and temporal variability at these depths is small. The major finding is that after 2013, the DCIL with a core at ∼700 m became a persistent thermohaline feature; in the first part of the observation period, waters at this depth were only intermittently overlain by warm intrusions (compare also profiles in Figure S2b with much older profiles in Figure S3b). Therefore, the WIL and DCIL can be regarded as variable elements of the vertical stratification. Their appearance over the past 15 years parallels the continuous increase in Rρ (Figure 3c).
Below 1,000 m, the temperature variations are characterized by warm anomalies originating from deeper depths ( Figure 1c). Four floats that operated almost simultaneously from 2005 to 2009 registered a "salinity wave," with a minimum in 2007 ( Figure 3b). They were deployed northeast of the Bosporus Strait as tandems of two floats per release. The short distance from the strait (see Figure S4 for their trajectories) would explain the high salinity values at the release positions. However, many other floats sampled this region ( Figure 1a) and never registered values as high as those of these four floats. Moreover, after a year of operation, salinity reached a minimum, and a continuous increase then occurred until the present salinity levels were reached. Notably, these high-amplitude oscillations were detected not only in the near-Bosporus area but also in the eastern basin. This "salinity wave" could be due to salinity intrusions deeper than 1,500 m resulting in a doubling of the salinity range in 2005-2009 compared to the rest of the period of observations.
There is a persistent increase in temperature in the WIL after 2014 (Figure 3a), illustrating that the changes in the Bosporus intrusions parallel the recent warming in the upper Black Sea (Stanev et al., 2019;Stanev & Chtirkova, 2021). It seems thus very plausible that the temperature of the inflowing water may have also increased in the past decade because of the warming trends in the Mediterranean. The comparison of the data in 2000s with those of the R/V Knorr cruise in 1988 (J. W. Murray et al., 1991), the latter of which is depicted by the red circle symbol in Figures 2k and S3k, shows that salinity remained almost the same, but θ decreased by ∼0.005°C.

Heat and Salt Balances
Most intrusions occur down to 600-700 m, which is in agreement with the observations of Ozsoy et al. (1993) and modeling results of Stanev et al. (2004). However, the "salinity wave" detected below ∼1,700 m supports the statement of J. W. Murray et al. (2006) that "occasional or rare ventilation events" can reach the bottom. As demonstrated by V. N. Eremeev et al. (1997Eremeev et al. ( , 1998, a salinity flux into the BCL needs to be postulated to adequately represent the thermohaline structure of deep Black Sea waters. Without a salt flux, convection due to geothermal heat flow causes the upper boundary of the BCL to continuously ascend. Adding a negative haline buoyancy flux B salt = gβQ W S, which opposes the positive heat buoyancy flux B heat = −gαQ T /(ρ 0 c W ), would prevent this. In other words, the potential energy released by the temperature field (or fraction m of it) is used to lift the salt (Turner, 1965 , it follows that a value of Q T = 0.04 W/m 2 would correspond to Q W ∼ 10 −10 m/s, or the annual addition of ∼1 km 3 water in the BCL (area is taken as 4 × 10 6 km 2 and m = 1). This volume is ∼1/300 of the inflow through the Bosporus Strait. If m = 0.15, as in the experiments of Turner (1965), the needed annual volume of water from Bosporus origin is 0.15 km 3 . How does the heat flux from the gravity flow that reached the bottom compare against Q T ? Knowing that β/α > 5 and taking for salinity and temperature differences between Marmara Sea and Black Sea waters ΔS = 18 psu and ΔT = 3°C, it follows that R ρ Bo = ßΔS/αΔT > 30. This number reflects the small available potential energy stored initially in the temperature (unstable component). Knowing that gravity flow mixes temperature and salt at the same rate, it follows that Q T Bo /Q T < 30 (if m = 1). One can thus conclude that the warming of the BCL by gravity flow is negligible compared to that by geothermal flow. Therefore, to the statement of J. W. Murray et al. (2006) "the only source of salt (and warm) water is through the Bosporus, and the only source of cold (and fresh) water is from the surface," one needs to add geothermal flow, which is fundamental for the properties of Black Sea water in the DTL and BCL. Notably, this flow is 5 times smaller than the heat flux through the Arctic staircases reported by Timmermans et al. (2008) but is comparable to the estimates of Padman and Dillon (1987). Here, we remember that the Arctic Ocean, like the Black Sea, is predominantly stratified by salinity.

Vertical Stratification Above the DCIL
Starting from the sea surface, the first element of vertical stratification is the mixed surface layer. The baroclinic layer, where the gravity currents from Bosporus and dynamics of the front trigger isopycnal mixing, extends to depths of ∼600 m. Considering that diapycnal turbulent mixing is proportional to the curvature of the θ-S line (McDougall, 1984) and taking into consideration the curvature of the θ-S diagrams in CIL ( Figure 2j) and DTL (Figure 2k), one can conclude that those are layers where diapycnal mixing plays a substantial role. CIL and DCIL can be considered the natural upper and lower boundaries of the baroclinic layer. Between them, from σ θ ∼ 15.8 kgm −3 to σ θ ∼ 16.8 kgm −3 , we observe straight θ-S lines (see also Figure S2), demonstrating that in most cases, temperature and salinity mix at equal rates (presumably due to fully developed turbulent diffusion and entrainment). Stanev and Chtirkova (2021) explained the different slopes of linear segments of the θ-S relationship as being due to several extreme cooling events and warming climates in the last 15 years. J. W. Murray et al. (1991) and Ozsoy et al. (1991) reported cold water intrusions down to 600 m and explained them as being due to mixing of water from the Bosporus and water from the CIL. In the past 15 years, warm winters have resulted in a substantial reduction in the cold water volume and oxygen content in the CIL (Capet et al., 2016;Stanev et al., 2019). Cold water intrusions were rare, but warm intrusions became dominant. One can thus explain the origin of the WIL and DCIL as resulting from the variability of the properties of waters originating from Bosporus and the warming of the CIL. One simple scenario would suggest that the vertical temperature profiles above ∼600 m move back and forth (compare Figures 2b and S3b), reducing the temperatures of the WIL in the cold phases and warming it in the warm phases. Thus, the WIL and DCIL pair cannot be considered in isolation from each other. The DCIL, like the CIL, is a variable end member that strongly responds to climate change and resulting in changes in the upper ocean. Recent climatic changes have made the WIL-DCIL pair more distinguishable than in the past.
There were no cold intrusions at 750 m recorded by profiling floats during the last 15 years, which justifies the following two questions. (1) Is the DCIL a relict water mass or is it intermittently refilled by cold water intrusions? (2) How low the turbulence has to be to avoid destroying the DCIL? Taking for the thickness of DCIL 100 m and using for the coefficient of vertical diffusion the "canonical" value K = 10 −5 m 2 s −1 yields a characteristic time T DCIL of ∼30 years. This time would be much longer if K << 10 −5 m 2 s −1 , which could be the case in the nontidal Black Sea (M. Gregg & Ozsoy, 1999; M. C. Gregg & Yakushev, 2005). Approximately 30 years have passed since J. W. Murray et al. (1991) showed that there is a temperature minimum at ∼600 m. This minimum was ∼0.005°C cooler and ∼100 deeper than the minimum in Figure 2b (we remember that J. W. Murray et al., 1991 showed only one profile). Without continuity of observations over at least several decades, the answer to question (1) is still unknown. As far as the answer to question (2) is concerned, it cannot be excluded that low turbulent diffusion at the bottom of the pycnocline contributes to the persistence of DCILs.

Vertical Stratification Below the DCIL
The temperature below the DCIL shows a linear profile, while the salinity profile is curved (Figures 2b and  2e). This is reflected in the curved θ-S distribution in DTL. These different θ and S profiles are due to differ-ent distributions of sources and sinks. For temperature, we assume that there are no sinks between the top of the BCL and DCIL. If K = 10 −4 m 2 s −1 in the rather homogenous layers below the pycnocline and Q T = 0.04 W/m 2 , the slope of the linear θ-profile equals that in the observations. Obviously, the geothermal flows impact not only the BCL (up to 1,700 m) but also the θ profile in the transition layer between the BCL and the baroclinic ocean. As shown by Stanev et al. (2004), a realistic salinity profile can be reproduced in a 1-D model depending on the ratio between entrainment and detrainment; that is, the curved profile of salinity is due to the dynamics of gravity flow in the DTL. The different distribution of sources of heat and salt (salt originates only from Bosporus, heat has a source at the bottom) explains the differences in the respective θ and S profiles and the specific shape of Rρ, the latter sets the conditions for existence of double diffusion above the BCL and in most of the water column up to the DCIL.

Conclusions
The CIL and DCIL appear to be the natural upper and lower boundaries of the baroclinic layer. Below DCIL is the DTL, where the θ-S lines change direction from almost normal to isopycnal (in the halocline) to tangential (in the BCL). Therefore, the DTL acts as a transition layer between the baroclinic ocean, which is dominated by isopycnal mixing maintained by frontal dynamics and intrusions of waters of Bosporus origin, and the BCL. In this transition layer, the vertical profiles of temperature and salinity largely differ because of the different distributions of their sources and sinks.
In the 1990s, a number of deep and cold temperature intrusions were observed, but they have rarely appeared in recent years. After 2013, the WIL-DCIL became a persistent thermohaline feature due to the warming of the waters from the Bosporus and waters in the CIL. DCILs can be regarded as a variable thermohaline end member that responds to changes in the upper layers and properties of gravity currents.
Four profiling floats registered a "salinity wave" at the base of the DTL. It is not plausible that the four floats were all malfunctioning, which suggests that we discovered very deep salinity intrusions not previously reported. This finding provides observational support for the concept that such a flow must exist to close physical balances controlling the thermohaline state of deep layers. The concept developed here that deep water variability caused by the interaction between the upper ocean and deep sea through gravity flows presents a generalization of earlier concepts, according to which the temporal variability of Black Sea water masses occurs in the layers above the permanent pycnocline.
BCL is not homogenous and stationary, as previously claimed. Its upper boundary reveals large spatial-temporal variability. Temperature anomalies from the BCL can be traced in the DTL up to at least 1,400 m, particularly over the shallower bottom. We hope that our results could motivate similar studies in other inland ocean basins or world oceans (remember the similarity between double diffusion in the Black Sea and in high latitudes, Ruddick and Richards, 2003;Kelley et al., 2003), as well as numerical modeling, which could test various scenarios about the role of geothermal flows and double diffusion in ocean dynamics.