Two hydrological surveys carried out in the northern Black Sea in summer 2016 and 2017 are processed with a hydrodynamic model that also assimilates observational data, which made it possible to more accurately describe the meso- and submesoscale features of hydrophysical fields and determine their possible formation mechanisms. High spatial resolution (horizontal grid of similar to 1.6 x 1.6 km and 27 vertical horizons) and ERA5 atmospheric forcing is used in calculations. The energy terms in the equations of the kinetic and potential energy budget for each year were analyzed to consider possible physical eddy formation mechanisms (baroclinic instability, current flow around coastline irregularities). Such specific features of circulation as the Rim Current along the coast, anticyclonic eddies near the southeastern coast of Crimea, and the area of cyclonic vorticity in the eastern deep-water part of the sea are observed for both years. Along the coast, under the action of weak winds, small-scale eddies were generated when the current was flowing around irregularities in the coastline and bottom topography. A large anticyclonic eddy was formed between 33 degrees and 34 degrees E in 2016 and between 31 degrees and 32 degrees E in 2017. With increased wind action in 2017, more intense currents developed and eddy formations in the upper layer of water were less pronounced than in 2016.

Purpose. The study is purposed at analyzing the available potential energy and its budget components in the Black Sea based on the results of numerical circulation modeling using a new temperature and salinity approximation scheme in the advective transport operator. Methods and Results. Two numerical experiments were carried out based on the MHI model versions differing from each other in their approximation schemes of advective terms. The difference between the schemes is that in experiment 1, the condition of conserving temperature and salinity in the first and second degrees is satisfied, whereas in experiment 2 - temperature in the first and third degrees and salinity in the first and fifth degrees are conserved. It is found that application of the new scheme is accompanied by an increase in the available potential energy reserve by on average 30% over a year. The difference is conditioned by a decrease in both horizontal diffusion in a warm season and consumption of available potential energy through the buoyancy work in a cold season. The modeling results validated by the temperature and salinity measurement data from the MHI Oceanographic Data Bank show that application of the new approximation scheme permits to specify the density field and the energy characteristics in the Black Sea upper layer. Below the 300 m horizon, the discrepancies between the model and in-situ thermohaline fields in two experiments are minor, whereas the qualitative and quantitative distinctions in energy fields are significant: difference in the values of available potential energy in the basin central and periphery parts as well as the area of zones with the extreme buoyancy work values increase. Conclusions. Application of the new approximation scheme of temperature and salinity in the advective transport operator makes it possible to specify the field density and, as a consequence, to obtain more accurate estimates of the available potential energy of sea circulation. In the Black Sea upper layer (the main pycnocline layer and above), the difference between the fields of energy characteristics calculated in two experiments is due to the differences in spatial distribution of density anomalies, at that the anomaly absolute values and the maximum energy values in the experiments are close in their magnitudes. Below the pycnocline layer, application of the new scheme is followed by the growth of available potential energy since the temperature and salinity changes lead to an increase in the gradients of density anomalies normal to the coast.

In this work, based on the results of predictive calculations, the accuracy of reproducing the Black Sea circulation is analyzed using new approximations of nonlinear terms in the transport equations, ensuring the conservation of temperature and salinity to a power greater than two. Numerical experiments have been carried out that differ in schemes for calculating temperature and salinity. In the first experiment, traditional schemes were used to ensure the conservation of temperature and salinity in the first and second degrees; in the second one, the temperature was maintained in the first and fifth degrees and salinity in the first and third; in the third experiment, the temperature was maintained in the first and third and salinity in the first and fifth degrees. Calculations were performed on the basis of MHI model with a resolution of 1.6 km and accounting a realistic atmospheric forcing for 2016. The validation of results was carried out based on comparison of model fields with data from contact and satellite measurements of temperature and salinity in 2016. An analysis of average and root mean square errors showed that, compared to the traditional approximation, the new difference schemes for the advection–diffusion equations of heat and salt, ensuring the preservation of predictive parameters to a power greater than two, improve the accuracy of reproducing of the Black Sea salinity in the upper 100-m layer throughout the year. Root mean square errors in the salinity field decrease by 15–20

The reasons for the origin of narrow time-dependent currents formed in the Black Sea in the lower region of the constant pycnocline and deeper are analyzed on the basis of the results of numerical modeling. The prepositions for the generation of deep-water countercurrents in the hydrophysical fields of the Black Sea are studied with reference to the example of its north-east region, where they manifest themselves most frequently. In September 2016 and February 2017 the countercurrents in the region of the North-Caucasian coast were fixed according to the observation data of the ARGO profiling float ID6901833. On the basis of the numerical model of the Marine Hydrophysical Institute (MHI) with a 1 km-resolution and the assimilated data of the hydrological observations of the temperature and salinity the hydrophysical fields of the Black Sea are numerically simulated for the period of 2016–2017. The results of the calculations are used to reproduce the variations in the deep-water flow directions in the above-noted region and to analyze the fields of the main geophysical parameters, together with their derivative parameters. The effect of the mesoscale anticyclonic eddies and the density gradients on the velocity field structure and variability is illustrated. It is established that countercurrents propagated during several days in the anticyclonic direction, along the continental slope on the horizons from 50–100 to 500 m, and their formation took place in the conditions of the attenuation of the cyclonic Black Sea Rim Current in the upper sea layer and the intensification of the Kerch anticyclone.

Оценки бюджета доступной потенциальной энергии в черном море при использовании новых схем аппроксимации уравнений адвекции-диффузии тепла и соли 1Демышев С.Г.,

A four-dimensional and energy analysis of hydrophysical fields in the limited area of the Black Sea was carried out on the basis of assimilation of hydrological data in the numerical model (autumn–winter season of 2016). The Rim Current was clearly reconstructed. Multi-scale eddies could be generated between the shore and the Rim Current during some weakening of the wind forcing. Cyclonic and anticyclonic eddies were noticed in the western area, they could merge into larger one during the further calculation. The most energetically significant components in the kinetic and potential energy budget equations were found and analyzed from 15th of November to 5th of December, 2016. Possible mechanisms of circulation features of the Black Sea were determined, analyzing of energy fields (for example, baroclinic and/or barotropic instability). The obtained results were compared with all available data of instrumental measurements.

Purpose. The study is aimed at identifying possible physical mechanisms for the variability of available potential energy density and buoyancy fluxes in the upper active layer of the Black Sea. Methods and Results. Spatial distribution of the available potential energy density and buoyancy fluxes was studied based on analyzing the thermohaline characteristics of the Black Sea circulation in 2011 and 2016 resulted from the numerical experiments performed using the Black Sea dynamics model developed in the Marine Hydrophysical Institute. The model included the EMODNet bathymetry and the SKIRON system data on wind velocity, heat fluxes, precipitation, evaporation, and sea surface temperature. The numerical experiments provided the daily fields of current velocities, temperature and salinity based on which the density of available potential energy and the buoyancy work were calculated. It is shown that the spatial-temporal variability of the available potential energy density in the Black Sea was formed by the mechanisms different for the upper 30-m layer and for the main halocline layer. The buoyancy work was revealed to be of seasonal variability.Conclusions. In the upper layer, the variability of the available potential energy density is related primarily to the propagation of freshened river waters, whereas in the main halocline layer (75-150 m), the field structure is conditioned by mesoscale dynamics. In the first case, the increased values of the available potential energy density are observed during a year on the northwestern shelf and on the basin periphery; in the central part of the sea, the distribution of available potential energy density is determined by the atmospheric conditions. In the layer below 75 m, the maximum values of the available potential energy density correspond to the anticyclonic eddies. In consequence of the intensive water mixing in the upper active layer during the cold period of a year, the buoyancy work is conditioned by vertical velocity. In a spring-summer period, a two-layer structure of the field is observed which governed by the sign of density anomalies. The upper layer thickness constitutes 20- 30 m and corresponds to the depth of seasonal thermocline. In the main halocline, the highest absolute values of the buoyancy work are observed in the zones of intense mesoscale anticyclones.

Purpose. The study is purposed at analyzing the physical mechanisms of formation of the Black and Marmara seas circulation structures based on the numerical experiments with climatic boundary conditions. Methods and Results. To investigate the reasons for the formation of circulation features, the energetic approach was applied that permitted to calculate the work of the forces affecting the marine environment. Location in the same geographical region determines similarity of atmospheric conditions for the Black and Marmara seas, and a clearly pronounced two -layer water stratification in both basins is related to a significant difference in salinity of the Black Sea and Mediterranean waters. To analyze the mechanisms of circulation variability, the mean and eddy fields formed under the impact of climatic atmospheric forcing and calculated using a numerical model of sea dynamics were considered. Wind influence, thermohaline fluxes on the sea surface, buoyancy work, friction, and diffusion were quantitatively assessed based on calculation of the Lorenz energy cycle components. The common features were found in the mechanisms of mesoscale variability, and the differences - in the mechanisms of large-scale circulation variability. Conclusions. It is shown that the main source of energy for the Black Sea mean circulation is wind stress work, and as for the Marmara Sea, the dominant factor is buoyancy work. For both basins, variability of the eddy kinetic energy characterizing the mesoscale dynamics is conditioned by baroclinic instability. At that, about a quarter of the available potential energy in the Black Sea, and about a half of it in the Marmara Sea is transformed into the eddy kinetic energy.

The purpose of this work is to determine the initial Cs137 concentration field in the Black Sea immediately after the Chernobyl accident using spatially and time-distributed measurement data based on the adjoint equation method. The calculation of the flow velocities was carried out using a three-dimensional model of the Black Sea circulation MGI with a horizontal grid step of 1.6 km. When calculating the currents, the wind effect was set according to SKIRON data. The method of adjoint equations is used to determine the location of a possible radioactive fallout according to measurements that were carried out on the 33rd flight of the NIS “Akademik Vernadsky” in June-July 1986. The National Centers for Environmental Prediction (NCEP) data on the wind situation and precipitation intensity are analyzed. The information of the IRSN (Institute of Nuclear and Radiation Safety of France) on the processes of transfer of radioactive contamination from the Chernobyl nuclear power plant towards the Black Sea is considered. Based on the solution of the adjoint problem, a possible area of radioactive fallout was determined, the location of which coincides with IRSN data on areas of increased isotope concentration in the atmosphere over the Black Sea region in late April–early May 1986.

This work presents an analysis of the Lorenz energy cycles derived from the simulation results of the Black Sea circulation. Three numerical experiments are carried out based on an eddy-resolving z-model with a horizontal resolution of 1.6 km and taking into account different atmospheric forcing: climatic data, 2011, and 2016. The annual mean circulation for these time intervals reflects the climatic basin-scale, basin-scale (2011) and eddy (2016) regimes. Main differences between experiments are (1) the intensity of atmospheric fluxes and (2) SST assimilation and direct consideration of shortwave radiation in the realistic forcing simulations. The Lorenz energy cycles components are considered in detail. Some common features between climatic and realistic energetics are detected. The annual mean energy conversion from mean motion to the eddy is observed for all circulation regimes. Also, it is obtained that the annual mean buoyancy work enhances the mean current for all experiments, which evidences about maintaining of isopycnal surfaces slope such that a condition for converting available potential energy into kinetic energy is realized. Qualitative difference in the energy transfers for the climatic calculation, basin-scale and eddy regimes is revealed. Conversion from the eddy kinetic energy to eddy available potential energy is observed only for climatic circulation. For the basin-scale circulation the eddy kinetic energy is increasing mainly due to the transfer from the mean current kinetic energy through barotropic instability. The growth of the eddy kinetic energy for the eddy regime is provided by conversion of the available potential energy due to baroclinic instability.

Fields of currents and arrays of energy budget components were investigated with the help of the numerical model of dynamics using hydrological data from 89th cruise of the R/V Professor Vodyanitsky. To implement the procedure of data assimilation, we used a four-dimensional analysis procedure, based on a Kalman filtering, taking into account the heterogeneity and non-isotropy of error estimates of thermohaline characteristics. Wind action and vertical friction made a significant contribution in the change of kinetic energy, vertical turbulent diffusion and advection of potential energy—in the change of potential energy. The following features of circulation were obtained in the numerical experiment for the autumn season of 2016: anticyclonic eddies near Sevastopol, cyclonic and anticyclonic eddies at the south-eastern coasts of Crimea and other parts of area under consideration, a flow of the Rim Current along the Crimean coast. High values of work of the wind force and vertical dissipation were observed in the zones of formation of mesoscale eddies. Negative values of the buoyancy work were noticed to the west of the region and along the eastern coast of Crimea.

Simulation results of the Black Sea dynamics for two periods when the annual mean circulation corresponded to the basin-scale and eddy regimes (2011 and 2016) are considered in the paper. Numerical experiments are carried out using the MHI model and considering the realistic atmospheric forcing from SKIRON. The seasonal variability of dynamic and thermohaline fields, as well as the kinetic and available potential energy, and their conversion rates are estimated. According to the model data on the seasonal mean distribution of currents velocity, it is found that in 2011 the RIM Current is detected in all seasons, and the most intense mesoscale eddies developed on its periphery over the continental slope in the warm period of the year; in 2016, separate cyclonic jets in the area of the continental slope are observed in the northern and southwestern parts of the basin during cold seasons, and mesoscale eddies are propagated in the central part of the sea throughout the year. The change in the mean current kinetic energy is determined by the circulation regime: energy maxima are revealed in the spring of 2011 and in the winter of 2016, when the mean current was the most intense. The distribution of the mean available potential energy is predominantly seasonal, the time variability is qualitatively similar for both modes and is provided by an increase in the density anomaly due to seawater heating. The eddy kinetic energy characterizing the mesoscale variability depends both on the circulation regime and on the season. In the spring 2011, the mean current and eddy kinetic energies are comparable; in 2016, the maximum eddy energy exceeded the mean current kinetic energy. In autumn and winter, for both calculations, the increase in eddy energy occurs due to the energy transfer from the wind and the mean current through the barotropic instability mechanism. In summer when wind activity weakens, in the basin-scale circulation mode, mesoscale variability is supported by commensurate contributions from barotropic and baroclinic instability; in the eddy circulation mode – mainly due to the conversion of available potential energy through baroclinic instability.

The aim of the presented study is to investigate one remarkable feature of the Black Sea deep-water circulation. These are unsteady narrow anticyclonic currents that propagate under the main pycnocline in the direction opposite to the surface circulation and are called undercurrents. According to observation data, undercurrents were discovered in several field expeditions, and were also revealed in some results of the Black Sea dynamic modeling. However, due to the lack of regular observations, it was not entirely clear whether they were a real feature of the Black Sea current field or an artifact of the experiments carried out. In this work, to assess the spatial variability of the Black Sea current field and identify undercurrents, the results of modeling the Black Sea circulation for several periods were analyzed. Simulations were carried out using the MHI model, and the results were validated based on deep-water field observation data on temperature and salinity. As well, in the northeastern part of the sea the simulated currents were compared with the data of ADCP deep-water velocity measurements (with Aqualog profiler). It is shown that undercurrents are more often formed in the spring–summer period and their lifetime is from one to several weeks. And although the length of undercurrents along the continental slope can reach several hundred kilometers, their width is only 8–12 km. Such characteristics of undercurrents explain the difficulty of their detection and identification in previous works.

Based on the numerical MHI model of 1.6 km horizontal resolution, a prognostic experiment was carried out to reconstruct the circulation of the Black Sea in 2011. The temperature and salinity profiling data of ARGO floats obtained for this year are used to validate the calculations results. As well, the simulation results are agreed with the data of deep-water measurements of the current velocity in June 2011 in the region of the North Caucasian coast (northeastern part of the Black Sea). The qualitative and quantitative characteristics of the deep-water currents in the northeastern part of the Black Sea are obtained.

Purpose. The study is aimed at evaluating effectiveness of the procedure of the observational data assimilation using the Kalman filter algorithm as compared to sequential analysis of the hydrophysical fields based on the optimal interpolation method, and at analyzing the mesoscale features of coastal circulation near the western Crimea coast and in the Sevastopol region. Methods and Results. Based on the hydrodynamic model adapted to the Black Sea coastal zone conditions including the open boundary and on the temperature and salinity data from the hydrological survey in 2007, the dynamic and energy characteristics of the Black Sea coastal circulation were calculated with high spatial resolution (horizontal grid is ~1.6×1.6 km and 30 vertical horizons). The hydrophysical fields were reconstructed using two algorithms of data assimilation: the sequential optimal interpolation and the modified Kalman filter. The kinetic energy changed mainly due to the wind action, vertical friction and the work of pressure forces; the potential energy – due to the potential energy advection and the horizontal turbulent diffusion. The following circulation features were reconstructed: the anticyclonic eddy with the radius about 15 km in the Kalamitsky Bay in the water upper layer, the anticyclonic eddy with the radius about 15 km between 32.2 and 32.6° E in the whole water layer, the intense current near Sevastopol and along the Crimea western coast directed to the north and northwest, and the submesoscale eddies of different signs of rotation in the upper layer. Conclusions. It is shown that having been taken into account, heterogeneity and non-isotropy of the error estimates of the temperature and salinity fields relative to the correlation function lead to qualitative and quantitative differences in the hydrodynamic fields (amplification of currents, change of the currents’ direction and eddy formations were better pronounced). At the same time, the mean square errors of the thermohaline fields’ estimates decreased. Formation of the anticyclonic eddy with the radius about 15 km in the Kalamitsky Bay could be related to the current shear instability. Submesoscale eddies with the diameters less than 5 km were formed when the current flowed around the coastline and the bottom topography inhomogeneities

Purpose. The study is aimed at evaluating effectiveness of the procedure of the observational data assimilation using the Kalman filter algorithm as compared to sequential analysis of the hydrophysical fields based on the optimal interpolation method, and at analyzing the mesoscale features of coastal circulation near the western Crimea coast and in the Sevastopol region. Methods and Results. Based on the hydrodynamic model adapted to the Black Sea coastal zone conditions including the open boundary and on the temperature and salinity data from the hydrological survey in 2007, the dynamic and energy characteristics of the Black Sea coastal circulation were calculated with high spatial resolution (horizontal grid is ~ 1.6 × 1.6 km and 30 vertical horizons). The hydrophysical fields were reconstructed using two algorithms of data assimilation: the sequential optimal interpolation and the modified Kalman filter. The kinetic energy changed mainly due to the wind action, vertical friction and the work of pressure forces; the potential energy – due to the potential energy advection and the horizontal turbulent diffusion. The following circulation features were reconstructed: the anticyclonic eddy with the radius about 15 km in the Kalamita Bay in the water upper layer, the anticyclonic eddy with the radius about 15 km between 32.2 and 32.6° E in the whole water layer, the intense current near Sevastopol and along the Crimea western coast directed to the north and northwest, and the submesoscale eddies of different signs of rotation in the upper layer. Conclusions. It is shown that having been taken into account, heterogeneity and non-isotropy of the error estimates of the temperature and salinity fields relative to the correlation function lead to qualitative and quantitative differences in the hydrodynamic fields (amplification of currents, change of the currents’ direction and eddy formations were better pronounced). At the same time, the mean square errors of the thermohaline fields’ estimates decreased. Formation of the anticyclonic eddy with the radius about 15 km in the Kalamita Bay could be related to the current shear instability. Submesoscale eddies with the diameters less than 5 km were formed when the current flowed around the coastline and the bottom topography inhomogeneities.

Numerical simulation results of the Black Sea circulation obtained by four ocean dynamics models are compared to each other and to in situ data in order to determine the features of the Black Sea deep-water circulation such as deep-water undercurrents. The year 2011 is chosen as the test period due to the availability of deep-sea observations, including ARGO profiles and ADCP current velocities. Validation of the simulation results is based on comparison with the temperature and salinity measured by the ARGO floats. Anticyclonic currents (undercurrents) under the cyclonic Rim Current are detected by the results of all numerical models near the North Caucasian coast. The main characteristics of undercurrents are consistent with in situ data on current velocity up to a depth of 1000 m obtained by the Aqualog probe at the IO RAS test site near Gelendzhik in June 2011. The analysis of the spatio-temporal variability of the modeled salinity and velocity fields reveals that the most probable origin of the undercurrents is the horizontal density gradient of seawater in the region.

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. New array of the temperature and salinity climatic fields was assessed by the results of numerical experiments. In the experiment, annual variation of the Black Sea hydrophysical parameters was reconstructed by the numerical model. Modeling included the scheme of assimilating the data of the climatic temperature and salinity array assessed. In contrast to the averaged data of the field observations, the modeled fields are compliant with equations of motion. Besides the temperature and salinity three-dimensional fields, the three-dimensional climatic fields of the Black Sea currents were also reconstructed for each day of a climatic year that is quite impossible using the observational data only. Spatial-temporal variability of the modeled three-dimensional fields was analyzed. The integral characteristics of the Black Sea water dynamics for the recent 30-year climatic period were studied and compared with the analogous ones for the previous century. Simulation was carried out by three-dimensional non-linear model of the Black Sea dynamics developed in Marine Hydrophysical Institute. The horizontal resolution of the model was 5 km, and the EMODNet bathymetry was used. The performed calculations showed that the increased spatial resolution of the temperature and salinity climatic array for the recent period made it possible to reconstruct the dynamics of the Black Sea in all layers in more detail. At the same time, significant small-scale variability of salinity fields was revealed. It was most pronounced at the deep-water horizons. Conclusions. Modeling using a new array of thermohaline fields revealed an increase in the integral temperature of the upper mixed layer in comparison with the experiment with assimilation of the previous version of the climatic array. At that, thinning and «break» of the cold intermediate layer found in the central part of the sea, indicates warming of the sea upper layer during the last 30 years. The highest noise detected at the deep-water horizons in the modeled salinity fields is related to quantity and quality of the salinity data resulted from the field observations. Taking into account insufficient calibration facilities for measuring seawater electrical conductivity, the next version of climatic TS-array requires a more strict procedure for verifying and processing the observation data obtained in the deep-sea layers.

Purpose. The aim of the present article is to study propagation of contamination in the Sevastopol coastal zone using the dynamic model of high spatial discretization and which takes into account actual atmospheric forcing. Location of possible contamination sources is to be calculated and, hence, determined by applying the adjoint equations method using the measurement data assimilation. Methods and Results. The currents' field was calculated using the three-dimensional baroclinic model of the Black Sea water circulation developed in the Marine Hydrophysical Institute, RAS. The model is characterized by high degree of spatial discretization. The simulation included application of the SCIRON data on actual atmospheric forcing. The adjoint equations method was used for defying location of possible contamination sources. The model currents in the coastal zone were analyzed for the chosen time period. The admixture distribution from the initial contamination location in the Black Sea water area nearby the Gerakleisky Peninsula was calculated. Having been integrated, a series of the adjoint problems permitted to determine location of the contamination source. Conclusions. Based on the results of the numerical experiments on integrating a series of the adjoint problems, defined is the area where a possible contamination source can be located. The location of this area agrees well with the initial distribution of concentration that, in case the information on the admixture character is available, permits to define the place where it enters the marine environment. The proposed approaches can be used for solving various ecological problems as well as for interpreting and planning the field experiments on studying sewage propagation in the coastal zone.