Black Sea Dynamics Research Articles

The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model

Abstract The problem of variational assimilation of observational data for the sea thermodynamics model is considered with the aim to reconstruct heat fluxes on the sea surface. The local sensitivity of functionals of the solution to the observational data and input data for heat fluxes is studied in the considered problem and the results of numerical experiments are presented for the Black Sea dynamics model.

Variational Data Assimilation for Ocean Thermodynamics Model and Sensitivity of Marine Characteristics to Observation Errors

The methodology of variational assimilation of observational data for the restoration of the initial state and heat fluxes for the mathematical model of sea thermodynamics is presented. An algorithm is developed for estimating the sensitivity of a model solution to errors in observational data. Calculation of the gradient of the response function of the model solution is based on the use of the Hessian of the cost functional. The results of numerical experiments for the Black Sea dynamics model developed at INM RAS are presented.

Numerical Study of Variability of Hydrological Regime for the Southeastern Part of the Black Sea (2010-2021)

The study and forecast of mesoscale dynamic processes in the coastal/shelf zones of seas and oceans is one of the main issues of physical oceanography, because these zones experience the most significant anthropogenic load. Circulation processes, which are closely related to temperature and salinity fields, make a significant contribution to the distribution of various impurities of anthropogenic and natural origin in the marine environment. In the present paper, a high-resolution numerical regional model of the Black Sea dynamics of M. Nodia Institute of Geophysics of Ivane Javakhishvili Tbilisi State University (RM-IG) is used to simulate and study some peculiarities of regional hydrophysical processes occurring in 2010-2021 in the southeastern part of the Black Sea covering Georgian sector of the Black Sea and surrounding water area. The RM-IG is based on a primitive system of ocean hydro and thermodynamics equations in hydrostatic approximation written in the Cartesian coordinate system and is implemented with a spatial resolution of 1 km under real atmospheric forcing.

Sensitivity of Functionals of the Solution to the Variational Assimilation Problem to the Input Data on the Heat Flux for a Model of Sea Thermodynamics

For the mathematical model of the sea thermodynamics developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, the problem of variational assimilation of observational data in order to recover heat fluxes on the sea surface is considered. The sensitivity of functionals of the solution to the input data on the heat flux in this problem is studied, and the results of numerical experiments for the model of Black Sea dynamics are presented.

Restricted Influence Over the Black Sea: The Limitations of the European Union’s Role

The Black Sea has been an important region for the international actors to consider with its countries with diverse backgrounds, complicated relations, and attempts to its region-building. European Union has been involved in Black Sea dynamics, yet the effectiveness of its role in the region is questionable. This study aims to show European Union’s limitations on a more significant role in the Black Sea region. The article explains three main limitations: seeing its role mainly from a trade perspective, the clashing interests of several international actors, and differences among member states. At first, the article focuses on European Union’s involvement in the Black Sea to acknowledge these limitations. The specific focus on the Russian-Ukrainian war provides a fresh look at the European Union’s role. How these limitations are reflected in this context can give a chance to the European Union for a more significant role while presenting new challenges to tackle. However, this study argues that current European Union policies do not provide a comprehensive approach. The article suggests that having a security dimension in its Black Sea policies, establishing more comprehensive relations with other international actors, and providing unanimity among member states about the Black Sea policies can help the European Union to overcome its limitations.

Sensitivity of functionals of the solution to a variational data assimilation problem with heat flux reconstruction for the sea thermodynamics model

Abstract The problem of variational observation data assimilation is considered for the mathematical thermodynamics model developed at the Marchuk Institute of Numerical Mathematics of RAS with the aim to reconstruct the sea surface heat flux. The sensitivity of functionals of solutions to observation data is studied for the considered variational assimilation problem and the results of numerical experiments for the Black Sea dynamics problem are presented.

ПРОСТРАНСТВЕННО-ВРЕМЕННАЯ ИЗМЕНЧИВОСТЬ ГИДРОФИЗИЧЕСКИХ И ЭНЕРГЕТИЧЕСКИХ ХАРАКТЕРИСТИК ЦИРКУЛЯЦИИ ЧЕРНОГО МОРЯ ПРИ ДОМИНИРОВАНИИ ДВИЖЕНИЙ РАЗНЫХ МАСШТАБОВ

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.

ANALYSIS OF THE LORENZ ENERGY CYCLE FOR DIFFERENT REGIMES OF THE BLACK SEA CIRCULATION

The Lorentz energy cycle components are calculated from numerically simulated data on the Black Sea dynamics for three regimes: climatic circulation, basin-scale (2011), and eddy (2016) circulations. The some common features have been found between climatic and realistic energy. The mean annual conversion of energy from mean motion to eddy motion is observed for all circulation regimes. The annual mean buoyancy work increases the mean current for all experiments, which indicates that the slope of the isopycnal surfaces remains such that the condition for converting the available potential energy into kinetic energy is realized. The qualitative difference is that the conversion of eddy kinetic energy into available potential energy is observed only for climatic circulation. For basin-scale circulation, the variability of the eddy kinetic energy is determined by the flux formed by the transformation of kinetic energy due to the barotropic instability of the mean current. For the eddy regime, the growth in the eddy kinetic energy is a result of the available potential energy conversion into kinetic energy due to baroclinic instability. The circulation regime, as well as the qualitative and quantitative difference in the magnitudes and directions of energy conversion, are primarily associated with atmospheric forcing.

Variational data assimilation for a sea dynamics model

Abstract The 4D variational data assimilation technique is presented for modelling the sea dynamics problems, developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The approach is based on the splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system that involves the adjoint equations and observation and background error covariances. Efficient algorithms for solving the variational data assimilation problems are presented based on iterative processes with a special choice of iterative parameters. The technique is illustrated for the Black Sea dynamics model with variational data assimilation to restore the sea surface heat fluxes.

Assessment of the Black Sea Temperature and Salinity Climatic Fields for the Recent Climatological Period (1991–2020)

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.

Otsenka klimaticheskikh poley temperatury i solenosti vod Chernogo morya dlya sovremennogo perioda (1991–2020)

Purpose. The study is aimed at assessing a new climatic array of the Black Sea temperature and salinity calculated using hydrological observations for the standard (according to the World Meteorological Organization definition) 30-year climatological period 1991–2020. Methods and Results. New array of the temperature and salinity climatic fields was assessed based on analyzing the results of numerical experiments. In the experiment, annual variation of the Black Sea hydrophysical parameters was reproduced 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 model fields were matched from the viewpoint of the motion equations. Besides the temperature and salinity three-dimensional fields, the three-dimensional climatic fields of the Black Sea currents were also reproduced for each day of a climatic year that is quite impossible using the instrumental measurements 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 performed at the grid with the 5 km horizontal resolution using the EMODNet bathymetry by means of the three-dimensional non-linear model of the Black Sea dynamics developed in Marine Hydrophysical Institute. Having been analyzed, the performed calculations showed that the increased spatial resolution of the temperature and salinity climatic array for the recent period made it possible to reproduce dynamics in all the layers of the Black Sea waters in more details. At the same time, a significant small-scale variability, most pronounced at the deep-water horizons, was present in the salinity fields. Conclusions. As compared to the experiment with assimilation of the previous version of the climatic array, the modeling based on the new array of the thermohaline fields revealed increase in the integral temperature of the upper mixed layer. 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 noisiness 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 metrological facilities for measuring seawater electrical conductivity, the next version of climatic array requires a more strict procedure for verifying and processing the observation data obtained in the deep-sea layers.

Restoring the Boundary Condition and the Initial State in the Variational Data Assimilation Problem for the Black Sea Dynamics Model

In the present paper, we formulate an inverse problem of assimilation of sea surface temperature for a sea thermodynamics model aimed at the reconstruction of the heat flux and the initial state. We assume, that the unique function which is obtained by observation data processing is the function of sea surface temperature (SST). Numerical experiments on restoring the surface heat flux and the initial state for the system of the Black Sea primitive equation hydrodynamics model (temperature, salinity, velocity, and sea surface level) with assimilation procedure were carried. The results of the numerical experiments are presented.

Numerical solution of the problem of variational data assimilation to restore heat fluxes and initial state for the ocean thermodynamics model

Abstract For the model of ocean thermodynamics developed at the Institute of Numerical Mathematics of RAS, the problem of variational data assimilation is considered in order to restore heat fluxes on the ocean surface and initial state of the model. Iterative solution algorithms are proposed for the optimality system, justification of these algorithms is given based on properties of the control operator. The results of numerical experiments for the model of the Black Sea dynamics are presented.

Variatsionnaya assimilyatsiya dannykh nablyudeniy v matematicheskoy modeli dinamiki Chernogo morya

Variatsionnaya assimilyatsiya dannykh nablyudeniy v matematicheskoy modeli dinamiki Chernogo morya

,E. I. Parmuzin*, , , N. R. Lezina

,E. I. Parmuzin*, , , N. R. Lezina

Numerical Modeling of Water Dynamics of Russian Zone of the Black Sea within the Framework of Operational Oceanography Tasks

Modeling of the Black Sea waters dynamics (Russian zone) was conducted within the framework of the European ARENA and ECOOP projects and Russian project JISWO on the basis of Princeton Ocean Model (POM). Nowcasting and three days forecasting of the Black Sea dynamics was carried out in a daily mode with horizontal resolution of ~1 km along the Russian coast of the basin. Examples of calculations are presented and their comparison with space remote sensing and in situ (hydrological measurements) data is fulfilled, results of model validation are discussed. Model data reproduce observed real dynamic structures. Increasing a spatial permit of processes allows reproduce in calculations the detail of hydrological structure, which does not principally find displaying in large-scale models (vortexes with horizontal spatial sizes ~10 km). The conclusion that the proposed modeling technology can adequately monitor the variability of the waters of the region with the spatial and temporal resolution, unattainable using only field data, can prove important for operational oceanography.

Study of the Black Sea dynamics on the basis of reanalysis results

The Black Sea dynamics during 25 years is analysed using numerical simulation and assimilation of remote sensing data. Numerical circulation model has horizontal space resolution of 4.8 km and 40 vertical levels. It includes a turbulent model of the Mellor-Yamada type. Results of simulation were validated by comparing with temperature and salinity profiles from hydrological surveys. Analysis of the results shows that the temperature of the sea upper layer grows. Salinity of upper 30m layer also increases, but in the layer 30-100m it decreases. The results of simulation reproduce authentically circulation in the upper layer of the Black Sea. According to simulation, mean currents, directed opposite to the surface one, are observed at a depth of more than 400 m.

A Tidal Semidiurnal Harmonic in the Black Sea Dynamics according to Numerical Modeling Results

The parameters of barotropic and baroclinic oscillations in the subinertial range have been obtained by numerical simulations of the Black Sea circulation using a model developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences. The structures and periods of barotropic and baroclinic seiches are in good agreement with the known theoretical predictions and results of numerical modeling of seiches obtained for the Black Sea subbasins.

The Role of the Bottom Relief and the β-effect in the Black Sea Dynamics

The Role of the Bottom Relief and the β-effect in the Black Sea Dynamics

Rol' rel'efa dna i β-effekta v dinamike Chernogo morya

Rol' rel'efa dna i β-effekta v dinamike Chernogo morya