Assimilation of climatic data in a model of circulation of waters in the Black Sea with regard for the space and time behavior of the variances and cross-covariance functions of forecast errors

We propose an improvement of the algorithm of joint assimilation of the data on climatic temperature, salinity, and altimetric sea level in a model of circulation. Unlike the previous works, the variances of the forecast errors of temperature and salinity and the cross-covariance functions of of the forecast errors of salinity-level and temperature-level depend on the dynamics of waters. It is shown that the structure of the fields of cross-covariance functions in the upper mixed layer is formed by the vertical turbulent diffusion of the variances of forecast errors of temperature and salinity. At greater depths, these statistical characteristics are mainly determined by the vertical advection. We compared the results of calculations with and without taking into account the dynamics of the statistical characteristics. The analysis of the influence of the dynamics of these characteristics makes it possible to reconstruct the mutually adapted climatic fields of temperature, salinity, and horizontal and vertical current velocities in the Black Sea with the assimilation of data in the numerical model in each time step. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 18–31, July–August, 2008.     

Assimilation of climatic hydrological data in a Black-Sea model based on the algorithm of adaptive statistics of prognostic errors

We propose an algorithm of adaptive statistics of prognostic errors aimed at the assimilation of the climatic temperature and salinity fields in a model of dynamics of the sea. The algorithm is used for the numerical solution of the proposed differential equations for the dispersions of prognostic errors of temperature and salinity. The sources in the equations of advective diffusion of heat and salt depend on the four-dimensional dispersions of prognostic errors and one-dimensional (along the vertical coordinate) dispersions of measurement errors. The dispersions of prognostic errors are corrected at the times of assimilation of the data. We perform the reconstruction and analysis of the climatic fields of currents in the Black Sea. It is shown that the structure of the fields of dispersions in the upper mixed layer is determined by the vertical diffusion. Below this layer, the distribution of dispersions depends on the vertical advection. The algorithm of adaptive statistics of prognostic errors allows us to reconstruct the improved mutually adapted hydrophysical parameters with regard for the dynamics of the dispersions of errors. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 26–37, January–February, 2008.     

Method and results of assimilation of climatic data on temperature,salinity, and sea level into a numerical model of the Black Sea

A method for combined assimilation of climatic hydrologic fields of temperature, salinity, and the climatic dynamic level of the Black Sea into a model of sea dynamics is proposed. The monthly mean fields of the dynamic sea level were obtained from the results of assimilation of satellite altimetry data into the model. The statistical characteristics of errors in the forecasts of the level, salinity, and temperature were assumed to be proportional to the statistical characteristics of the differences between monthly mean climatic fields of temperature, salinity, and sea level calculated by means of assimilating altimetry observations of the sea level and analogous climatic hydrologic fields. The climatic fields of currents are reconstructed and analyzed. The assimilation of the climatic altimetry level allows the reproduction (in current fields) of quasi-stationary synoptic anticyclonic eddies located along the periphery of the Black Sea Rim Current.     

A Procedure of Reconstruction of the Climatic Seasonal Circulation in the Black Sea Based on the Assimilation of Hydrological Data in the Model

We propose a procedure of reconstruction of the continuous (in time) climatic annual behavior of circulation in the Black Sea based on the successive assimilation of the climatic distributions of temperature and salinity in the complete nonlinear model. We use monthly average arrays interpolated for each day of a year by expanding in harmonic functions of time. Various procedures aimed at the assimilation of data are studied by taking into account the variance of measurement errors. Our main attention is given to the analysis of qualitative and quantitative characteristics of vertical motions in the sea depending on the quality of the data and parameters of the model. The main version of calculations is illustrated by the maps of annual variability of the fields of sea level, horizontal currents, and vertical velocity.     

Long-Term Variations of the Thermohaline and Dynamic Characteristics of the Black Sea According to the Climatic Data on Temperature and Salinity and Their Assimilation in the Model

We compare the thermohaline and dynamic characteristics of the Black Sea reconstructed by using two versions of climatic temperature and salinity fields:old (1903–1982)and new (1903–2003). The fields are reconstructed with the help of continuous assimilation of the climatic temperature and salinity in the model. It is shown that the climatic thermohaline fields constructed with regard for the data of observations for the last 20 yr are characterized by an insignificant elevation of the halocline (pycnocline)in the winter-spring period and the elevation of the upper boundary of the cold intermediate layer in the spring-summer period. The intensity of surface geostrophic currents is greater than the same quantity computed on the basis of the old climatic data for the whole year. The horizontal currents in the sea computed according to the new climatic data are more intense. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 11–30, May–June, 2005.     

Seasonal variability of climatic currents in the Caspian Sea reconstructed by assimilation of climatic temperature and salinity into the model of water circulation

We present the results of an analysis of the seasonal variability of current fields in the Caspian Sea, reconstructed by assimilation of climatic temperature and salinity into the primitive-equation model of water circulation on the basis of an algorithm for adaptive statistics of prediction errors. The sources in heat and salt transfer-diffusion equations depend on the spatial and temporal variability of the variances of prediction errors and one-dimensional (in the vertical coordinate) variances of measurement errors for temperature and salinity. The variances of prediction errors are adjusted at the moments of data assimilation in accordance with a simplified Kalman filter. The climatic circulation of waters in the Caspian Sea is shown to be highly varying. The maximum of its intensity over the entire depth is reached in February. The minimum of kinetic energy is observed in April. The currents in deep-sea areas are determined by the balance between wind and baroclinic factors of the formation of circulation with wind currents prevalent.     

Numerical model of the hydrodynamics of the Black Sea and the Sea of Azov with variational initialization of temperature and salinity

A numerical primitive-equation model of the hydrodynamics of the Black Sea and the Sea of Azov in σ-coordinates is proposed. The model has a resolution of ～4 × 4 km in horizontal coordinates with 40-σ levels in the vertical and includes the four-dimensional variational initialization of temperature and salinity fields. A numerical initialization algorithm combines splitting methods and adjoint equations. Flow, temperature, sea level, and salinity fields driven by atmospheric forcing are calculated for the year 2008. The calculations are made in a variational initialization — prediction regime. Temperature and salinity fields are initialized at the end of each month. The optimality system includes forward and adjoint transport-diffusion equations for heat and salt that are linearized on the assimilation interval. Results of three numerical experiments with different sets of assimilated data in comparison with the prediction obtained from the forward model are discussed.     

Estimation of the long-term variability of hydrophysical characteristics of the Black Sea based on the assimilation of the climatic hydrological fields L and altimetry data

To study the long-term variability of the thermohaline and dynamic characteristics of the Black Sea, we use three versions of climatic fields, namely, the fields reconstructed in the model according to the old (1903–1982) and new (1903–2003) hydrological climatic data arrays of temperature and salinity and according to the data of satellite altimetry. The analysis of the altimetry-based climatic fields confirms the distinctions (established earlier according to the old and new data arrays) in the seasonal variability of the integral characteristics of temperature and salinity and in the structures of hydrophysical fields in the sea. It is shown that, in the winter-spring season, the thermohaline fields reconstructed according to the new and altimetry data arrays are characterized by a small elevation of the halocline (pycnocline) and the upper boundary of the cold intermediate layer. In all seasons, the altimetry-based surface geostrophic currents contain numerous mesoscale eddies with different signs of rotation. Moreover, in all seasons, the Rim Current reconstructed according to the altimetry data is characterized by a narrower jet almost along the entire its length. This jet is especially intense near the coasts of West Anatolia. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 3–17, July–August, 2006.     

A numerical experiment on computations of the Black Sea density fields and current velocities during summer

A near-bottom pressure equation consistent with the original set of difference equations is derived in the framework of a numerical energetically-balanced model. The model is used to simulate numerically three-dimensional density and current velocity fields and in the Black Sea for a specific season. The climatic values of temperature, salinity, and tangential wind stress during summer are applied as the original conditions. Analysis of the hydrophysical fields at the final moment of integrating is performed. The difference between new data and data derived earlier is demonstrated.Translated by V. Puchkin.     

Seasonal variability of the water circulation in the southern ocean and heat, salt, and mass exchange in the Antarctic region and adjacent oceans

The hydrographic fields in the Arctic region are calculated with a three-dimensional nonlinear model of the general circulation in the World Ocean using climatic databases on temperature, salinity, and wind stress. The calculation results show that the seasonal variability of the fields is negligible. The salinity distribution almost does not change from season to season, and slight temperature differences are found only in the upper layer. In the winter period, a moderate intensification of the currents is observed. The formation of an intermediate low-salinity layer is revealed at the Subantarctic front, where the intensive turbulence and transverse circulation in the Antarctic Circumpolar Current near the front result in the sinking of the surface low-salinity waters down to intermediate depths. The low-salinity water propagates in the oceans at intermediate depths northward from the front by advection. The integral values of the seasonal transport of mass, heat, and salt in various sections are presented in tables, and the distributions of appropriate characteristics in these sections are shown in figures. According to the calculations, the highest seasonal variations of heat, salt, and mass exchange in the Antarctic region and adjacent oceans are found in the Atlantic sector.     

海洋岛附近海域春季海洋水文测量结果分析

利用2006年4月在海洋岛附近海域的CTD测量资料,系统分析了该海域温度、盐度、密度和声速的平面分布和垂直分布特征,并探讨了其形成机理。分析指出:4月份是海洋岛附近海域季节性跃层的生成期,海区会产生正跃层、逆跃层、冷中间层、暖中间层等复杂的垂直结构;中间层和底层水文要素受海流的影响较大,而表层水文要素主要受海面风场和气温的影响。     

Seasonal Variations and Transformations of Climatic Currents with Depth on the Basis of Assimilation of New Climatic Data on Temperature and Salinity in a Model of the Black Sea

The seasonal climatic circulation of the sea reconstructed on the basis of assimilation of new arrays of many-year average hydrological data in a model is analyzed. Five layers are discovered in the structure of climatic currents in the sea in depth: the surface Ekman layer (∼ 10 m), a layer with small vertical gradients of the kinetic energy (∼ 10–60 m), a layer with relatively high vertical gradients of the kinetic energy (∼ 60–150 m), a layer with gradual decrease in the kinetic energy and intensification (from 250–350 m) of the east cyclonic gyre and Batumi anticyclonic eddy (∼ 150–1000 m), and an abyssal layer characterized by an almost barotropic velocity (∼ 1000–2000 m). The specific features of the seasonal evolution of currents at these depths are investigated. It is shown that the key role in the formation of deep-water circulation of the sea is played by the south east flow, east cyclonic gyre, and Batumi anticyclonic eddy. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 28–45, November–December, 2005.     

A comparison between 3DVAR and EnOI techniques for satellite altimetry data assimilation

Two conceptually different assimilation schemes, three dimensional variational (3DVAR) assimilation and Ensemble Optimum Interpolation (EnOI) are compared in the context of satellite altimetric data assimilation. Similarities and differences of the two schemes are briefly discussed and their impacts on the model simulation are investigated.With a tropical Pacific ocean model, two assimilation experiments of sea level anomaly (SLA) data from TOPEX/Poseidon are performed for 5 years from 1997 to 2001. Annual mean states of temperature and salinity fields are compared with analysis data and some independent observations. It is found that EnOI generally produces moderate improvements on both temperature and salinity fields, while changes induced by 3DVAR assimilation are strong and vary remarkably in different areas. For instance, 3DVAR tends to excessively modify the temperature field along the thermocline depth and even deteriorate the simulation, but it is more effective than EnOI below the thermocline depth. However, for the salinity field 3DVAR outperforms EnOI nearly for almost the whole layer. As the difference relative to the WOA01 analysis is compared, it is apparently reduced to below 0.3 psu in most areas in the 3DVAR experiment. On the other hand, the pattern of difference in the EnOI experiment resembles that of the simulation and the magnitude is only diminished to some extent. One advantage of EnOI is that it yields more consistent improvements even in areas where there are large model errors. It is more reliable than 3DVAR in such a sense. It is also revealed that the T–S relation plays a very important role in altimetric data assimilation. Further, the distinct performance of the two schemes can be partly accounted for by their inherent assumptions and settings.     

Numerical modeling of ocean hydrodynamics with variational assimilation of observational data

Models and methods of the numerical modeling of ocean hydrodynamics dating back to the pioneering works of A.S. Sarkisyan are considered, with emphasis on the formulation of problems and algorithms of mathematical modeling and the four-dimensional variational assimilation of observational data. An algorithm is proposed for studying the sensitivity of the optimal solution to observational data errors in a seasurface temperature assimilation problem in order to retrieve heat fluxes on the surface. An example of a solution of the optimal problem of the World Ocean hydrodynamics with the assimilation of climatic temperature and salinity observations is offered.     

Assimilation of the climatic hydrological data in the σ-coordinate model of the black sea by the algorithm of adaptive statistics

We realize the algorithm of adaptive statistics of forecasting errors for the assimilation of the climatic fields of temperature and salinity in the σ-coordinate model of the dynamics of the Black Sea. The principal relations of this algorithm and its simplified version based on the Kalman filter are presented. The distinctive features of realization of the algorithm specified by the model are discussed. We also present the results of comparison of the hydrophysical fields of the Black Sea reconstructed according to the algorithm of adaptive statistics and a simplified scheme of assimilation of the climatic data. It is shown that the dependence of sources in the transport equations (heat and salt diffusion) on the four-dimensional variances of forecasting errors and threedimensional measurement errors enables one to reconstruct the mutually adapted climatic parameters of the sea more exactly.     

利用热带太平洋TAO浮标阵列评估全球高分辨率浪-潮-流耦合模式同化结果

In order to evaluate the assimilation results from a global high resolution ocean model, the buoy observations from tropical atmosphere ocean(TAO) during August 2014 to July 2015 are employed. The horizontal resolution of wave-tide-circulation coupled ocean model developed by The First Institute of Oceanography(FIOCOM model) is 0.1°×0.1°, and ensemble adjustment Kalman filter is used to assimilate the sea surface temperature(SST), sea level anomaly(SLA) and Argo temperature/salinity profiles. The simulation results with and without data assimilation are examined. First, the overall statistic errors of model results are analyzed. The scatter diagrams of model simulations versus observations and corresponding error probability density distribution show that the errors of all the observed variables, including the temperature, isotherm depth of 20°C(D20), salinity and two horizontal component of velocity are reduced to some extent with a maximum improvement of 54% after assimilation. Second, time-averaged variables are used to investigate the horizontal and vertical structures of the model results. Owing to the data assimilation, the biases of the time-averaged distribution are reduced more than70% for the temperature and D20 especially in the eastern Pacific. The obvious improvement of D20 which represents the upper mixed layer depth indicates that the structure of the temperature after the data assimilation becomes more close to the reality and the vertical structure of the upper ocean becomes more reasonable. At last,the physical processes of time series are compared with observations. The time evolution processes of all variables after the data assimilation are more consistent with the observations. The temperature bias and RMSE of D20 are reduced by 76% and 56% respectively with the data assimilation. More events during this period are also reproduced after the data assimilation. Under the condition of strong 2014/2016 El Ni?o, the Equatorial Undercurrent(EUC) from the TAO is gradually increased during August to November in 2014, and followed by a decreasing process. Since the improvement of the structure in the upper ocean, these events of the EUC can be clearly found in the assimilation results. In conclusion, the data assimilation in this global high resolution model has successfully reduced the model biases and improved the structures of the upper ocean, and the physical processes in reality can be well produced.     

Assimilation of hydrological observation data for calculating currents in seas and oceans

This paper considers the main steps in improving the methods for calculating the ocean (sea) dynamics on the basis of observational data on sea-water temperature and salinity. The results of diagnostic and adaptation calculations for the near-equatorial area of the West Atlantic in the area of the Lomonosov countercurrent formation are presented. We consider the problem of the complex use of measurements of temperature, salinity, and current velocity in the POLYMODE polygons with their assimilation into the model using a Kalman filter. The results of calculations of the coordinated fields with the mechanism of geostrophic adaptation and using asynchronous measurements obtained by the Razrezy program are given. We discuss further modifications of the assimilation algorithms for hydrological observation data in models of sea dynamics and the principles of adaptation of hydrophysical fields that made it possible to reconstruct the climate fields of the Black Sea and to reproduce the basin dynamics for 23 years.     

Numerical modelling of the Black Sea hydrodynamics with application to ecological problems

Computations involving a complete baroclinic model for the Black Sea are analysed. Monthly climatic temperature and salinity data were used. Dynamic fields were derived for each of the 12 months. The characteristics of the cold intermediate layer, which represents an essential feature of the Black Sea thermal structure, are examined.Translated by V. Puchkin.     

Three-dimensional structure of an observed cyclonic mesoscale eddy in the Northwest Pacific and its assimilation experiment

Mesoscale eddies play an important role in modulating the ocean circulation. Many previous studies on the threedimensional structure of mesoscale eddies were mainly based on composite analysis, and there are few targeted observations for individual eddies. A cyclonic eddy surveyed during an oceanographic cruise in the Northwest Pacific Ocean is investigated in this study. The three-dimensional structure of this cyclonic eddy is revealed by observations and simulated by the four-dimensional variational data assimilation(4 DVAR) system combined with the Regional Ocean Modeling System. The observation and assimilation results together present the characteristics of the cyclonic eddy. The cold eddy has an obvious dual-core structure of temperature anomaly.One core is at 50–150 m and another is at 300–550 m, which both have the average temperature anomaly of approximately-3.5°C. The salinity anomaly core is between 250 m and 500 m, which is approximately-0.3. The horizontal velocity structure is axis-asymmetric and it is enhanced on the eastern side of the cold eddy. In the assimilation experiment, sea level anomaly, sea surface temperature, and in situ measurements are assimilated into the system, and the results of assimilation are close to the observations. Based on the high-resolution assimilation output results, the study also diagnoses the vertical velocity in the mesoscale eddy, which reaches the maximum of approximately 10 m/d. The larger vertical velocity is found to be distributed in the range of 0.5 to 1 time of the normalized radius of the eddy. The validation of the simulation result shows that the 4 DVAR method is effective to reconstruct the three-dimensional structure of mesoscale eddy and the research is an application to study the mesoscale eddy in the Northwest Pacific by combining observation and assimilation methods.