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.     

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.     

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.     

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.     

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.     

Calculation of adapted black sea fields on the basis of assimilation of climatic temperature and salinity data into the model

A scheme of a periodic assimilation of climatic temperature and salinity data into a model is proposed. In accordance with the criteria chosen on the basis of numerical experiments, an optimum assimilation period of three hours is set. The proposed method allows a hydrodynamic adaptation of the fields of temperature, salinity, and flow velocity that are close to the climatic ones within the framework of the proposed criteria. The main feature of the adapted fields of vertical flows in the layer 0–700 m is their smooth character and an almost complete absence of small-scale noise. The extreme values of vertical velocity in this layer decrease by almost an order of magnitude as compared to analogous values calculated for the variant of data assimilation with a weak adjustment of fields.     

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.     

Improvement of short-termforecasting in the northwest Pacific through assimilating Argo data into initial fields

The impact of assimilating Argo data into an initial field on the short-term forecasting accuracy of temper- ature and salinity is quantitatively estimated by using a forecasting system of the western North Pacific, on the base of the Princeton ocean model with a generalized coordinate system （POMgcs）. This system uses a sequential multigrid three-dimensional variational （3DVAR） analysis scheme to assimilate observation da- ta. Two numerical experiments were conducted with and without Argo temperature and salinity profile data besides conventional temperature and salinity profile data and sea surface height anomaly （SSHa） and sea surface temperature （SST） in the process of assimilating data into the initial fields. The forecast errors are estimated by using independent temperature and salinity profiles during the forecasting period, including the vertical distributions of the horizontally averaged root mean square errors （H-RMSEs） and the horizontal distributions of the vertically averaged mean errors （MEs） and the temporal variation of spatially averaged root mean square errors （S-RMSEs）. Comparison between the two experiments shows that the assimila- tion of Argo data significantly improves the forecast accuracy, with 24% reduction of H-RMSE maximum for the temperature, and the salinity forecasts are improved more obviously, averagely dropping of 50% for H-RMSEs in depth shallower than 300 m. Such improvement is caused by relatively uniform sampling of both temperature and salinity from the Argo drifters in time and space.     

Reconstruction of the seasonal climate of the Black Sea on the basis of available hydrological data

We analyze the seasonal variability of the climatic hydrophysical fields of the Black Sea reporduced in three numerical experiments carried out according to the model of circulation. The numerical predictions are performed for a period of 12.5 yr on the basis of the hydrological data accumulated in 1983–1995. The monthly average climatic fields of the current speed are reconstructed according to the data on the climatic fields of temperature and salinity by the method of hydrodynamic adaptation (standard). It is shown that, in prognostic calculations, the seasonal variability of temperature and salinity is qualitatively close to the “standard” dependence. At the same time, the quantitative difference between the climatic behavior of the model and the standard dependence may be significant. The annual cycle of the currents is characterized by the intensification of the Main Black-Sea Current in winter. The structure of the hydrophysical fields of the sea in the model becomes much more realistic if it is based on the actual hydrological data. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

南海及邻近海域大气-海浪-海洋耦合精细化数值预报系统研制

本文主要介绍了南海及邻近海域大气-海浪-海洋耦合精细化数值预报系统的研制概况。预报区域为99°E~135°E,15°S~45°N,包括渤海、黄海、东海和南海及其周边海域。为了给耦合预报模式提供较准确的预报初始场,在预报开始之前,分别进行了海浪模式和海洋模式的前24小时同化后报模拟。海浪模式和海洋模式都采用了集合调整Kalman滤波同化方法,海浪模式同化了Jason-2有效波高数据;海洋模式同化了SST数据、MADT数据和ARGO剖面数据。为了改进海洋温度和盐度的模拟,我们在海洋模式的垂向混合方案中引入波致混合和内波致混合的作用。预报系统的运行主要包括两个阶段,首先海浪模式和海洋模式进行了2014年1月至2015年10月底的同化后报模拟,强迫场源自欧洲气象中心的六小时的再分析数据产品。然后耦合预报系统将同化后报模拟的结果作为初始场进行了14个月的耦合预报。预报产品包括大气产品（气温、风速风向、气压等）、海浪产品（有效波高和波向等）、海流产品（温度、盐度和海流等）。一系列观测资料的检验比较表明该大气-海浪-海洋耦合精细化数值预报系统的预报结果较为可靠,可以为南海及周边海洋资源开发和安全保障提供数据和信息产品服务。     

Statistical structure of the large-scale fields of temperature and salinity in the Black Sea

In order to reconstruct the large-scale temperature and salinity fields by the method of optimal interpolation of the archival data, we compute the correlation functions and analyze the space and time variations of the statistical structure of the fields. On the sea surface, the thermohaline fields are spatially inhomogeneous. Thus, the correlation functions are anisotropic in the region of the northwest shelf and close to isotropic in the inner parts of the sea. The values of correlation length vary from season to season. In the layer of pycnocline, the temperature and salinity fields are anisotropic. In the zonal direction, the correlation length is 2–3 times greater than in the meridional direction. The indicated anisotropy becomes stronger in the winter season and weaker in the summer season as a consequence of the seasonal variability of large-scale circulation. We study the dependence of the error of reconstruction of the fields by the method of optimal interpolation on the form of approximation of the correlation functions with regard for anisotropy. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 51–65, January–February, 2008.     

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.     

Reconstruction of the space and time variability of thermohaline fields in the Sevastopol Bay

The aim of the present work is to reconstruct the space and time variability of the three-dimensional fields of currents, temperature, salinity, and density in the Sevastopol Bay under the influence of the actual external factors in 1999. For this purpose, we use a version of the numerical multilayer model on the σ-coordinates. A vast array of the data of observations accumulated as a result of regular monitoring of the Sevastopol Bay contains, in particular, the data on the sea-surface temperature measured with six-hour intervals (at the hydrometeorological station located near the center of the bay) and almost monthly vertical profiles of temperature and salinity obtained at seven hydrological stations. The comparison of the numerical results with the data of observations enables us to conclude that, in general, the model fairly correctly describes the space structure and rearrangements of the fields of temperature and salinity. Among the most important distinctions, we can mention the fact that the fresh river water penetrating into the bay is mixed with seawater faster than predicted by the model. We also discuss the causes of these distinctions. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 23–39, September–October, 2008.     

Analysis of the Black-Sea climatic fields below the main pycnocline obtained on the basis of assimilation of the archival data on temperature and salinity in the numerical hydrodynamic model

We study model climatic temperature and salinity fields and the fields of currents in the 350–1000-m layer. The following specific features are revealed: Colder waters are observed in the regions with anticyclonic vorticity. At the same time, warmer waters are detected in the regions with cyclonic vorticity. This temperature effect can be explained by the elevation of temperature with depth below the main pycnocline. In the region of the Sevastopol anticyclone, at depths greater than 500 m, we observe a zone of cyclonic rotation of waters. Near the Caucasian coast, in the region of Gelendzhik, we reveal a narrow jet current existing at a depth of 350 m from March till July. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp.3–15, January–February, 2009.     

Comparative analysis of the North Atlantic surface circulation reproduced by three different methods

Calculation results are presented for long-term mean annual surface currents in the North Atlantic based on direct drifter measurements and numerical experiments with the ocean general circulation model using both climatic arrays of hydrological data World Ocean Atlas 2009 and Argo profiling data. The calculations show that the technique suggested for model calculations of oceanographic characteristics of the World Ocean with the use of Argo data significantly improves the climatic fields of the temperature and salinity even on a coarse grid. The comparison of the model calculation results with drifter data showed that the temperature and salinity fields found from Argo data with the use of data variational interpolation on a regular grid allow the calculation of realistic currents and can be successfully used as initial conditions in hydrodynamic models of the ocean dynamics.     

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.     

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.     

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.