A simple numerical dynamic-stochastic model of the ocean's synoptic variability closed at the second moment level

The results of numerical experiments involving a dynamic-stochastic model closed at the second moment level are reported. Specific features of the model are the possibility of using it neglecting viscosity coefficients, as well as in energy and enstrophy conservation at the prediction stage. The model is fairly effective in saving computer time. The model prognostic fields are less smoothed than those produced by a model with similar characteristics of the computed grid area and with biharmonic viscosity.Translated by Vladimir A. Puchkin.     

Optimization of the data assimilation algorithm in a model for synoptic dynamics of the velocity field

The results of numerical experiments involving data assimilation by a non-linear model for synoptic dynamics of the ocean are given. The results of application of simplified optimal filtration algorithms (with the correlation error function being parametrized for both linear and non-linear variants) and of the optimal interpolation are intercompared. The use of a non-linear equation to predict average values and a linear one to predict dispersion in the filtration algorithm is suggested as most appropriate for the cases, when anisotropy of the correlation function is to be included. In other cases, it is considered worth-while to apply optimal interpolation.Translated by V. Puchkin.     

Effectiveness of data assimilation using probabilistic techniques in a model for synoptic velocity field evolution

The results of numerical experiments involving data assimilation by linear and non-linear models for synoptic ocean dynamics are presented. This paper considers the model's response to data assimilation at diverse values of the relative error in the determination of the initial fields and space-time discreteness of data assimilation. The data obtained using the optimal filtering are compared with those provided by the optimal interpolation (OI). A qualitative difference in the response of the linear and non-linear models to data assimilation is noted. The limiting values of the time-space discreteness of observations assimilation are determined, which allow correct application of OI.Translated by Vladimir A. Puchkin.     

Assessment of the effectiveness of POLYMODE data assimilation by a numerical barotropic model for synoptic motions

This paper considers the results of numerical experiments involving POLYMODE data assimilation by a barotropic model for synoptic ocean dynamics. The model's response the data assimilation for various space-time discretenesses of assimilation is studied. Results derived from the application of optimal interpolation algorithms and modified optimal filtration algorithms are compared. Qualitative similarity to the calculations carried out through the simulation modelling technique is noted. Optimal assimilation algorithms are determined, depending on the space-time discreteness used. An optimal sampling discreteness for the POLYMODE conditions is suggested.Translated by Vladimir A. Puchkin.     

Numerical experiments on the four-dimensional assimilation of the observation data derived in the Black Sea in June 1984 on the basis of a numerical energy-balanced model

A procedure for the four-dimensional (4D) analysis of the hydrophysical fields in the Black Sea with an assimilation of the temperature and salinity (T, S) data was realized on the basis of a numerical model which involves the primitive equations of motion, and the heat and salt advection equations. Two experiments were carried out which differed by the observation data assimilation procedure. Analysis has shown that the observation data assimilation procedure realized using the energy-balanced model allows the reproduction of some synoptic features of the circulation in the Black Sea. A comparison of two computations demonstrates the efficiency of assimilating the measurement data on the basis of the 4D analysis as compared with the sequential objective analysis.Translated by Mikhail M. Trufanov.     

Numerical modeling of currents in the Drake Passage with assimilation of the experimental data of 2003

Computation of ocean currents in the Drake Passage is carried out with variational assimilation of the data of the hydrographical section across the Drake Passage carried out on December 11–15, 2003, and other data. A stream-eddy structure of the easterly Antarctic Circumpolar Current and a westerly current on the Antarctic Slope are obtained. Water transports by the different current field components and the integral transport across the Drake Passage are estimated. The necessity of direct current measurements in the Drake Passage for a correct estimate of the transport is confirmed.     

Dynamic-stochastic model for assimilation of remotely-sensed sea surface temperature data

We consider the possibility of assimilating sea surface temperature data by a combined ocean dynamics model incorporating a three-dimensional hydrodynamic model for synoptic variability for the considered ocean area and an integral model block describing the upper mixed layer. Model numerical simulations and experiments involving satellite-derived data are analysed.Translated by V. Puchkin.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

海洋环流模式中卫星遥感资料同化的应用进展

物理海洋研究长久以来一直受到观测资料不足的制约,然而这一状况随着现代观测技术的迅猛发展得到了很大的改善。卫星遥感技术的发展提供了覆盖全球的、连续、实时的卫星观测数据,这是其他任何资料都无法比拟的。这些数据大部分难以直接运用来改善气候预测或数值模拟分析,然而资料同化技术的出现和发展改善了这一情况。     

A new decomposition model of sea level variability for the sea level anomaly time series prediction

Rising sea level is of great significance to coastal societies; predicting sea level extent in coastal regions is critical. When carrying out predictions, the subsequences obtained using decomposition methods may exhibit a certain regularity and therefore can provide multidimensional information that can be used to improve prediction models. Traditional decomposition methods such as seasonal and trend decomposition using Loess(STL) focus mostly on the fluctuating trend of time series and ignore ...     

Comparison of methods for argo drifters data assimilation into a hydrodynamical model of the ocean

Different data assimilation methods such as an extended Kalman filter, the optimal interpolation method, and a method based on the Fokker-Planck equation applications are considered. Data from the ARGO drifters are assimilated into the HYCOM shallow water model (University of Miami, USA). Throughout the study, the schemes and methods of parallel computations with an MPI library are used. The results of the computations with assimilations are compared between themselves and with independent observations. The method based on the Fokker-Planck equation and the extended Kalman filter are preferable because they give better results than the optimal interpolation scheme. The various model characteristics of the ocean, such as the heat content fields and others, are analyzed after the data assimilation.     

Weak constraint data assimilation for tides in the Arctic Ocean

Estimation of the open-boundary inputs solving a weak constraint variational formulation for an Arctic tide model is considered as an ill-posed problem in the sense that the solution is very sensitive to the data noise and to grid size. Mathematically, spatial discretization of a cost function to be minimized and penalization of normal flow through the open boundary act as regularization of the problem. An heuristic choosing rule for the regularization parameter is applied to assess a suitable spatial resolution and the weight referred to the open boundary penalty. It is shown that these provide a better fit of the solution to a control data set compared with a finer grid, the value of the energy flux through the open boundary being in agreement with other model estimates. The M₂ solution obtained is much closer to the control data than other modern solutions while the accuracy of the simulated K₁ constituent is within the same error level. The tidal maps for these waves exhibit certain distinctions in comparison with other charts.     

Simultaneous assimilation of surface drifter data, satellite and in situ observations for improved estimates of meso-scale variability in the Kuroshio Extension Region

In order to better estimate meso-scale variabilities in the energetic Kuroshio Extension (KE) region, simultaneous assimilation of drifter-derived velocity data, together with satellite and in situ hydrographic data, is attempted by using a high-resolution 4-dimensional variational data assimilation (4D-VAR) system. Our experimental results, both with and without assimilation of drifter data (Exp. Drf and Exp. Ref, respectively) for the period during Aug–Oct 2005, show that the reproduced fields in Exp. Drf better reflect the observed meso-scale features such as the KE meandering jet and associated eddies. The adjoint sensitivity analysis indicates that our 4D-VAR system has the ability to provide a more realistic timeseries of the meandering jet structures that play a key role in the intergyre exchange between the subtropical and subarctic gyres in the North Pacific. In addition, the observed information from the surface drifters works to improve the subsurface structure. These results illustrate the advantage of our 4D-VAR simultaneous assimilation with the addition of drifter-derived surface velocity information.     

渤海M2分潮的伴随模式数值实验

根据渤海海域内M2潮汐调和常数的实测值,采用伴随方法来反演出开边界处的潮汐调和常数.为了取得较好的数值模拟结果,同时对给定的底摩擦系数进行了校正并对水深进行了微调.做了4个实验,并分别计算出调和常数的实测值与模拟值之差的绝对平均值:(1)只用19个验潮站的潮汐调和常数;振幅差为2.4cm,迟角差为5.0°.(2)只用37个观测点的高度计资料;振幅差为4.4cm,迟角差为5.7°.(3)同时利用19个验潮站的潮汐调和常数和37个观测点的高度计资料;振幅差为5.5cm,迟角差为8.5°.(4)同时利用19个验潮站的潮汐调和常数和14个观测点的高度计资料;振幅差为3.3cm,迟角差为5.6°.4个实验结果都较好地体现了渤海M₂潮波的特征.     

Evolution equation for the error correlation function of vorticity prediction used by a barotropic synoptic motion model to assimilate data

An exact equation is derived for the error correlation function of model processes, governed by a barotropic vortex balance equation in a linear approximation. This equation can be effectively applied to assimilate data with small spatial-temporal discreteness when the assumption on error correlation function's stationarity (homogeneity, isotropicity) proves to be incorrect and leads to unsatisfactory results.Translated by Vladimir A. Puchkin.     

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.