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.     

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.     

Spectral barotropic model for the prediction of synoptic currents in the open part of the ocean

We consider a quasigeostrophic spectral model used for the prediction of synoptic currents in the barotropic ocean. The spectral method is based on the expansion of the current function in a double series in cosines. An algorithm of numerical evaluation of the nonlinear term in the equation of potential eddy is described in detail. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 62–69, July–August, 2006.     

Collocation numerical model for synoptic eddy evolution in the ocean

A quasi-geostrophic model for synoptic eddy evolution in a confined oceanic area is examined. The numerical scheme is based on the combination of spline collocation, splitting, and Fourier series expansion by the dynamic operator's eigenfunctions over the vertical. The functions and their derivatives are approximated with cubic splines in a basis constituted by B-spline functions. A series of experiments focusing on eddy transformation were conducted. The acquired data confirmed the inference regarding the oscillatory nature of the energy exchange between the primary eddy and the secondary ones and showed how vortical formations affect the currents. The evidence obtained indicates that, vertically, the pattern of eddy propagation is complicated.Translated by Vladimir A. Puchkin.     

Numerical experiments with data assimilation in the simplest dynamic-stochastic model for the ocean's synoptic variability closed at the level of the second moments

The results of numerical experiments with data assimilation in a non-linear model of the synoptic dynamics of the world's oceans are reported. The model's response to the data assimilation is studied at different values of the relative error in determining the initial fields and assimilation discreteness. The results of application of the algorithms of optimum filtration and optimum interpolation are compared. The advantages of the filtration algorithm employed are discussed only for the case of small errors in determining the initial fields and low assimilation discreteness. The possibility of deterioration of the prediction estimates in data assimilation with discreteness less than the typical time of variability of the average fields is noted.Translated by Mikhail M. Trufanov.     

基于潮汐表数据同化的天文潮数值预报模型及其模拟预报效果

潮汐表是利用长期潮汐观测结果经调和分析实现的主要港湾潮汐预报结果,具有较高的预报精度,而通常的天文潮数值预报目前还难以达到潮汐表的预报精度.本研究在建立常规天文潮数值预报模型的基础上,建立了基于潮汐表数据同化的天文潮数值预报模型,并分别采用这2种模型预报福建沿岸海域的天文潮.其结果表明同化模型的预报结果无论是在潮时还是在潮高均明显优于常规模型;同化模型能显著地改善所研究的沿岸海域90个水位点中至少45个水位点的潮汐预报结果,而其他水位点的预报结果也有不同程度地改善.     

A global barotropic ocean model driven by synoptic atmospheric disturbances for detecting seafloor vertical displacements from in situ ocean bottom pressure measurements

A global barotropic ocean model forced by atmospheric disturbances is developed for the detection of seafloor vertical displacements from in situ ocean bottom pressure (OBP) data. The model accuracy is validated by deep-sea OBP data at more than 100 sites obtained over the global ocean. Parameters and boundary conditions including the horizontal resolution incorporated in the ocean model are tested in order to accurately simulate the nontidal (>2 days) OBP variations. The horizontal resolution is found to the factor that most significantly affects the simulated result. The finer the horizontal resolution applied, the smaller the model variability is. The model accuracy is highest when the horizontal resolution is 1/12°, but deteriorates when the horizontal resolution is finer than 1/12°. This may indicate a failure of the energy dissipation parameterization in the barotropic ocean model. Using the developed 1/12° model, the root-mean-square of the observed nontidal OBP component can be reduced by 18 % as an average of all the OBP data used. It is found that the 1/12° model is useful for the detection of a slow seafloor vertical displacement of centimeters related to the 2011 Tohoku-Oki earthquake from in situ OBP records near the hypocenter of the earthquake.     

A numerical model for wave motions and turbulence flows in front of a composite breakwater

A mathematical model based on the Volume-Averaged/Reynolds Averaged Navier-Stokes (VARANS) equations is developed to describe surface wave motions in the vicinity of a coastal structure, which could be either a rigid solid structure or a permeable structure or a combination of both. In the VARANS equations, the volume-averaged Reynolds stress is modeled by adopting the nonlinear eddy viscosity assumption. The model equations for the volume-averaged turbulent kinetic energy and its dissipation rate are derived by taking the volume-average of the standard k−ϵ equations. Because of the volume-averaging process, the effects of the small-scale turbulence in porous media are introduced. The performance of the model is checked by comparing numerical solutions with the experimental data related to a composite breakwater reported by Sakakiyama and Liu [Coast. Eng. 121 (2001) 117].     

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.     

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.     

A numerical investigation of western boundary currents in subtropical and subpolar gyres with a barotropic model

Dynamics of western boundary currents in the subtropical and subpolar gyres are studied as a source-sink flow of barotropic fluid by means of numerical integration of the time-dependent non-linear vorticity equation. The bottom topography consists of a continental shelf of uniform slope (120 km wide) parallel to the straight western coast and a flat bottom of uniform depth. The steady solution in the case of low Reynolds number (Re≦100) shows the vorticity balance of the western boundary current between theβ-, diffusion-, and bottom relief terms. The cuspidated flow of the western boundary current in the subpolar gyre is observed as a compensating flow for the subtropical western boundary current separating from the western coast. In the case of Re=350, the zonal current separating from the coast meanders with the wave length of the stationary Rossby waves. It is shown that in the present model the separation of the boundary current is controlled by the planetary vorticity (f) of the fluid particle in the boundary flow, with which the same particle flows out the eastern wall at the corresponding latitude. The decrease of the efflux width increases the intensity of the non-linear overshooting of the boundary current separating from the western coast.     

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.     

对地球系统模式FIO-ESM同化实验中北极海冰模拟的评估

本文评估了地球系统模式FIO-ESM(First Institute of Oceanography-Earth System Model)基于集合调整Kalman滤波同化实验对1992-2013年北极海冰的模拟能力。结果显示:尽管同化资料只包括了全球海表温度和全球海面高度异常两类数据,而并没有对海冰进行同化,但实验结果能很好地模拟出与观测相符的北极海冰基本态和长期变化趋势,卫星观测和FIO-ESM同化实验所得的北极海冰覆盖范围在1992-2013年间的线性变化趋势分别为-7.06×105和-6.44×105 km2/(10a),同化所得的逐月海冰覆盖范围异常和卫星观测之间的相关系数为0.78。与FIO-ESM参加CMIP5(Coupled Model Intercomparison Project Phase 5)实验结果相比,该同化结果所模拟的北极海冰覆盖范围的长期变化趋势和海冰密集度的空间变化趋势均与卫星观测更加吻合,这说明该同化可为利用FIO-ESM开展北极短期气候预测提供较好的预测初始场。     

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.     

A two-dimensional numerical model of tidal motions on the shelf of Guinea

The general statement of a non-linear problem in modelling a barotropic tide for the limited part of a real shelf and the problems related to artificial division of the computation area in the ocean by a liquid boundary are considered. Linear combinations of various types of boundary conditions and analytical expressions are used to describe the tidal wave structure at the liquid boundaries. The results of test computations for basins with the simplest outlines are given. The model is used to reconstruct the spatial distribution of characteristics of theM ₂ tide on the shelf of Guinea. The methods of computation and specification of unambiguously determined model parameters are described. Joint analysis of the modelling results and the field data has been carried out. The tidal map of theM ₂ wave is plotted for the area under investigation.Translated by Mikhail M. Trufanov.     

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.