Approximate Variational Method for Ocean Data Assimilation

An approximate variational method is proposed to assimilate an oceanographic data set with a numerical ocean model. In the approximate method, the adjoint equation to a governing equation is derived and then converted to a finite difference form, in contrast to the ordinary, exact variational method which is composed of a finite difference equation adjoint to the finite difference governing equation. A cumbersome derivation of the adjoint equation is avoided, and finite difference schemes used for the original governing equation are easily utilized for the adjoint equation. This method has been verified with twin experiments. The flow field in the twin experiments is composed of dipole eddies in a two-layer quasi-geostrophic model. Initial and boundary conditions are control variables. The descent converges towards the exact field within 50 iterations, showing that the fundamental problem of the method (an unstable descent with a large number of iterations) does not appear. The approximate method is promising and should be tried with real data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Pressure image assimilation for atmospheric motion estimation

The complexity of the laws of dynamics governing 3-D atmospheric flows associated with incomplete and noisy observations make the recovery of atmospheric dynamics from satellite image sequences very difficult. In this paper, we address the challenging problem of estimating physical sound and time-consistent horizontal motion fields at various atmospheric depths for a whole image sequence. Based on a vertical decomposition of the atmosphere, we propose a dynamically consistent atmospheric motion estimator relying on a multilayer dynamic model. This estimator is based on a weak constraint variational data assimilation scheme and is applied on noisy and incomplete pressure difference observations derived from satellite images. The dynamic model is a simplified vorticity-divergence form of a multilayer shallow-water model. Average horizontal motion fields are estimated for each layer. The performance of the proposed technique is assessed using synthetic examples and using real world meteorological satellite image sequences. In particular, it is shown that the estimator enables exploiting fine spatio-temporal image structures and succeeds in characterizing motion at small spatial scales.     

Reconstruction of hydrological fields and reproduction of climatic circulation of World Ocean waters

Due to a lack of observational data, the hydrological fields of temperature, salinity, and density used by oceanographers at present remain significantly smoothed. Specifically, this refers to the WOA data distributed freely by the group of Sidney Levitus. This study describes the history of synthesis of hydrological data and mathematical modeling with high resolution. Our aim is to minimize the drawbacks of original data of hydrological fields, improve them with the help of a mathematical model, and thus reproduce the current fields. The results of some realistic calculations are presented.     

Effect of the drag coefficient on a typhoon wave model

The effect of the drag coefficient on a typhoon wave model is investigated.Drag coefficients for Pingtan Island are derived from the progress of nine typhoons using COARE 3.0 software.The wind parameters are obtained using the Weather Research and Forecasting model.The simulation of wind agrees well with observations.Typhoon wave fields are then simulated using the third-generation wave model SWAN.The wave model includes exponential and linear growths of the wind input,which determine the wave-growth mode.A triple triangular mesh is adopted with spatial resolution as fine as 100 m nearshore.The SWAN model performs better when using the new drag coefficient rather than the original coefficient.     

Mean Dynamic Topography and Geostrophic Surface Currents in the Fram Strait Derived from Geodetic Data

Two mean dynamic topography (MDT) fields are determined in the Fram Strait between Svalbard and Greenland. New airborne gravity anomalies, older data, and two different mean sea surface (MSS) fields are combined using the least squares collocation (LSC) technique. The results are compared to an oceanographic MDT model and two synthetic MDT fields. The same main currents are seen in all fields. Additionally, smaller scale features are revealed in the new MDT fields. Geostrophic surface currents derived from the MDT models are compared to moorings and Lagrangian drifters. The agreement is desultory. The oceanographic data are an inadequate basis of comparison due to data gaps. Nevertheless, it is the only one available.     

A fully nonlinear Boussinesq model in generalized curvilinear coordinates

Based on the fully nonlinear Boussinesq equations in Cartesian coordinates, the equations in generalized coordinates are derived to adapt computations to irregularly shaped shorelines, such as harbors, bays and tidal inlets, and to make computations more efficient in large near-shore regions. Contravariant components of velocity vectors are employed in the derivation instead of the normal components in curvilinear coordinates or original components in Cartesian coordinates, which greatly simplifies the equations in generalized curvilinear coordinates. A high-order finite difference scheme with staggered grids in the image domain is adopted in the numerical model. The model is applied to five examples involving curvilinear coordinate systems. The results of these cases are in good agreement with analytical results, experimental data, and the results from the uniform grid model, which shows that the model has good accuracy and efficiency in dealing with the computations of nonlinear surface gravity waves in domains with complicated geometries.     

Wave height forecasting by the transfer function model

Three completing methods were introduced in this paper. The data were completed from 1983 to 1988 at the KL and PTC stations. The completed data were called original data. The completing methods were the transfer function with fixed-parameters then built the Transfer Function (TF) model between the two stations. The TF model was used to estimate the wave data of the future. The difference of the estimated data and the original data were conferred in this paper. Two types of forecasting differences were discussed here: (1) the input data year increases from 1 to 6 years, and the difference of the estimated data and the original data were then compared. (2) Use one-year data as the input series to forecast the data of the next five years, and then compare the differences of the estimated data and the original data. After comparing the differences we can know the results. The mean value and the standard deviation of the differences decrease and go more stable as the quantity of the input data year increases. The mean value and the standard deviation of the differences increase and go more unstable as the quantity of the forecasted data year increases. This model can be used to forecast the wave data.     

Estimation of 3-D current fields near the Rhine outflow from HF radar surface current data

HF radar systems are designed to measure spatially variable sea surface currents. A methodology was developed to complement these data with information about the current variability over the water column in a stratified shallow sea. Current profiles were estimated using a diagnostic model driven by surface current measurements from an HF radar system and by sea surface slopes derived from tide gauge data. The structure of the model has a physical basis but its parameters were derived from an analysis of in-situ current profile measurements. Application of the model to HF radar data from the SCAWVEX Rhine outflow experiment showed fair agreement with in-situ current data. As applications, estimation and tidal analysis of current fields are demonstrated.     

Four-dimensional analysis of the variability of hydrophysical fields in the tropical atlantic and on the shelf of guinea

The problem of monitoring of the mesoscale variability of hydrophysical fields in the shelf zone is considered. The usefulness of the data available in regional information centres is discussed. The possibility of monitoring the dynamics of the oceanic fields in the tropical Atlantic encompassing separate observation sites is demonstrated using the oceanographic databank of the scientific research centre (CERESCOR) in Conakry-Rogbane as an example. The results of assimilation of the hydrophysical survey data derived on the shelf in a telescopic model of the region are given.Translated by Mikhail M. Trufanov.     

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     

用气-水-土3层模型分析海水中水平电偶极子源的电磁场分布

由空气－海水－海底3层模型求得了海水中水平电偶极子源的电磁场分布。与以往不考虑空气层的两层模型的电磁场分布相比,它更接近于实际分布情况。文章还对不同海底电导率时水平电偶极子源的电场水平分量进行了数值计算和分析。     

Global historical archive of wind waves based on Voluntary Observing Ship data

A new global archive of wind wave characteristics has been developed based on Voluntary Observing Ship (VOS) data for the period of 1888–2015. In addition to the basic meteorological variables, we have derived the records of visually observed heights, periods, and wind sea and swell directions. The main parameters have been supplemented by significant wave height and dominant period estimates, as well as wave geometry characteristics: steepness, wave age, and wavelength. Multistage quality control has been applied to correct or eliminate spurious values. Data are presented as individual records for every month and as original monthly means fields for every parameter. Easy access and use, along with representative data, make the new archive particularly special and applicable in different ways without any additional preprocessing. Visual wave observations assimilated in the new archive can be used to develop global and regional climatologies, estimate extreme wave characteristics and long-term trends in wave climate, verify and compare them with satellite measurements and model analysis, and test the theoretical laws of ocean wave development and propagation.     

基于卫星数据改进计算白冠覆盖率的模型

本文基于白冠覆盖率的历史研究,总结了计算白冠覆盖率的参数化方案和海浪破碎统计模型,并分析比较其优缺点。通过结合基于卫星数据的参数化公式,利用最优拟合的方法,得到不同限制条件下模型中的系数C_en和n。通过分析考虑海浪破碎条件,确定了适用于一般海浪状况的系数值。通过比较白冠覆盖率的卫星数据和原始模型的模拟结果,可知改进后模型的结果更合理,同时与历史研究结论相符。文中还分析了从1998年到2008年十年平均的全球白冠覆盖率的季节性分布特征。在中高纬度海域,全年白冠覆盖率的值最大,而在低纬度和赤道海域,白冠覆盖率小于0.5%,全球白冠覆盖率的平均值大约为1% ~3%。北半球中高纬度海域的白冠覆盖率的季节性变化显著大于南半球。     

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.     

Optimal interpolation of the data of remote sensing of the sea surface

We analyze the statistical structure of the data of remote sensing of the fields of surface temperature and the concentration of chlorophyll in the northwest part of the Black Sea with an aim to apply the method of optimal interpolation to the restoration of the maps of these fields according to the restricted amounts of data. We determine the scales of smoothing for the selection of the random components of the fields and estimate their difference from the statistical model uniform and isotropic over the space correlation coefficients. The functions of spectral densities are constructed along various sections and the best intervals of discretization of the fields required to perform the optimal interpolation with given accuracy are determined. It is shown that the construction of the maps of fields under the conditions of controlled accuracy of reconstruction of their values remains possible even if the amounts of the input satellite data are significantly decreased. We consider a procedure of evaluation of the best possible amounts of data required for the use of the method of optimal interpolation. Some examples of application of this procedure to the data of remote sensing of the fields of surface temperature and the concentration of chlorophyll are presented.     

Model initialization in a tidally energetic regime: A dynamically adjusted objective analysis

A simple improvement to objective analysis of hydrographic data is proposed to eliminate spatial aliasing effects in tidally energetic regions. The proposed method consists of the evaluation of anomalies from observations with respect to circulation model fields. The procedure is run iteratively to achieve convergence. The method is applied in the Bay of Fundy and compared with traditional objective analysis procedures and dynamically adjusted climatological fields. The hydrographic skill (difference between observed and model temperature and salinity) of the dynamically adjusted objective analysis is significantly improved by reducing bias and correcting the vertical structure. Representation of the observed velocities is also improved. The resulting flow is consistent with the known circulation in the Bay.     

The reduction of plankton biomass induced by mesoscale stirring: A modeling study in the Benguela upwelling

Recent studies, both based on remote sensed data and coupled models, showed a reduction of biological productivity due to vigorous horizontal stirring in upwelling areas. In order to better understand this phenomenon, we consider a system of oceanic flow from the Benguela area coupled with a simple biogeochemical model of Nutrient-Phyto-Zooplankton (NPZ) type. For the flow three different surface velocity fields are considered: one derived from satellite altimetry data, and the other two from a regional numerical model at two different spatial resolutions. We compute horizontal particle dispersion in terms of Lyapunov exponents, and analyzed their correlations with phytoplankton concentrations. Our modeling approach confirms that in the south Benguela there is a reduction of biological activity when stirring is increased. Two-dimensional offshore advection and latitudinal difference in primary production, also mediated by the flow, seem to be the dominant processes involved. We estimate that mesoscale processes are responsible for 30–50% of the offshore fluxes of biological tracers. In the northern area, other factors not taken into account in our simulation are influencing the ecosystem. We suggest explanations for these results in the context of studies performed in other eastern boundary upwelling areas.     

太平洋海面粗糙度的计算及波长的提取

海面粗糙度对于海洋工程和海洋军事非常重要,但是海面粗糙度的现场观测资料非常少,波长更难观测。本文利用TOPEX高度计风速资料,实现了对海面粗糙度的反演。给出了一种提取波长的方法,通过验证表明利用该方法得到的波长精度较高。     

The induced electromagnetic field associated with submerged movingbodies in an unstratified conducting fluid

A mathematical model is proposed to investigate electromagnetic fields induced by the motion of conductive sea water in the wake of a moving body. An exact solution is obtained for the induced field. The results show that undersea mobile vehicles can generate measurable fields. The frequency-domain solution and its unique properties are also derived     

Numerical model of nonhydrostatic ocean dynamics based on methods of artificial compressibility and multicomponent splitting

An algorithm is proposed for solving three-dimensional ocean hydrodynamics equations without hydrostatic approximation and traditional simplification of Coriolis acceleration. It is based on multicomponent splitting of the modified model with artificial compressibility. The original system of equations is split into two subsystems describing the transport of three velocity components and adjustment of the density and velocity fields. At the adjustment stage, the horizontal velocity components are represented as a sum of the depth means and deviations; the two corresponding subsystems are derived. For barotropic dynamics, the compressibility effect is represented as the boundary condition at the free surface, while for the baroclinic subsystem, it is introduced as ε-regularization of the continuity equation. Then, the baroclinic equations are split into two subsystems describing the hydrostatic and nonhydrostatic dynamics. The nonhydrostatic dynamics is computed at a separate splitting stage. The algorithm is included into the Institute of Numerical Mathematics of the Russian Academy of Sciences model based on “primitive” equations and verified by solving the hydrodynamics problem for the Sea of Marmara.