Problems of variational assimilation of observational data for ocean general circulation models and methods for their solution

Problems of the variational assimilation of satellite observational data on the temperature and level of the ocean surface, as well as data on the temperature and salinity of the ocean from the ARGO system of buoys, are formulated with the use of the global three-dimensional model of ocean thermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). Algorithms for numerical solutions of the problems are developed and substantiated, and data assimilation blocks are developed and incorporated into the global three-dimensional model. Numerical experiments are performed with the use of the Indian Ocean or the entire World Ocean as examples. These numerical experiments support the theoretical conclusions and demonstrate that the use of a model with an assimilation block of operational observational data is expedient.     

中国海及邻近海域卫星观测资料同化试验

利用1个基于POMgcs海洋模式和多重网格三维变分同化方法建立的中国海及邻近海域海面高与三维温盐流数值预报模型,通过一系列数值试验,研究了同化卫星测高和卫星遥感海面温度观测资料对该模型预报能力的影响。试验结果表明,同化卫星测高资料可明显改善海面高度与三维温度和盐度的分析预报效果,使1 200 m以上的温度预报误差减小0.16℃,并能有效提高对海洋中尺度现象的预报能力;同化卫星遥感海面温度对100 m以上的温度和盐度的预报效果有所改善,可使海面温度的预报误差减小10%。     

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.     

A reduced-dynamics variational approach for the assimilation of altimeter data into eddy-resolving ocean models

A new method of assimilating sea surface height (SSH) data into ocean models is introduced and tested. Many features observable by satellite altimetry are approximated by the first baroclinic mode over much of the ocean, especially in the lower (but non-equatorial) and mid latitude regions. Based on this dynamical trait, a reduced-dynamics adjoint technique is developed and implemented with a three-dimensional model using vertical normal mode decomposition. To reduce the complexity of the variational data assimilation problem, the adjoint equations are based on a one-active-layer reduced-gravity model, which approximates the first baroclinic mode, as opposed to the full three-dimensional model equations. The reduced dimensionality of the adjoint model leads to lower computational cost than a traditional variational data assimilation algorithm. The technique is applicable to regions of the ocean where the SSH variability is dominated by the first baroclinic mode. The adjustment of the first baroclinic mode model fields dynamically transfers the SSH information to the deep ocean layers. The technique is developed in a modular fashion that can be readily implemented with many three-dimensional ocean models. For this study, the method is tested with the Navy Coastal Ocean Model (NCOM) configured to simulate the Gulf of Mexico.     

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.     

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.     

Impact of Ocean Mean Dynamic Topography on Satellite Data Assimilation

The response of an eddy-permitting ocean model to changes imposed by the use of different mean dynamic topographies (MDT) is analyzed in a multivariate assimilation context, allowing the evaluation of this impact, not only on the surface circulation, but also on the interior ocean representation. The assimilation scheme is a reduced-order sequential Kalman filter (SEEK). In a first set of experiments, high resolution sea surface temperature, along-track sea surface height and sea surface salinity from climatology are assimilated into a 1/3° resolution North and Tropical Atlantic version of the HYCOM model. In a second experiment, in situ profile data are assimilated in addition to the surface measurements.

The first set of experiments illustrates that important differences in the representation of the horizontal model circulation pattern are related to differences in the MDT used. The objective of assimilation is to improve the representation of the 3D ocean state. However, the imperfect representation of the mean dynamic topography appears to be an important limiting factor with regard to the degree of realism obtained in the simulated flow.

Vertical temperature and salinity profiles are key observations to drive a general circulation ocean model toward a more realistic state. The second set of experiments shows that assimilating them in addition to sea surface measurements is a far from trivial exercise. A specific difficulty is due to inconsistencies between the dynamic topography diagnosed from in situ observations and that diagnosed from sea surface height. These two fields obtained from different data sources do not contain exactly the same information. In order to overcome this difficulty, a strategy is proposed and validated.     

Impact of Ocean Mean Dynamic Topography on Satellite Data Assimilation

The response of an eddy-permitting ocean model to changes imposed by the use of different mean dynamic topographies (MDT) is analyzed in a multivariate assimilation context, allowing the evaluation of this impact, not only on the surface circulation, but also on the interior ocean representation. The assimilation scheme is a reduced-order sequential Kalman filter (SEEK). In a first set of experiments, high resolution sea surface temperature, along-track sea surface height and sea surface salinity from climatology are assimilated into a 1/3° resolution North and Tropical Atlantic version of the HYCOM model. In a second experiment, in situ profile data are assimilated in addition to the surface measurements.

The first set of experiments illustrates that important differences in the representation of the horizontal model circulation pattern are related to differences in the MDT used. The objective of assimilation is to improve the representation of the 3D ocean state. However, the imperfect representation of the mean dynamic topography appears to be an important limiting factor with regard to the degree of realism obtained in the simulated flow.

Vertical temperature and salinity profiles are key observations to drive a general circulation ocean model toward a more realistic state. The second set of experiments shows that assimilating them in addition to sea surface measurements is a far from trivial exercise. A specific difficulty is due to inconsistencies between the dynamic topography diagnosed from in situ observations and that diagnosed from sea surface height. These two fields obtained from different data sources do not contain exactly the same information. In order to overcome this difficulty, a strategy is proposed and validated.     

Oceanographic and sound speed fields for the ESME workbench

The authors describe the effort to provide three-dimensional global thermohaline and sound speed fields for use in the effects of sound in the marine environment (ESME) workbench suite of programs. The primary fields used are from the modular ocean data assimilation system (MODAS), developed by Fox et al. The system provides global thermohaline and sound speed fields on a daily basis using environmental inputs from the U.S. Navy as well as remote sensing of sea surface temperature and sea surface height. To examine the MODAS fields, the authors also used data from the Southern California Bight collected by the California Cooperative Fisheries Investigations as well as high-resolution hydrographic data collected over the continental shelf south of New England as part of the shelfbreak PRIMER experiment. MODAS performs well for features such as large-scale boundary currents and eddies but is more limited in resolving features such as shelfbreak and coastal fronts, which have small spatial and temporal correlation scales. Because of the considerable computational needs of other ESME modules and its use as a planning tool, the authors present a pragmatic approach for future applications.     

利用资料同化方法优化观测系统的空间布局:以泰国湾为例

海洋观测费用高昂，设计科学高效的观测系统可以充分发挥观测的效能。本文以泰国湾高频地波雷达观测系统为例，利用数据同化方法对观测系统进行了最优布局。首先基于FVCOM海洋数值模式建立了泰国湾海域高分辨率三维斜压水动力模式，在此基础上利用一种改进的高效集合卡曼滤波同化方法对岸基高频地波雷达表层海流观测系统开展观测效能评估数值实验。通过观测区域的不同组合方式将3个区域的雷达表层海流数据同化到数值模式中，实验结果表明，岸基高频地波雷达表层海流观测系统可有效降低高分辨数值模式的海流模拟误差。但不同观测区域的组合提供的观测数据对改善海流模拟的作用存在明显差别，泰国湾现有观测系统雷达站位布设方式应进一步优化。本文最后给出了研究区域最优观测站位的布局方案，可作为下一步观测系统进行布局调整的指导。     

表面波浪对海洋上层混合的作用

A new three-dimensional numerical model is derived through a wave average on the primitive N-S equations, in which both the＂Coriolis-Stokes forcing＂ and the＂Stokes-Vortex force＂ are considered. Three ideal experiments are run using the new model applied to the Princeton ocean model （POM）. Numerical results show that surface waves play an important role on the mixing of the upper ocean. The mixed layer is enhanced when wave effect is considered in conjunction with small Langmuir numbers. Both surface wave breaking and Stokes production can strengthen the turbulent mixing near the surface. However, the influence of wave breaking is limited to a thin layer, but Stokes drift can affect the whole mixed layer. Furthermore, the vertical mixing coefficients clearly rise in the mixed layer, and the upper ocean mixed layer is deepened especially in the Antarctic Circumpolar Current when the model is applied to global simulations. It indicates that the surface gravity waves are indispensable in enhancing the mixing in the upper ocean, and should be accounted for in ocean general circulation models.     

An experimenal analysis for the impact of 2D variation assimilation of satellite data on typhoon track simulation

A series of test simulations are performed to evaluate the impact of satellite-derived meteorological data on numerical typhoon track prediction. Geostationary meteorological satellite (GMS-5) and NOAA‘s TIROS operational vertical sounder (TOVS) observations are used in the experiments. A twodimensional variation assimilation scheme is developed to assimilate the satellite data directly into the Penn State-NCAR nonhydrostatic meteorological model (MM5). Three-dimensional objective analyses fields based on T213 results and routine observations are employed as the background fields of the initialization. The comparisons of the simulated typhoon tracks are also carried out, which correspond respectively to the initialization scheme with two-dimensional variation (2D- Var), three-dimensional observational nudging and direct assimilation of satellite data. It is found that, comparing with the experiments without satellite data assimilation, the first two assimilation schemes lead to significant improvements on typhoon track prediction. Track errors reduce by 18% at 12 h for 2D- Var and from about 16% at 24 h to about 35% at 48 h for observational nudging. The simulated results based on assimilating different kinds of satellite data are also compared.     

4DVAR Data Assimilation with the Regional Ocean Modeling System (ROMS): Impact on the Water Mass Distributions in the Yellow Sea

In this study, we evaluate the performance of the recently developed incremental strong constraint 4-dimensional variational (4DVAR) data assimilation applied to the Yellow Sea (YS) using the Regional Ocean Modeling System (ROMS). Two assimilation experiments are compared: assimilating remote-sensed sea surface temperature (SST) and both the SST and in-situ profiles measured by shipboard CTD casts into a regional ocean modeling from January to December of 2011. By comparing the two assimilation experiments against a free-run without data assimilation, we investigate how the assimilation affects the hydrographic structures in the YS. Results indicate that the SST assimilation notably improves the model behavior at the surface when compared to the non-assimilative free-run. The SST assimilation also has an impact on the subsurface water structure in the eastern YS; however, the improvement is seasonally dependent, that is, the correction becomes more effective in winter than in summer. This is due to a strong stratification in summer that prevents the assimilation of SST from affecting the subsurface temperature. A significant improvement to the subsurface temperature is made when the in-situ profiles of temperature and salinity are assimilated, forming a tongue-shaped YS bottom cold water from the YS toward the southwestern seas of Jeju Island.     

An ocean data assimilation system and reanalysis of the World Ocean hydrophysical fields

A new version of the ocean data assimilation system (ODAS) developed at the Hydrometcentre of Russia is presented. The assimilation is performed following the sequential scheme analysis–forecast–analysis. The main components of the ODAS are procedures for operational observation data processing, a variational analysis scheme, and an ocean general circulation model used to estimate the first guess fields involved in the analysis. In situ observations of temperature and salinity in the upper 1400-m ocean layer obtained from various observational platforms are used as input data. In the new ODAS version, the horizontal resolution of the assimilating model and of the output products is increased, the previous 2D-Var analysis scheme is replaced by a more general 3D-Var scheme, and a more flexible incremental analysis updating procedure is introduced to correct the model calculations. A reanalysis of the main World Ocean hydrophysical fields over the 2005–2015 period has been performed using the updated ODAS. The reanalysis results are compared with data from independent sources.     

Upper Ocean Four-Dimensional Variational Data Assimilation in the Arabian Sea and Bay of Bengal

A regional ocean circulation model with four-dimensional variational data assimilation scheme is configured to study the ocean state of the Indian Ocean region (65°E–95°E; 5°N–20°N) covering the Arabian Sea (AS) and Bay of Bengal (BoB). The state estimation setup uses 10 km horizontal resolution and 5 m vertical resolution in the upper ocean. The in-situ temperature and salinity, satellite-derived observations of sea surface height, and blended (in-situ and satellite-derived) observations of sea surface temperature alongwith their associated uncertainties are used for data assimilation with the regionally configured ocean model. The ocean state estimation is carried out for 61 days (1 June to 31 July 2013). The assimilated fields are closer to observations compared to other global state estimates. The mixed layer depth (MLD) of the region shows deepening during the period of assimilation with AS showing higher MLD compared to the BoB. An empirical forecast equation is derived for the prediction of MLD using the air–sea forcing variables as predictors. The surface and sub-surface (50 m) heat and salt budget tendencies of the region are also investigated. It is found that at the sub-surface, only the advection and diffusion temperature and salt tendencies are important.     

OSTIA数据在中国近海业务化环流模型中的同化应用

The prediction of sea surface temperature(SST) is an essential task for an operational ocean circulation model. A sea surface heat flux, an initial temperature field, and boundary conditions directly affect the accuracy of a SST simulation. Here two quick and convenient data assimilation methods are employed to improve the SST simulation in the domain of the Bohai Sea, the Yellow Sea and the East China Sea(BYECS). One is based on a surface net heat flux correction, named as Qcorrection(QC), which nudges the flux correction to the model equation; the other is ensemble optimal interpolation(En OI), which optimizes the model initial field. Based on such two methods, the SST data obtained from the operational SST and sea ice analysis(OSTIA) system are assimilated into an operational circulation model for the coastal seas of China. The results of the simulated SST based on four experiments, in 2011, have been analyzed. By comparing with the OSTIA SST, the domain averaged root mean square error(RMSE) of the four experiments is 1.74, 1.16, 1.30 and 0.91°C, respectively; the improvements of assimilation experiments Exps 2, 3 and 4 are about 33.3%, 25.3%, and 47.7%, respectively.Although both two methods are effective in assimilating the SST, the En OI shows more advantages than the QC,and the best result is achieved when the two methods are combined. Comparing with the observational data from coastal buoy stations, show that assimilating the high-resolution satellite SST products can effectively improve the SST prediction skill in coastal regions.     

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.     

基于神经网络的全球三维温盐场重构技术研究

文章利用果蝇优化广义回归神经网络算法FOAGRNN (fruit fly optimization algorithm, FOA; generalized regression neural network, GRNN)对SODA (simple ocean data assimilation)再分析数据进行训练, 构建海表温度、盐度、海面高度与次表层温盐场之间的投影关系模型, 并在全球范围使用SODA和卫星遥感数据评估了模型的应用性能。首先, 利用独立的2016年SODA海表数据作为模型输入进行理想重构试验, 结果显示全球重构温、盐平均均方根误差(MRMSE)分别为0.36℃和0.08‰, 与世界海洋图集WOA13资料相比减小约50%和60%。然后, 利用卫星观测的海表信息作为模型输入进行实际应用试验, 并与Argo观测剖面进行比较评估。试验结果表明, 重构模型能有效表征海水温、盐特征, 其中重构温、盐MRMSE分别为0.79℃和0.16‰, 相比WOA气候态减小27%和11%。误差的垂向分布显示, 重构温度RMSE从海表向下迅速增大, 至100m达到峰值1.35℃, 而后又迅速回落,至250m处为0.81℃, 跃层往下不断减小; 重构盐度RMSE基本随深度增大而减小, 误差峰值位于25m附近, 约为0.25‰。此外, Argo浮标跟踪分析和区域水团统计结果也表明模型能够较好地刻画海洋三维温盐场的内部结构特征。     

A singular evolutive extended Kalman filter to assimilate ocean color data in a coupled physical–biochemical model of the North Atlantic ocean

Within the European DIADEM project, a data assimilation system for coupled ocean circulation and marine ecosystem models has been implemented for the North Atlantic and the Nordic Seas. One objective of this project is to demonstrate the relevance of sophisticated methods to assimilate satellite data such as altimetry, surface temperature and ocean color, into realistic ocean models. In this paper, the singular evolutive extended Kalman (SEEK) filter, which is an advanced assimilation scheme where three-dimensional, multivariate error statistics are taken into account, is used to assimilate ocean color data into the biological component of the coupled system. The marine ecosystem model, derived from the FDM model [J. Mar. Res. 48 (1990) 591], includes 11 nitrogen and carbon compartments and describes the synthesis of organic matter in the euphotic zone, its consumption by animals of upper trophic levels, and the recycling of detritic material in the deep ocean. The circulation model coupled to the ecosystem is the Miami isopycnic coordinate ocean model (MICOM), which covers the Atlantic and the Arctic Oceans with an enhanced resolution in the North Atlantic basin. The model is forced with realistic ECMWF ocean/atmosphere fluxes, which permits to resolve the seasonal variability of the circulation and mixed layer properties. In the twin assimimation experiments reported here, the predictions of the coupled model are corrected every 10 days using pseudo-measurements of surface phytoplankton as a substitute to chlorophyll concentrations measured from space. The diagnostics of these experiments indicate that the assimilation is feasible with a reduced-order Kalman filter of small rank (of order 10) as long as a sufficiently good identification of the error structure is available. In addition, the control of non-observed quantities such as zooplankton and nitrate concentrations is made possible, owing to the multivariate nature of the analysis scheme. However, a too severe truncation of the error sub-space downgrades the propagation of surface information below the mixed layer. The reduction of the actual state vector to the surface layers is therefore investigated to improve the estimation process in the perspective of sea-viewing wide field-of-view sensor (SeaWiFS) data assimilation experiments.