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.     

An OSSE Study for Deep Argo Array using the GFDL Ensemble Coupled Data Assimilation System

An observing system simulation experiment (OSSE) using an ensemble coupled data assimilation system was designed to investigate the impact of deep ocean Argo profile assimilation in a biased numerical climate system. Based on the modern Argo observational array and an artificial extension to full depth, “observations” drawn from one coupled general circulation model (CM2.0) were assimilated into another model (CM2.1). Our results showed that coupled data assimilation with simultaneous atmospheric and oceanic constraints plays a significant role in preventing deep ocean drift. However, the extension of the Argo array to full depth did not significantly improve the quality of the oceanic climate estimation within the bias magnitude in the twin experiment. Even in the “identical” twin experiment for the deep Argo array from the same model (CM2.1) with the assimilation model, no significant changes were shown in the deep ocean, such as in the Atlantic meridional overturning circulation and the Antarctic bottom water cell. The small ensemble spread and corresponding weak constraints by the deep Argo profiles with medium spatial and temporal resolution may explain why the deep Argo profiles did not improve the deep ocean features in the assimilation system. Additional studies using different assimilation methods with improved spatial and temporal resolution of the deep Argo array are necessary in order to more thoroughly understand the impact of the deep Argo array on the assimilation system.     

基于ROMS和4DVAR的沿轨与网格化SSH数据同化效果评价

Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height(SSH) product are employed in the assimilation, including the gridded products from AVISO and the original along-track observations used in the generation. To explore their impact on the assimilation results, an experiment focus on the South China Sea(SCS) is conducted based on the Regional Ocean Modeling System(ROMS) and the four-dimensional variational data assimilation(4 DVAR) technology. The comparison with EN4 data set and Argo profile indicates that, the along-track SSH assimilation result presents to be more accurate than the gridded SSH assimilation, because some noises may have been introduced in the merging process. Moreover, the mesoscale eddy detection capability of the assimilation results is analyzed by a vector geometry–based algorithm. It is verified that, the assimilation of the gridded SSH shows superiority in describing the eddy's characteristics, since the complete structure of the ocean surface has been reconstructed by the original data merging.     

Variational data analysis with control of the forecast bias

We propose a methodology for the treatment of the systematic model error in variational data assimilation. The principle of the method is to add a systematic error correction term in the model equations and to include it in the variational assimilation control vector.
This method is applied to a simplified ocean circulation model in an identical twin experiment framework. It shows a noticeable improvement compared to the result of a classical variational assimilation scheme in which the systematic error is not corrected. The estimated systematic error correction term is sufficiently consistent with that needed by the model that it allows improvements not just to the analysis, but also during the forecast phase.     

The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part I - System overview and formulation

The Regional Ocean Modeling System (ROMS) is one of the few community ocean general circulation models for which a 4-dimensional variational data assimilation (4D-Var) capability has been developed. The ROMS 4D-Var capability is unique in that three variants of 4D-Var are supported: a primal formulation of incremental strong constraint 4D-Var (I4D-Var), a dual formulation based on a physical-space statistical analysis system (4D-PSAS), and a dual formulation representer-based variant of 4D-Var (R4D-Var). In each case, ROMS is used in conjunction with available observations to identify a best estimate of the ocean circulation based on a set of a priori hypotheses about errors in the initial conditions, boundary conditions, surface forcing, and errors in the model in the case of 4D-PSAS and R4D-Var. In the primal formulation of I4D-Var the search for the best circulation estimate is performed in the full space of the model control vector, while for the dual formulations of 4D-PSAS and R4D-Var only the sub-space of linear functions of the model state vector spanned by the observations (i.e. the dual space) is searched. In oceanographic applications, the number of observations is typically much less than the dimension of the model control vector, so there are clear advantages to limiting the search to the space spanned by the observations. In the case of 4D-PSAS and R4D-Var, the strong constraint assumption (i.e. that the model is error free) can be relaxed leading to the so-called weak constraint formulation. This paper describes the three aforementioned variants of 4D-Var as they are implemented in ROMS. Critical components that are common to each approach are conjugate gradient descent, preconditioning, and error covariance models, which are also described. Finally, several powerful 4D-Var diagnostic tools are discussed, namely computation of posterior errors, eigenvector analysis of the posterior error covariance, observation impact, and observation sensitivity.     

Assimilation of altimetry data in the numerical model of the circulation in the Black Sea: The model numerical experiments

The numerical algorithm of the Kalman optimum filtration generalized for the case of three-dimensional fields and a multicomponent vector of the ocean state, with level measurements discrete over space and time being available, is given. The results of model numerical experiments on the assimilation of data on the Black Sea level are given. An attempt to estimate the effect of the time interval of data input on the results of field reconstruction was made.Translated by Mikhail M. Trufanov.     

Coupling a two-way nested primitive equation model and a statistical SST predictor of the Ligurian Sea via data assimilation

A primitive equation model and a statistical predictor are coupled by data assimilation in order to combine the strength of both approaches. In this work, the system of two-way nested models centred in the Ligurian Sea and the satellite-based ocean forecasting (SOFT) system predicting the sea surface temperature (SST) are used. The data assimilation scheme is a simplified reduced order Kalman filter based on a constant error space. The assimilation of predicted SST improves the forecast of the hydrodynamic model compared to the forecast obtained by assimilating past SST observations used by the statistical predictor. This study shows that the SST of the SOFT predictor can be used to correct atmospheric heat fluxes. Traditionally this is done by relaxing the model SST towards the climatological SST. Therefore, the assimilation of SOFT SST and climatological SST are also compared.     

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.     

基于竞争遗传算法的海洋云平台资源调度模型研究

高质量的海洋自然资源管理离不开数据和信息的支撑。鉴于海洋数据的特殊性，海洋数据处理常涉及长时间序列或大空间范围的处理工作，对于此类密集型计算为主的数据处理，通用型云平台存在效率不高的突出问题。文章在全面分析Hadoop平台原生资源调度算法的基础上，结合海洋数据处理密集型计算的特点，创新性地提出了基于竞争模型的遗传算法任务调度策略(CGA),有效地解决了遗传算法求解速度受初始化种群与种群进化测量影响较大的问题。此外，为加快收敛速度，引入竞争机制，构建基于种群竞争的自适应进化模型。通过实际验证和比对，证明改进后的算法在收敛速度及收敛结果的稳定性上都优于传统算法，有效地改进了海洋云平台资源调度的能力，提升了海洋数据的处理效率。     

特征线计算格式下共轭方程两种导出途径的比较

共轭方程的导出是建立资料同化模型的关键，其导出方式有两种途径：AFD形式与FDA形式。在特征线计算格式基础上针对一类较广泛海洋动力控制方程分析了其两种共轭方程（AFD形式与FDA形式）之间的关系，并将理论结果应用于波谱共轭方程的讨论。     

A diagnostic stabilized finite-element ocean circulation model

A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuška–Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity–pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars.The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets.     

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.     

Optimal control of salinity boundary condition in a tidal model using a variational inverse method

A variational inverse data assimilation scheme is developed to estimate the salinity boundary conditions in a three-dimensional tidal hydrodynamic and salinity transport model. In this paper, the maximum incoming salinity value and the recovery time from the outflow salinity to the maximum incoming salinity at model open boundaries are treated as poorly known model control variables, and estimated using a variational inverse data assimilation scheme. The variational inverse model is tested in an idealized estuary using identical twin experiments, in which observed data are generated from the same model. Model tests with different initial guesses of the model control variables are conducted to evaluate the capability of the inverse model. A penalty technique is used to eliminate oscillations in the solution during the minimization process. The effects of preconditioning and penalty terms on the convergence rate are investigated. Model results demonstrate that the variational inverse model can be used to efficiently determine the optimal salinity open boundary conditions and improve the model state when there are no observed data available to specify the proper salinity open boundary conditions in a tidal model.     

大气-海洋-海浪耦合同化模式在台风过程模拟中的应用

基于MCT耦合器,利用中尺度大气模型WRF、海洋模型FVCOM和第三代海浪模型SWAN,实现大气、海洋和海浪的三者实时耦合计算,同时采用卫星微波辐射资料AMSU-A,通过WRF大气模式的资料同化模块WRFDA,实现对风场模拟的连续同化,从而建立起大气-海洋-海浪耦合与卫星数据同化的W-F-S-A耦合同化模式。将该模型应用于2014年台风“威马逊”的数值模拟,并与其他模型进行比较。结果表明,W-F-S-A耦合同化模式对于台风路径和风速的模拟结果优于单独耦合和单独同化结果,并且可以较好地模拟上层海洋对台风的响应特征。     

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.     

Numerical solution to the problem of variational assimilation of operational observational data on the ocean surface temperature

The problem of variational assimilation of satellite observational data on the ocean surface temperature is formulated and numerically investigated in order to reconstruct surface heat fluxes with the use of the global three-dimensional model of ocean hydrothermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), and observational data close to the data actually observed in specified time intervals. The algorithms of the numerical solution to the problem are elaborated and substantiated, and the data assimilation block is developed and incorporated into the global three-dimensional model. Numerical experiments are carried out with the use of the Indian Ocean water area as an example. The data on the ocean surface temperature over the year 2000 are used as observational data. Numerical experiments confirm the theoretical conclusions obtained and demonstrate the expediency of combining the model with a block of assimilating operational observational data on the surface temperature.     

Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar)

I present the derivation of the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar), which is developed for adopting a non-diagonal background error covariance matrix in nonlinear variational analyses (i.e., analyses employing a non-quadratic cost function). POpULar is based on the idea of a linear preconditioned conjugate gradient method widely adopted in ocean data assimilation systems. POpULar uses the background error covariance matrix as a preconditioner without any decomposition of the matrix. This preconditioning accelerates the convergence. Moreover, the inverse of the matrix is not required. POpULar therefore allows us easily to handle the correlations among deviations of control variables (i.e., the variables which will be analyzed) from their background in nonlinear problems. In order to demonstrate the usefulness of POpULar, we illustrate two effects which are often neglected in studies of ocean data assimilation before. One is the effect of correlations among the deviations of control variables in an adjoint analysis. The other is the nonlinear effect of sea surface dynamic height calculation required when sea surface height observation is employed in a three-dimensional ocean analysis. As the results, these effects are not so small to neglect.     

A comparison of sequential assimilation schemes for ocean prediction with the HYbrid Coordinate Ocean Model (HYCOM): Twin experiments with static forecast error covariances

We assess and compare four sequential data assimilation methods developed for HYCOM in an identical twin experiment framework. The methods considered are Multi-variate Optimal Interpolation (MVOI), Ensemble Optimal Interpolation (EnOI), the fixed basis version of the Singular Evolutive Extended Kalman Filter (SEEK) and the Ensemble Reduced Order Information Filter (EnROIF). All methods can be classified as statistical interpolation but differ mainly in how the forecast error covariances are modeled. Surface elevation and temperature data sampled from an 1/12° Gulf of Mexico HYCOM simulation designated as the truth are assimilated into an identical model starting from an erroneous initial state, and convergence of assimilative runs towards the truth is tracked. Sensitivity experiments are first performed to evaluate the impact of practical implementation choices such as the state vector structure, initialization procedures, correlation scales, covariance rank and details of handling multivariate datasets, and to identify an effective configuration for each assimilation method. The performance of the methods are then compared by examining the relative convergence of the assimilative runs towards the truth. All four methods show good skill and are able to enhance consistency between the assimilative and truth runs in both observed and unobserved model variables. Prediction errors in observed variables are typically less than the errors specified for the observations, and the differences between the assimilated products are small compared to the observation errors. For unobserved variables, RMS errors are reduced by 50% relative to a non-assimilative run and differ between schemes on average by about 5%. Dynamical consistency between the updated state space variables in the data assimilation algorithm, and the data adequately sampling significant dynamical features are the two crucial components for reliable predictions. The experiments presented here suggest that practical implementation details can have at least as much an impact on the accuracy of the assimilated product as the choice of assimilation technique itself. We also present a discussion of the numerical implementation and the computational requirements for the use of these methods in large scale applications.     

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.