Improving assimilation of SeaWiFS data by the application of bias correction with a local SEIK filter

Ocean-biogeochemical models show typically significant errors in the representation of chlorophyll concentrations. The model state can be improved by the assimilation of satellite chlorophyll data with algorithms based on the Kalman filter. However, these algorithms do usually not account for the possibility that the model prediction contains systematic errors in the form of model bias. Accounting explicitly for model biases can improve the assimilation performance. To study the effect of bias estimation on the estimation of surface chlorophyll concentrations, chlorophyll data from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) are assimilated on a daily basis into the NASA Ocean Biogeochemical Model (NOBM). The assimilation is performed by the ensemble-based SEIK filter combined with an online bias correction scheme. The SEIK filter is simplified here by the use of a static error covariance matrix. The performance of the filter algorithm is assessed by comparison with independent in situ data over the 7-year period 1998–2004. The bias correction results in significant improvements of the surface chlorophyll concentrations compared to the assimilation without bias estimation. With bias estimation, the daily surface chlorophyll estimates from the assimilation show about 3.3% lower error than SeaWiFS data. In contrast, the error in the global surface chlorophyll estimate without bias estimation is 10.9% larger than the error of SeaWiFS data.     

Validation of a hybrid optimal interpolation and Kalman filter scheme for sea surface temperature assimilation

A hybrid data assimilation scheme designed for operational assimilation of satellite sea surface temperatures (SST) into an ocean model has been developed and validated against in-situ observations. The scheme consists of an optimal interpolation (OI) part and a greatly simplified Kalman filter (KF) part.The OI is performed only in the longitudinal and latitudinal directions. A climatological field is used as a background field for the interpolation. It is constructed by fitting daily averages of satellite SST to the annual mean, annual, and semiannual harmonics in a 20 km by 20 km grid. The background error covariance is approximated by a spatially varying two-dimensional exponential covariance model. The parameters of the covariance model are fitted to the deviations of the satellite data from the background field using data from a full year.The simplified KF uses ocean model forecasts as a background field. It is based on the assumption that it is possible to neglect horizontal SST covariances in the filter and that the typical time scale for vertical mixing in the mixed layer is much shorter than the average time between observations. We therefore assume that the error variance in a column of water is evenly spread out throughout the mixed layer. The result of these simplifications is a computationally very efficient KF.A one year validation of the scheme is performed for year 2001 using an operational eddy resolving ocean model covering the North Sea and the Baltic Sea. It is found that assimilation of sea surface temperature data reduces the model root mean square error from 1.13 °C to 0.70 °C. The hybrid scheme is found to reduce the root mean square error slightly more than the simplified KF without OI to 0.66 °C. The inclusion of spatially varying satellite error variances does not improve the performance of the scheme significantly.     

Assimilation of buoy and satellite data in wave forecasts with integral control variables

The quality of numerical wave forecasts can be improved significantly by assimilating wave observations prior to the forecast. In the present study a technique for such assimilation is developed that exploits (a) the efficiency of a limited number of integral control variables, and (b) the effectiveness of variational (model-consistent) assimilation. The formal procedure is independent of the type of control variables and of the wave model (moreover, no adjoint wave model is required). In the present study, integral control variables are chosen to represent large-scale errors in the driving wind fields and uncertainties in the wave model. The assimilation technique is validated with observations of the ERS-1 satellite altimeter and two waverider buoys in two consecutive storms in the Norwegian Sea. The assimilation of the observations reduced the errors in the forecasted significant wave height at the buoy locations typically from 25% to 12%. For low-frequency waves the effect of the assimilation is similarly significant at one buoy location but marginal at the other buoy location.     

Data assimilation with the Ensemble Kalman Filter and the SEIK filter applied to a finite element model of the North Atlantic

Currently there are different approaches to filter algorithms based on the Kalman filter. One of the most used filter algorithms is the Ensemble Kalman Filter (EnKF). It uses a Monte Carlo approach to the filtering problem. Another approach is given by the Singular Evolutive Extended Kalman (SEEK) and Singular Evolutive Interpolated Kalman (SEIK) filters. These filters operate explicitly on a low-dimensional error space which is represented by an ensemble of model states. The EnKF and the SEIK filter have been implemented within a parallel data assimilation framework in the Finite Element Ocean Model FEOM. In order to compare the filter performances of the algorithms, several data assimilation experiments are performed. The filter algorithms have been applied with a model configuration of FEOM for the North Atlantic to assimilate the sea surface height in twin experiments. The dependence of the filter estimates on the represented error subspace is discussed. In the experiments the SEIK algorithm provides better estimates than the EnKF. Furthermore, the SEIK filter is much cheaper in terms of computing time.     

Assimilation of altimetric data in the mid-latitude oceans using the Singular Evolutive Extended Kalman filter with an eddy-resolving, primitive equation model

A new data assimilation scheme has been elaborated for ocean circulation models based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial error covariance matrix as a truncated series of orthogonal perturbations. This error sub-space evolves during the assimilation so as to capture the growing modes of the estimation error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filter considers a time-independent error sub-space, the apprentice filter progressively enriches the error sub-space with the information learned from the innovation vector after each analysis step, and the dynamical filter updates the error sub-space according to the model dynamics. The SEEK filter has been implemented to assimilate synthetic observations of the surface topography in a non-linear, primitive equation model that uses density as vertical coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a resolution of 20 km in the horizontal, and 4 levels in the vertical. The concept of twin experiments is used to demonstrate that the conventional SEEK filter must be complemented by a learning mechanism in order to model the misrepresented tail of the error covariance matrix. An approach based on the vertical physics of the isopycnal model, is shown particularly robust to control the velocity field in deep layers with surface observations only. The cost of the method makes it a suitable candidate for large-size assimilation problems and operational applications.     

Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: Twin experiments and real in-situ data assimilation

The Singular Evolutive Extended Kalman (SEEK) filter has been implemented to assimilate in-situ data in a 1D coupled physical-ecosystem model of the Ligurian Sea. The biogeochemical model describes the partly decoupled nitrogen and carbon cycles of the pelagic food web. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The data assimilation scheme (SEEK filter) parameterizes the error statistics by means of a set of empirical orthogonal functions (EOFs). Twin experiments are first performed with the aim to choose the suitable experimental protocol (observation and estimation vectors, number of EOFs, frequency of the assimilation,…) and to assess the SEEK filter performances. This protocol is then applied to perform real data assimilation experiments using the DYFAMED data base. By assimilating phytoplankton observations, the method has allowed to improve not only the representation of the phytoplankton community, but also of other variables such as zooplankton and bacteria that evolve with model dynamics and that are not corrected by the data assimilation scheme. The validation of the assimilation method and the improvement of model results are studied by means of suitable error measurements.     

The estimation of wave elevation and wave disturbance caused by the wave orbital motion of a fully submerged hydrofoil craft

The current control system of a fully submerged hydrofoil craft has manual input of fore-foil depth and control mode selection to improve the performance of the control system. However, the manual input needs skillful human operation and observation of waves the encountered to work well over a wide range of waves. In order to use information about the waves encountered in the control system, we considered the estimation of wave elevation and wave disturbance which was caused by the orbital motion of the waves in irregular waves. First, we investigated the wave disturbance by a fully submerged hydrofoil craft, in a state-space model of wave disturbance, and in hydrofoil craft motion, etc. We than considered estimations of the wave elevation and wave disturbance using a shaping filter, a Kalman filter, an autoregressive (AR) model, etc. Finally, we confirmed through simulations that the estimation results and estimation error of wave elevation and wave disturbance were valid.     

Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model

We consider the problem of combined state-parameter estimations in biased nonlinear models with non-Gaussian extensions of the Deterministic Ensemble Kalman Filter (DEnKF). We focus on the particular framework of ocean ecosystem models. Such models present important obstacles to the use of data assimilation methods based on Kalman filtering due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result.We present extensions of the DEnKF dealing with these difficulties by introducing a nonlinear change of variables (anamorphosis function) in order to execute the analysis step with Gaussian transformed variables and parameters. Several strategies to build the anamorphosis functions are investigated and compared within the framework of twin experiments realized in a simple 1D ocean ecosystem model. A solution to the problem of the specification of the observation error for transformed observations is suggested. The study highlights the inability of the plain DEnKF with a simple post-processing of the negative values to properly estimate parameters when constraints of positiveness apply to the variables. It goes on to show that the introduction of the Gaussian anamorphosis can remedy these assimilation biases.     

Comparison of robust H∞ filter and Kalman filter for initial alignment of inertial navigation system

There are many filtering methods that can be used for the initial alignment of an integrated inertial navigation system.This paper discussed the use of GPS,but focused on two kinds of filters for the initial alignment of an integrated strapdown inertial navigation system (SINS).One method is based on the Kalman filter (KF),and the other is based on the robust filter.Simulation results showed that the filter provides a quick transient response and a little more accurate estimate than KF,given substantial process noise or unknown noise statistics.So the robust filter is an effective and useful method for initial alignment of SINS.This research should make the use of SINS more popular,and is also a step for further research.     

Comparison of robust H∞ filter and Kalman filter for initial alignment of inertial navigation system

There are many filtering methods that can be used for the initial alignment of an integrated inertial navigation system. This paper discussed the use of GPS, but focused on two kinds of filters for the initial alignment of an integrated strapdown inertial navigation system (SINS). One method is based on the Kalman filter (KF), and the other is based on the robust filter. Simulation results showed that the filter provides a quick transient response and a little more accurate estimate than KF, given substantial process noise or unknown noise statistics. So the robust filter is an effective and useful method for initial alignment of SINS. This research should make the use of SINS more popular, and is also a step for further research.     

考虑舰体变形时的捷联惯性系统初始对准方法

为尽可能消除惯性测量组件（IMU）安装误差及挠曲变形对初始对准精度的影响，运用传递对准技术，建立系统方程和量测方程，采用扩展状态滤波器和速度加角速率匹配的方法，准确地估计出了这些误差，并对系统进行补偿。仿真结果表明，用速度加角速率匹配估计安装误差和挠曲变形比用速度加姿态匹配效果好，补偿了安装误差和挠曲变形后，系统的导航精度明显提高。     

Preoperational ocean forecasting in the southeastern Mediterranean Sea: Implementation and evaluation of the models and selection of the atmospheric forcing

Within the framework of several local and international programs, a quasi-operational ocean-forecasting system for the Southeastern Mediterranean Sea has been established and evaluated through a series of preoperational tests. The Princeton Ocean Model (POM) is used for simulating and predicting the hydrodynamics while the Wave Model (WAM) is used for predicting surface waves. Both models were set up to allow varying resolution and multiple nesting. In addition, POM was set up to be easily relocatable to allow rapid deployment of the model for any region of interest within the Mediterranean Sea. A common requirement for both models is the need for atmospheric forcing. Both models require time varying wind or wind stress. In addition, the hydrodynamic model requires initial conditions as well as time dependent surface heat fluxes, fresh water flux, and lateral boundary conditions at the open boundaries. Several sources of atmospheric forcing have been assessed based on their availability and their impact on the quality of the ocean models' forecasts. The various sources include operational forecast centers, other research centers, as well as running an in-house regional atmospheric model. For surface waves, higher spatial and temporal resolution of the winds plays a central role in improving the forecasts in terms of significant wave height and the timing of various high wave events. For the hydrodynamics, using the predicted wind stress and heat fluxes directly from an atmospheric model can potentially produce short range ocean forecasts that are nearly as good as hindcasts forced with gridded atmospheric analyses. Finally, a high-resolution, nested version of the model has shown to be stable under a variety of forcing conditions and time scales, thus indicating the robustness of the selected nesting strategy. For the southeastern corner of the Mediterranean, at forecast lead times of up to 4 days the high-resolution model shows improved skill over the coarser resolution driving model when compared to satellite derived sea surface temperatures. Most of the error appears to be due to the analysis error inherent in the initial conditions.     

Data assimilation into a Princeton Ocean Model of the Mediterranean Sea using advanced Kalman filters

This study investigates the effectiveness of the Singular Evolutive Extended Kalman filter (SEEK) and its variants (SEIK and SFEK filters) for data assimilation into a Princeton Ocean Model (POM) of the Mediterranean Sea. The SEEK filters are sub-optimal Kalman filters based on the approximation of the filter's error covariance matrices by singular low-rank matrices, reducing in this way extensive computational burden. At the initialization, the filters error covariance matrix is parameterized by a set of multivariate empirical orthogonal functions (EOFs) which describe the dominant modes of the system's variability. The Mediterranean model is implemented on a 1/4° × 1/4° horizontal grid with 25 sigma levels and is forced with 6-hour ECMWF re-analysis atmospheric data. Several twin experiments, in which pseudo-observations of altimetric data and/or data profiles were assimilated, were first performed to evaluate the filters performances and to study their sensitivities to different parameters and setups. The results of these experiments were very encouraging and helped in setting up an effective configuration for the assimilation of real data in near-real time situation. In the hindcast experiments, Topex/Poseidon and ERS weekly sea level anomaly data were first assimilated during 1993 and the filters solution was evaluated against independent Reynolds sea surface temperature (SST) analysis. The assimilation system was able to significantly enhance the consistency between the model and the assimilated data, although the improvement with respect to independent SST data was significantly less pronounced. The model SST was only improved after including SST data in the assimilation system.     

Comparison of robust H<Subscript>∞</Subscript> filter and Kalman filter for initial alignment of inertial navigation system

There are many filtering methods that can be used for the initial alignment of an integrated inertial navigation system. This paper discussed the use of GPS, but focused on two kinds of filters for the initial alignment of an integrated strapdown inertial navigation system （SINS）. One method is based on the Kalman filter （KF）, and the other is based on the robust filter. Simulation results showed that the filter provides a quick transient response and a little more accurate estimate than KF, given substantial process noise or unknown noise statistics. So the robust filter is an effective and useful method for initial alignment of SINS. This research should make the use of SINS more popular, and is also a step for further research.     

基于单水听器的移动声源运动参数估计

文章基于水声信道的多途结构,提出了一种利用舰船辐射噪声的单水听器声源运动参数估计方法。首先分析了自相关和倒谱多途时延估计方法,并针对传播水槽实验中随声源与单水听器距离增加自相关和倒谱时延峰信干比降低的问题,提出了基于自相关和倒谱的联合估计方法,提高了多途时延估计的稳健性;其次针对如何利用估计出的D-SR时延差这唯一信息进行运动参数估计的问题,通过逐步分析说明了径向匀速直线移动声源的运动参数估计问题可以在卡尔曼滤波(Kalman filter,KF)框架下进行求解;最后应用扩展卡尔曼滤波(extended Kalman filter,EKF)和迭代扩展卡尔曼滤波(iterated extended Kalman filter,IEKF)对水槽实验数据进行处理,所得结果表明:EKF和IEKF都能利用D-SR时延差信息估计出移动声源的距离、深度和速度,并且IEKF比EKF的跟踪效果更好,证明了方法的正确性和有效性。     

Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

This study considers advanced statistical approaches for sequential data assimilation. These are explored in the context of nowcasting and forecasting using nonlinear differential equation based marine ecosystem models assimilating sparse and noisy non-Gaussian multivariate observations. The statistical framework uses a state space model with the goal of estimating the time evolving probability distribution of the ecosystem state. Assimilation of observations relies on stochastic dynamic prediction and Bayesian principles. In this study, a new sequential data assimilation approach is introduced based on Markov Chain Monte Carlo (MCMC). The ecosystem state is represented by an ensemble, or sample, from which distributional properties, or summary statistical measures, can be derived. The Metropolis-Hastings based MCMC approach is compared and contrasted with two other sequential data assimilation approaches: sequential importance resampling, and the (approximate) ensemble Kalman filter (including computational comparisons). A simple illustrative application is provided based on a 0-D nonlinear plankton ecosystem model with multivariate non-Gaussian observations of the ecosystem state from a coastal ocean observatory. The MCMC approach is shown to be straightforward to implement and to effectively characterize the non-Gaussian ecosystem state in both nowcast and forecast experiments. Results are reported which illustrate how non-Gaussian information originates, and how it can be used to characterize ecosystem properties.     

恶劣海况下船舶航向控制仿真及应用研究

船舶在海面航行时,会受到风浪的干扰.此时,船舶航向控制困难,操舵频繁.采用Kalman滤波和模糊自整定PID控制,并基于线性化船舶运动方程的线性时,不变连续时间系统的设计方法得到的船舶操纵控制器,具有抗干扰能力强、鲁棒性好的特点,有效地解决了船舶在风浪干扰条件下的船舶航向控制时的操舵频繁与无效操舵问题.     

动力定位中跟踪环境力突变的自适应无迹卡尔曼滤波

无迹卡尔曼滤波可以在状态估计中滤去噪声干扰,已经被广泛应用于动力定位系统中.针对复杂海洋情况下动力定位系统需要准确、及时地估计当前时刻的状态而无迹卡尔曼滤波无法跟踪状态突变的问题,为此文章提出了一种自适应无迹卡尔曼滤波.通过及时判断状态值突变并适当调整后验均方差矩阵,可有效地跟踪船舶状态并减小实际位置与定点位置的偏差.仿真实验证明了算法的有效性.     

机动对SINS对准中惯性仪表误差估计的影响

为了尽可能估计出捷联惯导系统中惯性仪表的误差,建立捷联惯导系统误差方程和量测方程,运用传递对准技术,构建了速度匹配方式下的Kalman滤波器模型,研究了线加速和拐弯机动下对惯性仪表误差估计的影响,并对计算机仿真结果进行比较分析,仿真结果表明:线加速情况下可以提高陀螺漂移误差的估计精度,拐弯情况下可以提高加速度计偏置误差的估计精度。