Asynchronous data assimilation with the EnKF

This study revisits the problem of assimilation of asynchronous observations, or four-dimensional data assimilation, with the ensemble Kalman filter (EnKF). We show that for a system with perfect model and linear dynamics the ensemble Kalman smoother (EnKS) provides a simple and efficient solution for the problem: one just needs to use the ensemble observations (that is, the forecast observations for each ensemble member) from the time of observation during the update, for each assimilated observation. This recipe can be used for assimilating both past and future data; in the context of assimilating generic asynchronous observations we refer to it as the asynchronous EnKF. The asynchronous EnKF is essentially equivalent to the four-dimensional variational data assimilation (4D-Var). It requires only one forward integration of the system to obtain and store the data necessary for the analysis, and therefore is feasible for large-scale applications. Unlike 4D-Var, the asynchronous EnKF requires no tangent linear or adjoint model.     

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation (4D-Var) has been widely used in meteorological and oceanographic data assimilation. This method is usually implemented in the model space, known as primal approach (P4D-Var). Alternatively, physical space analysis system (4D-PSAS) is proposed to reduce the computation cost, in which the 4D-Var problem is solved in physical space (i.e., observation space). In this study, the conjugate gradient (CG) algorithm, implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process. The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed. In order to overcome the non-monotonic variation of gradient norm, a new algorithm, Minimum Residual (MINRES) algorithm, is implemented in the process of assimilation iteration in this study. Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function, greatly improves the convergence properties of 4D-PSAS as well, and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.     

基于四维变分同化方法的南海中尺度涡后报实验

海洋中尺度涡在本质上是属于满足准地转平衡的大尺度运动,因此理论上,其在短时间内的运动将主要受到准地转平衡关系的约束,而外部强迫场的影响在短期内不会明显改变其运动特征。基于上述思想,我们提出了一种基于四维变分同化初始场的中尺度涡旋预报方案。为了检验该方案的可行性,本文使用区域海洋模式(regional ocean modeling system, ROMS)和其内建的增量强约束四维变分同化(incremental strong constraint four dimensional variational, I4D-Var)模块,建立了一个南海海洋同化模拟系统。首先,通过I4D-Var方法将AVISO卫星高度计资料同化到海洋数值模拟中,获得了理想的中尺度涡同化模拟结果。同化、模式模拟和观测三者的中尺度涡统计结果表明,该同化系统模拟的南海中尺度涡的路径、半径、海表高度异常和振幅等特征信息与AVISO(Archiving ValidationandInterpolationofSatelliteOceanographicData)观测结果高度吻合,同时在深度上的分析表明,涡旋对应的温度、盐度和密度均得到有效的调整。然后,将该同化系统的模拟结果做为初始场,对某一特定时段的南海中尺度涡进行了后报模拟和结果的定量化分析。通过比较后报模拟与观测资料中对应涡旋的海表面高度异常(sea surface height anomalies, SSHA)相关系数、涡心差距和半径绝对误差,证明该方案的中尺度涡后报时效至少可达10 d以上。后报实验结果验证了该中尺度涡预报方案的可行性,从而为中尺度涡的预报提供一定的理论基础和可行性方案。     

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.     

The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part III - Observation impact and observation sensitivity in the California Current System

The critical role played by observations during ocean data assimilation was explored when the Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation system was applied sequentially to the California Current circulation. The adjoint of the 4D-Var gain matrix was used to quantify the impact of individual observations and observation platforms on different aspects of the 4D-Var circulation estimates during both analysis and subsequent forecast cycles. In this study we focus on the alongshore and cross-shore transport of the California Current System associated with wind-induced coastal upwelling along the central California coast. The majority of the observations available during any given analysis cycle are from satellite platforms in the form of SST and SSH, and on average these data exert the largest controlling influence on the analysis increments and forecast skill of coastal transport. However, subsurface in situ observations from Argo floats, CTDs, XBTs and tagged marine mammals often have a considerable impact on analyses and forecasts of coastal transport, even though these observations represent a relatively small fraction of the available data at any particular time.During 4D-Var the observations are used to correct for uncertainties in the model control variables, namely the initial conditions, surface forcing, and open boundary conditions. It is found that correcting for uncertainties in both the initial conditions and surface forcing has the largest impact on the analysis increments in alongshore transport, while the cross-shore transport is controlled mainly by the surface forcing. The memory of the circulation associated with the control variable increments was also explored in relation to 7 day forecasts of the coastal circulation. Despite the importance of correcting for surface forcing uncertainties during analysis cycles, the coastal transport during forecast cycles initialized from the analyses has less memory of the surface forcing corrections, and is controlled primarily by the analysis initial conditions.Using the adjoint of the entire 4D-Var system we have also explored the sensitivity of the coastal transport to changes in the observations and the observation array. A single integration of the adjoint of 4D-Var can be used to predict the change that occurs when observations from different platforms are omitted from the 4D-Var analysis. Thus observing system experiments can be performed for each data assimilation cycle at a fraction of the computational cost that would be required to repeat the 4D-Var analyses when observations are withheld. This is the third part of a three part series describing the ROMS 4D-Var systems.     

The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part II - Performance and application to the California Current System

The Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation systems have been systematically applied to the mesoscale circulation environment of the California Current to demonstrate the performance and practical utility of the various components of ROMS 4D-Var. In particular, we present a comparison of three approaches to 4D-Var, namely: the primal formulation of the incremental strong constraint approach; the dual formulation “physical-space statistical analysis system”; and the dual formulation indirect representer approach. In agreement with theoretical considerations all three approaches converge to the same ocean circulation estimate when using the same observations and prior information. However, the rate of convergence of the dual formulation was found to be inferior to that of the primal formulation. Other aspects of the 4D-Var performance that relate to the use of multiple outer-loops, preconditioning, and the weak constraint are also explored. A systematic evaluation of the impact of the various components of the 4D-Var control vector (i.e. the initial conditions, surface forcing and open boundary conditions) is also presented. It is shown that correcting for uncertainties in the model initial conditions exerts the largest influence on the ability of the model to fit the available observations. Various important diagnostics of 4D-Var are also examined, including estimates of the posterior error, the information content of the observation array, and innovation-based consistency checks on the prior error assumptions. Using these diagnostic tools, we find that more than 90% of the observations assimilated into the model provide redundant information. This is a symptom of the large percentage of satellite data that are used and to some extent the nature of the data processing employed. This is the second in a series of three papers describing the ROMS 4D-Var systems.     

解析四维集合变分参数优化方法研究

传统的四维变分数据同化方法在同化观测资料的同时可以对数值模式参数进行优化,然而传统的四维变分方法需要针对不同的数值模式编写特有的伴随模式,因此算法的可移植性差,同时计算时耗费大量资源。本文提出了一种新的基于解析四维集合变分的参数优化方法,该方法以迭代搜索得到的模式参数为基准展开扰动并构建样本集合,由此显式地计算协方差矩阵,并得到代价函数极小值的解析解,从而避免了伴随模式的使用。基于Lorenz-63模型对该方法进行单参数和多参数数值试验和优化效果检验,并在不同的同化时间窗口长度和观测采样间隔情况下,采用传统四维变分方法与之进行对比,结果显示,新方法表现出与传统四维变分相同的优化性能,都能有效收敛到真值,而新方法不需要计算伴随模式,可移植性好。本文还测试了不同的集合成员个数和模式参数真值的情况下新方法的同化效果,结果表明,新方法对集合样本个数及模型参数真值不敏感,采用较少的集合样本即可完成数据同化。     

变分同化方法反演海气耦合模型参数的研究

采用变分资料同化技术,结合最优控制思想,对一个海气耦合模型的模式参数和强迫项进行了反演,结果表明,采用该方法对模式进行优化,既可以补偿模式参数不准确性给预报带来的误差,又可以对模式参数本身进行修正和估计,为将来在实际应用中改善更复杂的预报模式、提高预报准确率提供了一个可借鉴的思路。     

Full Coupled Effects of Hull, Mooring and Risers Model in Time Domain Based on an Innovative Deep Draft Multi-Spar

The coupled hull, mooring and riser analysis techniques in time domain are widely recognized as the unique approach to predict the accurate global motions. However, these complex issues have not been perfectly solved due to a large number of nonlinear factors, e.g. forces nonlinearity, mooring nonlinearity, motion nonlinearity and so on. This paper investigates the coupled effects through the numerical uncoupled model, mooring coupled model and fully coupled model accounting mooring and risers based on a novel deep draft multi-spar which is especially designed for deepwater in 2009. The numerical static-offset, free-decay, wind-action tests are executed, and finally the three hours simulations are conducted under 100-year return period of GOM conditions involving wave, wind and current actions. The damping contributions, response characteristics and mooring line tensions are emphatically studied.     

Fully Coupled Effects of Hull, Mooring and Risers Model in Time Domain Based on An Innovative Deep Draft Multi-Spar

The coupled hull, mooring and riser analysis techniques in time domain are widely recognized as the unique approach to predict the accurate global motions. However, these complex issues have not been perfectly solved due to a large number of nonlinear factors, e.g. forces nonlinearity, mooring nonlinearity, motion nonlinearity and so on. This paper investigates the coupled effects through the numerical uncoupled model, mooring coupled model and fully coupled model accounting mooring and risers based on a novel deep draft multi-spar which is especially designed for deepwater in 2009. The numerical static-offset, free-decay, wind-action tests are executed, and finally three hours simulations are conducted under 100-year return period of GOM conditions involving wave, wind and current actions. The damping contributions, response characteristics and mooring line tensions are emphatically studied.     

IOCAS ICM及其ENSO实时预测试验和改进

厄尔尼诺和南方涛动(ENSO)是仅次于季节变化的最强年际气候变率信号,对全球气候和天气产生重要影响。准确、及时、有效地预报ENSO事件的发生和演变具有重大的实用意义。以中国科学院海洋研究所冠名的中等复杂程度海气耦合模式(IOCAS ICM),每月定期进行ENSO实时预报试验。IOCAS ICM实时预报结果目前收录于美国哥伦比亚大学国际气候研究所(IRI),以作进一步的集成分析和应用。该模式的大气部分是一个描述对海表温度(SST)年际异常响应的风应力异常经验模式,海洋部分包括了动力海洋模块、SST距平模块(嵌套于动力海洋模块中)和次表层上卷海温(T_e)距平模块三部分。IOCAS ICM的特点之一是开发了次表层海温反算优化这一创新技术,可有效改进热带太平洋SST异常的模拟和预报。IOCAS ICM和其他海气耦合模式的最新预报结果(以2017年9月为初条件)表明,2017年年末热带太平洋会处于一个SST冷异常态,最大变冷中心集中在赤道东太平洋,但并不足以达到拉尼娜(La Ni?a)事件的水平,SST冷异常可能会在2018年春季逐渐减弱,转化为中性状态。此外,本文还对四维变分资料同化方法(4D-Var)以及条件非线性最优扰动方法(CNOP)在IOCAS ICM中的应用进行了讨论。     

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.     

集合滤波和三维变分混合数据同化方法研究

发展了一种新的混合数据同化方法——基于集合滤波和三维变分的混合数据同化方法。该方法将集合调整卡尔曼滤波(ensemble adjustment Kalman filter,EAKF)得到的集合样本扰动通过一个转换矩阵的形式直接作用到背景场上,利用顺序滤波的思想得到分析场的一个扰动;然后在三维变分(three dimensional variational analysis,3D-Var)的框架下与观测数据进行拟合,从而给出分析场的最优估计。文中以Lorenz63模型为例,开展了理想数据同化试验,结果表明,相比于集合调整卡尔曼滤波,这种新的混合同化方法可以给出更好的同化结果。     

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.     

An experimental analysis for the impact of 3D 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 three-dimensional variational (3D-Var) assimilation scheme is developed to assimilate the satellite data directly into the Penn State-NCAR nonhydrostatic meteorological model (MM5). Three-dimensional objective analysis fields based on the T213 results and conventional observations are employed as the background fields of the initialization. The comparisons of the simulated typhoon tracks are carried out, which correspond respectively to assimilate different kinds of satellite data. It is found that, compared with the experiment without satellite data assimilation, the 3D-Var assimilation schemes lead to significant improvements on typhoon track prediction. Track errors reduce from approximately 25% at 24 h to approximately 30% at 48 h for 3D-Var assimilation experiments.     

Impacts of TRMM SRR assimilation on the numerical prediction of tropical cyclone

1 IntroductionObservation of the tropical rainfall is crucial forthe research on tropical weather and climate. Nu-merous studies have shown that the ingestion of rain-fall data into a numerical model can have considera-ble impacts on simulation results(Kr…     

Four-dimensional variational ocean reanalysis: a 30-year high-resolution dataset in the western North Pacific (FORA-WNP30)

We produced a four-dimensional variational ocean re-analysis for the Western North Pacific over 30 years (FORA-WNP30). It is the first-ever dataset covering the western North Pacific over 3 decades at eddy-resolving resolution. The four-dimensional variational analysis scheme version of the Meteorological Research Institute Multivariate Ocean Variational Estimation system (MOVE-4DVAR) is employed to conduct a long-term reanalysis experiment during 1982–2012. After evaluating the basic performance of FORA-WNP30, the interannual to decadal variability is analyzed. Overall, FORA-WNP30 reproduces basic features in the western North Pacific well. One of outstanding features in FORA-WNP30 is that anomalous events such as the Kuroshio large meander and anomalous intrusion of the Oyashio in the 1980s, when there were no altimeter data, are successfully reproduced. FORA-WNP30 is therefore a valuable dataset for a variety of oceanographic research topics and potentially for related fields such as climate study, meteorology and fisheries.     

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.     

A Finite-Difference Approach to the Time-Dependent Mild-Slope Equation

A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity.The Euler predictor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones,respectively,thus leading both the time and spatial derivatives to the second-order accuracy.The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift.Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach,respectively,and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor.From comparison of numerical results with theoretical or experimental ones,it is found that they are in reasonable agreement.