数据同化反演风应力拖曳系数以及垂向涡动黏性系数的分布

所作的孪生实验表明:通过利用变分优化控制技术将气象学和海洋学(表层和次表层)的观测资料同化到海洋的埃克曼层模型中,可将未知的边界条件(风应力拖曳系数)和垂向涡动黏性系数的分布同时反演出来.     

变分伴随数据同化在海表面温度预报中的应用研究

将变分伴随数据同化技术应用于海表面温度(SST)数值预报.采用中国近海海表面温度短期数值预报模式,将船舶测报海表面温度同化到该模型中,对SST初始场进行优化.文中给出了中国近海SST数值预报同化模型5d试报结果与观测值的比较,整个区域的均绝差由同化前的2.71℃降至0.87℃,即变分伴随数据同化对改进SST数值预报的效果是比较明显的,表明它可成为SST数值预报初始化的新方法.     

伴随同化方法在中国近海海洋数值模拟中的应用

简述了几种常用的资料同化方法,并较为详细地阐述了伴随同化方法的基本原理。基于其在潮汐模式中、在海水温度场中和在海洋生态模型中的应用等三方面综述了伴随方法在中国近海海洋数值模拟中的应用研究现状和进展。并对伴随方法的应用前景进行了初步的评述,指出该方法可对海洋观测方案的优化发挥重要作用,其在生态学流动力学模式中的应用亦应得到充分重视。     

资料同化中的伴随方法及其在海洋中的应用

较系统地综述了资料同化中各种方法的分类,并着重说明了伴随方法的基本原理和具体实现步骤。并总结了伴随方法在海洋中的应用现状,并指出由于观测资料特别是遥感资料的日益丰富,伴随方法将有广泛地应用前景。     

海洋生态模型中的伴随同化方法

伴随同化方法（简称“伴随法”）在1995年被首次应用于海洋生态模型,此后,它在海洋生态模型的研究中得到了广泛的应用.在本文中,作者详细阐述了海洋生态模型中伴随法的结构和特点,具体介绍了伴随法在海洋生态模型应用中的研究进展;并且以渤、黄海NPZD生态数值模式为例,展示了伴随法的优越性.     

海洋水温垂直分布数据同化方法研究

以一维海洋水温模型为例,利用伴随法进行海洋观测数据同化试验,以便为水温的数值预报提供较准确的初始场.文中利用泛函的Gâteaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立,并通过选择适当的差分格式离散伴随模型,使其保持连续时的伴随关系,同时给出了水温初始场最优化过程及相应的同化试验数值结果.     

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。     

数据同化在海洋数值产品制作及预报中的应用研究

讨论了海洋中数据同化的目的,意义,各种数据同化方法,国内外发展现状及其在海洋数值产品制作及预报中的应用。文中还介绍了数据同化方法中的客观分析法和伴随法的原理,结合海洋中的实际问题进行了数据同化试验,给出了相应的同化试验结果,并讨论了二阶伴随理论。     

伴随同化方法在渤、黄海生态模式中的应用——生态参数的空间分布

将伴随同化方法用于渤、黄海NPZD三维浮游生态动力学模型的研究中,利用1998年～2006年的SeaWiFS叶绿素资料作为观测数据进行同化实验,优化难以确定的生态参数.文中对参数在整个计算区域取常数时进行了优化,同时尝试了一种新的参数化方案,即在海区中选取一些点作为独立参数点,其它点的参数由独立参数点的值经过线性插值得到,优化独立点的参数后得到所有计算格点的参数.针对这两种不同的参数化方案做了一系列对比实验,结果表明利用伴随同化方法反演空间分布的参数能有效地提高数值模拟的精度.     

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 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.     

Correcting the errors in the initial conditions and wind stress in storm surge simulation using an adjoint optimal technique

An adjoint data assimilation methodology is applied to the Princeton Ocean Model and is evaluated by obtaining “optimal” initial conditions, sea surface forcing conditions, or both for coastal storm surge modelling. By prescribing different error sources and setting the corresponding control variables, we performed several sets of identical twin experiments by assimilating model-generated water levels. The experiment results show that, when the forecasting errors are caused by the initial (or surface boundary) conditions, adjusting initial (or surface boundary) conditions accordingly can significantly improve the storm surge simulation. However, when the forecasting errors are caused by surface boundary (or initial) conditions, data assimilation targeting improving the initial (or surface boundary) conditions is ineffective. When the forecasting errors are caused by both the initial and surface boundary conditions, adjusting both the initial and surface boundary conditions leads to the best results. In practice, we do not know whether the errors are caused by initial conditions or surface boundary conditions, therefore it is better to adjust both initial and surface boundary conditions in adjoint data assimilation.     

Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system

We describe the development and preliminary application of the inverse Regional Ocean Modeling System (ROMS), a four dimensional variational (4DVAR) data assimilation system for high-resolution basin-wide and coastal oceanic flows. Inverse ROMS makes use of the recently developed perturbation tangent linear (TL), representer tangent linear (RP) and adjoint (AD) models to implement an indirect representer-based generalized inverse modeling system. This modeling framework is modular. The TL, RP and AD models are used as stand-alone sub-models within the Inverse Ocean Modeling (IOM) system described in [Chua, B.S., Bennett, A.F., 2001. An inverse ocean modeling system. Ocean Modell. 3, 137–165.]. The system allows the assimilation of a wide range of observation types and uses an iterative algorithm to solve nonlinear assimilation problems. The assimilation is performed either under the perfect model assumption (strong constraint) or by also allowing for errors in the model dynamics (weak constraints). For the weak constraint case the TL and RP models are modified to include additional forcing terms on the right hand side of the model equations. These terms are needed to account for errors in the model dynamics.Inverse ROMS is tested in a realistic 3D baroclinic upwelling system with complex bottom topography, characterized by strong mesoscale eddy variability. We assimilate synthetic data for upper ocean (0–450 m) temperatures and currents over a period of 10 days using both a high resolution and a spatially and temporally aliased sampling array. During the assimilation period the flow field undergoes substantial changes from the initial state. This allows the inverse solution to extract the dynamically active information from the synthetic observations and improve the trajectory of the model state beyond the assimilation window. Both the strong and weak constraint assimilation experiments show forecast skill greater than persistence and climatology during the 10–20 days after the last observation is assimilated.Further investigation in the functional form of the model error covariance and in the use of the representer tangent linear model may lead to improvement in the forecast skill.     

南海潮汐的伴随同化数值模拟

把利用正交潮响应方法对 2 4 8个周期超过 6年的南中国海的TOPEX/Poseidon卫星高度计资料进行潮波分析提取的沿轨分潮调和常数同化到二维非线性潮汐数值模式中去 ,优化模型中的开边界条件和底摩擦系数 ,模拟了南海m1 和M2 分潮的潮汐。所用的同化方法是伴随同化。根据计算结果给出了m1 和M2 分潮的同潮图。计算结果与 5 9个验潮站资料的比较结果是 :m1 分潮的振幅和迟角的平均绝对误差分别是 4.8cm和 8.7°;M2 分潮的振幅和迟角的平均绝对误差分别是 4.3cm和 1 1 .0°,表明计算结果与验潮站资料符合良好。研究结果表明 ,利用伴随同化方法把TOPEX/Poseidon资料同化到潮汐数值模式中去对模式进行校正是有效的     

The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model

This paper compares contending advanced data assimilation algorithms using the same dynamical model and measurements. Assimilation experiments use the ensemble Kalman filter (EnKF), the ensemble Kalman smoother (EnKS) and the representer method involving a nonlinear model and synthetic measurements of a mesoscale eddy. Twin model experiments provide the “truth” and assimilated state. The difference between truth and assimilation state is a mispositioning of an eddy in the initial state affected by a temporal shift. The systems are constructed to represent the dynamics, error covariances and data density as similarly as possible, though because of the differing assumptions in the system derivations subtle differences do occur. The results reflect some of these differences in the tangent linear assumption made in the representer adjoint and the temporal covariance of the EnKF, which does not correct initial condition errors. These differences are assessed through the accuracy of each method as a function of measurement density. Results indicate that these methods are comparably accurate for sufficiently dense measurement networks; and each is able to correct the position of a purposefully misplaced mesoscale eddy. As measurement density is decreased, the EnKS and the representer method retain accuracy longer than the EnKF. While the representer method is more accurate than the sequential methods within the time period covered by the observations (particularly during the first part of the assimilation time), the representer method is less accurate during later times and during the forecast time period for sparse networks as the tangent linear assumption becomes less accurate. Furthermore, the representer method proves to be significantly more costly (2–4 times) than the EnKS and EnKF even with only a few outer iterations of the iterated indirect representer method.     

Efficiency of reduced-order, time-dependent adjoint data assimilation approaches

Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reduced-order optimization methods that reduce the size of the control vector by projecting it onto a limited number of basis functions were suggested. In this paper, we show that such order reduction can indeed speed up the initial convergence rate of an assimilation effort in the eastern subtropical North Atlantic using in situ and satellite data as constraints. However, an improved performance of the optimization was only obtained with a hybrid approach where the optimization is started in a reduced subspace but is continued subsequently using the full control space. In such an experiment about 50% of the computational cost can be saved as compared to the optimization in the full control space. Although several order-reduction approaches seem feasible, the best result was obtained by projecting the control vector onto Empirical Orthogonal Functions (EOFs) computed from a set of adjusted control vectors estimated previously from an optimization using the same model configuration.     

数据同化——它的缘起,含义和主要方法

我国已进入流体动力学的卫星观测世纪,数据同化（有时叫“四维同化”）,势必成为随之而来的重要课题之一。针对目前人们对这一课题尚无太多了解,从而在实际工作中产生一些混乱,笔者在本文就数据同化的必要性,它的含义,它的开创和现在研究、应用中的主要方法作一比较详细的论述。     

Application of Nonlinear Constraints in a Three-Dimensional Variational Ocean Analysis

Two kinds of nonlinear constraints, not previously studied in oceanography, have been adopted with the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar) in a three-dimensional oceanic variational analysis in the equatorial Pacific. One is the constraint for the variational Quality Control (QC) procedure and the other is used to avoid density and temperature inversions. Estimation of the large heat content anomaly in the upper ocean related to El Nino and La Nina phenomena is improved with the variational QC. For example, it prevents unusual but correct observation data on the thermocline deepening in the 1997/98 El Nino from being ignored. As a result, it improves the temperature field estimation in the eastern equatorial Pacific. The constraint for avoiding inversions prevents the low salinity layer at the surface and the barrier layer in the eastern equatorial Pacific in the El Nino period from being destroyed by the convective adjustment procedure performed after minimizing the cost function. Incorporating nonlinear constraints in variational analyses is thus a strong candidate for increasing the accuracy of analysis.     

Short-Range Prediction Experiments with Operational Data Assimilation System for the Kuroshio South of Japan

The short-range (one month) variability of the Kuroshio path was predicted in 84 experiments (90-day predictions) using a model in an operational data assimilation system based on data from 1993 to 1999. The predictions started from an initial condition or members of a set of initial conditions, obtained in a reanalysis experiment. The predictions represent the transition from straight to meander of the Kuroshio path, and the results have been analyzed according to previously proposed mechanisms of the transition with eddy propagation and interaction acting as a trigger of the meander and self-sustained oscillation. The reanalysis shows that the meander evolves due to eddy activity. Simulation (no assimilation) shows no meander state, even with the same atmospheric forcing as the prediction. It is suggested therefore that the initial condition contains information on the meander and the system can represent the evolution. Mean (standard deviation) values of the axis error for all 84 cases are 13, 17, and 20 (10, 10, and 12) km, in 138.5°E, in the 30-, 60-, and 90-day predictions respectively. The observed mean deviation from seasonal variation is 30 km. The predictive limit of the system is thus about 80 days. The time scale of the limit depends on which stage in the transition is adopted as the initial condition. The gradual decrease of the amplitude in a stage from meander to straight paths is also predicted. The predictive limit is about 20 days, which is shorter than the prediction of the opposite transition. This revised version was published online in July 2006 with corrections to the Cover Date.