集合资料同化方法的理论框架及其在海洋资料同化的研究展望

在海洋动力系统的数值模拟中,海洋资料同化是一种能够有效融合多源海洋观测资料和数值模式的方法。它不仅可以显著地提高数值模拟的效果,构造海洋再分析资料场,还能有效减少海洋和气候预报时模式初始条件的不确定性。因此,海洋资料同化对于海洋研究和业务化应用具有非常重要的意义。资料同化方法的研究一直是大气、海洋科学的热门课题之一。其中,集合卡尔曼滤波器(EnKF)是一种有效的资料同化方法,自提出以来经过了20多年的发展和改进,已经在海洋资料同化中得到了广泛的研究和应用。近年来,随着动力模式的不断发展和计算能力的提高,粒子滤波器由于不受模型线性和误差高斯分布假设的约束,也逐渐成为了当前资料同化方法研究的热点。本文分析和总结了目前关于集合卡尔曼滤波器和粒子滤波器的一些最新理论研究结果,在贝叶斯滤波理论的框架下讨论了这两类算法的关联和区别,以及各自在资料同化实践中的优势和不足。在此基础上,我们探讨了粒子滤波器应用于海洋模式资料同化的主要困难和目前可行的一些解决方法,展望了集合资料同化方法研究的新趋势,为集合资料同化方法的进一步发展和应用提供理论基础。     

拉格朗日资料同化的研究进展

拉格朗日资料对了解海洋环流和大气环流的动力学过程起到很重要的作用,同化拉格朗日资料有很大的必要性.拉格朗日观测工具主要提供的是水团或空气微团的位置和速度等信息,因为拉格朗日资料提供的是移动框架的数据而不是欧拉格点上的模式变量,所以随着拉格朗日观测覆盖大部分海洋和全球海洋环流模式的实现,采用先进的同化方法充分利用这些资料来提高分析预报准确性势在必行.在同化方法不断的发展中最优插值、变分同化、卡尔曼滤波这几种方法都有很好的应用.     

增量变分法融合多源SST

各种不同的观测资料有各自的特点,一种好的融合过程,必须把每一种资料的不同点与误差特点考虑进去.选用了Argo、MODIS、AVHRR、AMSRE、TMI等SST资料,应用增量变分法融合多源卫星SST资料,分析得到了中国近海高分辨率的SST分析产品.用最小二乘共轭梯度法求解三维增量变分法目标函数的最小化,并对三维增量变分法的实际应用方法作了说明.在相关性函数中,合理引入相关温度尺度参数后,能更好地利用SST分布场各点间的相关性与温度梯度场两者之间的关系.在实际应用中,根据前1天的分析温度值计算温度梯度函数,从而得到以实际温度场为基础确定的各向异性相关系数,解决了在大温度梯度区域与海岸上的相关系数的各向异性问题.使用三维增量变分法对AVHRR、MODIS、TMI、AMSRE的所有SST资料进行融合,从2006年融合得到的SST分析场可以明显地看出,多源融合SST分析场和TMI与AMSRE对应的3日平均SST的基本分布是一致的.多源SST融合集合了各卫星SST资料的优点,弥补了各卫星SST资料的不足,根据各种资料的准确度分配权重,最后通过最小二乘共轭梯度迭代法,得到了中国近海全覆盖的高分辨率的SST分析场.在近海区域实时观测资料少,各卫星资料的精度偏低且各卫星资料数据相互独立的情况下,多卫星资料融合有利于提高分析结果的准确性.因此要在近海区域得到实时的、准确的、高分辨率的SST分布就必须融合所有可融合的观测资料,本文在这方面做了初步有益的尝试.     

ARGO观测资料的2种同化方案

使用POM(Princeton Ocean Model)海洋环流模式模拟西北太平洋海域的温盐场,之后运行中国科学院大气物理研究所同化系统(Ocean Variational Analysis System,OVALS),使用Argo观测网格化产品进行2006年整个计算域三维变分同化。无论从平面分布还是断面分布来看,除海表面温度(SST)外,温度同化的效果都比较好,尤其是800 m水深以浅,均方差值甚至能减小1.0℃以上。而且随着同化积分时间的增加,同化后误差减小越来越显著,3、4月份的同化效果明显高于1、2月份。与OFES(OGCM for the Earth Simulator)海洋模式结果相比,同化在一定程度上改进了模拟结果。在POM(Princeton Ocean Model)数值模拟基础上,利用3个西太平洋代表性浮标的观测资料,运用松弛逼近法同化2006年6月断面数据。当松弛系数取0.5时,模拟时间大约半天,模拟值就能快速逼近或完全等于观测值。虽然只对观测剖面进行了数据同化,但该同化可以产生更大范围的效果,而且这种效果可以持续更长时间。     

基于CESM气候模式的同化模拟实验

利用nudging方法将GODAS次表层海温资料同化到"通用地球系统模式"(CESM)中,并分析了同化后的海温、降水、海表面气压等海洋、气象要素。结果表明,同化后的模拟结果与GODAS、NCEP、GPCP等资料的结果较为一致,较好的再现了中低纬海洋和大气的平均特征和随时间演变的规律,NINO3指数的相关系数达到0.90。但模拟结果仍存在一些问题,如大西洋西边界流偏强,赤道辐合带降水偏多等。     

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.     

Cycling the Representer Method for 4D-variational data assimilation with the Navy Coastal Ocean Model

The Cycling Representer Method, which is a technique for solving 4D-variational data assimilation problems, has been demonstrated to improve the assimilation accuracy with simpler nonlinear models. In this paper, the Cycling Representer Method will be used to assimilate an array of ADCP velocity observations with the Navy Coastal Ocean Model (NCOM). Experiments are performed in a high-resolution Mississippi Bight domain for the entire month of June, 2004 and demonstrate the usefulness of this assimilation technique in a realistic application.The Representer Method is solved by minimizing a cost function containing the weighted squared errors of velocity measurements, initial conditions, boundary conditions, and model dynamics. NCOM, however, is a highly nonlinear model and in order to converge towards the global minimum of this cost function, NCOM is linearized about a background state using tangent linearization. The stability of this tangent linearized model (TLM) is a very sensitive function of the background state, the level of nonlinearity of the model, open boundary conditions, and the complexity of the bathymetry and flow field. For the Mississippi Bight domain, the TLM is stable for only about a day. Due to this short TLM stability time period, the Representer Method is cycled by splitting the time period of the assimilation problem into short intervals. The interval time period needs to be such that it is short enough for the TLM to be stable, but long enough to minimize the loss of information due to reducing the temporal correlation of the dynamics and data. For each new cycle, a background is created as a nonlinear forecast from the previous cycle’s assimilated solution. This background, along with the data that falls within this new cycle, is then used to calculate a new assimilated solution. The experiments presented in this paper demonstrate the improvement of the assimilated solution as the time window of the cycles is reduced to 1 day. The 1-day cycling, however, was only optimal for the first half of the experiment. This is because there was a strong wind event near the middle of June that significantly reduced the stability of the 1-day cycling and caused substantial errors in the assimilation. Therefore, the 12-h cycling worked best for the second half of the experiment. This paper also demonstrates that the forecast skill is improved as the assimilation system progresses through the cycles.     

Weak constraint data assimilation for tides in the Arctic Ocean

Estimation of the open-boundary inputs solving a weak constraint variational formulation for an Arctic tide model is considered as an ill-posed problem in the sense that the solution is very sensitive to the data noise and to grid size. Mathematically, spatial discretization of a cost function to be minimized and penalization of normal flow through the open boundary act as regularization of the problem. An heuristic choosing rule for the regularization parameter is applied to assess a suitable spatial resolution and the weight referred to the open boundary penalty. It is shown that these provide a better fit of the solution to a control data set compared with a finer grid, the value of the energy flux through the open boundary being in agreement with other model estimates. The M₂ solution obtained is much closer to the control data than other modern solutions while the accuracy of the simulated K₁ constituent is within the same error level. The tidal maps for these waves exhibit certain distinctions in comparison with other charts.     

融合法及其在数据同化中的应用研究

根据预报值具有最小方差这一要求,详细推导了融合法在观测数据为一维、多维和维数不同的情况下的具体同化表达形式,同时还给出了不同情况下与同化表达式相对应的预报误差公式.利用这些公式,可以用融合法处理常见的海洋观测数据的同化问题.在陆架海模式HAMSOM基础上,以4月份的渤海海表温度为例,我们验证了同化公式的正确性,并给出了同化后较好的同化结果。最后将融合法的同化结果与卡尔曼滤波同化结果进行了对比.比较表明,融合法使用起来更简单,且能有效地处理常见的海洋观测数据.     

Ocean acoustic tomography as a data assimilation problem

The ocean acoustic tomographic (OAT) approach to sound speed field estimation is generalized to include a variety of sources of information of interest such as an oceanographic model of the sound speed field, direct local sound speed measurements, and a full field acoustic propagation model as well as measurements. The inverse problem is presented as a four-dimensional field estimation problem using a variational approach commonly used in oceanographic data assimilation. The current OAT approach is shown to be a special case of the general framework. The matched-field tomography (MFT) approach is also discussed within this context. A simple implementation of this novel approach is then investigated in the absence of a suitable oceanographic model, and acoustic propagation is accounted for using a standard parabolic equation model. The inverse equations derived are validated numerically through a simple inversion example, and some issues on environmental mismatch and computations are discussed. The developments then provide a basic framework for ongoing data-model melding in acoustically focused oceanographic sampling (AFOS) network     

Problems of operational data assimilation for marginal seas

Operational models based on the system of equations of geophysical thermohydrodynamics of the marine medium are considered, as are methods for an approximate reconstruction of the main geophysical fields from the data of deep-sea thermohaline measurements. The results of calculations for the White, Barents, and Kara seas are presented.     

El Niño phenomenon in simple ocean data assimilation data

[1]Battisti D S. 1988. The dynamics and     

黄海、渤海TOPEX/Poseidon高度计资料潮汐伴随同化

首先将大约10a的TOPEX/Poseidon(T/P)高度计资料沿星下轨迹点做潮汐调和分析,提取得到各分潮的调和常数,利用伴随同化方法,同化到二维非线性潮汐数值模式中,模拟了黄海、渤海区域M₂,S₂,O₁,K₁等4个潮汐分潮,并根据计算结果给出了各分潮的同潮图.将计算值与观测值的进行偏差统计,结果表明计算值与验潮站资料符合良好.研究过程中做了两类试验:一类试验是针对不同的参数进行优化,一类试验是针对不同的资料进行同化.第一类试验表明:将开边界条件和底摩擦系数同时作为模型优化的控制参数,其结果明显优于单独优化开边界条件;第二类试验表明:同时同化高度计资料与验潮站资料,比单独同化其中任一种资料,对模式计算结果都有较好的改进.研究结果表明,采用伴随同化方法,利用T/P高度计资料和验潮站资料作为同化数据能有效改进模拟结果,用来反演黄海、渤海的潮波系统是可行的.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

Numerical modeling of currents in the Drake Passage with assimilation of the experimental data of 2003

Computation of ocean currents in the Drake Passage is carried out with variational assimilation of the data of the hydrographical section across the Drake Passage carried out on December 11–15, 2003, and other data. A stream-eddy structure of the easterly Antarctic Circumpolar Current and a westerly current on the Antarctic Slope are obtained. Water transports by the different current field components and the integral transport across the Drake Passage are estimated. The necessity of direct current measurements in the Drake Passage for a correct estimate of the transport is confirmed.     

Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model

The representer method was used by [Ngodock, H.E., Jacobs, G.A., Chen, M., 2006. The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: a comparison study using a nonlinear reduced gravity ocean model. Ocean Modelling 12, 378–400] in a comparison study with the ensemble Kalman filter and smoother involving a 1.5 nonlinear reduced gravity idealized ocean model simulating the Loop Current (LC) and the Loop Current eddies (LCE) in the Gulf of Mexico. It was reported that the representer method was more accurate than its ensemble counterparts, yet it had difficulties fitting the data in the last month of the 4-month assimilation window when the data density was significantly decreased. The authors attributed this failure to increased advective nonlinearities in the presence of an eddy shedding causing the tangent linear model (TLM) to become inaccurate. In a separate study [Ngodock, H.E., Smith, S.R., Jacobs, G.A., 2007. Cycling the representer algorithm for variational data assimilation with the Lorenz attractor. Monthly Weather Review 135 (2), 373–386] applied the cycling representer algorithm to the Lorenz attractor and demonstrated that the cycling solution was able to accurately fit the data within each cycle and beyond the range of accuracy of the TLM, once adjustments were made in the early cycles, thus overcoming the difficulties of the non-cycling solution. The cycling algorithm is used here in assimilation experiments with the nonlinear reduced gravity model. It is shown that the cycling solution overcomes the difficulties encountered by the non-cycling solution due to a limited time range of accuracy of the TLM. Thus, for variational assimilation applications where the TLM accuracy is limited in time, the cycling representer becomes a very powerful and attractive alternative, given that its computational cost is significantly lower than that of the non-cycling algorithm.     

基于D-S理论的卫星遥感海表面温度和同化数据融合方法

利用卫星遥感获取海表面温度实时性强,但其数据质量随大气环境而波动;利用同化技术求解的海表面温度局部精度高,但覆盖面与实时性差.鉴于两种技术适应不同情况,拟使用信息融合技术实现两者优势互补,即根据各自的优势和局限性对数据点进行一致性评价和加权融合计算,在提高精度的同时对结果的不确定性进行量化和评价.以我国东部海域海表温度为例的采样试验结果表明,融合法更适应复杂的环境.     

集合变换卡尔曼滤波数据同化方法中的协方差局地化

在集合数据同化中,协方差局地化（covariance localization,CL）方法的使用存在限制。集合转换卡尔曼滤波（ensemble transform Kalman filter,ETKF）作为集合平方根滤波的变种方法,是一种应用较广、计算高效的数据同化方法。本文分析了CL方法应用于ETKF方法的困难,从而改进CL方法使其可以适用于ETKF方法。另外,结合浅水方程,利用Askey函数作为多元局地化函数,提出了一种适用于多元数值模型的CL方法。通过具体实验验证,得到了较好的分析结果。