中国近海现场海洋观测系统设计评估

中国科学院正在发展一个在中国近海(包括黄海、东海和南海)现场海洋观测系统。观测系统包括3个沿岸观测站点、4个近海离岸浮标和由观测船只按固定航线做的船舶观测断面。观测站点、浮标和断面的位置已经预先确定,这个计划在2008-2011实施。利用基于卡尔曼理论的样本集合方法对这样一个能够监测大尺度的季节和年季变率的观测系统设计进行了评估。根据卡尔曼滤波理论,用集合样本的方法能够给出经过同化这个观测系统位置的观测资料后能够减少多少分析误差和分析场的不确定性。用2个来自不同模式、不同分辨率的模式的结果作为集合样本来计算静态的背景误差协方差,这2套样本分别是来自分辨率是0.5°×0.5°的模式同化结果和高分辨0.125°×0.125°的模式结果。由这2个不同资料得到的结果是一致的。发现来自3个近岸和4个离岸浮标得到的观测能够有效地减少SST在渤海、黄海、东海和南海中部的分析误差。然而在越南东部和台湾东部海域,分析误差减少的百分比相对要小。最后,给出了中国近海最优的观测位置序列设计。     

现代海洋/大气资料同化方法的统一性及其应用进展

海洋／大气资料同化的理论基础是用数值模式作为动力学强迫对观测信息进行提炼，或者说，从包含观测误差(噪声)的空间分布不均匀的实测资料中依据动力系统自身的演化规律(动力学方程或模式)来确定海洋／大气系统状态的最优估计。本文对主要的现代海洋／大气资料同化方法，包括最优插值(()ptimal Interpolation，简称()Ⅰ)、变分方法(3—Dimensional Variational和4—Dimensional Variational，分别简称3DVAR和4DVAR)和滤波方法(Filtering)的原理、算法设计和实际应用进行系统地回顾，并对这些资料同化方法的优缺点进行分析和讨论。在滤波框架下，所有的现代资料同化方法都被统一了：()Ⅰ和3DVAR是不随时间变化的滤波器，4DVAR和卡曼滤波是线性滤波器，即非线性滤波的退化情形；而集合滤波能构建非线性的滤波器，因为集合在某种程度上体现了系统的非高斯信息。一个非线性滤波器的主要优点是能计算和应用随时间变化的各阶误差统计距，如误差协方差矩阵。将非线性滤波器计算的随时间变化的误差协方差矩阵引入到（）Ⅰ或4DVAR中，也许能实质性地改进这些传统方法。在实际应用中，方法的优劣可能取决于所选用的数值模式和可获得的计算资源，因此需针对不同的问题选取不同的资料同化方法。由于各种资料同化方法具有统一性，因此可建立测试系统来评价这些方法，从而对各种方法获得更深入的理解，改进现有的资料同化技术，并提高人们对海洋／大气环境的预测能力。     

利用资料同化方法优化观测系统的空间布局:以泰国湾为例

海洋观测费用高昂，设计科学高效的观测系统可以充分发挥观测的效能。本文以泰国湾高频地波雷达观测系统为例，利用数据同化方法对观测系统进行了最优布局。首先基于FVCOM海洋数值模式建立了泰国湾海域高分辨率三维斜压水动力模式，在此基础上利用一种改进的高效集合卡曼滤波同化方法对岸基高频地波雷达表层海流观测系统开展观测效能评估数值实验。通过观测区域的不同组合方式将3个区域的雷达表层海流数据同化到数值模式中，实验结果表明，岸基高频地波雷达表层海流观测系统可有效降低高分辨数值模式的海流模拟误差。但不同观测区域的组合提供的观测数据对改善海流模拟的作用存在明显差别，泰国湾现有观测系统雷达站位布设方式应进一步优化。本文最后给出了研究区域最优观测站位的布局方案，可作为下一步观测系统进行布局调整的指导。     

海洋资料同化对气候季节-年际预测技巧及初始场的影响试验

集合卡尔曼滤波(Ensemble Kalman filter, EnKF)是一种国内外广泛使用的海洋资料同化方案, 用集合成员的状态集合表征模式的背景误差协方差, 结合观测误差协方差, 计算卡尔曼增益矩阵, 有效地将观测信息添加到模式初始场中。由于季节、年际预测很大程度上受到初始场的影响, 因此资料同化可以提高模式的预测性能。本文在NUIST-CFS1.0预测系统逐日SST nudging的初始化方案上, 利用EnKF在每个月末将全场(full field)海表温度(sea surface temperature, SST)、温盐廓线(in-situ temperature and salinity profiles, T-S profiles)以及卫星观测海平面高度异常(sea level anomalies, SLA)观测资料同化到模式初始场中, 对比分析了无海洋资料同化以及加入同化后初始场的区别、加入海洋资料同化后模式提前1~24个月预测性能的差异以及对于厄尔尼诺-南方涛动(El Niño-southern oscillation, ENSO)预测技巧的影响。结果表明, 加入海洋资料同化能有效地改进初始场, 并且呈现随深度增加初始场改进越显著的特征。加入同化后, 对全球SST、次表层海水温度的平均预测技巧均有一定的提高, 也表现出随深度增加预测技巧改进越明显的特征。但加入海洋资料同化后, 模式对ENSO的预测技巧有所下降, 可能是由于模式误差的存在, 使得同化后的预测初始场从接近观测的状态又逐渐恢复到与模式动力相匹配的状态, 加剧了赤道太平洋冷舌偏西、中东部偏暖的气候平均态漂移。     

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。     

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.     

上海邻近海域风暴潮数据同化与特征分析

风暴潮是一种复杂的对众多因素敏感又备受关注的海洋现象。本文基于协方差局地化的集合卡尔曼滤波方法（EnKF）,选择201810号台风“安比”登陆上海的风暴潮过程,首次将海洋站和FVCOM数值模拟的不同来源、不同误差信息、不同时空分辨率的风暴潮进行数据同化融合,获得了逐72 h的上海海域风暴潮的最优解,进行了同化结果评估验证,并给出了集合样本数和Schur半径设置范围。结果表明,实测计算和数值模拟的风暴增减水之间均方根误差为0.20 m,实测和同化计算的风暴增减水之间均方根误差为0.07 m,准确度提高了65%;独立观测和同化计算的风暴增减水均方根误差为0.09 m,集合离散度与均方根误差比值为0.90,同化效果较好且可信;同化后的风暴增减水能够较好地刻画双峰增水、台风眼增水、增水锋面等特征,对于风暴潮研究、数值模拟结果订正、海洋防灾减灾等有重要意义。     

MASNUM-WAM海浪模式集合Kalman滤波同化研究——Ⅱ.集合样本对同化效果的影响

背景误差相关结构的确定是影响海浪同化效果的关键因素之一。集合Kalman滤波是一种较为成熟的同化方法,其可以对背景误差进行实时更新和动态估计,现已广泛应用于海洋和大气领域的研究。本文基于MASNUM-WAM海浪模式,分别采用静态样本集合Kalman滤波和EAKF方法,针对2014年全球海域开展海浪数据同化实验,同化资料为Jason-2卫星高度计数据,利用Saral卫星高度计资料对同化实验结果进行检验。结果表明,两组同化方案均有效提高了海浪模式的模拟水平,EAKF方案在风场变化较大的西风带区域表现显著优于静态样本集合Kalman滤波方案,但总体上两者相差不大。综合考虑计算成本和同化效果,静态样本集合Kalman滤波方案更适用于海浪业务化预报。     

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.     

集合同化方法在黄海海域海表面温度同化中的应用

The effects of sea surface temperature(SST) data assimilation in two regional ocean modeling systems were examined for the Yellow Sea(YS). The SST data from the Operational Sea Surface Temperature and Sea Ice Analysis(OSTIA) were assimilated. The National Marine Environmental Forecasting Center(NMEFC) modeling system uses the ensemble optimal interpolation method for ocean data assimilation and the Kunsan National University(KNU) modeling system uses the ensemble Kalman filter. Without data assimilation, the NMEFC modeling system was better in simulating the subsurface temperature while the KNU modeling system was better in simulating SST. The disparity between both modeling systems might be related to differences in calculating the surface heat flux, horizontal grid spacing, and atmospheric forcing data. The data assimilation reduced the root mean square error(RMSE) of the SST from 1.78°C(1.46°C) to 1.30°C(1.21°C) for the NMEFC(KNU) modeling system when the simulated temperature was compared to Optimum Interpolation Sea Surface Temperature(OISST) SST dataset. A comparison with the buoy SST data indicated a 41%(31%) decrease in the SST error for the NMEFC(KNU) modeling system by the data assimilation. In both data assimilative systems, the RMSE of the temperature was less than 1.5°C in the upper 20 m and approximately 3.1°C in the lower layer in October. In contrast, it was less than 1.0°C throughout the water column in February. This study suggests that assimilations of the observed temperature profiles are necessary in order to correct the lower layer temperature during the stratified season and an ocean modeling system with small grid spacing and optimal data assimilation method is preferable to ensure accurate predictions of the coastal ocean in the YS.     

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.     

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。     

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.     

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.     

海洋数据同化与数据融合技术应用综述

简述了不同数据同化和数据融合方法在海洋环境监测与预测方面的应用、国内外相关业务单位的海洋分析和预报系统的现状,以及海洋数据同化将来的业务化应用的发展趋势。四维变分和集合卡尔曼滤波正在成为国际上海洋环境分析与预报的主要应用方向,海-气耦合数据同化以及海冰数据同化是目前数据同化方法研究的热点。     

各向异性背景场误差协方差构建及在“凡亚比”台风的应用

利用相临过去时段预报结果中同一时刻不同时效的模式预报场差异,计算预报误差协方差,并基于集合-变分混合同化系统将其与静态背景场误差协方差结合,从而在同化系统中构建了具有各向异性和一定流依赖特征的背景场误差协方差。单点观测理想试验显示本方案改善了静态模型化背景场误差协方差的各向同性和流依赖性问题。“凡亚比”台风的一系列同化及模拟试验表明,从台风路径、强度等方面本文方案的效果都要优于三维变分法。本文方案在不需要集合预报,计算量与三维变分法相当的情况下,给同化系统引入了各向异性、一定流依赖特征的背景误差协方差,因此本方案适于在计算资源较为紧缺情况下,对时效要求较高的预报业务中应用。     

Inversion for Time-Evolving Sound-Speed Field in a Shallow Ocean by Ensemble Kalman Filtering

In the context of the recent Maritime Rapid Environmental Assessment/Blue Planet 2007 sea trial (MREA/BP07), this paper presents a range-resolving tomography method based on ensemble Kalman filtering of full-field acoustic measurements, dedicated to the monitoring of environmental parameters in coastal waters. The inverse problem is formulated in a state–space form wherein the time-varying sound-speed field (SSF) is assumed to follow a random walk with known statistics and the acoustic measurements are a nonlinear function of the SSF and the bottom properties. The state–space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Surface measurements augment the measurement vector to constrain the range-dependent structure of the SSF. Realistic scenarios of vertical slice shallow-water tomography experiments are simulated with an oceanic model, based on the MREA/BP07 experiment. Prior geoacoustic inversion on the same location gives the bottom acoustic properties that are input to the propagation model. Simulation results show that the proposed scheme enables the continuous tracking of the range-dependent SSF parameters and their associated uncertainties assimilating new measurements each hour. It is shown that ensemble methods are required to properly manage the nonlinearity of the model. The problem of the sensitivity to the vertical array (VA) configuration is also addressed.      

Observation bias correction with an ensemble Kalman filter

This paper considers the use of an ensemble Kalman filter to correct satellite radiance observations for state dependent biases. Our approach is to use state-space augmentation to estimate satellite biases as part of the ensemble data assimilation procedure. We illustrate our approach by applying it to a particular ensemble scheme—the local ensemble transform Kalman filter (LETKF)—to assimilate simulated biased atmospheric infrared sounder brightness temperature observations from 15 channels on the simplified parameterizations, primitive-equation dynamics (SPEEDY) model. The scheme we present successfully reduces both the observation bias and analysis error in perfect-model simulations.     

基于海气耦合模式的均权重粒子滤波与集合卡尔曼滤波比较研究

在大气和海洋环境研究中,粒子滤波(PF)由于在非线性数据同化方面突出的优势,逐渐成为研究热点。最近改进的均权重粒子滤波(EWPF)为粒子滤波的进一步发展指明了新方向。集合卡尔曼滤波方法 (EAKF)作为当前主要应用的数据同化方法,使用高斯假设和线性假设来解决非线性问题,然而对均权重粒子滤波方法和卡尔曼滤波方法在非线性模式下的同化结果和特点还缺少系统详细的比较研究。本文在非线性耦合气候模式下,比较研究两种同化方法,采用均方根误差(RMSE)作为评价比较标准。实验结果表明,在非线性低频观测耦合模式中EWPF结果均优于EAKF。同时根据RMSE的结果得出,EWPF的同化结果更接近观察结果,而EAKF的同化结果更接近模式真值。     

Parameter sensitivity of three Kalman filter schemes for assimilation of water levels in shelf sea models

In applications of data assimilation algorithms, a number of poorly known assimilation parameters usually need to be specified. Hence, the documented success of data assimilation methodologies must rely on a moderate sensitivity to these parameters. This contribution presents a parameter sensitivity study of three well known Kalman filter approaches for the assimilation of water levels in a three dimensional hydrodynamic modelling system. The filters considered are the ensemble Kalman filter (EnKF), the reduced rank square root Kalman filter (RRSQRT) and the steady Kalman filter. A sensitivity analysis of key parameters in the schemes is undertaken for a setup in an idealised bay. The sensitivity of the resulting root mean square error (RMSE) is shown to be low to moderate. Hence the schemes are robust within an acceptable range and their application even with misspecified parameters is to be encouraged in this perspective. However, the predicted uncertainty of the assimilation results are sensitive to the parameters and hence must be applied with care. The sensitivity study further demonstrates the effectiveness of the steady Kalman filter in the given system as well as the great impact of assimilating even very few measurements.