A comparison between 3DVAR and EnOI techniques for satellite altimetry data assimilation

Two conceptually different assimilation schemes, three dimensional variational (3DVAR) assimilation and Ensemble Optimum Interpolation (EnOI) are compared in the context of satellite altimetric data assimilation. Similarities and differences of the two schemes are briefly discussed and their impacts on the model simulation are investigated.With a tropical Pacific ocean model, two assimilation experiments of sea level anomaly (SLA) data from TOPEX/Poseidon are performed for 5 years from 1997 to 2001. Annual mean states of temperature and salinity fields are compared with analysis data and some independent observations. It is found that EnOI generally produces moderate improvements on both temperature and salinity fields, while changes induced by 3DVAR assimilation are strong and vary remarkably in different areas. For instance, 3DVAR tends to excessively modify the temperature field along the thermocline depth and even deteriorate the simulation, but it is more effective than EnOI below the thermocline depth. However, for the salinity field 3DVAR outperforms EnOI nearly for almost the whole layer. As the difference relative to the WOA01 analysis is compared, it is apparently reduced to below 0.3 psu in most areas in the 3DVAR experiment. On the other hand, the pattern of difference in the EnOI experiment resembles that of the simulation and the magnitude is only diminished to some extent. One advantage of EnOI is that it yields more consistent improvements even in areas where there are large model errors. It is more reliable than 3DVAR in such a sense. It is also revealed that the T–S relation plays a very important role in altimetric data assimilation. Further, the distinct performance of the two schemes can be partly accounted for by their inherent assumptions and settings.     

云尺度雷达资料的混合同化对台风“桑美”的数值模拟研究

本文采用基于WRFDA的集合-变分混合同化系统（En3DVAR）在云尺度分辨率下同化了雷达观测资料考察其对登陆台风"桑美"的影响。高时空分辨率的雷达径向风资料在台风登陆前的3 h同化窗内以每30 min的频率同化进WRF模式（Weather Research and Forecasting）。研究结果表明:En3DVAR试验在3 h同化窗内的均方根误差相比3DVAR试验改进显著,这可能得益于混合同化系统中提供的"流依赖"的集合协方差信息。系统性的诊断分析表明En3DVAR试验在台风内核区产生了较为明显正温度增量,对台风内核区的热力和动力结构均有较好调整,而3DVAR则在台风内核区产生了负温度增量;相比3DAVR试验,En3DVAR在采用了"流依赖"的集合协方差信息后还可以对背景场上的台风的位置进行系统性的偏差订正。总体而言,En3DVAR试验预报的台风路径和强度相比3DVAR改进显著,其正效果主要来源于混合背景误差协方差中的"流依赖"集合协方差信息。     

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。     

4DVAR data assimilation in the Intra-Americas Sea with the Regional Ocean Modeling System (ROMS)

We present the background, development, and preparation of a state-of-the-art 4D variational (4DVAR) data assimilation system in the Regional Ocean Modeling System (ROMS) with an application in the Intra-Americas Sea (IAS). This initial application with a coarse model shows the efficacy of the 4DVAR methodology for use within complex ocean environments, and serves as preparation for deploying an operational, real-time assimilation system onboard the Royal Caribbean Cruise Lines ship Explorer of the Seas. Assimilating satellite sea surface height and temperature observations with in situ data from the ship in 14 day cycles over 2 years from January 2005 through March 2007, reduces the observation-model misfit by over 75%. Using measures of the Loop Current dynamics, we show that the assimilated solution is consistent with observed statistics.     

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。     

Towards a true 4‐dimensional data assimilation algorithm: application of a cycling representer algorithm to a simple transport problem

3‐dimensional variational algorithms are widely used for atmospheric data assimilation at the present time, particularly on the synoptic and global scales. However, mesoscale and convective scale phenomena are considerably more chaotic and intermittent and it is clear that true 4‐dimensional data assimilation algorithms will be required to properly analyze these phenomena. In its most general form, the data assimilation problem can be posed as the minimization of a 4‐dimensional cost function with the forecast model as a weak constraint. This is a much more difficult problem than the widely discussed 4DVAR algorithm where the model is a strong constraint. Bennett and collaborators have considered a method of solution to the weak constraint problem, based on representer theory. However, their method is not suitable for the numerical weather prediction problem, because it does not cycle in time. In this paper, the representer method is modified to permit cycling in time, in a manner which is entirely internally consistent. The method was applied to a simple 1‐dimensional constituent transport problem where the signal was sampled (perfectly and imperfectly) with various sparse observation network configurations. The cycling representer algorithm discussed here successfully extracted the signal from the noisy, sparse observations     

4DVAR data assimilation in the Intra-Americas Sea with the Regional Ocean Modeling System (ROMS)

We present the background, development, and preparation of a state-of-the-art 4D variational (4DVAR) data assimilation system in the Regional Ocean Modeling System (ROMS) with an application in the Intra-Americas Sea (IAS). This initial application with a coarse model shows the efficacy of the 4DVAR methodology for use within complex ocean environments, and serves as preparation for deploying an operational, real-time assimilation system onboard the Royal Caribbean Cruise Lines ship Explorer of the Seas. Assimilating satellite sea surface height and temperature observations with in situ data from the ship in 14 day cycles over 2 years from January 2005 through March 2007, reduces the observation-model misfit by over 75%. Using measures of the Loop Current dynamics, we show that the assimilated solution is consistent with observed statistics.     

TRMM海表降水率同化在热带气旋Danas(2001) 数值模拟中的应用研究

研究了TRMM/TMI海表降水率资料的四维变分同化在热带气旋(TC)数值模拟中的作用.使用中尺度气象模式MM5设计了若干数值试验模拟了TC Danas(2001)由热带低压初生到台风生成的发展过程.在满足MM5模式动力约束的前提下,将TRMM海表降水率资料直接同化进入较高分辨率(18 km)的模式初始场.结果表明,使用MM5模式的4D-VAR同化系统直接同化TRMM/TMI海表降水率资料是可行的.这种做法提高了TRMM资料的利用率,不仅在模式初始场中加入了更多实测信息,而且避免了两次同化(1DVAR+4DVAR)可能引起的误差.直接同化TRMM资料通过调整气压、温度、湿度等要素初始场,改善了模式对热带气旋结构(如暖心、涡度、散度)的描述和降水的模拟.在此基础上,同化不仅改进了对Danas强度的模拟,而且成功地模拟了热带气旋环境场的演变过程,因而改进了路径的模拟.     

直接同化卫星辐射数据的黄海海雾数值试验研究

基于中尺度大气模式WRF及其3DVAR.模块,采用循环3DVAR数据同化方案,针对6次明显的黄海海雾过程,实施了一系列直接同化ATOVS卫星辐射数据数值试验.在试验中设计了不同化任何观测数据、仅同化GTS常规数据、仅直接同化辐射数据,同时同化二者,以及同化不同疏密程度辐射数据的对比研究方案.利用地面水平能见度与卫星云图对模拟的海雾雾区进行了评估,并比较了各种同化方案所形成初始场的差异.对试验结果的统计分析表明:同化试验较好地再现了影响海雾的天气系统,模拟雾区与实际观测较为吻合,并且初始温度场和湿度场对比不同化任何观测数据的试验有明显的改善;仅同化辐射数据的结果略优于仅同化常规数据的结果,疏化或者只同化海上辐射数据几乎不影响模拟的雾区,但却可以大幅节约计算资源;同时同化常规数据与辐射数据的结果为单独同化它们所得结果的综合体现,总体效果最好.     

不同 AMDAR资料同化时间窗对台风“摩羯”预报影响研究

2018年第14号台风“摩羯”对山东造成了大范围暴雨和大风天气,基于WRF（Weather Research and Forecasting）模式及其Hybrid-3DVAR混合同化预报系统,对Hybrid-3DVAR不同集合协方差比例和不同航空气象数据转发（aircraft meteorological data relay,以下简称AMDAR）资料同化时间窗对台风“摩羯”预报的影响进行了数值研究。结果表明：加大集合协方差比例对台风“摩羯”路径预报有较大影响和改进;当全部取来自集合体的流依赖误差协方差时,预报的台风路径最好,降水预报也最接近实况;AMDAR资料同化对于台风路径和降水预报也有正的改进作用,但加大集合协方差比例到100%时对台风路径预报影响更大;不同资料同化时间窗会影响同化的AMDAR资料数量,从而影响台风降水精细化预报;45 min同化时间窗的要素预报误差最小,对台风造成的强降水精细特征预报最接近实况;不同资料同化时间窗主要影响台风降水预报落区分布,对台风路径预报影响相对较小。     

Assimilation of simulated altimeter data in a two-layer linear Rossby wave model using the variational method

The variational assimilation method has been examined for ability of reconstructing mesoscale features in altimeter data using a simple dynamic model. A one-dimensional, two-layer Rossby wave model in a cross-track channel has been chosen. The simulated data are constructed from a theoretical solution, which is composed of any combination of two normal vertical (barotropic and baroclinic) modes. The data are collected along tracks and with repeat periods similar to those of the Geosat altimeter. The phase space of control variables is composed of initial and boundary conditions. A cost function is defined to measure differences between the simulated data and the model solution. Regularization (smoothing) terms are also included in the cost function in the form of secon-order spatial and time derivatives of the solution. In this paper, two potential problems existing in the altimeter data assimilation are addressed: one is low cross-track resolution, and the other is vertical projection of the data measured at the sea surface. A succesful metho is developed for reconstructing Rossby waves with wavelengths as short as twice the track intervals for any combination of two vertical modes. A key component to efficient assimilation is a preparation step prior to the actual variational assimilation: a uniform ratio of pressure amplitudes in the two layers is included as an optimization parameter. Starting with the first guess from the preparation step, the variational method is carried out based on adjoint equations without such constraint. Separation of the control variables into the two subsets of the initial and the boundary conditions is found useful. Characteristics of the Hessian matrix are related to the performance of this technique. The method developed for the linear system implies steps to be included in data assimilation for nonlinear meanders and eddies in a major current system as well.     

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…     

多普勒雷达资料同化在台风“灿都”(2010)预报中的应用研究

文章基于中尺度天气预报模式(WRF)及其三维变分同化系统(WRF-3DVAR), 采用了两部雷达径向风资料, 进行单一时间分析以初始化台风“灿都”(Chanthu), 比较研究了同化雷达径向速度(V_r)对台风“灿都”分析和预报的影响。结果表明: 同化雷达径向风的作用主要体现在台风强度和环流结构的调整, 且在同化达到一定时长后, 对改进同化后的预报分析有积极效应。同化试验改进台风的初始风场以及台风环流中心的热力和动力结构、强度和位置, 进而提高18h预报的台风结构、路径、强度。     

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.     

Incremental 4D-VAR assimilation scheme based on Lorenz model

Four-dimensional variational(4D-VAR) data assimilation method is a perfect data assimilation solution in theory, but the compu- tational issue is quite difficult in operational implementation. The incremental 4D-VAR assimilation scheme is set up in order to re- duce the computational cost. It is shown that the accuracy of the observations, the length of the assimilation window and the choice of the first guess have an important influence on the assimilation outcome through the contrast experiment. Compared with the standard 4D-VAR assimilation scheme, the incremental 4D-VAR assimilation scheme shows its advantage in the computation speed through an assimilation experiment.     

双多普勒雷达资料同化在飓风“艾克”预报中的应用研究

本文采用美国国家大气研究中心（NCAR）开发的中尺度数值模式WRFV3.7及其三维变分同化系统WRF-3DVAR对2008年飓风“艾克”进行了数值模拟研究。利用多普勒天气雷达观测资料具有高时空分辨率的优点,将美国两部多普勒天气雷达资料进行速度退模糊等必要质量控制后同化进中尺度数值模式,考察雷达资料同化对飓风“艾克”预报的改进程度。试验结果表明:将雷达资料用于对流尺度分辨率下飓风初始化需要对变分同化系统中特征尺度化因子进行优化调整,使观测资料能够以较为合理的方式调整模式初始场并进而改进预报;雷达径向风同化可以有效调整模式初始场中的飓风动力和热力结构,而经过尺度化因子调整后的雷达径向风同化则在飓风观测中心位置产生较为合理的气旋性风场增量,提供更为确切的中小尺度信息,使模式初始场更加接近观测并进而改进对飓风路径和强度的预报。     

An OSSE Study for Deep Argo Array using the GFDL Ensemble Coupled Data Assimilation System

An observing system simulation experiment (OSSE) using an ensemble coupled data assimilation system was designed to investigate the impact of deep ocean Argo profile assimilation in a biased numerical climate system. Based on the modern Argo observational array and an artificial extension to full depth, “observations” drawn from one coupled general circulation model (CM2.0) were assimilated into another model (CM2.1). Our results showed that coupled data assimilation with simultaneous atmospheric and oceanic constraints plays a significant role in preventing deep ocean drift. However, the extension of the Argo array to full depth did not significantly improve the quality of the oceanic climate estimation within the bias magnitude in the twin experiment. Even in the “identical” twin experiment for the deep Argo array from the same model (CM2.1) with the assimilation model, no significant changes were shown in the deep ocean, such as in the Atlantic meridional overturning circulation and the Antarctic bottom water cell. The small ensemble spread and corresponding weak constraints by the deep Argo profiles with medium spatial and temporal resolution may explain why the deep Argo profiles did not improve the deep ocean features in the assimilation system. Additional studies using different assimilation methods with improved spatial and temporal resolution of the deep Argo array are necessary in order to more thoroughly understand the impact of the deep Argo array on the assimilation system.     

利用循环3DVAR改进黄海海雾数值模拟初始场Ⅰ:WRF数值试验

以如何提高黄海海雾数值模拟初始场质量为研究目的,利用WRF模式及其先进的3DVAR同化模块,设计并构建了循环3DVAR同化方案。以2006年3月6~8日的1次大范围黄海海雾过程为研究对象,利用该同化方案进行了一系列WRF数值模拟对比试验。模拟结果显示,循环3DVAR同化方案能有效改进黄海海雾数值模拟初始场质量,主要体现在增加低层大气温度层结构的稳定性与改变大气边界层下层的风场结构,从而导致海雾的模拟结果显著改善。研究结果表明进行海雾数值模拟时,必须高度重视其初始场质量。     

EnKF集合同化下黄海海雾数值确定性预报初始场构造方法的探究

在黄海海雾的数值模拟中,EnKF（ensemble Kalman filter）是一种优于3DVAR（three-dimensional variational）的数据同化方法。研究发现,对EnKF初始场集合体采取常用的集合平均所产生的确定性预报初始场,会出现初始场中海雾在预报开始后就迅速消失以及接下来海雾难以生成的异常现象。通过详细的海雾个例研究,清晰地揭示并解释了此现象,指出这是集合平均造成初始场中云水与温度湿度之间存在不协调关系所导致的后果,并提出了一种择优加权平均方法来取代常用的集合平均。研究结果表明,海雾确定性预报采用择优加权平均所构建的初始场,可以消除上述异常现象,显著改进海雾模拟效果。     

Improvement of short-termforecasting in the northwest Pacific through assimilating Argo data into initial fields

The impact of assimilating Argo data into an initial field on the short-term forecasting accuracy of temper- ature and salinity is quantitatively estimated by using a forecasting system of the western North Pacific, on the base of the Princeton ocean model with a generalized coordinate system （POMgcs）. This system uses a sequential multigrid three-dimensional variational （3DVAR） analysis scheme to assimilate observation da- ta. Two numerical experiments were conducted with and without Argo temperature and salinity profile data besides conventional temperature and salinity profile data and sea surface height anomaly （SSHa） and sea surface temperature （SST） in the process of assimilating data into the initial fields. The forecast errors are estimated by using independent temperature and salinity profiles during the forecasting period, including the vertical distributions of the horizontally averaged root mean square errors （H-RMSEs） and the horizontal distributions of the vertically averaged mean errors （MEs） and the temporal variation of spatially averaged root mean square errors （S-RMSEs）. Comparison between the two experiments shows that the assimila- tion of Argo data significantly improves the forecast accuracy, with 24% reduction of H-RMSE maximum for the temperature, and the salinity forecasts are improved more obviously, averagely dropping of 50% for H-RMSEs in depth shallower than 300 m. Such improvement is caused by relatively uniform sampling of both temperature and salinity from the Argo drifters in time and space.