两种四维奇异值分解同化方法的比较及误差分析

4DSVD是最近提出的一种新的资料同化方法。目前还存在一些需要解决的问题,比如如何选取样本,如何得到支撑大气吸引子的基向量以及选取基向量的个数问题等等。作者利用奇异值分解(SVD)与经验正交函数分解(EOF)两种方法来获得支撑大气吸引子的基向量,推导了基于这两种方法的4DSVD分析场的理论公式,并用简单的数值试验比较了基于这两种方法的4DSVD分析场的空间相关系数和误差,初步分析了分析场与基向量个数的关系以及与样本选取的关系和分析误差的来源及各种误差对分析误差影响的相对大小。结果表明,用SVD方法作为获得支撑大气吸引子基向量的方法得到的分析场较EOF方法稳定,分析场与基向量个数有密切关系,观测误差、模式误差和观测代表性误差是分析误差的主要来源,且其引起的分析误差随着基向量个数增多而增大。     

An Ensemble-Based Three-Dimensional Variational Assimilation Method for Land Data Assimilation

Land surface models are often highly nonlinear with model physics that contain parameterized discontinuities. These model attributes severely limit the application of advanced variational data assimilation methods into land data assimilation. The ensemble Kalman filter （EnKF） has been widely employed for land data assimilation because of its simple conceptual formulation and relative ease of implementation. An updated ensemble-based three-dimensional variational assimilation （En3-DVar） method is proposed for land data assimilation This new method incorporates Monte Carlo sampling strategies into the 3-D variational data assimilation framework. The proper orthogonal decomposition （POD） technique is used to efficiently approximate a forecast ensemble produced by the Monte Carlo method in a 3-D space that uses a set of base vectors that span the ensemble. The data assimilation process is thus significantly simplified. Our assimilation experiments indicate that this new En3-DVar method considerably outperforms the EnKF method by increasing assimilation precision. Furthermore, computational costs for the new En3-DVar method are much lower than for the EnKF method.     

中尺度数值模式MM5的四维变分资料同化系统

应用伴随方法求解以数值预报方程作为约束条件的四维变分资料同化方案，关键问题是如何构造伴随模式。以中尺度数值模式MM5为例，讨论了如何用伴随码技术建立MM5伴随模式，以及伴随模式系统中权重、尺度因子的选取；最后对MM5伴随模式系统进行了梯度检验，并利用实际资料进行四维变分资料同化试验。试验表明该系统有较强的同化能力，能够提高MM5降水预报的准确性。     

在四维变分同化中运用集合协方差的试验

利用浅水方程模式和模式模拟资料进行数值试验比较3种不同的背景误差协方差矩阵处理方法对四维变分(4DVAR)资料同化的影响.3种背景误差协方差矩阵分别是:(1)对单一变量将背景误差协方差矩阵简化为对角矩阵;(2)将背景误差协方差矩阵的作用简化为高斯过滤;(3)由预报集合生成背景误差协方差矩阵并利用奇异值分解技术解决矩阵的求逆.通过一系列数值试验,比较不同观测密度、不同观测误差下3种背景误差协方差处理方法对4DVAR同化效果的影响.结果表明,背景误差协方差的结构对4DVAR有重大影响.当观测资料的空间密度不够高时,采用对角矩阵得不到满意的结果.高斯过滤方案可以明显改善同化结果,但是对背景误差特征长度比较敏感.第3种方法采用的背景误差协方差矩阵是流型依赖的,而且并不以显式的方式出现在目标函数中.避免了对它求逆的复杂运算.由于做了降维处理,在观测点的密度较低和观测误差较大时可望取得较好的同化结果,同化效果较为稳定.     

Adaptive observations in the context of 4D-Var data assimilation

Summary The design of adaptive observations strategies must account for the particular properties of the data assimilation method. A new adjoint sensitivity approach to the targeted observations problem is proposed in the context of four-dimensional variational data assimilation (4D-Var). The method is based on a periodic update of the adjoint sensitivity field that takes into account the interaction between time distributed adaptive and routine observations. Information provided by all previously located observations is used to identify best locations for new targeted observations. Adaptive observations at distinct instants in time are selected in a sequential manner such that the method is only suboptimal. The selection algorithm proceeds backward in time and requires only one additional adjoint model integration in the assimilation window. Therefore, the method is very efficient and is suitable for practical applications. A comparative performance analysis is presented using the traditional adjoint sensitivity method as well as the total energy singular vectors technique as alternative adaptive strategies. Numerical experiments are performed in the twin experiments framework using a two-dimensional global shallow water model in spherical coordinates and an explicit Turkel-Zwas discretization scheme. Data from a NASA 500mb analysis valid for 00Z 16 Mar 2001 6h obtained with the GEOS-3 model was used to specify the geopotential height at the initial time and the initial velocities were obtained from a geostrophic balance. Numerical results show that the new adaptive observations approach is a promising method for targeted observations and its implementation is feasible for large scale atmospheric models.     

The use of successive dynamic initialization by nudging to simulate cyclogenesis during GALE IOP 1

Summary Synoptic/diagnostic case studies have increasingly come to rely on numerical simulations started from some initial state after which the model generated fields receive no further information from observed data. The purpose of this paper is to demonstrate the use of a dynamic data assimilation technique based on nudging to create a dynamically consistent high-resolution four-dimensional data set that can be used for synoptic diagnostic studies. The nudging technique is applied in the Goddard Mesoscale Atmospheric Simulation System (GMASS) using the 3-h radiosonde data collected during GALE IOP 1. A unique aspect of this application is nudging toward data analyses for which the areal coverage shifts with time. One of the two nudging simulations assimilates surface pressure in addition to the temperature, mixing ratio, and wind components. The nudging values are determined by linear interpolation between 3-h observation times. Assuming a linear variation of the assimilated value in time leads to estimates of the nudging coefficients which take into account the accuracy of the observations.Both nudging simulations are more accurate in terms of S hand root-mean-square error (RMSE) scores than a control sunulation without successive initialization. The nudging simulation with surface pressure is more accurate than the nudging simulation without surface pressure assimilation for this case. The simulation with surface pressure nudging captures the surface cyclogenesis and the associated strong rise-fall couplet in the 500 hPa height field. It also exhibits the strongest ageostrophic flow and exit region vertical circulation associated with a jet streak on the western side of the intensifying upper-level trough.The data sets made possible by the dynamic assimilation/ simulation cycles are dynamically consistent, have high spatial and temporal resolution and are ideally suited for diagnostic studies. Examples presented include the evolution of the ageostrophic flow associated with the exit region of an upper-level jet propagating toward the base of an intensifying trough with increasing cyclonic curvature of the flow. The nudging simulation with surface pressure provides the resolution and accuracy required to depict the rapid transformation (within a 12-h period) of the exit region ageostrophic flow from predominantly cross contour to along contour as the jet streak approaches the base of the trough.With 19 Figures     

多普勒雷达四维变分分析系统概述

《热带气象学报》是中国气象局广州热带海洋气象研究所主办的学术期刊,由气象出版社出版;其前身是《热带气象》,创刊于1984年,已经连续出版20年了。《热带气象学报》主要刊登热带大气科学的基础理论研究及应用研究方面的论文、热带地区天气预报的先进方法和成功的经验、推动学科发展的综合评述和学术动态。当前一段时间的刊登重点是:海气相互作用,中低纬大气环流相互作用,低频振荡及遥相关,低纬大气环流异常及其机制,热带大气环流异常对全球天气、气候的影响以及季风动力学、热带气旋动力学与运动学等的学术成果。由于国家重视气象科学研究,…     

Dynamical and Microphysical Retrieval from Simulated Doppler Radar Observations Using the 4DVAR Assimilation Technique

Based on a cloud model and the four-dimensional variational (4DVAR) data assimilation method developed by Sun and Crook (1997), simulated experiments of dynamical and microphysical retrieval from Doppler radar data were performed. The 4DVAR data assimilation technique was applied to a cloud scale model with a warm rain parameterization scheme. The 3D wind, thermodynamical, and microphysical fields were determined by minimizing a cost function, defined by the difference between both radar observed radial velocities and reflectivities and their model predictions. The adjoint of the numerical model was used to provide the gradient of the cost function with respect to the control variables. Experiments have demonstrated that the 4DVAR assimilation method is able to retrieve the detailed structure of wind, thermodynamics, and microphysics by using either dual-Doppler or single-Doppler information. The quality of retrieval depends strongly on the magnitude of constraint with respect to the variables. Retrieving the temperature field, cloud water and water vapor is more difficult than the recovery of the wind field and rainwater. Accurate thermodynamic retrieval requires a longer assimilation period. The inclusion of a background term, even mean fields from a single sounding, helped reduce the retrieval errors. Less accurate velocity fields were obtained when single-Doppler data were used. It was found that the retrieved velocity is sensitive to the location of the retrieval domain relative to the radars while the other fields have very little changes. Two radar volumetric scans are generally adequate for providing the evolution, although the use of additional volumes improves the retrieval. As the amount of the observations decreases, the performance of the retrieval is degraded. However, the missing observations can be compensated by adding a background term to the cost function. The technique is robust to random errors in radial velocity and calibration errors in reflectivity. The boundary conditions from the dual-Doppler synthesized winds are sufficient for the retrieval. When the retrieval is mainly controlled by the observations in the regions away from the boundaries, the simple boundary conditions from velocity azimuth display (VAD) analysis are also available. The microphysical retrieval is sensitive to model errors.     

气象场观测误差和四维同化数值模拟试验

本文对气象观测中的随机误差和四维同化进行了数值摸拟试验。用五层原始方程模式,以1975年4月19日20时的观测资料作初始场进行六天预报。把每小时的预报结果贮存起来,作为没有误差的“真实大气观测资料”,然后在原来的初始场上加上一个随机误差场,用一个物理过程比前者稍差的同样模式进行数值预报,把“真实资料”不断嵌入模式中去进行四维同化试验。 误差场是用概率统计中产生伪随机数的办法产生以模拟观测误差的随机情况。 四维同化的试验结果表明:最优同化频率,不仅与观测资料误差有关,而且还与整个同化过程的长短有关。     

SVD-En3DVar方法同化多普勒雷达速度观测资料 II. 实际资料试验

文章的第Ⅰ部分(徐道生等,2011)将基于SVD (singular value decomposition)技术和预报集合的三维变分同化方法(SVD-En3DVar)用于同化模拟的雷达速度观测资料,试验表明,通过3DVar (three-dimensional variational technique)方法产生预报...     

由大尺度观测提取中尺度信息的可能性研究

利用浅水方程模式和变分四维同化方法对由大尺度观测提取中尺度信息的可能性进行了模拟试验研究。试验的初始场是在平直气流上叠加一个半径为 5倍格距的圆形涡旋。分别设定观测点的间距是 5 ,7和 9倍格距 ,观测的时间间隔分别是 1,2和 3h ,同化时间为 6h或 12h ,考察同化产生的初始场。试验结果是 :观测点的间距是 5倍格距时 ,由观测给出的分析场不能反映涡旋的基本特征 ,而在同化产生的初始场中 ,涡旋的基本结构清楚 ,但强度有所削弱。增加观测次数或者延长同化时间 ,可以改善同化的结果。对于移动较快的系统 ,同化的结果较好。当观测点的间距是 9倍格距时 ,同化的结果与分析场相比已无明显改进。     

FOUR-DIMENSIONAL DATA QUALITY CONTROL THROUGH THE ADJOINT APPROACH*

Using the variational four-dimensional (4-D) data assimilation technique (the adjoint method), we defined the error/mean-error ratios (EMER) of observational data. The plausibility of marking the gross error using the EMER is investigated theoretically under some assumptions.Idealized numerical experiments are carried out using the simple Lorenz model to test the quality control scheme.     

FOUR-DIMENSIONAL DATA QUALITY CONTROL THROUGH THE ADJOINT APPROACH

Using the variational four-dimensional (4-D) data assimilation technique (the adjointmethod), we defined the error/mean-error ratios (EMER) of observational data. The plausibilityof marking the gross error using the EMER is investigated theoretically under some assumptions.Idealized numerical experiments are carried out using the simple Lorenz model to test the qualitycontrol scheme.     

多普勒雷达资料4DVAR同化反演的模拟研究

利用Sun等建立的同化模式和四维变分同化方法对多普勒雷达资料反演大气风场、热力场和微物理场进行了模拟试验研究.反演的基本思路是将4DVAR同化方法应用到三维云模式,定义价值函数表征雷达资料与模式预报结果之间的差别,通过极小化价值函数得到反演场,价值函数相对模式控制变量的梯度由伴随模式求取.试验结果表明,4DVAR同化技术能够从单(双)多普勒雷达资料反演大气三维风场、热力场和微物理场.各个变量反演精度高低与同化过程中变量受约束的大小程度呈正相关.速度场和雨水场反演精度较高,温度场、云水和水汽的反演精度次之,温度场的准确反演需要较长的同化时间.价值函数中加入背景场,哪怕是单点探空给出的平均场信息也有利于提高反演精度.在采用单部多普勒雷达资料进行反演时,速度场的反演误差较大.反演区相对雷达站的位置变化对速度场反演结果有一定的影响,而对其他变量的反演影响很小.两个时次的雷达观测资料基本足够提供反演所需的时间演变信息,同化更多时次的雷达资料,反演效果改进很小.雷达观测资料的缺值会显著降低同化效果,甚至可能导致同化失败,引入背景场可以改善这一状况.4DVAR同化技术对于雷达观测资料误差不太敏感.利用双多普勒雷达合成风场提供水平风场边界条件是比较准确可靠的.在反演主体离边界较远时,VAD风场也基本可用作水平风场边界条件.微物理场的反演对模式中的微物理参数化方案较敏感.     

Testing a four-dimensional variational data assimilation method using an improved intermediate coupled model for ENSO analysis and prediction

A four-dimensional variational (4D-Var) data assimilation method is implemented in an improved intermediate coupled model (ICM) of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The “observation” of the SST anomaly, which is sampled from a “truth” model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.     

加密探空资料同化对一次降水预报能力改进研究

通过设计不同的试验方案,将加密探空资料同化到WRF模式中,对一次层状云系的降水过程进行了数值模拟.采用实时四维资料同化的方法,使得背景场和观测资料相协调,在一定程度上解决了模式的spin up问题.将温度同化到模式里,改变了模式原有的热力场,使得模式动力场随之改变,模式模拟的结果更接近实际观测.经过松弛(nudging)之后,得到的雷达回波、高度场、温度和实况很像,降水也要比不加探空资料的降水更接近实况.鉴于只有两个地方的探空资料,并不能覆盖整个模式区域,以及同化过程还需要改进,模式模拟的结果和实际观测之间还有一定的差异,有待更深入的研究.     

用一种新的同化方法同化降水量资料

Observations of accumulated precipitation are extremely valuable for effectively improving rainfall analysis and forecast. It is, however, difficult to use such observations directly through sequential assimilation methods, such as three-dimensional variational data assimilation or an Ensemble Kalman Filter. In this study, the authors illustrate a new approach that makes effective use of precipitation data to improve rainfall forecast. The new method directly obtains an optimal solution in a reduced space by fitting observations with historical time series generated by the model; it also avoids the implementation of tangent linear model and its adjoint. A lot of historical samples are produced as the ensemble of precipitation observations with the fully nonlinear forecast model. The results show that the new approach is capable of extracting information from precipitation observations to improve the analysis and forecast. This method provides comparable performance with the standard four- dimensional variational data assimilation at a much lower computational cost.     

四维变分同化技术在优化Z-C预测模式初始场中的应用试验

文中使用四维变分同化技术将海温观测资料同化到Zebiak-Cane模式中,通过优化模式的初始场提高了模式的预报技巧.通过用理想场进行检验,说明所建立的同化伴随模式是正确的 .用文中建立的四维变分同化模式以1997年1月为初始场所做的预报结果与实况相比,结果较好.这对今后ENSO预报打下了良好的基础.     

Assessment of Data Assimilation Approaches for the Simulation of a Monsoon Depression Over the Indian Monsoon Region

A low pressure system that formed on 21 September 2006 over eastern India/Bay of Bengal intensified into a monsoon depression resulting in copious rainfall over north-eastern and central parts of India. Four numerical experiments are performed to examine the performance of assimilation schemes in simulating this monsoon depression using the Fifth Generation Mesoscale Model (MM5). Forecasts from a base simulation (with no data assimilation), a four-dimensional data assimilation (FDDA) system, a simple surface data assimilation (SDA) system coupled with FDDA, and a flux-adjusting SDA system (FASDAS) coupled with FDDA are compared with each other and with observations. The model is initialized with Global Forecast System (GFS) forecast fields starting from 19 September 2006, with assimilation being done for the first 24 hours using conventional observations, sounding and surface data of temperature and moisture from Advanced TIROS Operational Vertical Sounder satellite and surface wind data over the ocean from QuikSCAT. Forecasts are then made from these assimilated states. In general, results indicate that the FASDAS forecast provides more realistic prognostic fields as compared to the other three forecasts. When compared with other forecasts, results indicate that the FASDAS forecast yielded lower root-mean-square (r.m.s.) errors for the pressure field and improved simulations of surface/near-surface temperature, moisture, sensible and latent heat fluxes, and potential vorticity. Heat and moisture budget analyses to assess the simulation of convection revealed that the two forecasts with the surface data assimilation (SDA and FASDAS) are superior to the base and FDDA forecasts. An important conclusion is that, even though monsoon depressions are large synoptic systems, mesoscale features including rainfall are affected by surface processes. Enhanced representation of land-surface processes provides a significant improvement in the model performance even under active monsoon conditions where the synoptic forcings are expected to be dominant.     

台风数值模拟中bogus涡旋四维变分同化的研究

研究用MM5四维变分同化系统同化bogus涡旋变量对台风数值模拟的影响,对2002年13号台风Phanfone进行48h预报,结果表明：用四维变分方法同化bogus涡旋变量效果优于在背景场中直接植入模型涡旋的传统bogus技术。同时同化bogus涡旋的风、气压、温度和比湿效果不如只同化气压和其中任一变量。同化bogus涡旋的气压和比湿,能够调整模式初始场的其他变量,得到结构更清晰、与环境场更协调的初始涡旋,从而在一定程度上提高了台风Phanfone路径和强度预报的准确性。