EnKF协方差膨胀算法对雷达资料同化的影响研究

基于集合卡尔曼滤波(EnKF)方法同化模拟雷达径向风和回波,引入具有时空自适应理论优势的贝叶斯膨胀算法,通过与常数膨胀算法的对比,分析了两种协方差膨胀算法对EnKF同化效果的影响。结果表明:在对流区域的北侧,由贝叶斯膨胀算法分析得到的回波在水平和垂直结构上均增强;在对流区域,由贝叶斯膨胀算法分析得到的各变量的集合离散度增大,均方根误差减小,水平和垂直速度增大,冷池强度减弱;模拟还发现贝叶斯膨胀算法提高了强对流系统的模拟效果,回波强度增强,阵风锋区内水平和垂直风速增大。这表明贝叶斯膨胀算法有效地改进了基于常数膨胀算法的EnKF同化雷达资料的效果。     

GRAPES集合卡尔曼滤波资料同化系统Ⅰ:系统设计及初步试验

集合卡尔曼滤波资料同化方法,可以用集合样本统计出随天气形势变化的误差协方差,是当前资料同化领域的研究热点。主要介绍了GRAPES集合卡尔曼滤波资料同化系统的设计以及初步的试验结果。针对集合卡尔曼滤波同化实际观测资料难以实施的问题,采用成批观测同化的顺序同化方法进行多变量的集合卡尔曼滤波同化;为了滤除有限集合数造成的误差相关噪音和缓解求逆矩阵不满秩的问题,在水平和垂直方向都采用了Schur滤波;建立了与GRAPES预报模式的垂直坐标和预报变量一致的模式面集合卡尔曼滤波系统;集合样本的生成考虑了模式变量的空间相关和模式变量之间的相关,通过利用三维变分分析中的控制变量变换得到模式变量扰动场。通过比较GRAPES集合卡尔曼滤波资料同化系统和GRAPES区域三维变分资料同化系统的单点观测资料同化分析结果,对比背景误差相关系数的分布,验证了GRAPES集合卡尔曼滤波系统的正确性。此外,同化区域探空观测资料试验结果表明,GRAPES集合卡尔曼滤波资料同化系统能够得到合理的分析,并且具有实际运行能力。对分析结果进行12h预报表明,GRAPES集合卡尔曼滤波资料同化系统的分析协调性不如三维变分资料同化系统。     

集合变分混合同化背景误差协方差流依赖性分析

通过单点观测试验的方法,对集合变分混合同化背景误差协方差的流依赖特征、流依赖性影响因子、产生原因,以及集合预报方法对流依赖性的影响进行了研究。结果表明:由于引入了集合信息,集合变分混合同化的分析增量与天气系统的分布有关,具有非均匀、各向异性的特征;这种流依赖特征对混合系数敏感,当集合协方差所占权重很小时,分析增量仍呈现出均匀、各向同性特征;混合同化背景误差协方差的流依赖特征不仅与集合样本有关,还与构造集合协方差的ETKF方法有关,只引入与环流形势密切相关的集合样本并不能使分析增量表现出显著的流依赖性,集合样本和ETKF方法共同作用才能将流依赖信息引入到混合协方差中,使分析增量出现流依赖特征;不同集合预报方法对混合协方差的流依赖特征有显著影响,考虑初值和物理过程的超级集合,以及在超级集合样本上再进行ETKF更新扰动后样本构造的混合协方差流依赖特征更加显著。     

GSI同化系统的背景误差协方差特征及对预报的影响

在同化系统中使用更合理的背景误差协方差对于得到更良好的同化效果至关重要。首先采用NMC方法针对中国区域构建更适合WRF-ARW区域预报系统的B矩阵,并对比分析了其与GSI同化系统预设的NCEP预报系统的B矩阵在分析变量间的平衡关系、分析控制变量的标准差、水平和垂直特征尺度等方面的特征差异。参照这些特征差异设计单点观测试验、背景误差协方差调优参数敏感性试验,确定针对中国区域构建B矩阵的最佳调优参数。并讨论其对一次季风低压强降水天气过程的循环同化和预报效果的影响。结果表明,采用最佳调优参数使用针对中国区域构建B矩阵的试验(Sen6)对V风分量场和相对湿度场的预报性能改进显著,同时也引出了GSI同化系统背景误差协方差参数调优(尤其是水平特征尺度参数调整)的两难问题。在此基础上,采用Hybrid同化方法使用针对中国区域构建B矩阵的循环同化试验(Hyb3)可以进一步改善预报效果,并在一定程度上修正个例模拟雨带的位置。     

混合误差协方差用于集合平方根滤波同化的试验

在集合卡尔曼滤波方法中, 根据预报集合统计提供的依流型而变的预报误差协方差对同化起到决定性的作用。但在集合样本容量不足及模式存在系统误差时, 由预报集合估计的预报误差协方差会出现明显偏差。既要减小这种估计偏差对同化产生的影响而又不增加计算量, 一种可供选择的方法是将定常或准定常的高斯型预报误差协方差和由预报集合估计的预报误差协方差加权平均用于集合卡尔曼滤波同化。利用浅水方程模式, 通过观测系统模拟试验检验在不同的模式误差、 集合成员数以及观测密度条件下, 将这种混合预报误差协方差矩阵用于在集合平方根滤波的效果。试验结果表明, 当预报集合成员数较多而模式又无误差时, 不必采用混合的预报误差协方差矩阵, 否则, 采用混合的预报误差协方差矩阵都有可能改进分析和预报。混合预报误差协方差的最优的权重系数与模式误差关系密切, 模式误差越大, 定常预报误差协方差的权重越大。最优的权重系数与集合成员数及观测密度也有一定关系。     

集合卡尔曼滤波同化中雷达位置的敏感性研究

针对对流尺度集合卡尔曼滤波（EnKF）雷达资料同化中雷达位置对同化的影响进行研究。为了考察强对流出现在雷达不同方位时集合卡尔曼滤波同化雷达资料的能力,以一个理想风暴为例,设计了8个均匀分布在模拟区域周围的模拟雷达进行试验。单雷达同化试验中,初期同化对雷达位置较敏感,而十几个循环后对雷达方位的敏感性降低。造成初期同化效果较差的雷达观测位于模拟区域正南和正北方向,这两部雷达与模拟区域中心的连线垂直于风暴移动方向（即环境气流的方向）。双雷达试验的结果表明,正东、正南、正西和正北方向的雷达组合观测会使同化初期误差较大,这说明并不是所有与风暴连线成90°的雷达组合都能在短时同化中得到合理的分析结果,还需要都处于模拟区域对角线上（即与环境气流成45°夹角）,同化效果才较好。短时同化后的确定性预报结果表明,较大分析误差也会导致较大预报误差。这些分析误差主要是由于同化初期不准确的集合平均场驱动出的不合理的背景误差协方差造成的。当背景场随着同化循环得到改进后,驱动出的合理的背景误差协方差使得不同位置雷达同化造成的差异逐步减小。基于上述结果,引入迭代集合均方根滤波（iEnSRF）算法,结果显示使用该算法后,雷达位置对同化效果的影响减小,同化不同位置的雷达资料均能有效降低分析和预报误差。      

区域三维变分同化中背景误差协方差的模拟

背景误差协方差(B)是变分同化中的一个重要部分,极大地影响同化系统输出的分析场.由于计算和指定B中有关统计量需要巨大的资料存储量和计算量,因此进行相关的研究较为困难.本文首先论述了B在变分同化中的重要性以及进行模拟的必要性;接着介绍了美国NMC方法的原理,并研究将其应用到区域三维变分同化中的方法;然后利用WRF模式生成的预报场差值集合对有关统计量进行了估计.揭示了以下结论:通过使用平衡变换和回归系数,控制变量被限制在较小范围内,保证了分析场的质量;流函数第一全局特征向量在200 hPa附近的最大分量,表示了急流层中强西风误差;流函数前五个全局特征向量在低层与中高层之间是负相关的;非平衡温度和相对湿度的特征长度尺度比流函数和非平衡速度势的值要小,说明它们是局地性较强的量.流函数和非平衡速度势的特征长度尺度随垂直模态数的增大快速减小,而相对湿度和非平衡温度的特征长度尺度随垂直模态数的变化较为平缓.     

基于云依赖背景场误差协方差的雷达资料同化及对降雨预报影响研究

传统变分同化方法中使用各向同性和均质的背景场误差协方差,忽略了背景场误差协方差的天气系统依赖性,而在变分框架下引入集合流依赖的背景场误差协方差还需要额外的集合预报.为在变分同化中引入更合理的背景场误差协方差,通过引入云指数构建"云依赖"背景场误差协方差,提出了一种云依赖背景场误差协方差的同化方案,并应用于雷达等多源观测...     

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.     

集合卡尔曼滤波数据同化在一维波动方程中的应用

简要回顾了集合卡尔曼滤波(EnKF：Ensemble Kalman Filter)数据同化方法的发展历史,并介绍了EnKF数据同化方法的基本原理,利用一维非线性波动方程进行了数值试验。EnKF数据同化方法的实现过程简单可行。避免了EKF中协方差演变方程预报过程中出现的计算不准确和关于协方差矩阵的大量数据的存储问题,最主要的是EnKF可以有效控制模式变量估计误差方差的增长,改善预报效果。     

A Time-Averaged Covariance Method in the EnKF for Argo Data Assimilation

In the ensemble Kalman filter (EnKF), ensemble size is one of the key factors that significantly affects the performance of a data assimilation system. A relatively small ensemble size often must be chosen because of the limitations of computational resources, which often biases the estimation of the background error covariance matrix. This is an issue of particular concern in Argo data assimilation, where the most complex state-of-the-art models are often used. In this study, we propose a time-averaged covariance method to estimate the background error covariance matrix. This method assumes that the statistical properties of the background errors do not change significantly at neighbouring analysis steps during a short time window, allowing the ensembles generated at previous steps to be used in present steps. As such, a joint ensemble matrix combining ensembles of previous and present steps can be constructed to form a larger ensemble for estimating the background error covariance. This method can enlarge the ensemble size without increasing the number of model integrations, and this method is equivalent to estimating the background error covariance matrix using the mean ensemble covariance averaged over several assimilation steps. We apply this method to the assimilation of Argo and altimetry datasets with an oceanic general circulation model.

Experiments show that the use of this time-averaged covariance can improve the performance of the EnKF by reducing the root mean square error (RMSE) and improving the estimation of error covariance structure as well as the relationship between ensemble spread and RMSE.

RÉSUMÉ [Traduit par la rédaction] Dans le filtre de Kalman d'ensemble (EnKF), la taille de l'ensemble est l'un des facteurs clés qui ont une influence importante sur la performance d'un système d'assimilation de données. Il faut souvent choisir une taille d'ensemble assez petite à cause des limites des ressources informatiques, ce qui biaise souvent l'estimation de la matrice de covariance de l'erreur de fond. Cette question revêt une importance particulière pour l'assimilation des données Argo, qui fait souvent appel à des modèles de pointe très complexes. Dans cette étude, nous proposons une méthode de covariance moyennée dans le temps pour estimer la matrice de covariance de l'erreur de fond. Cette méthode suppose que les propriétés statistiques des erreurs de fond ne changent pas de façon importante d'une étape d'analyse à la suivante durant un court laps de temps, ce qui permet d'utiliser dans les étapes courantes les ensembles générés aux étapes précédentes. Ainsi, on peut construire une matrice d'ensembles conjoints combinant les ensembles des étapes précédentes et courantes pour former un plus grand ensemble dans le but d'estimer la covariance de l'erreur de fond. Cette méthode peut accroître la taille de l'ensemble sans augmenter le nombre d'intégrations du modèle; elle équivaut à estimer la matrice de covariance de l'erreur de fond en utilisant la covariance moyenne de l'ensemble calculée sur plusieurs étapes d'assimilation. Nous appliquons cette méthode à l'assimilation des ensembles de données Argo et d'altimétrie avec un modèle de circulation océanique générale.

Des essais montrent que l'emploi de cette covariance moyennée dans le temps peut améliorer la performance de l'EnKF en réduisant l’écart-type et en améliorant l'estimation de la structure de la covariance de l'erreur de même que la relation entre l'étalement et l'écart-type l'ensemble.     

Improvement in Background Error Covariances Using Ensemble Forecasts for Assimilation of High-Resolution Satellite Data

Satellite data obtained over synoptic data-sparse regions such as an ocean contribute toward improving the quality of the initial state of limited-area models. Background error covariances are crucial to the proper distribution of satellite-observed information in variational data assimilation. In the NMC (National Meteorological Center) method, background error covariances are underestimated over data-sparse regions such as an ocean because of small differences between different forecast times. Thus, it is necessary to reconstruct and tune the background error covariances so as to maximize the usefulness of the satellite data for the initial state of limited-area models, especially over an ocean where there is a lack of conventional data. In this study, we attempted to estimate background error covariances so as to provide adequate error statistics for data-sparse regions by using ensemble forecasts of optimal perturbations using bred vectors. The background error covariances estimated by the ensemble method reduced the overestimation of error amplitude obtained by the NMC method. By employing an appropriate horizontal length scale to exclude spurious correlations, the ensemble method produced better results than the NMC method in the assimilation of retrieved satellite data. Because the ensemble method distributes observed information over a limited local area, it would be more useful in the analysis of high-resolution satellite data. Accordingly, the performance of forecast models can be improved over the area where the satellite data are assimilated.     

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.     

EnKF Assimilation of Satellite-retrieved Cloud Water Path to Improve Tropical Cyclone Rainfall Forecast

Tropical cyclone (TC) rainfall forecast has remained a challenge. To create initial conditions with high quality for simulation, the present study implemented a data assimilation scheme based on the EnKF method to ingest the satellite-retrieved cloud water path ( C w ) and tested it in WRF. The scheme uses the vertical integration of forecasted cloud water content to transform control variables to the observation space, and creates the correlations between C w and control variables in the flow-dependent background error covariance based on all the ensemble members, so that the observed cloud information can affect the background temperature and humidity. For two typhoons in 2018 (Yagi and Rumiba), assimilating C w significantly increases the simulated rainfalls and TC intensities. In terms of the average equitable threat score of daily moderate to heavy rainfall (5?120 mm), the improvements are over 130%, and the dry biases are cut by about 30%. Such improvements are traced down to the fact that C w assimilation increases the moisture content, especially that further away from the TC center, which provides more precipitable water for the rainfall,strengthens the TC and broadens the TC size via latent heat release and internal wind field adjustment.     

FY-2E卫星云导风定高误差及在同化中的应用

FY-2E气象卫星云导风产品观测误差较大的主要原因是高度指定存在较大误差。针对该问题,采用一维变分方法对云导风高度进行调整。统计分析表明:经高度调整后的FY-2E气象卫星云导风产品质量得到很大改善;采用新息向量法,选取零阶Bessel函数模型,在观测空间分离背景误差和观测误差方差得到云导风的观测误差。运用GRAPES全球模式进行数值模拟,结果表明:采用新的观测误差方案和经过高度调整后的云导风产品能提高数值模式在北半球的短期预报能力,高层的改进效果明显好于中低层。并根据云导风反演原理及算法,讨论了FY-2E气象卫星云导风高度指定系统性偏高的主要原因,以求进一步改善云导风产品的质量。     

Data Assimilation Method Based on the Constraints of Confidence Region

The ensemble Kalman filter(En KF) is a distinguished data assimilation method that is widely used and studied in various fields including methodology and oceanography. However, due to the limited sample size or imprecise dynamics model, it is usually easy for the forecast error variance to be underestimated, which further leads to the phenomenon of filter divergence.Additionally, the assimilation results of the initial stage are poor if the initial condition settings differ greatly from the true initial state. To address these problems, the variance inflation procedure is usually adopted. In this paper, we propose a new method based on the constraints of a confidence region constructed by the observations, called En CR, to estimate the inflation parameter of the forecast error variance of the En KF method. In the new method, the state estimate is more robust to both the inaccurate forecast models and initial condition settings. The new method is compared with other adaptive data assimilation methods in the Lorenz-63 and Lorenz-96 models under various model parameter settings. The simulation results show that the new method performs better than the competing methods.     

Wind Speed and Altitude Dependent AMDAR Observational Error and Its Impacts on Data Assimilation and Forecasting

Aircraft Meteorological Data Relay (AMDAR) observations have been widely used in numerical weather prediction (NWP) because of its high spatiotemporal resolution. The observational error of AMDAR is influenced by aircraft flight altitude and atmospheric condition. In this study, the wind speed and altitude dependent observational error of AMDAR is estimated. The statistical results show that the temperature and the observational error in wind speeds slightly decrease as altitude increases, and the observational error in wind speed increases as wind speed increases. Pseudo single AMDAR observation assimilation tests demonstrate that the wind speed and altitude dependent observational error can provide more reasonable analysis increment. Furthermore, to assess the performance of wind speed and altitude dependent observational error on data assimilation and forecasting, two-month 3-hourly cycling data assimilation and forecast experiments based on the Weather Research and Forecasting Model (WRF) and its Data Assimilation system (WRFDA) are performed for the period during 1 September-31 October, 2017. The results of the two-month 3-hourly cycling experiments indicate that new observational error improves analysis and forecast of wind field and geo-potential height, and has slight improvements on temperature. The Fractions Skill Score (FSS) of the 6-h accumulated precipitation shows that new wind speed and altitude dependent observational error leads to better precipitation forecast skill than the default observational error in the WRFDA does.     

Application of Nonlinear Balance Scheme in Three-Dimensional Variational Data Assimilation

The dynamical constrains in three-dimensional variational data assimilation are discussed when consid- ering the impact of stream divergence and convergence on the pressure and wind fields.For the analysis of severe tropical cyclone,frontal structures,and other rapidly changing structures,the geostrophic balance and linear balance cannot properly represent the relationship between wind and pressure fields.However,the nonlinear balance incremental equation takes into account the information of flow-dependent background, and makes response to the flow-dependent background covariance in the 3D-Var system.Results indicate that the application of the nonlinear balance equation to 3D-Var system improves the quality of severe trop- ical cyclone assimilation system,which has some positive effects on intensity prediction of tropical cyclones.     

贝叶斯膨胀算法对EnSRF雷达资料同化的影响研究

本文针对2009年6月5日发生在我国华东地区的一次中尺度对流过程（Mesoscale Convective System,简称MCS）,基于集合均方根滤波（Ensemble Square Root Filter,简称EnSRF）方法同化多部多普勒天气雷达资料,引入具有时空自适应理论优势的贝叶斯膨胀算法,通过与常数膨胀算法的对比,分析了两种膨胀算法对EnSRF同化效果的影响。结果表明:贝叶斯膨胀算法同化的雷达组合反射率因子在强对流中心处有所增强,改善了基于常数膨胀算法的EnSRF同化强对流系统偏弱的问题。相比常数膨胀算法,贝叶斯膨胀算法同化的冷池结构更合理,径向风和反射率因子的均方根误差均减少。进一步探讨贝叶斯膨胀算法对同化效果改善的原因,结果发现:贝叶斯膨胀参数的分布与反射率因子的均方根误差分布十分吻合,这表明贝叶斯膨胀算法可以在背景场均方根误差较大,即背景场与观测差距较大时,给出较大的膨胀参数,进而增加集合的背景场误差,使得观测权重增大,从而给出了较大的分析增量。对集合平均分析场进行了1小时的确定性预报发现,贝叶斯膨胀算法提高了预报模式对安徽与江苏交界处的强对流系统的模拟效果,回波强度更强,冷池强度和范围更大,且对于不同组合反射率因子的阀值,贝叶斯膨胀算法的评分（Equitable Threat Score,简称ETS）均高于常数膨胀算法。这表明贝叶斯膨胀算法有效地改进了基于常数膨胀算法的EnSRF同化雷达资料的效果。