两种样本生成方法对DRP-4DVar同化方法性能影响的比较及分析

降维投影四维变分同化方法(DRP-4DVar)利用历史预报的集合来统计背景误差协方差,并将分析变量投影到样本空间下求解代价函数,因而集合样本的质量对DRP-4DVar同化方法的性能有着重要影响.文中尝试使用三维变分(3DVar)控制变量的扰动方法来产生集合样本,并与原来的历史预报扰动方法做比较.历史预报扰动样本具有随流...     

集合降维变分同化中的初始扰动和局地化

集合降维变分同化方法ERDVar不需要求解切线性模式和伴随模式，不仅能减少同化计算量，而且能够提供“流依赖”的背景误差协方差矩阵。本文提出用NMC初始扰动生成方法和分区同化方案，来解决初始扰动样本生成问题和全球同化局地化问题，最终实现将ERDVar应用到全球中期数值预报模式T106L19。试验结果表明：①使用ERDVar方法能够有效提取真实增量信息，提高全球同化精度。②用NMC方法产生的扰动样本反映预报误差结构特征，在预报过程中不容易衰减，同化后至少使预报误差降低10%。③与全球ERDVar同化试验相比，分区ERDVar同化试验各变量平均的均方根误差降低14%，计算代价进一步降低。分区ERDVar方法和NMC样本的联合应用使同化改进效果更稳定。     

集合四维变分资料同化研究进展

背景误差协方差矩阵的精确定义是构建高水平资料同化系统的先决条件。传统四维变分资料同化(4D-Var)方法将观测资料处理转化成以动力模式为约束的泛函极小化问题,通过调整控制变量,使指定时间窗口内由控制变量得到的模式预报结果与实际观测资料之间的偏差达到最小。该方法在同化窗口内可以利用模式的切线性和伴随隐式地改变背景误差协方差,能够在某种程度上满足快速发展的天气过程。但是大部分业务中心的四维变分资料同化系统仍采用静态化的背景误差协方差矩阵模型来缓解背景误差协方差矩阵的维度问题,即矩阵维数远大于可用信息量。随着计算机科学的迅猛发展,维度问题可以进一步通过集合的方法缓解。集合四维变分资料同化就是基于这一目标通过构造多个能反映出背景误差协方差分布特征的样本集合来弥补可用信息量的不足。该方法目前已在ECMWF、Mete-France等业务中心实现业务化,为确定性四维变分资料同化系统提供流依赖背景误差协方差估计。简要介绍了集合四维变分资料同化方法的基本原理;其次以ECMWF为例,概述了四维变分资料同化系统的业务现状,重点阐述了系统在开发过程中需要解决的扰动、滤波、校正等一些关键技术;最后探讨集合四维变分资料同化系统目前存在的问题和未来可能的研究方向。     

流依赖球面小波背景误差协方差模型设计和初步试验

基于资料同化集合设计了流依赖球面小波背景场误差协方差模型中背景误差方差和局地垂直相关协方差的统计计算方法。为了提高背景误差方差的估计精度,采用客观滤波技术来减少因集合样本个数不足而引入的随机取样噪声。最后在银河四维变分同化业务系统(YH4DVar)上设计了集合资料同化的试验系统,以流依赖背景误差方差为重点验证了模型的有效性。结果表明:基于流依赖球面小波背景误差协方差模型能够有效估计出随天气状态变化的背景场误差方差,对台风等剧烈变化的天气过程的同化分析和预报都具有一定的正效果。      

基于优化样本组合的集合-变分混合同化方案研究

为有效引入“流依赖”的背景场误差协方差,同时降低集合预报带来的计算量,尝试通过优选与同化时刻天气形势更相似的历史预报样本,并结合预报过程中的时间滞后样本,将两种样本引入集合-变分混合同化系统中,构建基于优选历史预报样本和时间滞后样本的集合-变分混合同化方案。单点观测理想试验表明,优选历史预报样本结合时间滞后样本,既能够缓解样本不足所导致的采样误差,又能够为同化系统提供“流依赖”的背景场误差协方差。连续一周的循环同化及预报试验结果显示,相较于ERA5资料和探空资料,三维变分方案整体表现稍差,样本组合混合同化方案分析场和预报场的均方根误差最小,且比仅用时间滞后样本的混合同化方案有所改进;降水评分整体也表现最优,尤其对中雨和暴雨的模拟改进较明显,较好地模拟出了强降水中心的强度和位置,且改善了降水过报的问题。      

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。     

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...     

数值模式误差对降水四维变分资料同化及预报的影响

利用一个无量纲的水汽发展方程,针对同化时间窗口内出现和不出现降水两种情况,分析了不同模式误差和初始误差对降水四维变分资料同化预报效果的影响。结果表明,应用四维变分资料同化方法进行降水预报前,应该充分考虑数值模式中的误差,才能得到比较满意的同化及预报结果。假定同化窗口内获得的比湿观测场是准确的,当不存在模式误差时,四维变分资料同化方法可以有效地消除初始场误差,找到比湿真实初始场;而存在模式误差时,四维变分资料同化后的模式初始场会偏离真实的比湿初始场,并且模式误差越大,偏离程度越严重。在一些模式误差情况下,由于模式误差在同化窗口及延伸预报时段的作用不同,进行四维变分资料同化处理后,尽管累积降水量的预报结果在同化时间窗口内优于同化前的预报,而在最终预报时刻反而差于同化前。     

基于混合集合同化方案的台风“海鸥”的数值模拟研究

混合变分/集合同化是基于变分+集合思路新兴发展起来的一种资料同化方法。利用WRF和WRFDA最新版本3.5构建混合集合同化的流程,通过单点试验直观体现出混合集合同化方案“流依赖”背景误差协方差的影响。对台风“海鸥”路径和强度的模拟和分析表明,混合集合同化方案在台风路径和强度的预报上要强于三维变分同化方案。对比两种方案同化后的分析场表明,混合集合同化方案分析出的台风中心强度优于三维变分同化方案分析结果,其原因一方面是混合集合同化方案初始场是采用集合平均的结果,另一方面是混合集合同化方案采用“流依赖”背景误差协方差的影响,这两个因素对台风的预报准确性有一定作用。      

数值天气预报中集合-变分混合资料同化及其研究进展

数值天气预报中混合资料同化是结合集合预报与变分同化方法各自优势研究发展的一种新型资料同化方案。它在变分资料同化框架的基础上,利用集合预报扰动场信息的优点,构造具有流依赖属性的背景误差协方差结构,克服变分同化中固定、均匀及各向同性的背景误差协方差的缺陷,改善对不同天气系统预报误差协方差的表达能力,从而改善分析和预报的质量。近年来,基于集合与变分方法的混合资料同化快速成为数值预报资料同化发展的新趋势,具有良好的业务应用潜力。对集合与变分混合资料同化的研究进展进行综述,在简要介绍数值天气预报中资料同化发展趋势的基础上,分析混合资料同化方案的理论框架和优势,总结混合资料同化的发展和研究成果,并讨论我国研究和发展混合资料同化的基础和前景及面临的问题,指出混合资料同化发展中亟需研究的关键科学问题。      

Sensitivity of the DRP-4DVar Performance to Perturbation Samples Obtained by Two Different Methods

The dimension-reduced projection four-dimensional variational data assimilation (DRP-4DVar) approach utilizes the ensemble of historical forecasts to estimate the background error covariance (BEC) and directly obtains the analysis in the ensemble space.As a result,the quality of ensemble members significantly affects the DRP-4DVar performance.The historical-forecast-based initial perturbation samples are flow-dependent and can describe the error-growth pattern of the atmospheric model and the balanced relat...     

The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System: Single-point Experiment

A four dimensional variational data assimilation (4DVar) based on a dimension-reduced projection (DRP-4DVar) has been developed as a hybrid of the 4DVar and Ensemble Kalman filter (EnKF) concepts. Its good flow-dependent features are demonstrated in single-point experiments through comparisons with adjoint-based 4DVar and three-dimensional variational data (3DVar) assimilations using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5). The results reveal that DRP-4DVar can reasonably generate a background error covariance matrix (simply B-matrix) during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar are anisotropic and no longer symmetric with respect to observation location due to the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.     

An Extension of the Dimension-Reduced Projection 4DVar

This paper extends the dimension-reduced pro- jection four-dimensional variational assimilation method （DRP-4DVar） by adding a nonlinear correction process, thereby forming the DRP-4DVar with a nonlinear correction, which shall hereafter be referred to as the NC-DRP- 4DVar. A preliminary test is conducted using the Lorenz-96 model in one single-window experiment and several multiple-window experiments. The results of the single-window experiment show that compared with the adjoint-based traditional 4DVar, the final convergence of the cost function for the NC-DRP-4DVar is almost the same as that using the traditional 4DVar, but with much less computation. Furthermore, the 30-window assimilation experiments demonstrate that the NC-DRP-4DVar can alleviate the linearity approximation error and reduce the root mean square error significantly.     

An Economical Approach to Four-dimensional Variational Data Assimilation

Four-dimensional variational data assimilation (4DVar) is one of the most promising methods to provide optimal analysis for numerical weather prediction (NWP). Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimension-reduced projection (DRP), which is called ``DRP-4DVar." The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation. To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.     

Impact of Analysis-time Tuning on the Performance of the DRP-4DVar Approach

In this study we extend the dimension-reduced projection-four dimensional variational data assimilation (DRP-4DVar) approach to allow the analysis time to be tunable, so that the intervals between analysis time and observation times can be shortened. Due to the limits of the perfect-model assumption and the tangentlinear hypothesis, the analysis-time tuning is expected to have the potential to further improve analyses and forecasts. Various sensitivity experiments using the Lorenz-96 model are conducted to test the impact of analysistime tuning on the performance of the new approach under perfect and imperfect model scenarios, respectively. Comparing three DRP-4DVar schemes having the analysis time at the start, middle, and end of the assimilation window, respectively, it is found that the scheme with the analysis time in the middle of the window outperforms the others, on the whole. Moreover, the advantage of this scheme is more pronounced when a longer assimilation window is adopted or more observations are assimilated.     

GRAPES Hybrid-3DVar对台风苏迪罗的数值试验

为了把反映天气形势变化的背景误差协方差引入到变分分析系统中来提高分析质量,本文在GRAPES区域三维变分框架的基础上通过扩展控制变量方法实现动态与静态背景误差协方差耦合,建立混合三维变分分析系统（GRAPES Hybrid-3DVar）。通过控制变量扰动产生的集合样本进行单点观测分析试验验证Hybrid-3DVar及其局地化方案的合理性,并针对台风苏迪罗进行实际观测资料同化和数值预报试验,结果表明:用集合样本描述的背景误差协方差是随着天气流型变化的,动力场和质量场的离散度在台风中心处最大,因而混合同化的分析增量包含更多细微结构和中小尺度信息;其分析和24 h内预报要素质量优于3DVar,24 h内降水强度和落区预报也更准确,混合同化分析改善了3DVar分析的降水空报问题;同时混合同化分析的24 h内台风路径预报也最接近实况,台风强度预报在48 h之内都比3DVar更接近观测。     

物理滤波初始化四维变分在临近预报中的应用

运用WRF模式（Weather Research and Forecasting Model,天气研究和预报模式）和WRFDA同化（WRF Data Assimilation,WRF资料同化）系统,探究采用物理滤波初始化四维变分同化方法提高数值预报在临近预报时效的预报能力的可能性。通过采用12 min同化窗,在不显著增加计算量的情况下,得到更协调的模式初始场,从而提高模式预报能力。选取2018年8月华北地区17个降水个例进行研究,结果表明:采用物理滤波初始化四维变分同化技术能够明显改进模式短时临近降水预报能力,明显提高对大量级降水预报的ETS评分,6 h累积降水大于25.0 mm量级的ETS评分由0.125提高到0.190,且6 h累积降水大于60.0 mm量级的ETS评分由0.016提高到0.081。研究还表明:同化雷达风场通过改进初始动力场使次网格尺度降水过程（积云参数化）快速响应,可提高短时临近时段的降水预报能力。     

SVD-En3DVar方法同化多普勒雷达速度观测资料 I. 模拟资料试验

利用WRF模式及模式模拟的资料,开展了利用SVD-En3DVar(基于集合和SVD技术的三维变分同化方法)方法同化雷达径向速度资料的试验.由于雷达观测经常出现大面积空缺,同化时引入了一种局地化方法避免远距离虚假相关的影响.试验着重研究了不同的初始扰动样本产生方法以及不同的样本积分时间对同化结果的影响.提出了一种为预报集...     

Reducing the prediction uncertainties of high-impact weather and climate events: An overview of studies at LASG

This paper summarizes recent progress at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences in studies on targeted observations, data assimilation, and ensemble prediction, which are three effective strategies to reduce the prediction uncertainties and improve the forecast skill of weather and climate events. Considering the limitations of traditional targeted observation approaches, LASG researchers have developed a conditional nonlinear optimal perturbation-based targeted observation strategy to optimize the design of the observing network. This strategy has been employed to identify sensitive areas for targeted observations of the El Niño–Southern Oscillation, Indian Ocean dipole, and tropical cyclones, and has been demonstrated to be effective in improving the forecast skill of these events. To assimilate the targeted observations into the initial state of a numerical model, a dimension-reducedprojection- based four-dimensional variational data assimilation (DRP-4DVar) approach has been proposed and is used operationally to supply accurate initial conditions in numerical forecasts. The performance of DRP-4DVar is good, and its computational cost is much lower than the standard 4DVar approach. Besides, ensemble prediction, which is a practical approach to generate probabilistic forecasts of the future state of a particular system, can be used to reduce the prediction uncertainties of single forecasts by taking the ensemble mean of forecast members. In this field, LASG researchers have proposed an ensemble forecast method that uses nonlinear local Lyapunov vectors (NLLVs) to yield ensemble initial perturbations. Its application in simple models has shown that NLLVs are more useful than bred vectors and singular vectors in improving the skill of the ensemble forecast. Therefore, NLLVs represent a candidate for possible development as an ensemble method in operational forecasts. Despite the considerable efforts made towards developing these methods to reduce prediction uncertainties, much challenging but highly important work remains in terms of improving the methods to further increase the skill in forecasting such weather and climate events.