预分析初始扰动样本对降维投影四维变分同化性能的影响

降维投影四维变分同化(DRP-4DVar)方法的背景误差协方差是由基于历史预报的扰动样本统计得到的,为了改进降维投影四维变分同化系统中背景误差协方差的流依赖特性,提出了对初始扰动样本进行预分析的新思路,即在对背景场分析之前,利用降维投影四维变分同化系统本身对每个样本进行预先分析,使得统计出的背景误差协方差随实际的天气形势而变化,从而实现其在真正意义上的流依赖,且在循环同化时能够避免滤波发散现象的出现。试验结果表明,对样本进行预先分析能够通过改善同化系统中背景误差协方差的空间结构和流依赖特性,来进一步改进降维投影四维变分同化方法的性能,为数值模式提供更精确的初始场,从而提高了基本模式变量的预报精度,并改善了对强降水的模拟能力。相比较而言,对所有初始扰动样本都进行了预分析的同化试验能够得到最优的分析和预报。     

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合提供初始扰动场的新方法,这一方法将温度和比湿的伪随机扰动场当作观测增量,通过3DVar (three-dimensional variational technique)系统生成所有变量的初始扰动场.试验表明,用这种方法给出的初始扰动样本各个变量间有较好的协调性,积分后扰动不会快速衰减,可以减少模式调整的时间,达到缩短同化循环时间窗的目的.同化雷达径向风资料后对12小时内的温度,湿度和水平风的预报都有所改进,对降水的预报也有一定改进.     

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...     

基于历史样本投影的四维变分陆面数据同化方法及其初步应用

法面临着计算量上的挑战。本研究将一种历史样本投影的四维变分同化方法(Historical-Sample-Projection4DVar,简写为HSP-4DVar)应用于陆面数据同化,建立起CoLM陆面模型的HSP-4DVar系统。相比其他四维变分同化方法,HSP-4DVar的分析值是显式求解,不需要编写和使用伴随模式,从而大大节省了计算量,是一种易于实现的同化方案。通过同化56个月的土壤湿度观测数据表明,新的陆面同化系统不仅省时,而且能够有效吸取观测信息,使得同化后的均方根误差显著降低,各层土壤湿度模拟都有所改善,陆表1000mm层的改善最为明显。     

基于观测扰动的集合预报EDA初值扰动方法研究

北京城市气象研究院初步发展了3 km分辨率的华北对流尺度集合预报系统.为构建适用于该系统的初值扰动,设计了观测随机扰动方案,并与全球集合预报动力降尺度背景场相结合,利用三维变分同化方法构建了集合资料同化(EDA)初值扰动;开展了EDA方案在华北对流尺度集合预报系统中的批量试验,并与动力降尺度初值扰动方法进行了对比.结果...     

华南暴雨区域集合预报中不同同化方案的影响试验研究

基于全球集合预报系统(GEFS)资料,利用WRF中尺度模式及GEFS动力降尺度获取区域集合预报初值场,通过对同化后的分析场进行模式积分实现华南前汛期区域集合预报。对2019年6月10日的一次华南前汛期暴雨过程进行不同同化方案的试验:混合同化(Hybrid)、三维变分(3Dvar)、集合卡尔曼滤波(EnKF)和对比试验(Ctrl)四组试验的对比分析,探讨具有不同背景误差协方差矩阵的同化方案对区域集合预报集合扰动和集合离散随时间演变特征的影响,评估不同试验的降水模拟效果。(1) Hybrid对模式初始场有较好的改善作用,而3DVar和EnKF对初始场的改善作用不明显。(2) 对风场、温度场和湿度场,在前期预报中Hybrid的预报误差小于3DVar和EnKF,在中后期的预报中,3DVar和EnKF的预报误差得到改善,且好于Hybrid。同样,集合扰动能量,Hybrid和Ctrl在前期预报发展好于3DVar和EnKF,而在中后期的预报3DVar和EnKF好于Hybrid和Ctrl。(3) 从24 h累积降水评分中,整体上同化试验好于Ctrl,3DVar和EnKF好于Hybrid,且3DVar对大中雨级别的降水评分较好,而EnKF对暴雨以上级别的降水评分较好。(4) 对于集合统计检验分析,同化试验的AUC值都大于Ctrl的AUC值,24 h累积降水量阈值在10~100 mm的AUC值,3DVar最好;而125 mm阈值的AUC值,EnKF最好。      

使用混合样本的集合四维变分同化试验研究

基于集合和奇异值分解的四维变分同化方法(SVD-En4DVar)的同化效果对采用的预报样本容量有很强的依赖性,其中一个重要原因是在SVD-En4DVar中分析变量被表示为按照扰动预报集合提取的奇异向量作线性展开的形式,这种展开存在截断误差,过少的样本数会造成过大的截断误差。为了在不增加计算量的情况下增加用于同化的样本,从而改善同化效果,本文提出了流依赖的预报样本与定常样本相混合的方法。定常样本有两种生成方法：第一种是按照给定的统计结构给出伪随机扰动场直接叠加到四维背景场上而完全不经过模式积分;第二种是在第一个同化循环时将伪随机扰动场叠加到初始背景场,然后在分析时间窗内积分模式得到扰动预报样本,最后将其中一部分保留不动作为后面同化循环的定常样本。利用浅水方程模式和80个变量的Lorenz-96模式及模拟资料进行数值试验,比较不同样本结构的同化效果。结果表明,在浅水方程模式的同化中,完全采用大容量的定常样本仍然可以得到较好的结果,但对Lorenz-96模式效果不好。采用混合样本后,这两类模式的同化都可以得到较好的结果,在相同的计算时间下,混合样本方法可以明显提高同化精度,其中第二种产生定常样本的方法要好于第一种。     

基于扰动模式的四维变分资料同化系统框架的设计完善和数值试验

为了建立一个应用于区域数值预报的四维变分资料同化（4DVar）系统,在近期开发的扰动预报模式GRAPES_PF基础上,开发完善增量四维变分同化系统框架。该框架中暂不包含物理过程（长短波辐射、边界层过程、对流参数化和云微物理等）。对比业务使用的GRAPES 3DVar系统,增加了温度控制变量。将无量纲Exner气压与流函数的线性风压平衡方程直接在地形追随垂直坐标面上求解,且通过广义共轭余差法（GCR）求解扰动亥姆霍兹（Helmholtz）伴随方程。利用人造“探空”资料对2015年10月台风“彩虹”进行了理想数值试验。试验结果表明,所开发的扰动四维变分同化框架得到了预期的结果,即同化更多资料并反复受到模式约束的四维变分同化系统能有效改善初值质量,进而改善区域数值预报。建立的区域四维变分同化框架合理可行,为进一步发展包含完整物理过程的区域四维变分同化系统奠定了研究基础。      

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。     

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...     

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...     

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.     

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.     

A new DRP-4DVar-based coupled data assimilation system for decadal predictions using a fast online localization technique

Climate Dynamics - A new coupled data assimilation (CDA) system based on dimension-reduced projection four-dimensional variational data assimilation (DRP-4DVar) for decadal predictions is developed...     

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.     

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.     

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.     

A New Approach to Data Assimilation

A significant attempt to design a timesaving and efficient four-dimensional variational data assimilation (4DVar) has been made in this paper, and a new approach to data assimilation, which is noted as 'three-dimensional variational data assimilation of mapped observation (3DVM)' is proposed, based on the new concept of mapped observation and the new idea of backward 4DVar. Like the available 4DVar, 3DVM produces an optimal initial condition (IC) that is consistent with the prediction model due to the inclusion of model constraints and best fits the observations in the assimilation window through the model solution trajectory. Different from the 4DVar, the IC derived from 3DVM is located at the end of the assimilation window rather than at the beginning conventionally. This change greatly reduces the computing cost for the new approach, which is almost the same as that of the three-dimensional variational data assimilation (3DVar). Especially, such a change is able to improve assimilation accuracy because it does not need the tangential linear and adjoint approximations to calculate the gradient of cost function. Therefore, in numerical test, the new approach produces better IC than 4DVar does for 72-h simulation of TY9914 (Dan), by assimilating the three-dimensional fields of temperature and wind retrieved from the Advanced Microwave Sounding Unit-A (AMSU-A) observations. Meanwhile, it takes only 1/7 of the computing cost that the 4DVar requires for the same initialization with the same retrieved data.     

Initialization and simulation of a landfalling typhoon using a variational bogus mapped data assimilation (BMDA)

Summary Recently, a new data assimilation method called “3-dimensional variational data assimilation of mapped observation (3DVM)” has been developed by the authors. We have shown that the new method is very efficient and inexpensive compared with its counterpart 4-dimensional variational data assimilation (4DVar). The new method has been implemented into the Penn State/NCAR mesoscale model MM5V1 (MM5_3DVM). In this study, we apply the new method to the bogus data assimilation (BDA) available in the original MM5 with the 4DVar. By the new approach, a specified sea-level pressure (SLP) field (bogus data) is incorporated into MM5 through the 3DVM (for convenient, we call it variational bogus mapped data assimilation – BMDA) instead of the original 4DVar data assimilation. To demonstrate the effectiveness of the new 3DVM method, initialization and simulation of a landfalling typhoon – typhoon Dan (1999) over the western North Pacific with the new method are compared with that with its counterpart 4DVar in MM5. Results show that the initial structure and the simulated intensity and track are improved more significantly using 3DVM than 4DVar. Sensitivity experiments also show that the simulated typhoon track and intensity are more sensitive to the size of the assimilation window in the 4DVar than that in the 3DVM. Meanwhile, 3DVM takes much less computing cost than its counterpart 4DVar for a given time window.