模式误差弱约束四维变分同化研究

经典四维变分同化(four dimensional variational data assimilation,简称4dvar)中认为模式是完美的, 而实际数值模式中存在的模式误差将对变分同化效果产生直接影响, 弱约束4dvar的提出为4dvar中考虑模式误差的影响提供了一种可行途径. 研究了基于模式误差控制变量的弱约束4dvar基本理论, 并在一维浅水方程组中对其同化效果及估计模式误差的有效性进行相关数值实验研究. 结果表明,在模式误差不可忽略的情况下,模式误差弱约束4dvar在整个区间 (包括同化区间和预报区间)上预报误差均比传统4dvar小, 在模式误差相对较大时改进效果更明显,具有明显优越性; 并且,模式误差弱约束4dvar能有效估计模式误差大小及分布形式.     

变分同化中水平误差函数的正交小波模拟新方法

背景误差协方差是变分资料同化系统中的一个重要组成部分,能将观测信息从观测点传播到周围的模式格点和垂直层上.为了模拟背景误差协方差中水平误差函数的非均匀性和各向异性,提出了一种用正交小波变换模拟水平误差函数的新方法.试验结果表明：新方法能模拟出水平误差函数中固有的非均匀性和各向异性,极好地表示了背景误差协方差中固有的结构和特征. 关键词： 变分资料同化 背景误差协方差 二维正交小波 水平误差函数     

优化模式物理参数的扩展四维变分同化方法

数值模拟的一个重要误差来源是模式物理参数,为提高模拟准确率,如何改进模式物理参数是亟需解决的问题.本文对经典四维变分同化技术进行了改进,提出了一种新的利用观测资料来同时优化模式初始场和物理参数的扩展四维变分同化方法,并以Ekman边界层模式和Lorenz模式为例进行了数值试验.结果表明,利用本文提出的新方法,通过对观测资料的变分同化,可以在实现对模式初始场进行优化的同时,纠正了模式物理参数中的误差,从而有效提高了模式的模拟准确率.该方法对于改进数值模式物理参数有着重要的促进意义.     

GPS掩星一维弯曲角算子在四维变分资料同化系统中的实现方法研究

GPS无线电掩星资料的良好特性使其作为十分重要的观测资料在欧洲 及美国数值天气预报中效果明显. 本文设计了一维弯曲角算子在四维变分资料同化系统中的实现方法和质量控制策略. 详细阐述了一维弯曲角正演算子及其切线性/伴随算子在全球四维变分资料同化系统中的实现步骤和过程, 其中折射率计算中采用Rüeger的折射率最佳平均因子的三项表达式, 计算出更加精确的折射率值. 对2012年8月份的GPS无线电掩星资料进行了观测误差统计, 引入了更加符合四维变分资料同化系统实际情况的一维弯曲角观测误差模型和质量控制策略. 同时, 对比了观测误差统计试验中同化GPS无线电掩星资料的模式背景场和未同化GPS无线电掩星资料的背景场的观测误差统计结果, 发现同化GPS无线电掩星资料之后的观测误差统计结果在全球区域正作用十分明显, 尤其是在中低纬度地区, 高度在10 km 以上的区域观测误差减小十分明显. 关键词： GPS无线电掩星 一维弯曲角算子 四维变分同化系统 质量控制     

数字滤波弱约束四维变分同化在台风初始化中的应用(Ⅱ):数字滤波权重选择

数字滤波权重的选择是影响台风路径和强度预报的重要因素,某些个例中直接决定着台风数值模拟的成功与否,合适的数字滤波权重非常重要.本文利用2010年3个台风7个不同初始时刻个例,开展数字滤波弱约束四维变分同化(4D-Var)台风初始化试验,分析不同数字滤波权重对台风路径和强度预报的影响;基于上述台风路径和强度预报后验统计信息,以及台风中心区域800 km范围和整个模拟区域3 h平均地面气压倾向信息,提出一种bogus资料同化台风初始化中数字滤波权重优选方案,并进行理论解释说明;同时,指出bogus资料同化台风初始化中,常规数字滤波权重为1000更合理,明显有别于常规天气和暴雨天气权重设置.     

基于区域逐步分析的集合变分资料同化方法

集合变分数据同化方法的同化效果对集合样本容量具有很强的依赖性,研究发现此问题的出现是因为其计算过程中分析增量被表示为集合扰动向量或其展开正交基向量的线性组合.这样的处理方法虽然避免了计算梯度而引入伴随模式,但是因为物理控制变量个数远大于集合样本容量,就会导致物理量的同化分析值对集合样本容量很敏感.根据此原因,提出了区域逐步分析方法,减小了同化分析区域内物理变量个数与集合样本容量数之间的比值,使问题得到解决.利用浅水方程模式进行资料同化数值试验表明,基于区域逐步分析的集合变分资料同化方法可以得到较好的结果,能明显提高同化的精度.     

Impact of GNSS radio occultation bending angle data assimilation in YH4DVAR system

Global Navigation Satellite System （GNSS） radio occultation measurements have been assimilated into the four- dimensional variational data assimilation system （YH4DVAR） using a one-dimensional bending angle operator （GBAO） as a new type of observation. For the sake of verifying the impact of GNSS radio occultation （RO） measurements to the data assimilation system, three experiments have been conducted. The statistical results of the analysis error experiment and forecast skill experiment show that the GNSS RO measurements have an impact on the analysis system. The typhoon forecast experiment shows the impact on the important weather process. They all have a positive impact on the weather forecast. Lastly, we look forward to future work on the observation system simulation experiment （OSSE） to investigate the impact of GNSS RO measurements as a function of observation number, which is an effective method to estimate the saturation of the observation number.     

Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The data contain errors (observation and background errors), hence there will be errors in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can often be approximated by the inverse Hessian of the cost functional. Here we focus on highly nonlinear dynamics, in which case this approximation may not be valid. The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance. Two new methods for computing this covariance are presented: the fully nonlinear ensemble method with sampling error compensation and the ‘effective inverse Hessian’ method. The second method relies on the efficient computation of the inverse Hessian by the quasi-Newton BFGS method with preconditioning. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term.     

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction(NWP). Considering the continuous evolution of the atmosphere, the observed data(ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers’ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.     

资料同化中的数字滤波弱约束试验及分析

气象数值预报中,由于分析过程引入初始非平衡,从而引起虚假快波振荡,重力波控制弱约束把资料分析过程和初始化过程结合在一起,通过数字滤波弱约束在极小化过程中实现对分析场的平衡约束,克服非平衡问题. 以2008年初的一次南方雨雪天气为研究个例,进行了数字滤波弱约束的同化试验和预报试验,结果表明,数字滤波弱约束4D-Var能充分控制快波振荡的出现和初始调整现象,使得到的分析场不仅能更好的逼近观测,而且能更好地与模式动力相协调. 预报检验的结果表明,在同化过程中施加数字滤波弱约束,能有效滤除由于地形或观测资料等因素 关键词： 变分同化 初始非平衡 数字滤波 弱约束     

Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re_τ = 590) and flow over a cylinder (Re_D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.