小集合数条件下的数据同化策略研究

基于集合的数据同化方法近年来得到广泛的重视和研究,已经逐步实验在业务大气数据同化系统中来替代变分类方法。集合Kalman滤波方法高度依赖于集合的大小,集合数过小会带来欠采样,协方差低估,滤波发散和远距离的虚假相关等问题。局地化技术可以有效改善小集合带来的相关问题。在Lorenz-96模型的基础上,研究有无局地化的效果差异,探讨小集合条件下的局地化技术的优劣性;提出一种基于功率谱密度（PSD）判断集合数据同化效果的办法。实验证明：在有限集合数下,采用Kalman增益值和PSD可以评价同化效果,结合局地化技术,可以获得效率更高的同化算法。     

观测误差协方差估计下的集合鲁棒滤波数据同化方法

在数据同化方法中,观测误差协方差矩阵是相关的,且与时间和状态有一定的依赖性。针对这种相关特性,将鲁棒滤波方法与观测误差协方差估计方法相结合,得到随状态时间变化的观测误差协方差,提出一种带有观测误差估计的鲁棒数据同化新方法,更新观测误差协方差,改善估计效果。从分析误差协方差,转移矩阵特征值放大等角度优化同化方法。利用非线性Lorenz-96混沌系统,对三种不同优化角度下带有观测误差估计的鲁棒滤波和原鲁棒滤波方法的鲁棒性和同化精度进行评估,并比较分析了两种方法在模型误差、观测数目和性能水平系数变化时的性能。结果表明：观测误差估计技术能够提高状态估计的精确性,带有观测误差估计的鲁棒滤波对系统参数变化具有较好的鲁棒性。     

球面小波背景误差协方差模型的设计

在全球变分资料同化系统中设计和实现了基于球面小波的背景误差协方差（B）模型。引入框架理论构造了球面小波函数;设计了一个基于球面小波变换的全球B矩阵模型;分别通过理想数值试验和在全球变分同化系统中的实现对新模型的有效性进行了验证。试验结果表明：基于球面小波的背景误差协方差模拟方法能够克服由有限背景误差样本引入的取样噪声,能估计出真实的背景误差相关函数;在全球变分同化系统中新模型能够模拟出在物理和动力上正确和有效的背景误差结构函数。     

协方差矩阵加权波束形成及应用

在逆波束形成方法的基础上提出一种改进的协方差矩阵加权波束形成方法，它根据阵元的分布情况对阵元接收信号的协方差矩阵进行直接加权，使得环境噪声相关比较强的协方差元素得到抑制，环境噪声相关性比较弱的部分被加强，降低噪声增益，从而达到提高阵增益的目的。文中给出了两种协方差加权方法。并且计算了在各向均匀噪声环境下的阵增益。从阵增益和误差稳定性两个方面与CBF和MVDR方法进行了对比，验证了该方法的正确性。     

基于无迹变换的协方差交集算法研究

针对分布式数据观测系统中数据融合存在数据线性化过程误差较大、滤波过程中的错误无法修正的问题,提出了一种基于无迹变换的协方差交集算法。该算法首先对系统数据进行无迹变换,然后对数据采用协方差交集算法滤波,可得到较好的滤波性能。实验结果表明,该算法弥补了协方差交集算法的不足,能够修正数据线性化误差及滤波产生的错误,是一种有效的数据融合算法。     

误差系数对变分同化的质量影响研究

误差是变分同化过程中不可避免的话题,背景场误差和观测场误差又是整个同化过程误差的主要部分。论文通过简单地对变分同化基本原理、背景误差协方差矩阵以及观测误差协方差矩阵建模之后,通过数值模拟实验,分析了背景误差系数和观测误差系数变化给同化带来的影响,结果表明,无论哪种误差系数,系数越大,同化质量越低,波动越大,但是并不影响整个同化过程对的收敛性。     

协作多点传输中基于空间协方差动态更新的码本自适应方法

针对典型码本自适应算法的信道协方差矩阵反馈时间间隔过长,导致高速环境下系统性能迅速恶化的缺点,提出了一种基于信道协方差矩阵动态更新的码本自适应改进算法。基于协方差矩阵和码本之间的等效关系和均方误差最小的原则,在接收端将协方差矩阵拆分成一个固定参数和一个码本向量,并向发射端反馈该码本向量。然后,在发射端利用反馈的码本向量及本地固定参数和上一时刻的协方差矩阵,重构当前时刻的协方差矩阵。仿真结果表明,较之典型算法,提出的算法具有更好的性能表现,尤其在高速环境下,可以获得近2dB的增益。     

基于Lorenz-96模型的顺序数据同化方法比较研究

顺序数据同化方法在数据同化系统中得到了广泛的应用,其性能各有优缺。选择3种典型的顺序数据同化算法,即集合Kalman滤波,集合转换Kalman滤波和确定性Kalman滤波,使用经典的Lorenz-96模型进行敏感性实验,研究不同的关键参数变化,如集合数目变化、观测数变化、误差放大因子变化和定位半径变化时对同化效果的影响。实验表明：集合数目和观测数目的多少直接影响3种方法的同化效果;协方差放大因子和定位半径的选择会提高同化精度。综合比较,确定性集合Kalman滤波算法是一种具有较强鲁棒性的滤波算法,能够在集合数较小的情况下达到较好的同化效果。     

混合模型算法中协方差矩阵及其导数信息的存储设计

针对用极大似然方法和限制极大似然方法进行混合模型的参数估计,设计并实现了随机效应的协方差矩阵和观测误差的协方差矩阵及其导数信息的切实可行的存储方案。     

测量误差协方差矩阵的鲁棒估计

由于经典的误差协方差阵间接估计方法对于过失误差存在非常敏感,本文提出了一种基于Hampel三截尾估计的间接估计方法,在无过失误差和存在过失误差的情况下都能给出测量误差协方差矩阵可靠的估计,两个仿真实例表明了算法的鲁棒性。     

基于双EnKF的土壤水分与土壤属性参数同时估计

为提高土壤水分数据同化结果的精度,将基于双集合卡尔曼滤波(Dual Ensemble Kalman Filter,DEnKF)的状态-参数估计方案与简单生物圈模型(simple biosphere model 2,SiB2)相结合,同时更新土壤水分和优化模型参数(土壤属性参数)。选用2008年6月1日~10月29日黑河上游阿柔冻融观测站为参考站,开展了同化表层土壤水分观测数据的实验。研究结果表明:DEnKF可同时优化土壤属性参数和改进土壤水分估计,该方法对表层土壤水分估计的精度0.04高于EnKF算法的精度0.05。当观测数据稀少时,DEnKF算法仍然可以得到较高精度的土壤水分估计,3层土壤水分的估计精度在0.02~0.05之间。     

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood.An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.     

Experiments of one-dimensional soil moisture assimilation system based on ensemble Kalman filter

Ensemble Kalman filter is a new sequential data assimilation algorithm which was originally developed for atmospheric and oceanographic data assimilation. It can be applied to calculate error covariance matrix through Monte-Carlo simulation. This approach is able to resolve the nonlinearity and discontinuity existed within model operator and observation operator. When observation data are assimilated at each time step, error covariances are estimated from the phase-space distribution of an ensemble of model states. The error statistics is then used to calculate Kalman gain matrix and analysis increments. In this study, we develop a one-dimensional soil moisture data assimilation system based on ensemble Kalman filter, the Simple Biosphere Model (SiB2) and microwave radiation transfer model (AIEM, advanced integration equation model). We conduct numerical experiments to assimilate in situ soil surface moisture measurements and low-frequency passive microwave remote sensing data into a land surface model, respectively. The results indicate that data assimilation can significantly improve the soil surface moisture estimation. The improvement in root zone is related to the model bias errors at surface layer and root zone. The soil moisture does not vary significantly in deep layer. Additionally, the ensemble Kalman filter is predominant in dealing with the nonlinearity of model operator and observation operator. It is practical and effective for assimilating observations in situ and remotely sensed data into land surface models.     

Notes and correspondence on ensemble-based three-dimensional variational filters

Several ensemble-based three-dimensional variational (3D-Var) filters are compared. These schemes replace the static background error covariance of the traditional 3D-Var with the ensemble forecast error covariance, but generate analysis ensemble anomalies (perturbations) in different ways. However, it is demonstrated in this paper that they are all theoretically equivalent to the ensemble transformation Kalman filter (ETKF). Furthermore, a new method named EnPSAS is presented. The analysis shows that EnPSAS has a small condition number and can apply covariance localization more easily than other ensemble-based 3D-Var methods.     

An evaluation of the nonlinear/non-Gaussian filters for the sequential data assimilation

This paper aims to investigate several new nonlinear/non-Gaussian filters in the context of the sequential data assimilation. The unscented Kalman filter (UKF), the ensemble Kalman filter (EnKF), the sampling importance resampling particle filter (SIR-PF) and the unscented particle filter (UPF) are described in the state-space model framework in the Bayesian filtering background. We first evaluated those methods with a simple highly nonlinear Lorenz model and a scalar nonlinear non-Gaussian model to investigate the filter stability and the error sensitivity, and then their abilities in the one-dimensional estimation of the soil moisture content with the synthetic microwave brightness temperature assimilation experiment in the land surface model VIC-3L. All the results are compared with the EnKF. The advantages and disadvantages of each filter are discussed.The results in the Lorenz model showed that the particle filters are suitable for the large measurement interval assimilation and that the Kalman filters were suitable for the frequent measurement assimilation as well as small measurement uncertainties. The EnKF also showed its feasibility for the non-Gaussian noise. The performance of the SIR-PF was actually not as good as that of the UKF or the EnKF regarding a very small observation noise level compared with the uncertainties in the system. In the one-dimensional brightness temperature assimilation experiment, the UKF, the EnKF and the SIR-PF all proved to be flexible and reliable nonlinear filter algorithms for the low dimensional sequential land data assimilation application. For the high dimensional land surface system that takes the horizontal error correlations into account, the UKF is restricted by its computational demand in the covariance propagation; we must use the EnKF, the SIR-PF and other covariance reduction algorithms. The large computational cost prevents the UPF from being applied in practice.     

Ensemble member generation for sequential data assimilation

Using an ensemble of model forecasts to describe forecast error covariance extends linear sequential data assimilation schemes to nonlinear applications. This approach forms the basis of the Ensemble Kalman Filter and derivative filters such as the Ensemble Square Root Filter. While ensemble data assimilation approaches are commonly reported in the scientific literature, clear guidelines for effective ensemble member generation remain scarce. As the efficiency of the filter is reliant on the accurate determination of forecast error covariance from the ensemble, this paper describes an approach for the systematic determination of random error. Forecast error results from three factors: errors in initial condition, forcing data and model equations. The method outlined in this paper explicitly acknowledges each of these sources in the generation of an ensemble. The initial condition perturbation approach presented optimally spans the dynamic range of the model states and allows an appropriate ensemble size to be determined. The forcing data perturbation approach treats forcing observations differently according to their nature. While error from model physics is not dealt with in detail, discussion of some commonly used approaches and their limitations is provided. The paper concludes with an example application for a synthetic coastal hydrodynamic experiment assimilating sea surface temperature (SST) data, which shows better prediction capability when contrasted with standard approaches in the literature.