中文摘要：

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。

英文摘要：

The ensemble-based 4DVar approach with SVD technique（SVD-En4DVar） may be subject to significant uncertainties due to the size of forecast ensemble.Especially,the less ensemble size will cause more truncation errors when the analysis variables are expressed as a linear expansion with the leading singular vectors extracted from an ensemble of the perturbed forecasts.In order to improve assimilation skills by increasing sample members but without addition computational costs,a hybrid sample analysis scheme is developed.In this scheme some time-invariant samples are added to the flow-dependent samples obtained by the short-range forecasts over the analysis time window.The static samples can be produced by two approaches.In the first approach,the initial pseudo random fields with a specified statistic structure are added directly to the background field in 4D space without operating by the model integration.In the second approach,the static samples are obtained by integrating the model over the first analysis time window with the initial fields superposed the pseudo random fields on the initial background field.This implies that the partial flow-dependent samples yielded in the first assimilation circle will be used as the static samples in the subsequent circles.The numerical experiments on the different sample structures are tested with the shallow-water-equation model and Lorenz-96 model with 80 variables.When only large size of static sample ensemble is used,the better assimilation skills can be found in the shallow-water-equation model but not for Lorenz-96 model.However,two models perform well when hybrid samples are used.For the same computation costs,the hybrid sample analysis scheme can obviously improve assimilation accuracy and the second approach for statically sampling is better than the first one.