集合资料同化中方差滤波技术研究及试验

Investigations and experiments of variances filtering technology in the Ensemble Data Assimilation

本文基于YH4DVAR业务系统构建了集合资料同化试验平台,利用10个集合样本统计得到的流依赖背景误差能显著改进业务应用中背景误差方差的结构和大小.但是受样本数的限制,背景误差方差的集合估计值中引入了大量的随机取样噪声.为了降低噪声对估计值的影响,本文采用谱滤波方法,根据信号和噪声尺度的统计特征构造一个低通滤波器来滤除背景误差方差估计值中的大部分随机取样噪声.在2013年第九号台风"飞燕"的集合方差滤波试验中,10个样本的滤波结果优于30个样本的集合估计值.谱滤波方法的成功应用有效降低了集合资料同化系统对集合样本数的要求,将是集合资料同化系统未来业务化运行的一项不可或缺的关键技术.

Ensemble Data Assimilation（EDA）system is able to provide flow-dependent estimates of background error covariances matrix.Therefore,it is possible to overcome the shortcomings of quasi-static or climatic covariance models currently used in most of the variational data assimilation systems.However,the finite ensemble size implies a detrimental sampling noise for the background error variances estimation.To resolve this problem,a spectral filtering technique is employed to formulate a low-passing filter whose truncation wave number is determined according to the typical horizontal length scales of noises and valuable signals.The rationality and efficiency of this technique are analysed in a typhoon assimilation experiment.The method of spectral filtering was used to filter sampling noise in the EDA raw background error estimation.At first,an experimental EDA system was built based on the operational YH4 DVAR analysis.This system consisted 10 lower resolution members generated by perturbing observations,sea surface temperature（SST）fields and model physical tendencies.Secondly,the vorticity background error of the 9th typhoon in 2013 calculated from 10,20 and 30members respectively were compared with the operational one.Though EDA estimates showed superiority to the later,its slow rate convergence of sampling noise with respect to ensemble size and the limited ensemble dimensions made the filtering process still necessary.FollowingRaynaud′s theory,the sampling noise power spectrum was calculated from the expectation of the ensemble-based error covariance matrix.Then,a smooth spectral filter was applied to the 10 member raw estimate.The filter′s truncation wave number was determined according to the typical horizontal length scales of noises and valuable signals.The filtered result was compared with 30 member raw estimate.In this typhoon assimilation experiment,flow-dependent background error variances can be estimated accurately from the experimental EDA system with 10,20 or 30 members.Corresponding to the operational one,the location of the maximum of vorticity background error on model level 91 is closer to the center position of typhoon,and its structure also exactly represents the uncertainty in the background state in this dynamically active areas.With similar structure,the difference between those estimates is the levels of sampling noise,the larger size the lower level.In operational context,it is reasonable to choose 10 members′estimate as the raw signal.After the spherical spectral transform,the separation in spectral space of the signal（10member variance estimate）from the sampling noise power is clear up to about wavenumber195.This corresponds to the definition of a truncation wavenumber（Ntrunc）.Based on the Ntrunc,a smooth filtering is designed whose coefficient is close to 0when wavenumber is equal or bigger than Ntrunc.Otherwise,the coefficient is a sinusoidal function of wavenumber.It enables us to get rid of some large oscillations in the raw filter whose coefficient is determined directly by the noiseto-signal ratio.The application of those low-pass filters in spectral space can be seen as a weighted spatial averaging technique in grid-point space,which enables the large-scale signal of interest to be extracted while filtering out the small-scale sampling noise effectively.The two filtered vorticity background error fields are similar in large-scale,but the smooth filter reveals a heavier filtering as coefficients beyond the Ntruncare set to 0.Whatever,10-members′filtered variances exhibit better performance than 30-members′s estimations while saving computer resource obviously.An ensemble data assimilation system is built to provide flow-dependent estimates of background error statistics for operational data assimilation YH4 DVAR.A spectral filtering method is used to deal with the sampling noise caused by limited ensemble members.The employed smooth filter enables the large-scale signal of interest to be preserved while filtering out the small-scale sampling noise.For this reason,it can reduce the size of EDA system running in operational context.Further work is using heterogeneous filter that depends on the geographical position to deal with error structures of varying scales,and in particular to extract localised patterns of useful signal which is often smoothed out by smooth filter.