Ensemble Data Assimilation And Its Background-error Variances Filtering

The modeling and specification of the background error covariance matrix(B)are important elements in most variational data assimilation system.It determines how information spread and keep balance to nearby area.However,since the hurge dimensionality of B and lackage of knowledge concerning the statistical properties,several hypotheses of homogeneity,isotropy as well as static are ofter made in order to produce a viable computational algorithm.This kind of processing ignores the characteristics of heterogeneity,anisotropy and flow-dependent in B,which is especially obvious when dealing with the rapid development of frontal and typhoon systems.This article focuses on how to improve the statistical methods and efficiency of flow-dependent background error covariance.The main work is as follows:(1)In Four-dimensional variational data assimilation,a more efficient spatial averaging filtering scheme is designed to eliminate the sampling noise deduced by Lanczos algorithm in the diagnosis of background error variance.Compared with operational methods,this scheme can not only improve the filtering effect but also reduce the computational cost.Firstly,the relationship between spatial correlation length of sampling noise and background error variance is studied.Secondly,the influence of vertical layer and atmospheric variables on the optimal average length is studied.Finally,the scheme is applied to the actual operational system to analyze the impact of this method on the skill of assimilation and forecast.One-month experimental results show that this scheme can reduce the need of sample size and improve the quality of background error variance,what the most important is that it has positive effects on forecast and analysis.In addition,the spatial average filtering method simplifies the calculation process,and own more computational scallable and efficiency than operatioanl method.(2)In order to obtain a more realistic flow-dependent background error covariance,an experimental ensemble four-dimensional variational data assimilation system(En4DVar)was initially implemented based on the deterministic four-dimensional variational data assimilation system(YH4DVAR).By perturbing the background field,observation data and SST,a number of independent samples that characterize the uncertainty of the background field are constructed.Those samples offer the possibility of calculate of covariances‘of the day'in YH4DVAR system.Local vertical correlation covariance in wavelet flow-dependent background error covariance model is also designed and tested.Our results show that this model can effectively estimate the variance of the background field with the diversification of the weather conditions,and has some positive effects on the assimilation and prediction of severe weather such as typhoons.(3)Due to the limitation of computational resources,the ensemble size of En4Dvar is limited less thano(7)10 ~2(8).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 lower-passing filter.Firstly,the spatial correlation length-scale of the sampling noise is quantitaive deduced from climatological background error.Secondly,a low-pass filter is proposed based on this relation.The truncated wave number of the filter can be calculated according to the energy spectrum of the background error and corresponding nosie.Finally,the spectral method is applied to the simple one-dimensional tool model,the two-dimensional barotropic vorticity equation equation as well as the En4DVar experimental system respectively.The results show that the accuratcy of 10-member filtered result produced by spectral filtering denoising method can comparable to that of 50 samples.(4)A non-Gaussian noise wavelet threshold denoising method(NGWT)is proposed.As the sampling noise in background error variance has some spatial correlation and scale dependence,the sampling noise no longer strickly obeys the Gaussian distribution.Firstly,a wavelet threshold denoising method(GWT)with spectral and spatial localization is introduced to eliminate the sampling noise of the background error variance.Then,the GWT method is improved according to the non-Gaussian features of the sampling noise,the proposed method is able to automatically calculate and correct the threshold to reduce the residual error caused by excessive noise energy level in some scales,thus improving the filtering effect.Finally,the robustness of the proposed method is tested in a one-dimensional ideal model and real ensemble data assimilation system(En4DVar).(5)Combined with the idea of spectral filtering,a constraint-based wavelet threshold denoising method(CWTDNM)is proposed based on the fourth idea.That is,by introducing a new constraint parameter,the noise on each scale,especially on larger scales,is concerned.The CWTDNM method is validated in the 2D Diving wave model wave model.After filtering,both root mean square error and peak signal to noise ratio are slightly better than the pre-improvement method.