Fitting model fields to observations by using singular value decomposition: An ensemble‐based 4DVar approach

Qiu, Chongjian; Shao, Aimei; Xu, Qin; Li, Wei

doi:10.1029/2006jd007994

Cited by 38 publications

(60 citation statements)

References 50 publications

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“…Wang et al, 2008aWang et al, , 2008bClayton et al, 2013), the 'En4DVar' (e.g. Zhang et al, 2009;Zhang and Zhang, 2012) and the '4DEnVar' assimilation methods (Qiu et al, 2007;Liu et al, 2008;Tian et al, 2008;Wang et al, 2010;Tian et al, 2011;Tian and Xie, 2012). The 'hybrid 4DVar' denotes 4DVar methods using a combination of climatological and ensemble covariances.…”

Section: Introductionmentioning

confidence: 99%

A non-linear least squares enhanced POD-4DVar algorithm for data assimilation

Tian

Feng

2015

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T This paper presents a novel non-linear least squares enhanced proper orthogonal decomposition (POD)-based 4DVar algorithm (referred as NLS-4DVar) for the non-linear ensemble-based 4DVar. In the algorithm, the GaussÁNewton iterative method is employed to handle the non-quadratic non-linearity of the 4DVar cost function while the overall structure of the algorithm still resembles the original POD-4DVar algorithm. It is proved that the original POD-4DVar algorithm is a special case of the proposed NLS-4DVar algorithm under the assumption of the linear relationship between the model perturbations (MPs) and the simulated observation perturbations (OPs). Under the assumption it is also shown that the solution of POD-4DVar algorithm coincides with the solution of the proposed NLS-4DVar algorithm. On the contrary, if the linear relationship assumption is dropped, the solution of the POD-4DVar algorithm is only the first iteration of the proposed NLS-4DVar algorithm. As a result, our analysis provides an explanation for the degraded and inaccurate performance of the POD-4DVar algorithm when the underlying forecast model or (and) the observation operator is strongly non-linear. The potential merits and advantages of the proposed NLS-4DVar are demonstrated by a group of Observing System Simulation Experiments with Advanced Research WRF (ARW) using accumulated rainfall-observations.

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Section: Introductionmentioning

confidence: 99%

A non-linear least squares enhanced POD-4DVar algorithm for data assimilation

Tian

Feng

2015

Tellus A: Dynamic Meteorology and Oceanography

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“…The DRP-4DVar method with a wide range of the EOF truncation number surpasses the ETKF and the 4DEnVar methods in analysis RMSE. This explains the successful applications of the DRP-4DVar method as well as other 4DEnVar methods [20,24,34,38,56], without special optimization of the truncation number. Yet, optimizing the EOF truncation number makes sense.…”

Section: Discussionmentioning

confidence: 99%

“…Zhao et al developed a DRP-4DVar assimilation system based on MM5, and successfully assimilated the simulated sea level pressure observations to improve the typhoon-track forecasts in the observing system simulation experiments (OSSEs) [39]. However, previous studies paid little attention to the EOF-, SVD-, or POD-based techniques and their related parameters (e.g., truncation number) in the 4DEnVar method family [20,24,25,40]. Investigating and understanding the role of EOF is of great importance for the study of these 4DEnVars since the basis vectors expressing the analysis variables in the 4D space are constructed by the technique.…”

Section: Introductionmentioning

confidence: 99%

Evaluating the Role of the EOF Analysis in 4DEnVar Methods

et al. 2017

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Abstract:The four-dimensional variational data assimilation (4DVar) method is one of the most popular techniques used in numerical weather prediction. Nevertheless, the needs of the adjoint model and the linearization of the forecast model largely limit the wider applications of 4DVar. 4D ensemble-variational data assimilation methods (4DEnVars) exploit the strengths of the Ensemble Kalman Filter and 4DVar, and use the ensemble trajectories to directly estimate four-dimensional background error covariance. This study evaluates the role of the empirical orthogonal function (EOF) analysis in 4DEnVars. The widely-recognized 4DEnVar method DRP-4DVar (the Dimension-reduced projection 4DVar) is adopted as the representation of EOF analyses in this study. The performance of the Dimension-reduced projection 4DVar (DRP-4DVar), 4DEnVar (i.e., another traditional 4DEnVar scheme without EOF transformation), and the Ensemble Transform Kalman Filter (ETKF) was compared to demonstrate the effect of the EOF analysis in DRP-4DVar. Sensitivity experiments indicate that EOF analyses construct basis vectors in eigenvalue space and the dimension reduction in the DRP-4DVar approach helps improve computational efficiency and analysis accuracy. When compared with 4DEnVar and the ETKF, the DRP-4DVar demonstrates similar analysis root-mean-square error (RMSE) to 4DEnVar, whereas it surpasses the ETKF by 22.3%. In addition, sensitivity experiments of DRP-4DVar on the ensemble size, the assimilation window length, and the standard deviation of the initial perturbation imply that the DRP-4DVar with the optimized EOF truncation number is robust to a wide range of the parameters, but extremely low values should be avoided. The results presented here suggest the potential wide application of EOF analysis in the hybrid 4DEnVar methods.

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“…Many developments have recently been reported on assimilation methods and systems and their applications for land, atmosphere and ocean research (Zhu et al, 2007;Wang and Mu, 2008;Li et al, 2007;Qiu et al, 2007;Yang et al, 2007;Wang et al, 2010;Zhang et al, 2012). Tian et al (2011) developed a proper orthogonal decomposition (POD)-based ensemble four-dimensional variational assimilation method (PODEn4DVar), which incorporates advantages of both ensemble and variational methods and is suitable for GRACE data assimilation.…”

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confidence: 99%

GRACE terrestrial water storage data assimilation based on the ensemble four-dimensional variational method PODEn4DVar: Method and validation

Sun

Xie

Tian

2015

Sci. China Earth Sci.

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Seasonal and interannual changes in the Earth's gravity field are mainly due to mass exchange among the atmosphere, ocean, and continental water sources. The terrestrial water storage changes, detected as gravity changes by the Gravity Recovery and Climate Experiment (GRACE) satellites, are mainly caused by precipitation, evapotranspiration, river transportation and downward infiltration processes. In this study, a land data assimilation system LDAS-G was developed to assimilate the GRACE terrestrial water storage (TWS) data into the Community Land Model (CLM3.5) using the POD-based ensemble four-dimensional variational assimilation method PODEn4DVar, disaggregating the GRACE large-scale terrestrial water storage changes vertically and in time, and placing constraints on the simulation of vertical hydrological variables to improve land surface hydrological simulations. The ideal experiments conducted at a single point and assimilation experiments carried out over China by the LDAS-G data assimilation system showed that the system developed in this study improved the simulation of land surface hydrological variables, indicating the potential of GRACE data assimilation in large-scale land surface hydrological research and applications. data assimilation, land surface model, terrestrial water storage, ensemble four-dimensional variational data assimilation method Citation:Sun Q, Xie Z H, Tian X J, et al. 2015. GRACE terrestrial water storage data assimilation based on the ensemble four-dimensional variational method

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Fitting model fields to observations by using singular value decomposition: An ensemble‐based 4DVar approach

Cited by 38 publications

References 50 publications

A non-linear least squares enhanced POD-4DVar algorithm for data assimilation

A non-linear least squares enhanced POD-4DVar algorithm for data assimilation

Evaluating the Role of the EOF Analysis in 4DEnVar Methods

GRACE terrestrial water storage data assimilation based on the ensemble four-dimensional variational method PODEn4DVar: Method and validation

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