An economical approach to four-dimensional variational data assimilation

Wang, Bin; Liu, Juanjuan; Wang, Shudong; Cheng, Wei; Liang, Juan; Liu, Chengsi; Xiao, Qingnong; Kuo, Ying‐Hwa

doi:10.1007/s00376-009-9122-3

Cited by 78 publications

(88 citation statements)

References 36 publications

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“…The main idea of DRP-4DVar is to combine 4DVar and EnKF to produce a superior hybrid approach. In order to benefit from using the statedependent uncertainty provided by EnKF, Wang et al (2010) used initial perturbation samples to estimate the B-matrix as in EnKF:…”

Section: Methodsmentioning

confidence: 99%

“…Recently, several researchers have proposed a variety of hybrid methods (Lorenc, 2003;Hunt et al, 2004;Liu et al, 2008Liu et al, , 2009Zhang et al, 2009;Wang et al, 2010). The main thrust behind the hybrid methods is that the ensemble-based background error covariance statistics are provided to the variational data assimilation.…”

Section: Introductionmentioning

confidence: 99%

“…Despite the many differences between the various ensemble-based algorithms, all are comprised of a finite number of samples and short-range forecast cycles (Hamill, 2000). The DRP-4DVar approach (Wang et al, 2010) is one of these various hybrid schemes, and its B-matrix is modeled using the ensemble of forecasts, these ensembles are produced by the historical time series of model forecasts, so ensure it to flow dependency globally. Thépaut et al (1993) showed how complex a forecast error covariance could be when it evolved according to the primitive equations.…”

Section: Introductionmentioning

confidence: 99%

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The structure of background-error covariance in a four-dimensional variational data assimilation system: Single-point experiment

Liu

Wang

2010

Adv. Atmos. Sci.

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A four dimensional variational data assimilation (4DVar) based on a dimension-reduced projection (DRP4DVar) has been developed as a hybrid of the 4DVar and Ensemble Kalman filter (EnKF) concepts. Its good flow-dependent features are demonstrated in single-point experiments through comparisons with adjointbased 4DVar and three-dimensional variational data (3DVar) assimilations using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5). The results reveal that DRP-4DVar can reasonably generate a background error covariance matrix (simply B-matrix) during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar are anisotropic and no longer symmetric with respect to observation location due to the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.Key words: DRP-4DVar, data assimilation, flow dependence, single-point experiment Citation: Liu, J. J., B. Wang, and S. D. Wang, 2010: The structure of background-error covariance in a four-dimensional variational data assimilation system: single-point experiment.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The structure of background-error covariance in a four-dimensional variational data assimilation system: Single-point experiment

Liu

Wang

2010

Adv. Atmos. Sci.

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“…Lorenc, 2003;Harlim and Hunt, 2007;Tian et al, 2008Tian et al, , 2011Wang et al, 2010;Zhang et al, 2009;Cheng et al, 2010;Zhang and Zhang, 2012;Wang et al, 2013). According to the classification suggested by Andrew C. Lorenc (http:// www.wcrp-climate.org/WGNE/BlueBook/2013/individualarticles/01_Lorenc_Andrew_EnVar_nomenclature.pdf), the existing composite methods in the literature can be roughly divided into three groups, namely, the 'hybrid' (e.g.…”

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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“…However, the "signal-to-noise" problem has not yet been resolved, and thus CarbonTracker also has to assimilate natural CO 2 emissions at the ecological scale only. In Tan-Tracker (Tian et al, 2014), a fourdimensional (4-D) moving sampling strategy (Wang et al, 2010) is used to generate the flux ensemble members, and so the surface CO 2 fluxes can be optimized as a whole at the grid scale. In this work, the persistence dynamical model taken by Peters et al (2005) was further developed for the purpose of resolving the "signal-to-noise" problem, to optimize the surface CO 2 fluxes as a whole at the grid scale.…”

Section: Z Peng Et Al: a Regional Carbon Data Assimilation Systemmentioning

confidence: 99%

A regional carbon data assimilation system and its preliminary evaluation in East Asia

et al. 2015

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Abstract. In order to optimize surface CO 2 fluxes at grid scales, a regional surface CO 2 flux inversion system (Carbon Flux Inversion system and Community Multi-scale Air Quality, CFI-CMAQ) has been developed by applying the ensemble Kalman filter (EnKF) to constrain the CO 2 concentrations and applying the ensemble Kalman smoother (EnKS) to optimize the surface CO 2 fluxes. The smoothing operator is associated with the atmospheric transport model to constitute a persistence dynamical model to forecast the surface CO 2 flux scaling factors. In this implementation, the "signalto-noise" problem can be avoided; plus, any useful observed information achieved by the current assimilation cycle can be transferred into the next assimilation cycle. Thus, the surface CO 2 fluxes can be optimized as a whole at the grid scale in CFI-CMAQ. The performance of CFI-CMAQ was quantitatively evaluated through a set of Observing System Simulation Experiments (OSSEs) by assimilating CO 2 retrievals from GOSAT (Greenhouse Gases Observing Satellite). The results showed that the CO 2 concentration assimilation using EnKF could constrain the CO 2 concentration effectively, illustrating that the simultaneous assimilation of CO 2 concentrations can provide convincing CO 2 initial analysis fields for CO 2 flux inversion. In addition, the CO 2 flux optimization using EnKS demonstrated that CFI-CMAQ could, in general, reproduce true fluxes at grid scales with acceptable bias. Two further sets of numerical experiments were conducted to investigate the sensitivities of the inflation factor of scaling factors and the smoother window. The results showed that the ability of CFI-CMAQ to optimize CO 2 fluxes greatly relied on the choice of the inflation factor. However, the smoother window had a slight influence on the optimized results. CFI-CMAQ performed very well even with a short lag-window (e.g. 3 days).

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An economical approach to four-dimensional variational data assimilation

Cited by 78 publications

References 36 publications

The structure of background-error covariance in a four-dimensional variational data assimilation system: Single-point experiment

The structure of background-error covariance in a four-dimensional variational data assimilation system: Single-point experiment

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

A regional carbon data assimilation system and its preliminary evaluation in East Asia

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