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

Liu, Juanjuan; Wang, Bin; Wang, Shudong

doi:10.1007/s00376-010-9067-6

Cited by 5 publications

(6 citation statements)

References 25 publications

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“…Extremely short assimilation window lengths lead to failure of the assimilation analysis when the RMSE is larger than 1.00. This result is also in accordance with previous studies on the assimilation window length in 4DVar and the DRP-4DVar methods [7,36].…”

Section: Resultssupporting

confidence: 82%

“…This result is also in accordance with previous studies on the assimilation window length in 4DVar and the DRP-4DVar methods [7,36]. Figure 5.…”

Section: Resultssupporting

confidence: 82%

“…The DRP-4DVar method with the optimized EOF truncation number is robust to the variation of pertinent parameters, though extremely low parameter values should be avoided. Results of the sensitivity experiments on the parameters (i.e., the ensemble size, the assimilation window length, and the standard deviation of the initial perturbation for each assimilation window) also agree with previous studies on EnKF, 4DVar, 4DEnVar, and DRP-4DVar [7,22,36,55,57], Thus, refinement of the EOF truncation number is attractive for cases with a high requirement of the computational efficiency and the analysis accuracy, particularly for applications on operational numerical system (e.g., [39]). …”

Section: Discussionsupporting

confidence: 76%

“…The X en and Y en are generated by either historical sampling (e.g., [34]) or ensemble forecast for the assimilation window (e.g., [36,37,46]), and this study focuses on the latter scenario. Further, the background ensemble perturbations X en are assumed to be a Gaussian distribution with X en = 0 and given standard deviations.…”

Section: The Drp-4dvar and The 4denvar Methodsmentioning

confidence: 99%

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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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Section: Resultssupporting

confidence: 82%

“…This result is also in accordance with previous studies on the assimilation window length in 4DVar and the DRP-4DVar methods [7,36]. Figure 5.…”

Section: Resultssupporting

confidence: 82%

Section: Discussionsupporting

confidence: 76%

Section: The Drp-4dvar and The 4denvar Methodsmentioning

confidence: 99%

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Evaluating the Role of the EOF Analysis in 4DEnVar Methods

et al. 2017

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“…In this theory, the forecast error covariance, also known as background error covariance (BEC), is of central importance (Fu et al, 2004;Wang et al, 2010). BEC is the most complicated part in the practical data assimilation formulation and often incurs the largest computational cost in a data assimilation system (Derber and Bouttier, 1999;Liu et al, 2010). Representing BEC in aerosol data assimilation associated with a meteorology-chemistry model is more complicated than that associated with a meteorology-only model, because a sophisticated meteorology-chemistry model may explicitly treat more than a dozen variables, representing different aerosol species along with multiple size bins.…”

Section: Introductionmentioning

confidence: 99%

Background error statistics for aerosol variables from WRF/Chem predictions in Southern California

Zang

Hao

Pan

et al. 2015

Asia-Pacific J Atmos Sci

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Background error covariance (BEC) is crucial in data assimilation. This paper addresses the multivariate BEC associated with black carbon, organic carbon, nitrates, sulfates, and other constituents of aerosol species. These aerosol species are modeled and predicted using the Model for Simulating Aerosol Interactions and Chemistry scheme (MOSAIC) in the Weather Research and Forecasting/Chemistry (WRF/Chem) model at a resolution of 4 km in Southern California. The BEC is estimated from the differences between the 36-hour and 12-hour forecasts using the NMC method. The results indicated that the maximum background error standard deviation is associated with nitrate and is larger than that of black carbon, organic carbon, and sulfate. The horizontal and vertical scale of the correlation of nitrate is much smaller than that of other species. A significant cross-correlation is found between the species of black carbon and organic carbon. The cross-correlations between nitrate and other variables are relatively smaller and exhibit a relatively smaller length scale. Single observation data assimilation experiments are performed to illustrate the effect of the BEC on analysis increments.

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