The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation

Courtier, Philippe; Andersson, Erik; Heckley, W. A.; Vasiljevic, Drasko; Hamrud, Mats; Hollingsworth, A.; Rabier, Florence; Fisher, Michael; Pailleux, Jean

doi:10.1002/qj.49712455002

Cited by 381 publications

(355 citation statements)

References 54 publications

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“…To achieve this, a variety of data assimilation techniques have been developed to improve the initial fields of the forecast. Current variational data assimilation methods are 3D-Var or 4D-Var (Courtier et al, 1998;Barker et al, 2004;Wulfmeyer et al, 2006;Huang et al, 2009) and the ensemble Kalman filter (EnKF; Evensen, 1994Evensen, , 2003Warrach-Sagi and Wulfmeyer, 2010) for surface and atmospheric data assimilation. Most assimilation schemes include conventional observations like SYNOP stations or radiosondes (TEMP).…”

Section: Introductionmentioning

confidence: 99%

High‐resolution simulation over central Europe: assimilation experiments during COPS IOP 9c

Schwitalla

Bauer

Wulfmeyer

et al. 2011

Quart J Royal Meteoro Soc

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The impact of assimilating conventional and Global Positioning System (GPS)ZenithA further comparison with the operational high-resolution models of DWD during this COPS IOP reveals a strong dependence on the initial boundary-layer wind field especially as the near-surface wind field is better represented in the ECMWF analysis than in the COSMO analysis.As this is, to our knowledge, the first study applying a convection-permitting configuration of WRF over Europe, it can be used as a guidance for further studies.

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Section: Introductionmentioning

confidence: 99%

High‐resolution simulation over central Europe: assimilation experiments during COPS IOP 9c

Schwitalla

Bauer

Wulfmeyer

et al. 2011

Quart J Royal Meteoro Soc

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“…Some models of the background correlation matrix are based on a diagonal assumption in spectral space (Courtier et al, 1998) leading to homogeneous covariances. More recently, the diagonal assumption in wavelet space has been introduced in order to model some heterogeneous correlations (Fisher, 2003).…”

Section: Introductionmentioning

confidence: 99%

Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation

Pannekoucke

Massart

2008

Quart J Royal Meteoro Soc

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ABSTRACT:As the background-error covariance matrix is a key component of any assimilation system, its modelling is an important step. Usually, this matrix is decomposed into correlations and standard deviations matrices. An interesting method for modelling the correlation matrix of the background error for complex geometry, like an ocean grid, consists in computing correlation functions using a diffusion operator. The background-error correlation functions can be estimated for example from an ensemble of perturbed forecasts. The diffusion operator is able to represent heterogeneous correlation functions at a reasonable numerical cost. But a first challenge resides in the determination of the local diffusion tensor corresponding to the local correlation function. Then the second challenge resides in the determination of the normalization to make sure that the matrix modelled through the diffusion operator is a correlation matrix. In this article, we propose to build a background-error correlation matrix using a diffusion operator based on a local diffusion tensor. The estimation of this local tensor is performed using an ensemble of perturbed forecasts. A validation within a randomization method illustrates the feasibility and the accuracy of the proposed method. In particular, it is shown that the local geographical variations of diagnosed correlation functions (through an ensemble of perturbed forecast) are well represented. This is first illustrated in an analytical one-dimensional framework. In that context, the diffusion field and the normalization field are deduced from a given correlation length-scale field. The resulting length-scales are shown to correspond to the initial length-scale when the given length-scale field spectrum is red. The approximate normalization, computed from the local length-scale, is close to the true normalization under the same condition of a red spectrum.Then, the method is illustrated in a real context using an ensemble of perturbed forecasts from the MOCAGE-PALM assimilation system. In that case, length-scale and anisotropy diagnosis reveal the complexity of the correlation of stratospheric ozone forecast errors. The local diffusion tensor deduced from these diagnoses is shown be able to represent such an existing heterogeneity and anisotropy. As in the one-dimensional case, the approximate normalization, based on the local diffusion tensor, appears to be a really good approximation of the true normalization.

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“…For example, the 3D-Var [11] and 4D-Var [12] methods have entered into common usage. In general, such methods can be viewed as inverse problems in that they attempt to reconstruct continuous scalar fields based on a discrete (and often sparse) set of measurements.…”

Section: Related Workmentioning

confidence: 99%

Interpolating sparse scattered data using flow information

Streletz

Gebbie

Kreylos

et al. 2016

Journal of Computational Science

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a b s t r a c tScattered data interpolation and approximation techniques allow for the reconstruction of a scalar field based upon a finite number of scattered samples of the field. In general, the fidelity of the reconstruction with respect to the original scalar field tends to deteriorate as the number of samples decreases. For the situation of very sparse sampling, the results may not be acceptable at all. However, if it is known that the scalar field of interest is correlated with a known flow field -as is the case when the scalar field represents the value of an oceanographic tracer that propagates under the influence of the ocean's flow -then this knowledge can be exploited to enhance the scattered data reconstruction method. One way to exploit flow field information is to use it to construct a modified notion of distance between points. Replacing the standard Euclidean distance metric with a flow-field-aware notion of distance provides a method for extending standard scattered data interpolation methods into flow-based methods that produce superior results for very sparse data. The resulting reconstructions typically have lower root-mean-square errors than reconstructions that do not use the flow information, and qualitatively they often appear physically more realistic.

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The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation

Cited by 381 publications

References 54 publications

High‐resolution simulation over central Europe: assimilation experiments during COPS IOP 9c

High‐resolution simulation over central Europe: assimilation experiments during COPS IOP 9c

Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation

Interpolating sparse scattered data using flow information

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