Representation of correlation functions in variational assimilation using an implicit diffusion operator

Mirouze, Isabelle; Weaver, Anthony

doi:10.1002/qj.643

Cited by 82 publications

(123 citation statements)

References 65 publications

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“…Second, this approach is quite simple in an infinite or periodic domain but has to be adapted in the case of boundary conditions. These limitations were explored by Mirouze and Weaver (2010). The authors detail the correlation function obtained by the solution of the one-dimensional diffusion equation using an implicit time integration, as a function of the number of time steps M (i.e.…”

Section: Background Error Vertical Correlationsmentioning

confidence: 99%

“…This methodology was here derived and the vertical correlation is built by solving two one-dimensional diffusion equations: one with a Dirichlet boundary condition and the other with a Neumann one, using an implicit time integration. Our adaptation of the Mirouze and Weaver (2010) methodology greatly improves the treatment near boundaries, but not at the boundaries themselves. Nevertheless, the uppermost data value we used (see section 2.3) is located at a distance of 3 grid points from the top of the model vertical grid.…”

Section: Background Error Vertical Correlationsmentioning

confidence: 99%

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Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses

Massart

Piacentini

Pannekoucke

2011

Quart J Royal Meteoro Soc

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An ensemble method combined with a four-dimensional variational data assimilation system is used to provide monthly estimates of the background error covariance matrix for global stratospheric and upper tropospheric ozone for the year 2008. The system is composed of the Mocage chemical transport model and the Valentina assimilation system. The ensemble was obtained from parallel analyses of perturbed data from the Microwave Limb Sounder (MLS) instrument. The monthly estimates of background error covariances have then been introduced in the assimilation suite. To assess the separate contribution of each of its components, a number of analyses were realized, using only some estimated components of the background error covariances and a basic model for the others. The evaluation is realized by comparing the analyses with independent ozone profiles (from ozonesondes) and total ozone columns (from the Ozone Monitoring Instrument). It demonstrates that using the estimated statistics compared to basic models for the background error covariance matrix globally slightly improves the analysis quality; however, using the estimated statistics more largely improves the analysis quality for special situations encountered in April and October. In these situations, the most important parameter for the analysis quality is the use of estimated correlations. Copyright c 2011 Royal Meteorological SocietyKey Words: data assimilation; atmospheric chemistry; background error covariance matrix

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Section: Background Error Vertical Correlationsmentioning

confidence: 99%

Section: Background Error Vertical Correlationsmentioning

confidence: 99%

Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses

Massart

Piacentini

Pannekoucke

2011

Quart J Royal Meteoro Soc

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“…Xu, 2005;Pannekoucke and Massart, 2008;Mirouze and Weaver, 2010). Of particular interest are the iBEC models described by positive-definite polynomials of the diffusion operator…”

Section: Introductionmentioning

confidence: 99%

On the correlation functions associated with polynomials of the diffusion operator

Yaremchuk

Smith

2011

Quart J Royal Meteoro Soc

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“…Thus, this allows us to locally adjust the intensity of the smoothing. The local length-scale L(x) of the averaging kernel at the position x is determined from the local diffusion coefficient ν (or tensor in the multi-dimensional case): ν(x) = L 2 (x)/2 (Pannekoucke and Massart, 2008;Pannekoucke, 2009;Mirouze and Weaver, 2010).…”

Section: Heterogeneous Diffusionmentioning

confidence: 99%

Heterogeneous filtering of ensemble‐based background‐error variances

Raynaud

Pannekoucke

2012

Quart J Royal Meteoro Soc

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Background-error variances estimated from a finite size ensemble of data assimilations are affected by sampling noise, which degrades the accuracy of the variance estimates. Previous work highlighted the close link between the spatial structures of background error and the associated sampling noise, and demonstrated the ability of local spatial averaging to remove this sampling noise.Existing filtering techniques commonly assume a homogeneous smoothing of the estimated variances. However, this assumption can be inadequate to represent error structures of varying scales, e.g. small-scale errors associated with localized severe weather events. To answer this problem, this article introduces and examines a heterogeneous filter based on the knowledge of the local spatial properties of the sampling noise. The filtering is realized with a diffusion process, and the diffusion coefficient is parametrized according to the local correlation length-scale of the sampling noise. This enables the diffusion coefficient to vary spatially in such a way as to encourage smoothing in regions where the background error is large scale in preference to regions where the error is small scale.A simulated 1D framework is considered to test the proposed approach. It is shown that the filtering using a spatially varying diffusion coefficient is able to preserve high-frequency variance structures, while this information tends to be smoothed with homogeneous filtering. The benefits of applying heterogeneous filtering are particularly pronounced with small ensemble sizes and in the vicinity of localized variance maxima.

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Representation of correlation functions in variational assimilation using an implicit diffusion operator

Cited by 82 publications

References 65 publications

Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses

Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses

On the correlation functions associated with polynomials of the diffusion operator

Heterogeneous filtering of ensemble‐based background‐error variances

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