Dynamical structure functions in a four‐dimensional variational assimilation: A case study

Thépaut, Jean‐Noël; Courtier, Philippe; Belaud, Gilles; Lemaitre, G.

doi:10.1002/qj.49712253012

Cited by 109 publications

(73 citation statements)

References 32 publications

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“…The analysis increments due to a single observation can directly be associated with the multivariate structure functions, that is a single row or column of B, and their flow dependencies in the case of 4D-Var. Single observation impact experiments with the ECMWF 3D-Var and 4D-Var were carried out by The´paut et al (1996). Based on the theoretical equivalence between 4D-Var and the Extended Kalman Filter (EKF) (Ghil and Malanotte-Rizzoli, 1991), the analysis increments from these experiments were used to investigate the dynamical structure functions implied in the ECMWF 4D-Var.…”

Section: Implicit Dynamical Structure Functionsmentioning

confidence: 99%

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Four-dimensional variational data assimilation for a limited area model

Gustafsson

Huang

Yang

et al. 2012

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C TA 4-dimensional variational data assimilation (4D-Var) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system is described in this article. The innovative approaches to the multi-incremental formulation, the weak digital filter constraint and the semi-Lagrangian time integration are highlighted with some details. The implicit dynamical structure functions are discussed using single observation experiments, and the sensitivity to various parameters of the 4D-Var formulation is illustrated. To assess the meteorological impact of HIRLAM 4D-Var, data assimilation experiments for five periods of 1 month each were performed, using HIRLAM 3D-Var as a reference. It is shown that the HIRLAM 4D-Var consistently out-performs the HIRLAM 3D-Var, in particular for cases with strong mesoscale storm developments. The computational performance of the HIRLAM 4D-Var is also discussed.

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Section: Implicit Dynamical Structure Functionsmentioning

confidence: 99%

“…One of the most important aspects of 4D-Var is its implicit flow-dependent assimilation structure functions (The´paut et al, 1996). 4D-Var takes the time dimension into account through the forecast model.…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional variational data assimilation for a limited area model

Gustafsson

Huang

Yang

et al. 2012

Tellus A: Dynamic Meteorology and Oceanography

View full text Add to dashboard Cite

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“…As illustrated by several authors (Thépaut et al, 1996;Ingleby, 2001), background-error covariances in NWP models are heterogeneous. From a climatological point of view, correlation length-scales are rather high over the oceans while smaller values are observed in the midlatitude storm-track regions, for instance.…”

Section: Homogeneous Diffusionmentioning

confidence: 99%

“…Such experimental settings may simulate what we observe in the vicinity of lows and troughs (e.g. midlatitude storms), which are characterized by high variances and small length-scales (Thépaut et al, 1996;Pannekoucke et al, 2007;Raynaud et al, 2009). As explained in the previous sections, the optimization of the homogeneous and heterogeneous filters is based on different metrics.…”

Section: Optimization Of the Heterogeneous Filtermentioning

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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“…4D-Var can then outperform 3D-Var if the model has significant skill in evolving the background-error covariance matrix, even though the assimilation cycle is started with a climatological estimate. Though a 6 h or 12 h forecast from a climatological estimate is clearly insufficient to obtain a good estimate, extra value may still be obtained over allowing no evolution at all, as demonstrated, for instance, by Thépaut et al (1996). Conventional 4D-Var will give an optimal estimate of the atmospheric state if the forecast model is perfect and a linearised perturbation model can accurately evolve perturbations to a model state.…”

Section: Introductionmentioning

confidence: 99%

A demonstration of 4D‐Var using a time‐distributed background term

Cullen

2010

Quart J Royal Meteoro Soc

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The standard four-dimensional variational data assimilation (4D-Var) method used at several major operational centres minimises a cost function which consists of a background term evaluated at the start of the assimilation window and a sum of observation terms evaluated throughout the assimilation window. This method can be interpreted as a smoother in which the background term is evolved in time using the forecast model, and the observations assimilated sequentially. However, in operational practice, the initial estimate of the background error is climatological and highly simplified, so that it is not clear whether this interpretation is useful. We thus interpret the background term as a regularisation term, rather than as an estimate of the true background error. We demonstrate this approach using a toy model whose solutions contain two time-scales: a slow scale which can be accurately predicted and a fast scale where the model errors are too large for deterministic prediction to be possible. This represents a common situation in operational predictions. We show that, if the regularisation term is only evaluated at the beginning of the assimilation window, as in standard 4D-Var, it is less effective at controlling rapidly growing modes. This can be resolved by applying the regularisation with equal weight throughout the window. The effect is that, in poorly observed situations, better forecasts of the slow modes can be obtained by directing information from the observations onto the slow modes rather than the unpredictable fast modes.

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Dynamical structure functions in a four‐dimensional variational assimilation: A case study

Cited by 109 publications

References 32 publications

Four-dimensional variational data assimilation for a limited area model

Four-dimensional variational data assimilation for a limited area model

Heterogeneous filtering of ensemble‐based background‐error variances

A demonstration of 4D‐Var using a time‐distributed background term

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