Impact of non‐smooth observation operators on variational and sequential data assimilation for a limited‐area shallow‐water equation model

Steward, Jeffrey L.; Navon, I. M.; Zupanski, Milija; Karmitsa, Napsu

doi:10.1002/qj.935

Cited by 24 publications

(14 citation statements)

References 41 publications

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“…The SWM has been used for a variety of assimilation experiments e.g. Lawless et al (2005Lawless et al ( , 2008; Katz et al (2011);Steward et al (2012). As an idealised system, it allows clearer understanding of the results without the obfuscating complexity of a more realistic system.…”

Section: Shallow Water Modelmentioning

confidence: 99%

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Stewart¹,

Dance²,

Nichols

2013

Tellus A: Dynamic Meteorology and Oceanography

108

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A B S T R A C T Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or 'truth' trajectory, as well as with analyses using the 'true' observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

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Section: Shallow Water Modelmentioning

confidence: 99%

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Stewart¹,

Dance²,

Nichols

2013

Tellus A: Dynamic Meteorology and Oceanography

108

View full text Add to dashboard Cite

show abstract

“…Examples discussed here include so-called variational methods, but there is much more to explore, like iterative Tikhonov regularisation. Of specific mention is are variants that can handle non-smooth problems, see, e.g., Steward et al (2012) for a geophysical example. All these methods can be part of the proposal densities in the Bayesian framework, and this seems to be the natural way to combine the Bayesian and the inverse problems fields, and indeed their communities.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear Data Assimilation

Leeuwen

Cheng

Reich

2015

Frontiers in Applied Dynamical Systems: Reviews and Tutorials

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The Frontiers in Applied Dynamical Systems (FIADS) covers emerging topics and significant developments in the field of applied dynamical systems. It is a collection of invited review articles by leading researchers in dynamical systems, their applications and related areas. Contributions in this series should be seen as a portal for a broad audience of researchers in dynamical systems at all levels and can serve as advanced teaching aids for graduate students. Each contribution provides an informal outline of a specific area, an interesting application, a recent technique, or a "how-to" for analytical methods and for computational algorithms, and a list of key references. All articles will be refereed.

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“…For general nonlinear or even non-smooth radiative transfer operators (Steward et al, 2012), the utility of higher-order elements in a Taylor expansion may be questionable. Also, the development of the second-order term may be time consuming and difficult in the case of complex observation operators, especially when the observation operators cannot be localized.…”

Section: G Wu Et Al: Improving the Etkf Using Second-order Informationmentioning

confidence: 99%

Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

Wang

et al. 2014

Nonlin. Processes Geophys.

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Abstract. The ensemble transform Kalman filter (ETKF) assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the ensemble Kalman filter (EnKF), the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem in the minimization of a nonlinear objective function similar to 4D-Var is that the nonlinear operator and its tangent-linear operator have to be calculated iteratively if the Hessian is not preconditioned or if the Hessian has to be calculated several times. This may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate.This study attempts to solve these problems. First, we apply the second-order Taylor approximation to the nonlinear observation operator in which the operator, its tangentlinear operator and Hessian are calculated only once. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz 96 model shows that using the secondorder Taylor approximation of the nonlinear observation operator leads to a reduction in the analysis error compared with the traditional linear approximation method. Furthermore, the proposed inflation scheme leads to a reduction in the analysis error compared with the procedure using the traditional inflation scheme.

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Impact of non‐smooth observation operators on variational and sequential data assimilation for a limited‐area shallow‐water equation model

Cited by 24 publications

References 41 publications

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Nonlinear Data Assimilation

Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

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