Comparison between Four-Dimensional LETKF and Ensemble-Based Variational Data Assimilation with Observation Localization

Yokota, Sho; Kunii, Masaru; Aonashi, Kazumasa; Origuchi, Seiji

doi:10.2151/sola.2016-019

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…In the 4D-Var-BenkfL system, it is not necessarily zero even at an analysis grid point away from an observation location because the localization scale is defined by r a and the analysis increment evolves in time according to the model dynamics. Similar difference between 4D-Var and LETKF was also observed in Yokota et al (2016).…”

Section: Single-observation Experimentssupporting

confidence: 82%

Mesoscale Hybrid Data Assimilation System based on JMA Nonhydrostatic Model

Ito

Kunii²,

Kawabata³

et al. 2016

Mon. Wea. Rev.

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This paper discusses the benefits of using a hybrid ensemble Kalman filter and four-dimensional variational (4D-Var) data assimilation (DA) system rather than a 4D-Var system employing the National Meteorological Center (NMC, now known as NCEP) method (4D-Var-Bnmc) to predict severe weather events. An adjoint-based 4D-Var system was employed with a background error covariance matrix [Formula: see text] constructed from the NMC method and perturbations in a local ensemble transform Kalman filter system. The DA systems are based on the Japan Meteorological Agency’s nonhydrostatic model. To reduce the sampling noise, three types of implementation (the spatial localization, spectral localization, and neighboring ensemble approaches) were tested. The assimilation of a pseudosingle observation of sea level pressure located at a tropical cyclone (TC) center yielded analysis increments physically consistent with what is expected of a mature TC in the hybrid systems at the beginning of the assimilation window, whereas analogous experiments performed using the 4D-Var-Bnmc system did not. At the end, the structures of the 4D-Var-based increments became similar to one another, while the analysis increment by the 4D-Var-Bnmc system was broad in the horizontal direction. Realistic DA experiments showed that all of the hybrid systems provided initial conditions that yielded more accurate TC track and intensity forecasts than those achievable by the 4D-Var-Bnmc system. The hybrid systems also yielded some statistically significant improvements in forecasting local heavy rainfall events in terms of fraction skill scores when a 160 km × 160 km window size was used. The overall skills of the hybrid systems were relatively independent of the choice of implementation.

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Section: Single-observation Experimentssupporting

confidence: 82%

Mesoscale Hybrid Data Assimilation System based on JMA Nonhydrostatic Model

Ito

Kunii²,

Kawabata³

et al. 2016

Mon. Wea. Rev.

Self Cite

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“…The quality of an estimate with the 4DEnVar can thus be poor if there are insufficient ensemble members. In practical applications of the 4DEnVar, a localization technique is usually used to avoid this problem (e.g., Buehner, 2005;Liu et al, 2009;Buehner et al, 2010;Yokota et al, 2016). However, the present paper does not consider localization because the focus here is on the basic behavior of the 4DEnVar.…”

Section: The 4d Variational Data Assimilation (4denvar)mentioning

confidence: 99%

“…However, the ensemblebased methods basically seek the solution within a lowerdimensional subspace spanned by the ensemble members. In many applications in atmospheric sciences, it has been demonstrated that the localization of the covariance matrix is useful for coping with high-dimensional problems (e.g., Buehner, 2005;Liu et al, 2009;Buehner et al, 2010;Yokota et al, 2016). However, it has not necessarily been clarified how general high-dimensional problems, in which the localization of the covariance matrix might not be appropriate, can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble.…”

Section: Introductionmentioning

confidence: 99%

Behavior of the iterative ensemble-based variational method in nonlinear problems

Nakano

2021

Nonlin. Processes Geophys.

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Abstract. The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4D ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, are solved by applying this method iteratively. However, the ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members. It is not necessarily trivial how high-dimensional problems can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in high-dimensional nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in a high-dimensional context. It is shown that the ensemble-based algorithm can solve high-dimensional problems by distributing the ensemble in different subspace at each iteration. The findings as the results of the present study were also experimentally supported.

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Section: Introductionmentioning

confidence: 99%

Behavior of the iterative ensemble-based variational method in nonlinear problems

Nakano¹

2020

Preprint

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The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4-dimensional ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, where system nonlinearity is significant, are solved by applying this method iteratively. However, it is not necessarily trivial how the algorithm works in highly uncertain problems where nonlinearity is not negligible. In the present study, an 5 ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in nonlinear context. The findings as the results of the present study were also experimentally supported. https://doi.org/10.5194/npg-2020-9 Preprint. Discussion started: 17 April 2020 c Author(s) 2020. CC BY 4.0 License.Several studies have suggested that estimation in nonlinear problems can be improved by iterative algorithms in which 25 the ensemble is repeatedly updated in each iteration (e.g., Gu and Oliver, 2007;Kalnay and Yang, 2010; Chen and Oliver, 2012; Sakov, 2013, 2014;Raanes et al., 2019). These iterative algorithms can be regarded as a variant of the 4DEnVar method based on an approximation of the Gauss-Newton method or the Levenberg-Marquardt method. The Gauss-Newton and the Levenberg-Marquardt methods are variants of the Newton-Raphson method for solving nonlinear least squares problems by using the Jacobian of a nonlinear function. Thus, when the Gauss-Newton or the Levenberg-Marquardt framework 30 is strictly applied to data assimilation problems, the tangent linear of the system model is required. Indeed, if the tangent linear of the system model is obtained, 4-dimensional variational data assimilation problems can be solved with the incremental formulation (Courtier et al., 1994) which can be regarded as an instance of the Gauss-Newton framework (Lawless et al., 2005). The ensemble-based methods avoid computing the Jacobian of a nonlinear system model by a low-rank linear approximation using the ensemble. This ensemble-based approximation is justified if linearity can be assumed over the range where the 35 ensemble members are distributed. However, it has not necessarily been clarified how the algorithm works in highly uncertain problems where nonlinearity is not negligible.The present study aims to reformulate an ensemble-based iterative algorithm in order to analyze its behavior in nonlinear problems. We then explore the conditions for achieving monotonic convergence to a local maximum of the objective function in nonlinear context. The monotonic convergence means that the discrepancies between estimates and observations are reduced 40 in each iteration. It is thus ensured that the algorithm would attain a satisfactory result in nonlinear problems. This study is originally moti...

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Comparison between Four-Dimensional LETKF and Ensemble-Based Variational Data Assimilation with Observation Localization

Cited by 5 publications

References 19 publications

Mesoscale Hybrid Data Assimilation System based on JMA Nonhydrostatic Model

Mesoscale Hybrid Data Assimilation System based on JMA Nonhydrostatic Model

Behavior of the iterative ensemble-based variational method in nonlinear problems

Behavior of the iterative ensemble-based variational method in nonlinear problems

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