Ensemble Generation for Models of Multimodal Systems

Miller, Robert N.; Ehret, Laura L.

doi:10.1175/1520-0493(2002)130<2313:egfmom>2.0.co;2

Cited by 23 publications

(11 citation statements)

References 49 publications

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“…These are discarded in the EnKF (see Evensen and van Leeuwen, 2000), and a fully nonlinear filter is expected to improve the results when used with nonlinear dynamical models with multi-modal behavior where the predicted error statistics are far from Gaussian. Implementations of nonlinear filters based on either kernel approximation or particle interpretations have been proposed by Miller et al (1999), Anderson and Anderson (1999), Pham (2001), Ehret (2002), andvan Leeuwen (2003), although more research is needed before these can claimed to be practical for realistic high-dimensional systems.…”

Section: Nonlinear Filters and Smoothersmentioning

confidence: 99%

The Ensemble Kalman Filter: theoretical formulation and practical implementation

Evensen¹

2003

Ocean Dynamics

3,698

2,898

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The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

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Section: Nonlinear Filters and Smoothersmentioning

confidence: 99%

The Ensemble Kalman Filter: theoretical formulation and practical implementation

Evensen¹

2003

Ocean Dynamics

3,698

2,898

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“…(4a) and (4b). The first is the pure prediction problem, in real-time or in hindcast, which starts from realistic initial conditions P(0) [54,64]. The second is the reanalysis or full assimilation problem, including possibly both filtering and smoothing, which computes uncertainties after the data collection and can lead to close to stationary errors if the observation system is well chosen/adapted.…”

Section: Fundamental Equationsmentioning

confidence: 99%

Uncertainty estimation and prediction for interdisciplinary ocean dynamics

Lermusiaux

2006

Journal of Computational Physics

160

121

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Scientific computations for the quantification, estimation and prediction of uncertainties for ocean dynamics are developed and exemplified. Primary characteristics of ocean data, models and uncertainties are reviewed and quantitative data assimilation concepts defined. Challenges involved in realistic data-driven simulations of uncertainties for four-dimensional interdisciplinary ocean processes are emphasized. Equations governing uncertainties in the Bayesian probabilistic sense are summarized. Stochastic forcing formulations are introduced and a new stochastic-deterministic ocean model is presented. The computational methodology and numerical system, Error Subspace Statistical Estimation, that is used for the efficient estimation and prediction of oceanic uncertainties based on these equations is then outlined. Capabilities of the ESSE system are illustrated in three data-assimilative applications: estimation of uncertainties for physical-biogeochemical fields, transfers of ocean physics uncertainties to acoustics, and real-time stochastic ensemble predictions with assimilation of a wide range of data types. Relationships with other modern uncertainty quantification schemes and promising research directions are discussed.

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“…In practice, however, specific implementations may have different constants of proportionality, and ingenious sampling schemes may even lead to better convergence as a function of N. To this end, two important issues in ensemble filtering are (i) sampling from the unknown initial PDF and (ii) maintaining sufficient spread of the numerically evolving PDF to keep sampling the nonGaussian features of the true PDF. The overall purpose is to generate perturbations that are effective in guiding the perturbed trajectories in the most likely directions of system evolution (Miller and Ehret 2002). Two approaches that are widely used in numerical weather prediction to achieve this purpose are bred vectors (Toth and Kalnay 1993;Kalnay 2003) and singular vectors (Molteni et al 1996;Ehrendorfer and Tribbia 1997).…”

Section: Discussionmentioning

confidence: 99%

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Chin

Turmon

Jewell

et al. 2007

Monthly Weather Review

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Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

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Ensemble Generation for Models of Multimodal Systems

Cited by 23 publications

References 49 publications

The Ensemble Kalman Filter: theoretical formulation and practical implementation

The Ensemble Kalman Filter: theoretical formulation and practical implementation

Uncertainty estimation and prediction for interdisciplinary ocean dynamics

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

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