Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

Liu, Bo; Ait‐El‐Fquih, Boujemaa; Hoteit, Ibrahim

doi:10.1175/mwr-d-14-00292.1

Cited by 26 publications

(13 citation statements)

References 61 publications

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“…We assume that

H_{n}^{x}

and

H_{n}^{z}

are linear for simplicity, but the proposed ensemble schemes can be easily extended to the case of nonlinear observation operators as discussed for example in Liu et al . (2016). The model noise terms,

η^{x} = {η_{n}^{x}}_{n \in ℕ}

and

η^{z} = {η_{n}^{z}}_{n \in ℕ}

, and the observation noise terms,

ε^{x} = {ε_{n}^{x}}_{n \in ℕ}

and

ε^{z} = {ε_{n}^{z}}_{n \in ℕ}

, are assumed to be independent, jointly independent and independent of the initial states x 0 and z 0 .…”

Section: The Classical Enkf For Owc Systemsmentioning

confidence: 99%

Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

Raboudi

Ait‐El‐Fquih

Subramanian

et al. 2020

Quart J Royal Meteoro Soc

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This study investigates the filtering problem with one‐way coupled (OWC) state‐space systems, for which the joint ensemble Kalman filter (EnKF) is the standard solution. In this approach, the states of the two coupled sub‐systems are jointly updated with all incoming observations. This enables transfer of the information across the sub‐systems, which should provide coupled‐state estimates in better agreement with the observations. The state estimates of the joint EnKF highly depend on the relevance of the joint ensembles' cross‐covariances between the sub‐systems' variables. In this work, we propose a new joint EnKF scheme based on the One‐Step‐Ahead (OSA) smoothing formulation of the filtering problem for efficient assimilation into OWC systems. The scheme introduces an extra smoothing step for both states' sub‐systems with the future observations, followed by an analysis step for each sub‐system state using only its own observation, all within a Bayesian‐consistent framework. The extra OSA smoothing step enables us to more efficiently exploit the observations, to enhance the representativeness of the EnKF covariances, and to mitigate for reported inconsistencies in the joint EnKF analysis step. We demonstrate the relevance of the proposed approach by presenting and analyzing results of various numerical experiments conducted with a OWC Lorenz‐96 model.

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“…We assume that

H_{n}^{x}

and

H_{n}^{z}

η^{x} = {η_{n}^{x}}_{n \in ℕ}

and

η^{z} = {η_{n}^{z}}_{n \in ℕ}

, and the observation noise terms,

ε^{x} = {ε_{n}^{x}}_{n \in ℕ}

and

ε^{z} = {ε_{n}^{z}}_{n \in ℕ}

, are assumed to be independent, jointly independent and independent of the initial states x 0 and z 0 .…”

Section: The Classical Enkf For Owc Systemsmentioning

confidence: 99%

Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

Raboudi

Ait‐El‐Fquih

Subramanian

et al. 2020

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, the covariance of each kernel is estimated from the inter-model differences even though autocorrelation of the individual models is lost. This is a very common choice in kernel-based probability density approximations (Liu et al, 2016;Silverman, 1986).…”

Section: Kernel Modelmentioning

confidence: 99%

Combining a pollen and macrofossil synthesis with climate simulations for spatial reconstructions of European climate using Bayesian filtering

2019

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Abstract. Probabilistic spatial reconstructions of past climate states are valuable to quantitatively study the climate system under different forcing conditions because they combine the information contained in a proxy synthesis into a comprehensible product. Unfortunately, they are subject to a complex uncertainty structure due to complicated proxy–climate relations and sparse data, which makes interpolation between samples difficult. Bayesian hierarchical models feature promising properties to handle these issues, like the possibility to include multiple sources of information and to quantify uncertainties in a statistically rigorous way. We present a Bayesian framework that combines a network of pollen and macrofossil samples with a spatial prior distribution estimated from a multi-model ensemble of climate simulations. The use of climate simulation output aims at a physically reasonable spatial interpolation of proxy data on a regional scale. To transfer the pollen data into (local) climate information, we invert a forward version of the probabilistic indicator taxa model. The Bayesian inference is performed using Markov chain Monte Carlo methods following a Metropolis-within-Gibbs strategy. Different ways to incorporate the climate simulations into the Bayesian framework are compared using identical twin and cross-validation experiments. Then, we reconstruct the mean temperature of the warmest and mean temperature of the coldest month during the mid-Holocene in Europe using a published pollen and macrofossil synthesis in combination with the Paleoclimate Modelling Intercomparison Project Phase III mid-Holocene ensemble. The output of our Bayesian model is a spatially distributed probability distribution that facilitates quantitative analyses that account for uncertainties.

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“…Even though systematic errors in the system and model noise (issue (i)) may be partially treated using well-known parameter estimation techniques (e.g., Dee, 2005;Gharamti et al, 2015;Dreano et al, 2017;Ait-El-Fquih and Hoteit, 2018;Sakov et al, 2018), and those in the filter (issue (ii)) by for instance relaxing the Gaussian assumption made on the analysis pdf to a Gaussian mixture through the use of an ensemble Gaussian mixture filter (e.g., Hoteit et al, 2008;Frei and Künsch, 2013;Liu et al, 2015), sampling errors are inevitable. Many applications have demonstrated that the EnKF can tolerate sampling errors by applying auxiliary techniques, the most standard of which are covariance inflation (Anderson, 2001) and covariance localization (Houtekamer and Mitchell, 1998); other techniques have also been proposed, for example, Hamill and Snyder (2000), Song et al (2010), and Luo and Hoteit (2011).…”

Section: Introductionmentioning

confidence: 99%

A particle‐filter based adaptive inflation scheme for the ensemble Kalman filter

Ait‐El‐Fquih

Hoteit

2020

Quart J Royal Meteoro Soc

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An adaptive covariance inflation scheme is proposed for the ensemble Kalman filter (EnKF) to mitigate the loss of ensemble variance. Adaptive inflation methods are mostly based on a Bayesian approach, which considers the inflation factor as a random variable with a given prior probability distribution and then combines it with the inflation likelihood through Bayes' rule to obtain its posterior distribution. In this work, we introduce a numerical implementation of this generic Bayesian approach that uses a particle filter (PF) to compute a Monte Carlo approximation of the inflation posterior distribution. To alleviate the sample attrition issue, the proposed PF employs an artificial dynamical model for the inflation factor based on the well‐known smoothing‐kernel West and Liu model. The positivity constraint on the inflation factor is further imposed through an inverse‐Gamma transition density, with parameters that suggest analytical expressions. The resulting PF–EnKF scheme is straightforward to implement, and can use different numbers of particles in its EnKF and PF components. Numerical experiments are conducted with the Lorenz‐96 model to demonstrate the effectiveness of the proposed method under various experimental scenarios.

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Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

Cited by 26 publications

References 61 publications

Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

Combining a pollen and macrofossil synthesis with climate simulations for spatial reconstructions of European climate using Bayesian filtering

A particle‐filter based adaptive inflation scheme for the ensemble Kalman filter

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