TY - JOUR
T1 - A Variational Bayesian Approach for Ensemble Filtering of Stochastically Parametrized Systems
AU - Ait-El-Fquih, Boujemaa
AU - C. Subramanian, Aneesh
AU - Hoteit, Ibrahim
N1 - KAUST Repository Item: Exported on 2023-05-12
Acknowledgements: Research reported here was supported by King Abdullah University of Science and Technology (KAUST). The authors thank the anonymous reviewers for the valuable and constructive comments
PY - 2023/5/7
Y1 - 2023/5/7
N2 - Modern climate models use both deterministic and stochastic parameterization schemes to represent uncertainties in their physics and inputs. This work considers the problem of estimating the involved parameters of such systems simultaneously with their state through data assimilation. Standard state-parameters filtering schemes cannot be applied to such systems owing to the posterior dependency between the stochastic parameters and the “dynamical” augmented-state, defined as the state augmented by the deterministic parameters. We resort to the variational Bayesian (VB) approach to break this dependency, by approximating the joint posterior probability density function (pdf) of the augmented-state and the stochastic parameters with a separable product of two marginal pdfs that minimizes the Kullback-Leibler divergence. The resulting marginal pdf of the augmented-state is then sampled using a one-step-ahead smoothing-based ensemble Kalman filter (EnKF-OSAS), whereas a closed-form is derived for the marginal pdf of the stochastic parameters. The proposed approach combines the effectiveness of the OSAS filtering approach to mitigate inconsistency issues that often arise with the joint EnKF, with the advantage of obtaining a full posterior pdf for the stochastic parameters, which is not possible with the traditional maximum likelihood method. We demonstrate the relevance of the proposed approach through extensive numerical experiments with a one-scale Lorenz-96 model, which includes a stochastic parametrization representing subgrid-scale effects.
AB - Modern climate models use both deterministic and stochastic parameterization schemes to represent uncertainties in their physics and inputs. This work considers the problem of estimating the involved parameters of such systems simultaneously with their state through data assimilation. Standard state-parameters filtering schemes cannot be applied to such systems owing to the posterior dependency between the stochastic parameters and the “dynamical” augmented-state, defined as the state augmented by the deterministic parameters. We resort to the variational Bayesian (VB) approach to break this dependency, by approximating the joint posterior probability density function (pdf) of the augmented-state and the stochastic parameters with a separable product of two marginal pdfs that minimizes the Kullback-Leibler divergence. The resulting marginal pdf of the augmented-state is then sampled using a one-step-ahead smoothing-based ensemble Kalman filter (EnKF-OSAS), whereas a closed-form is derived for the marginal pdf of the stochastic parameters. The proposed approach combines the effectiveness of the OSAS filtering approach to mitigate inconsistency issues that often arise with the joint EnKF, with the advantage of obtaining a full posterior pdf for the stochastic parameters, which is not possible with the traditional maximum likelihood method. We demonstrate the relevance of the proposed approach through extensive numerical experiments with a one-scale Lorenz-96 model, which includes a stochastic parametrization representing subgrid-scale effects.
UR - http://hdl.handle.net/10754/691647
UR - https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4481
U2 - 10.1002/qj.4481
DO - 10.1002/qj.4481
M3 - Article
SN - 0035-9009
JO - Quarterly Journal of the Royal Meteorological Society
JF - Quarterly Journal of the Royal Meteorological Society
ER -