Stochastic parameterization identification using ensemble Kalman filtering combined with maximum likelihood methods

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the best possible stochastic parameterization from noisy data. Sta...

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Bibliographic Details
Published in:Tellus. Series A, Dynamic meteorology and oceanography Vol. 70; no. 1; pp. 1 - 17
Main Authors: Pulido, Manuel, Tandeo, Pierre, Bocquet, Marc, Carrassi, Alberto, Lucini, Magdalena
Format: Journal Article
Language:English
Published: Stockholm Taylor & Francis 01.01.2018
Stockholm University Press
Subjects:
Bayesian analysis
Data collection
Dynamics
Earth Sciences
Engineering Sciences
expectation-maximization algorithm
Kalman filters
Machine learning
Markov chains
Meteorology
model error estimation
Modelling
Ocean, Atmosphere
parameter estimation
Parameterization
Parameters
Probability theory
Sciences of the Universe
Signal and Image processing
Statistical methods
stochastic parameterization
Teaching methods
ISSN:1600-0870, 0280-6495, 1600-0870
Online Access:Get full text
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Summary:For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the best possible stochastic parameterization from noisy data. State-of-the-art sequential estimation methods such as Kalman and particle filters do not achieve this goal successfully because both suffer from the collapse of the posterior distribution of the parameters. To overcome this intrinsic limitation, we propose two statistical learning methods. They are based on the combination of the ensemble Kalman filter (EnKF) with either the expectation-maximization (EM) or the Newton-Raphson (NR) used to maximize a likelihood associated to the parameters to be estimated. The EM and NR are applied primarily in the statistics and machine learning communities and are brought here in the context of data assimilation for the geosciences. The methods are derived using a Bayesian approach for a hidden Markov model and they are applied to infer deterministic and stochastic physical parameters from noisy observations in coarse-grained dynamical models. Numerical experiments are conducted using the Lorenz-96 dynamical system with one and two scales as a proof of concept. The imperfect coarse-grained model is modelled through a one-scale Lorenz-96 system in which a stochastic parameterization is incorporated to represent the small-scale dynamics. The algorithms are able to identify the optimal stochastic parameterization with good accuracy under moderate observational noise. The proposed EnKF-EM and EnKF-NR are promising efficient statistical learning methods for developing stochastic parameterizations in high-dimensional geophysical models.
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ISSN:1600-0870
0280-6495
1600-0870
DOI:10.1080/16000870.2018.1442099