Stochastic parameterization identification using ensemble Kalman filtering combined with expectation-maximization and Newton-Raphson maximum likelihood methods

Abstract

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-the-art sequential estimation methods such as Kalman and particle filters do not achieve this goal succesfully because both suffer from the collapse of the parameter posterior distribution. To overcome this intrinsic limitation, we propose two statistical learning methods. They are based on the combination of two methodologies: the maximization of the likelihood via Expectation-Maximization (EM) and Newton-Raphson (NR) algorithms which are mainly applied in the statistic and machine learning communities, and the ensemble Kalman filter (EnKF). The methods are derived using a Bayesian approach for a hidden Markov model. 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 incorpored to represent the small-scale dynamics. The algorithms are able to identify an optimal stochastic parameterization with a good accuracy under moderate observational noise. The proposed EnKF-EM and EnKF-NR are promising statistical learning methods for developing stochastic parameterizations in high-dimensional geophysical models.

References in corpus (2)

• Estimating model evidence using data assimilation
• DADA: Data Assimilation for the Detection and Attribution of Weather- and Climate-related Events

Cited by in corpus (9)

• Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation
• Adaptive covariance inflation in the ensemble Kalman filter by Gaussian scale mixtures
• Evaluation of Machine Learning Techniques for Forecast Uncertainty Quantification
• Model error covariance estimation in particle and ensemble Kalman filters using an online expectation-maximization algorithm
• Inference of stochastic parameterizations for model error treatment using nested ensemble Kalman filters
• Model uncertainty estimation using the expectation maximization algorithm and a particle flow filter
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps