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

• Autores: Pulido, Manuel Arturo; Tandeo, Pierre; Bocquet, Marc; Carrasi, Alberto; Lucini, María Magdalena
• Año de publicación: 2018
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: EXPECTATION–MAXIMIZATION ALGORITHM; MODEL ERROR ESTIMATION; PARAMETER ESTIMATION; STOCHASTIC PARAMETERIZATION
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina
Fil: Tandeo, Pierre. Centre National de la Recherche Scientifique; Francia. Universite de Bretagne Occidentale; Francia
Fil: Bocquet, Marc. Université Paris-Est; Francia
Fil: Carrasi, Alberto. Nansen Environmental and Remote Sensing Center; Noruega
Fil: Lucini, María Magdalena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina