Estimation of physical parameters under location uncertainty using an Ensemble$^2$-Expectation-Maximization algorithm

Yin Yang 1 Etienne Mémin 2
2 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : Estimating the parameters of geophysical dynamic models is an important task in Data Assimilation (DA) technique used for forecast initialization and reanalysis. In the past, most parameter estimation strategies were derived by state augmentation, yielding algorithms that are easy to implement but may exhibit convergence difficulties. The Expectation-Maximization (EM) algorithm is considered advantageous because it employs two iterative steps to estimate the model state and the model parameter separately. In this work, we propose a novel ensemble formulation of the Maximization step in EM that allows a direct optimal estimation of physical parameters using iterative methods for linear systems. This departs from current EM formulations that are only capable of dealing with additive model error structures. This contribution shows how the EM technique can be used for dynamics identification problem with a model error parameterized as arbitrary complex form. The proposed technique is here used for the identification of stochastic subgrid terms that account for processes unresolved by a geophysical fluid model. This method, along with the augmented state technique, are evaluated to estimate such subgrid terms through high resolution data. Compared to the augmented state technique, our method is shown to yield considerably more accurate parameters. In addition, in terms of prediction capacity, it leads to smaller generalization error as caused by the overfitting of the trained model on presented data and eventually better forecasts.
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https://hal.inria.fr/hal-01944730
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Submitted on : Thursday, December 6, 2018 - 9:16:51 AM
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Yin Yang, Etienne Mémin. Estimation of physical parameters under location uncertainty using an Ensemble$^2$-Expectation-Maximization algorithm. Quaterly journal of the royal meteorological society, Wiley, In press, pp.1-47. ⟨10.1002/qj.3438⟩. ⟨hal-01944730⟩

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