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

MANUEL PULIDO; TANDEO, PIERRE; BOCQUET, MARC; CARRASI, ALBERTO; LUCINI, MARÍA MAGDALENA

TELLUS B

WILEY-BLACKWELL PUBLISHING, INC

Lugar: Londres; Año: 2018 vol. 70 p. 1 - 15

0280-6509

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamicalequations while small-scale processes are represented via parameterizations. This work proposes a method foridentifying the best possible stochastic parameterization from noisy data. State-of-the-art sequential estimation methodssuch as Kalman and particle filters do not achieve this goal successfully because both suffer from the collapse of theposterior distribution of the parameters. To overcome this intrinsic limitation, we propose two statistical learningmethods. 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 beestimated. The EM and NR are applied primarily in the statistics and machine learning communities and are brought herein the context of data assimilation for the geosciences. The methods are derived using a Bayesian approach for a hiddenMarkov model and they are applied to infer deterministic and stochastic physical parameters from noisy observations incoarse-grained dynamical models. Numerical experiments are conducted using the Lorenz-96 dynamical system withone and two scales as a proof of concept. The imperfect coarse-grained model is modelled through a one-scale Lorenz96system in which a stochastic parameterization is incorporated to represent the small-scale dynamics. The algorithmsare 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 stochasticparameterizations in high-dimensional geophysical models.