Noise Parameter Estimation in Stochastic Dynamical Systems using Expectation Maximization Algorithm

PULIDO, MANUEL ARTURO; TANDEO, PIERRE; LUCINI, MARÍA MAGDALENA

Valdivia

Conferencia; XIX Conference on Nonequilibrium Statistical Mechanics and nonlinear Physics,; 2016

The Expectation-Maximization algorithm (EM) is a widely used methodology to maximize the likelihood function in a broad spectrum of applications. One of the big advantages of the EM algorithm is that the implementation is rather straigthforward. Recently the EM algorithm was applied to a highly nonlinear observation operator, specifically an orographic subgrid-scale parameterization (which is present in several state-of-the-art numerical weather forecast models inclucing the ECMWF forecast model) and showed to be able to estimate the true subgrid-scale parameters with good accuracy while standard ensemble Kalman filter techniques failed.In this work, we apply the EM algorithm to estimate stochastic physical and statistical parameters in chaotic nonlinear dynamical systems. The EM algorithm is used in conjunction with an ensemble Kalman filter (EnKF) and smoother, the last are used to obtain the intermidiate function conditioned to the observations and unknown parameters. A Newton-Raphson algorithm that maximizes the observation likelihood function is also implemented for comparison with the EM algorithm. The evaluation of the observation likelihood function also requires a Kalman filter and smoother. To that end, we implement an algorithm based on the ensemble-based Kalman filter which does not require the adjoint model for its application in nonlinear dynamical systems. The approach here proposed is evaluated in the one and two-scale Lorenz 96 systems. The EnKF-EM algorithm is able to estimate both the dynamical noise and measurement noise with a good degree of accuracy. These approaches are shown to be useful for stochastic parameterization development and setting.