INVESTIGADORES
LUCINI Maria magdalena
congresos y reuniones científicas
Título:
`Estimating model error covariances using Particle Filters''
Autor/es:
LUCINI MARIA MAGDALENA; VAN LEEWUEN, PETER JAN; PULIDO, MANUEL ARTURO; COCUCCI TADEO
Lugar:
Viena
Reunión:
Congreso; European Geosciences Union (EGU) General Assembly,; 2019
Resumen:
State-space models are used in data assimilation to mathematically describe the state of a hiddensystem by combining observations with a physical model. The formulation of these models usuallyinvolve statistical parameters that do not rely on physical constants and must be estimated, sincethey play a central role in the performance of the data assimilation method to be used. Among theseparameters, covariance matrices are introduced to prescribe statistical properties of the system andobservation noise (model and observation errors, respectively). The model error covariance matrixQ is, perhaps, the hardest to estimate since it depends on how well the model represents theunderlying physics. If a particle filter is to be used, a misspecification of Q has a strong impact onthe computation of the probability density functions involved in the particle filter algorithm, leadingto unreliable predictions and even to a total failure of the assimilation procedure. In this work, wepropose the combination of the Expectation-Maximization algorithm (EM) with an efficient particlefilter to estimate the model error covariance matrix Q, using a batch of observations. However,because the relation between the observations and the model error covariance is via the evolvingstate of the system under this covariance matrix, this is a complicated problem. Based on the EMalgorithm principles, the proposed solution method encompasses two stages: the expectation stage,in which a particle filter is used with the present estimate of the model error covariance as given tofind the probability density function that maximises the likelihood, followed by a maximization stagein which this expectation is maximised as function of the elements of the model error covariance.Since the problem is highly nonlinear an analytical solution for this maximum cannot be found andwe propose an original algorithm, that does not require a Particle Smoother, to find this maximum.We show that this methodology converges to the true model error covariances in twin experimentsusing the Lorenz-96 system, but at different rates and with different accuracies depending on systemparameters.