Abstract
Abstract. The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning parameter in EKF, which is often simply postulated by the user. In this paper, we study the filter likelihood technique for estimating the parameters of the model error covariance matrix. The approach is based on computing the likelihood of the covariance matrix parameters using the filtering output. We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned EKF in terms of the accuracy of the state estimates and model predictions. For our numerical experiments, we use the two-layer quasi-geostrophic model that is often used as a benchmark model for numerical weather prediction.
Highlights
In state estimation, or data assimilation, the goal is to estimate the dynamically changing state of the model, given incomplete and noisy observations
We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned extended Kalman filter (EKF) in terms of root mean squared errors of the state estimates and model predictions
We believe that the reason is that EKF is an approximative filter – it uses linearizations and assumes, for instance, that the model error and state are independent – and the imperfections in the method can to some extent be compensated for by calibrating the model error covariance matrix
Summary
Data assimilation, the goal is to estimate the dynamically changing state of the model, given incomplete and noisy observations. We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned EKF in terms of root mean squared (rms) errors of the state estimates and model predictions. In such a synthetic case, the truth is known, so the true model error can be studied by computing differences between the truth and the forecast model. The predictive distribution is given by the integral
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