Abstract
The ETKF rescaling scheme has been implemented into the HIRLAM forecasting system in order to estimate the uncertainty of the model state. The main purpose is to utilize this uncertainty information for modelling of flowdependent background error covariances within the framework of a hybrid variational ensemble data assimilation scheme. The effects of rank-deficiency in the ETKF formulation is explained and the need for variance inflation as a way to compensate for these effects is justified. A filter spin-up algorithm is proposed as a refinement of the variance inflation. The proposed spin-up algorithm will also act to prevent ensemble collapse since the ensemble will receive ‘fresh blood’ in the form of additional perturbation components, generated on the basis of a static background error covariance matrix. The resulting ETKF-based ensemble perturbations are compared with ensemble perturbations based on targeted singular vectors and are shown to have more realistic spectral characteristics.
Highlights
The Extended Kalman Filter (EKF, Kalman and Bucy, 1961) and the Unscented Filter (UF, Julier and Uhlmann, 1997) are two main strategies in sequential data assimilation for non-linear and/or non-Gaussian models
The objective of this study is to investigate the performance of the Ensemble Transform Kalman Filter (ETKF, Bishop et al, 2001) rescaling scheme within the HIRLAM forecasting system (Unden et al, 2002) primarily for operational applications
The ETKF rescaling scheme has been implemented into the HIRLAM variational data assimilation scheme in order to estimate the uncertainty about the model state estimate
Summary
The Extended Kalman Filter (EKF, Kalman and Bucy, 1961) and the Unscented Filter (UF, Julier and Uhlmann, 1997) are two main strategies in sequential data assimilation for non-linear and/or non-Gaussian models. The Ensemble Kalman Filters (EnKF, Evensen, 1994) provide a Monte Carlo approximation to the EKF, in which a sample of model states is used to estimate and propagate the mean and the covariance of the model state forward in time, based on a reduced rank approximation. In this approach the Kalman filtering becomes feasible even in the case of large dimensional systems. We outline the basic principles of linear filtering, we use a non-standard analysis technique to investigate limitations of the ETKF rescaling scheme imposed by the severe rank-deficiency and we propose a method to handle these limitations
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