Abstrakt
In meteorological and geophysical sciences, where the system state is a vector with big dimension, the most popular methods for data assimilation are filters based on Monte-Carlo approximation of the traditional Kalman filter. In these methods, the posterior distribution is approximated by a set of system states (so called ensemble).
Examples of these filters are ensemble Kalman filter (EnKF), ensemble Square-root filter and others. However, due to the computational cost, the ensemble is always very small and therefore provides a poor estimate of the prior covariance matrix, which negatively affects estimation of the posterior mean.
In practise, this problem is solved by several (more or less) heuristic methods like tapering or even diagonal approximation of the prior covariance matrix. In this contribution, we will present two methods for modelling of a covariance matrix that are applicable in Ensemble Kalman filter and that provides rigorous covariance regularization.