An ensemble Kalman filter using potential vorticity for atmospheric multiscale data assimilation
A multiscale data assimilation method for the ensemble Kalman filter (EnKF) is proposed for atmospheric models in the case where the ensemble size and observations of small scales are both insufficient. Dynamical state variables of a forecast ensemble are decomposed into balanced and unbalanced parts by applying potential vorticity (PV) inversion, in which PV anomalies are computed from spatially smoothed state variables. The mass variables of the two parts are adjusted to reduce additional sampling errors caused by the decomposition. The forecast error covariance between the two parts is ignored in the Kalman gain to suppress spurious error correlations. This approximation makes it possible to apply different covariance localizations to small and large scales.
The performance of the proposed method is demonstrated with a shallow water model through twin experiment in a perfect model scenario. Results using the same localization radius for the two parts show that the smaller the ensemble size is, the greater the degree of improvement over a conventional EnKF is in terms of the accuracy of analysis. The benefit of using the first-order direct PV inversion over the quasi-geostrophic inversion is marginal. When the ensemble size is large enough, the conventional EnKF outperforms the proposed method.
Dr. Tadashi Tsuyuki Meteorological College