Using orthogonal vectors to improve the ensemble space of the EnKF and its effect on data assimilation and forecasting

Abstract. The space spanned by the background ensemble provides a basis for correcting forecast errors in the ensemble Kalman filter. However, the ensemble space may not fully capture the forecast errors due to the limited ensemble size and systematic model errors, which affect the assimilation performance. This study proposes a new algorithm to generate pseudo members to properly expand the ensemble space during the analysis step. The pseudomembers adopt vectors orthogonal to the original ensemble and are included in the ensemble using the centered spherical simplex ensemble method. The new algorithm is investigated with a six-member ensemble Kalman filter implemented in the Lorenz 40-variable model. Our results suggest that orthogonal vectors with the ensemble singular vector or ensemble mean vector can serve as effective pseudomembers for improving the analysis accuracy, especially when the background has large errors.