Using orthogonal vectors to improve the ensemble space of the ensemble Kalman filter and itseffect on data assimilation and forecasting

The space spanned by the background ensemble provides a basis forcorrecting forecast errors in the ensemble Kalman filter. However, theensemble space may not fully capture the forecast errors due to the limitedensemble size and systematic model errors, which affect the assimilationperformance. This study proposes a new algorithm to generate pseudomembersto properly expand the ensemble space during the analysis step. Thepseudomembers adopt vectors orthogonal to the original ensemble and areincluded in the ensemble using the centered spherical simplex ensemblemethod. The new algorithm is investigated with a six-member ensemble Kalmanfilter implemented in the 40-variable Lorenz model. Our results suggest thatthe ensemble singular vector, the ensemble mean vector, and their orthogonalcomponents can serve as effective pseudomembers for improving the analysisaccuracy, especially when the background has large errors.