Using orthogonal vector to improve the ensemble space of the EnKF and its effect on data assimilation and forecasting
In the ensemble-based data assimilation, the ensemble space provides the space for correcting forecast errors. However, the use of limited ensemble size and model error can limit the ensemble space and thus affect the assimilation performance. This study proposes a new algorithm to generate pseudo ensemble members during analysis in order to expand the ensemble space in the right direction. The pseudo ensemble members are generated by the vectors orthogonal to the original ensemble and included by the centered spherical simplex ensemble method. Experiments are carried out with the LETKF implemented in the Lorenz 40-variable model. Different orthogonal vectors are generated from the null-space vector from SVD, ensemble singular vector and ensemble mean vector.
Results show that the assimilation performance can be improved with additional orthogonal vectors. Among all the orthogonal vectors, the ones that are extracted from the ensemble singular vector and mean state are particularly useful. The analysis error is reduced in the areas with large errors or fast growing errors, especially when the original ensemble was unable to capture the direction of forecast error.
Prof. Shu-Chih Yang Taiwan National Central University