The main goal of this work is to investigate techniques for treating model errors in the ensemble Kalman filter, and to develop a data assimilation system capable of assimilating real weather observations. An ensemble based data assimilation scheme - local ensemble transform Kalman filter (LETKF, Hunt 2005) is applied to the SPEEDY primitive equation global model (Molteni 2003). The model errors are introduced by assimilating observations from the NCEP/NCAR reanalysis data. The effect of model errors on LETKF is investigated. To deal with the model error, several model error correction methods are tested, including the 'covariance inflation', the Danforth et al (2006) low-order method, the Dee and da Silva method (1998) and its simplified version (Radakovich et al 2001). The performances of these methods are investigated and compared under the different observational networks. Finally the most accurate and efficient method will be chosen and applied to NASA fvGCM and NCEP GFS model to assimilate the real observations.