Spectral properties of the assimilated data and numerical model usually differ. In addition, ensemble Kalman filter algorithm depending on the size of the ensemble and choice of the localization matrix will modify spectral properties of the analysis. In this work we investigate the relation between the spectral properties of the observations, localization matrix used for ensemble Kalman filter, as well as the numerical model. Further, in the context of reduced order analysis there is a error contribution which is linked to the fraction of the background error that is not included in the analysis reduced space. Having in mind the spectrally consistent approach, the proper way of including this error in reduced rank algorithms and ways of modeling its covariance are discussed.