A study on the background error covariance for reduced-rank retrospective optimal interpolation with WRF

Abstract:

This study presents the investigation of the background error covariance for reduced-rank retrospective optimal interpolation (reduced-rank ROI). Retrospective optimal interpolation (ROI) algorithm which assimilates observations over the analysis window for variance-minimum estimate of an atmospheric state at the initial time of the analysis window is suggested in Song et al. (2009). The assimilation window of ROI is gradually increased. Song and Lim (2011) suggested reduced-rank ROI improved by incorporating eigen-decomposition and covariance inflation. In this study, the background error covariance for reduced-rank ROI algorithm is investigated with Weather Research and Forecasting model (WRF). Reduced-rank ROI is applied by incorporating eigen-decomposition of background error covariance from ensemble. The structure of the background error covariance is investigated from each eigenvectors. The data assimilation experiments with reduced-rank ROI are based on Observing System Simulation Experiments (OSSE). A regularly dense network, a regularly sparse network, and irregularly realistic network are used for observation networks. It is assumed that all observations are located at the model grid points. Analysis error with reduced-rank ROI decreases significantly. Vertical profiles of background error and analysis error shows overall analysis error reduction.