Effect of Multivariate Background Error Covariances on Analyses and Forecasts of Heavy Rainfall over the Korean Peninsula

In variational data assimilation methods, background error covariances determine the spatial and multivariate response of the analysis to an observation. Generally, the background error covariance matrix is calculated not in model space but in a control variable space, and the control variable transform is a key factor in background error covariance modeling. In the Weather Research and Forecasting Data Assimilation (WRFDA) system, the control variable transform consists of three parts, horizontal transform, vertical transform, and physical variable transform. The horizontal covariances are represented by a recursive filter, and the empirical orthogonal functions of vertical covariances are computed. The physical variable transform is related to multivariate covariances, and regression coefficient between streamfunction and velocity potential, streamfunction and temperature, or streamfunction and surface pressure is calculated. To investigate the effect of the background error covariance, three types of background error statistics are tested in assimilating radar data for heavy rainfall cases over the Korean Peninsula. The three types include global background error statistics, regional background error statistics without moisture-related multivariate covariances, and regional background error statistics with moisture-related multivariate covariances. A heavy rainfall case that occurred on 21 September 2010 is selected for data assimilation experiments. In this case, mesoscale convective system induced torrential rainfall over a localized area and a short period of time. The 12-h accumulated rainfall amount at Seoul was approximately 300 mm. Overall, rainfall forecasts are improved through the assimilation of radar data. The data assimilation experiment with global background error statistics shows less improvement than the experiment with regional background error statistics. When multivariate covariances related to moisture variable are included, the quality of the analysis and the corresponding forecast are improved, especially for the three dimensional variational data assimilation method. This is because in the four dimensional variational data assimilation method, covariances between moisture variable and the other variables can be provided through the model integration. Additionally, length scale of a recursive filter in the horizontal transform is tuned to determine the appropriate length scale for the assimilation of high-resolution radar data.