The optimization of error covariances in the KMA UM 4D-Var system using the forecast sensitivity to error covariance weightings

This study investigated the forecast sensitivity to error covariance weightings in the Korea Meteorological Administration (KMA) Unified Model (UM) 4D-Var system for the summer (June and July 2011) and winter (December 2011 and January 2012) months. The forecast sensitivity to error covariance weightings defines the gradient of the forecast error with respect to the weightings corresponding to error covariances in the data assimilation system. The sensitivity guidance provides that the covariance deflation will be helpful to reduce the forecast error if the derivatives are positive, whereas the covariance inflation will be helpful to reduce forecast error if the derivatives are negative.

In addition, this study estimated the optimized error covariances using the multiple linear regression of the sensitivity data corresponding to the summer and winter months, and investigated the forecast error reduction when the optimized error covariances were used in the KMA UM 4D-Var system for August 2011 and February 2012. The predictors (i.e., weightings) were estimated using the preconditioned conjugate gradient algorithm. The multiple linear regression method diagnosed that to reduce the forecast error the inflation of the background error covariance is be necessary by 30 %, whereas the deflation of most observation error covariances is necessary. More detailed results will be presented in the conference.