Refinement of the Use of Inhomogeneous Background Error Covariance Estimated from Historical Forecast Error Samples and its Impact on Short-Term Regional Numerical Weather Prediction

Background error covariance (BEC) is one of the key components in data assimilation systems for numerical weather prediction. Recently, a scheme of using an inhomogeneous and anisotropic BEC estimated from historical forecast error samples has been tested by utilizing the extended alpha control variable approach (BEC-CVA) in the framework of the variational Data Assimilation system for the Weather Research and Forecasting model (WRFDA). In this paper, the BEC-CVA approach is further examined by conducting single observation assimilation experiments and continuous-cycling data assimilation and forecasting experiments covering a 3-week period. Additional benefits of using a blending approach (BEC-BLD), which combines a static, homogeneous BEC and an inhomogeneous and anisotropic BEC, are also assessed. Single observation experiments indicate that the noise in the increments in BEC-CVA can be somehow reduced by using BEC-BLD, while the inhomogeneous and multivariable correlations from BEC-C VA are still taken into account. The impact of BEC-CVA and BEC-BLD on short-term weather forecasts is compared with the three-dimensional variational data assimilation scheme (3DVar) and also compared with the hybrid ensemble transform Kalman filter and 3DVar (ETKF-3DVar) in WRFDA. The results show that BEC-CVA and BEC-BLD outperform the use of 3DVar. BEC-CVA and BEC-BLD underperform ETKF-3DVar, as expected. However, the computational cost of BEC-CVA and BEC-BLD is considerably less expensive because no ensemble forecasts are required.