Impacts of different background error covariance matrices on 4DVAR data assimilation

A simple model of shallow water equation and simulated data are used to examine the impacts of different background error covariance matrices on the four-dimensional variational (4DVAR) data assimilation. Three different schemes of background error covariance matrix are compared: (1) a diagonal matrix; (2) a Gaussian form matrix with the homogeneous and isotropic assumption; (3) a singular vector decomposition (SVD) technique based on ensemble forecasts. Numerical results show that the background error covariance matrix plays an important role in 4DVAR data assimilation. When the spatial density of the observations is not high enough, the use of diagonal matrix produces a poor analysis. The Gaussian filter scheme improves the analysis results, but it is sensitive to the characteristic scale of the background error. The ensemble-based method shows a stable behavior and best performance, even in the case when the observations are sparse and the errors are large.

Preliminary tests with an advanced numerical model (e.g., the community mesoscale weather research and forecasting mode -- WRF model) will also be presented.